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Establishing an appropriate landing fee schedule at Vancouver International Airport Shanks, Andrew David 1974

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ESTABLISHING AN APPROPRIATE LANDING FEE SCHEDULE AT VANCOUVER INTERNATIONAL AIRPORT by ANDREW DAVID SHANKS B.A., University of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION i n the Department of Commerce We accept th i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1974 In p resent ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and study. I f u r t h e r agree tha t permiss ion for e x t e n s i v e copying of t h i s t h e s i s fo r s c h o l a r l y purposes may be granted by the Head of my Department o r by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be al lowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date i ABSTRACT The l a s t twenty years has seen a tremendous increase i n aviation a c t i v i t y within Canada. A i r l i n k s have been established and improved and safety standards upgraded to the point where the a i r can now be regarded as the optimum environment i n which to t r a v e l . Because of i t s tremendous popularity, f l y i n g has also placed demands on the public purse. Every year more money i s allocated to the aviation sector. U n t i l recently, t h i s outflow of funds continued v i r t u a l l y unchecked. With an increasing awareness of ecological balance and the impending depletion of non-renewable resources, public opinion has begun to question the v i a b i l i t y of increased aviation investment. In consideration of these factors, t h i s work has invest-igated the economic theory upon which r a t i o n a l p r i c i n g i s based. Given the current l e v e l of investment, the f i r s t chapter examines the r e l a t i o n s h i p between the present l e v e l of demand for aviation services, and the appropriate l e v e l of price to be assessed against t h i s demand. Demand i s also used to formulate a decision frame-work for future investment i n a i r p o r t s . Succeeding chapters introduce research conducted i n the United States which attempts to r e l a t e the economic theory pre-sented above to a p r a c t i c a l p r i c i n g schedule. The f i n a l chapter incorporates a l l of the work described above. Using the Airborne Instrument Laboratory, A i r p o r t Capacity Handbook, the p r a c t i c a l capacity of Vancouver International A i r p o r t (movements per hour) i s calculated. Consideration i s given to i i p r e v a i l i n g weather patterns as well as the configuration and c h a r a c t e r i s t i c s of the runways to a r r i v e at the annual capacity of the a i r p o r t . This capacity figure i s then used to determine how appropriate the current levels of landing fees are at Vancouver International A i r p o r t . Ratios of processing time are determined for A i r Carrier and General Aviation a i r c r a f t . These r a t i o s , which r e f l e c t the time required for an a i r c r a f t of one class to land r e l a t i v e to the time required for an a i r c r a f t of the other class to land, are calculated for various mixes of the a i r c r a f t population. Using these r a t i o s and weighting them with the f r e -quency with which each r a t i o could be expected to occur, a schedule of opportunity cost (General Aviation - A i r Carrier) i s prepared. By applying the l a t t e r schedule to the current l e v e l of landing fees, an alternate schedule of landing fees at Vancou-ver International A i r p o r t has been calculated. By observing how the l e v e l of charges at Vancouver International A i r p o r t has been, to some degree, responsible for the pattern of investment there, i t i s evident that considerable improvement i n the a l l o c a t i o n of resources can be effected by re v i s i n g t h i s schedule. Application of the resultant fee schedule w i l l not guarantee an improvement i n the economy but u t i l i z a t i o n of the p r i n c i p l e s inherent i n i t s derivation, w i l l c e r t a i n l y c l a r i f y the d i r e c t i o n change must take. i i i T A B L E O F C O N T E N T S Chapter Page INTRODUCTION I THE ECONOMICS OF AIRPORT DEMAND AND PRICING . 1 APPROACHES TO PEAK FOOD PRICING: A. Steiner 2 B. H i r s h l e i f e r 9 C. Williamson 13 II APPLICATION OF EFFICIENT PRICING RULES 30 III THE DEVELOPMENT OF A MODEL FOR PRICING RUNWAY CAPACITY 56 IV VANCOUVER INTERNATIONAL AIRPORT 95 A. Rationale for Expansion 95 B. Airport Capacity 100 C. Capacity Calculation 110 V DERIVATION OF LANDING FEE SCHEDULE 123 CONCLUSIONS 133 BIBLIOGRAPHY 140 APPENDIX "A" 142 APPENDIX "B" 153 i v L I S T O F T A B L E S Chapter I Chapter II Chapter III Table I Average Delays to Kennedy A r r i v a l s .... 65 Table II A r r i v a l Rates for Kennedy A r r i v a l s .... 70 Table III Delay Calculation—Schedule Evaluator Technique 77 Table IV Peak Average Delay 79 Table V Cost of Delay 87 Table VI Hourly Average of Expected Remaining Busy Period 89 Table VII Proportional Marginal Cost Prices for LaGuardia A i r p o r t 93 Chapter IV Table I Vancouver International Airport, Population D i s t r i b u t i o n 114 Table II Calculation of Multiple Runway Capacities 115 Table III Percent Annual Runway Use , 116 Table IV Capacity Calculation 118 Table V Capacity C a l c u l a t i o n — D a t a Revision . . . 120 Table VI Capacity C a l c u l a t i o n — F i n a l I t e r a t i o n . 121 Chapter V Table I Capacity of Vancouver International A i r -port under varying mines of a i r c r a f t population 127 Table II Processing Time Ratios, General A v i a t i o n — A i r C a r r i e r A i r c r a f t 127 Table III Vancouver International Airpor t , Peak movements, August, 1973 129 Conclusion Table I Proposed Fee Schedule, Vancouver International Airport 138 V L I S T O F F I G U R E S Chapter I Figure 1 Firm Peak Case 4 Figure 2 S h i f t i n g Peak Case 7 Figure 3 Short-Run and Long-Run Solutions, Discontinuous Cost Function 10 Figure 4 Short-Run and Long-Run Solutions, T r a d i t i o n a l (Continuous) Cost Function 14 Figure 5 General Solution 18 Figure 6 Unequal Demand Solution 23 Figure 7 I n d i v i s i b l e Plant Solution 28 Chapter II Chapter III Figure 1 Average Delay as a Function of Operational Frequency Figure 2 A r r i v a l Rate as a Function of Acceptance Rate Figure 3 Average Delay as a Function of Average A r r i v a l Rate Figure 4 Queue Length Chapter IV Figure 1 Vancouver International Airport 96 Figure 2 A i r Movement Forecast 99 Figure 3 AIL Delay as a Function of Movement Rate 102 Figure 4 Runway Configurations 107 Chapter V Conclusion Figure 1 Annual Costs and Revenues, C i v i l Aviation Infrastructure 136 v i ACKNOWLEDGEMENTS My sincere appreciation i s extended to Dr. Karl M. Ruppenthal for his suggestions and guidance. I am also indebted to Mr. Douglas G. Hosgood and Mr. Donald McLaughlin of the Ministry of Transport, Vancouver, B.C. for t h e i r invaluable assistance i n obtaining data. Further thanks to Miss Evelyn Heggelund and Miss V i c k i Blackmore for t h e i r generosity i n typing the paper. To my wife Glenis, for her i n f i n i t e patience and unflagging determination. v i i i Introduction The Ministry of Transport ( P a c i f i c Region) intends to expand the capacity of Vancouver International A i r p o r t by construct-ing an additional runway p a r a l l e l to the 08-26 f a c i l i t y . L i t t l e thought has been devoted to the question of economic j u s t i f i c a t i o n for the expansion. The schedule of landing fees at Vancouver International Airport encourages use by general aviation and a i r c a r r i e r a i r c r a f t . These fees discriminate between a i r c r a f t type but not time of use. P a r t i c u l a r a i r c r a f t can land at any time for the same pr i c e . Consequently, the a i r p o r t i s u t i l i z e d the most during the hours most convenient to business travel—between 7:00 a.m. and 9:00 a.m., and 6:00 p.m. and 8:00 p.m. Expansion of the a i r p o r t i s sought to accommodate the t r a f f i c which u t i l i z e s the runways at the peak hours. During the off-peak hours the runways are used much les s . I t i s the writer's hypothesis that the system of landing fees currently employed by the Ministry of Transport i s , to a large degree, responsible for the l e v e l and pattern of t r a f f i c using the a i r p o r t . This schedule of fees provides no incentive for u t i l i z a t i o n of f a c i l i t i e s at off-peak times, nor does i t r a t i o n capacity i n an economically e f f i c i e n t manner. I t i s f e l t that i f the l e v e l of landing fees was equated to the cost of providing the service, the demand for service would drop. Only users who placed a value on landing equal to the higher fees would be accommodated, and additional investment i n the a i r p o r t could be delayed or even avoided. i x The idea of equating cost and price to ensure e f f i c i e n c y i s not new. Under p e r f e c t l y competitive conditions marginal cost and price are equivalent. The application of t h i s concept to welfare economics, primarily the p r i c i n g of services, has attracted renewed attention i n recent years. Peak load p r i c i n g under con-s t r a i n t s , and i n the general case, i s the topic i n t h i s instance. P.O. Steiner, J . H i r s h l e i f e r and O.E. Williamson have incorporated marginal cost theory into a theory for p r i c i n g a commodity under varying conditions of demand. The commodity was a service and, by v i r t u e of i t s nature, was not storeable. Steiner was i n s t r u -mental i n devising a geometrical solution to the p r i c i n g problem. Unfortunately his technique was tenable only under very r e s t r i c t e d conditions. H i r s h l e i f e r modified Steiner's technique to comply with his own notion of discriminatory p r i c i n g . Williamson's work modified Steiner's approach and allowed marginal cost p r i c i n g theory to be applied to very general sit u a t i o n s . During the l a s t ten years, the concepts explored by the above authors have been examined i n the l i g h t of p r i c i n g the services of a i r p o r t s . J . Yance, A. C a r l i n & R. Parks, M.E. Levine, and J . Wardford examined the p r i c i n g schemes used at major American airports and concluded that the rules adhered to by policy-makers i n establishing prices did not conform to economic e f f i c i e n c y c r i t e r i a . C a r l i n & Park developed a p r i c i n g scheme based on the marginal delay costs that a i r c r a f t impose on each other when operating within a congested system. Michael E. Levine i n v e s t i -gated the dilemma of excess demand at major airpost. (U.S.) X Levine recommended a p r a c t i c a l approximation to marginal cost p r i c i n g but q u a l i f i e d his suggestions with recognition of the d i f f i c u l t y of ascertaining t h i s figure. He further suggested that marginal costs of operating and expanding f a c i l i t i e s be averaged over some period of time to avoid disruption due to highly variable prices. J . Yance has addressed the problem from a di f f e r e n t standpoint. Like the others, Yance questions the v a l i d i t y of weight based landing fees. He feels that a more s i g n i f i c a n t variable i s the length of time that a movement takes. Landing fees would, i n his view, better r e f l e c t the cost of a movement, i f they were proportional to the r e l a t i v e time demands of a i r c r a f t using an a i r p o r t at a given time. The present work incorporates the Yance technique of assessing landing charges. An analysis has been made of the t r a f f i c densities at Vancouver International A i r p o r t to determine i f the a i r p o r t i s currently operating at capacity. The Airborne Instruments Laboratory (AIL) c r i t e r i o n f or capacity operation was adopted: an a i r p o r t i s considered to be at capacity i f the average delay experienced by departing a i r c r a f t i s equal to four minutes. Using the Yance model, the time demands of a i r c a r r i e r a i r c r a f t r e l a t i v e to general aviation a i r c r a f t has been calculated This c a l c u l a t i o n has been repeated for various configurations of a i r c r a f t mix, weather conditions and season. Given the r e l a t i v e demands of these two c l a s s i f i c a t i o n s , a revised schedule of land-ing fees has been calculated. The revised schedule i s compared with the schedules at airports in three metropolitan (U.S.) areas where increases in the minimum level of landing fees precipitated a significant reduction in t r a f f i c . Based on the results of the above work, recommendations for future policy have also been made. Chapter I Before discussing the theory of peak load p r i c i n g i t may be worthwhile s t a t i n g the objectives of t h i s paper and the studies being reviewed. By adopting a scheme of p r i c i n g , one attempts to improve e f f i c i e n c y i n the a l l o c a t i o n of resources i n one sector of the economy. The sector i n question i s aviation-related a c t i v i t y emanating from Vancouver International A i r p o r t . No attempt w i l l be made to prescribe techniques which recover the f u l l costs of providing service or which enable the a i r p o r t to accommodate a l l demands. The sole aim of the application of peak load p r i c i n g theory to t r a f f i c at the a i r p o r t i s to maximize consumer welfare by improving the a l l o c a t i o n of resources currently employed there. The s o c i a l welfare function to be maximized i s defined i n terms of the so c a l l e d Marshallian "surplus" c r i t e r i o n . This d e f i n i t i o n disregards the d i s t r i b u t i o n of income for a l l i n d i v i d -uals. A d d i t i o n a l l y , a l l of the work reviewed assumes that the optimum conditions of production and exchange are s a t i s f i e d e lse-where i n the economy. This simplifying assumption should not detract from the value of these studies since i t obviates the requirement of "second-best" approaches and permits a p a r t i a l analysis of t h i s problem. The problem of peak load p r i c i n g has been addressed many times since the l a s t world war. Of the solutions presented i n the l i t e r a t u r e , f i v e predominate: Marcel Boiteux; Hendrik Houthakker; Peter Steiner; Jack H i r s h l e i f e r and Oliver Williamson. 2 . Three of these studies w i l l be elucidated i n t h i s presentation. Peter 0. S t e i n e r 1 presented an approach to peak load p r i c i n g i n an a r t i c l e published i n the Quarterly Journal of Economics, November 1967. Steiner's work, though dependent on some very r e s t r i c t i v e assumptions, provides a good point to begin the review. Steiner begins by assuming that only two kinds of costs are incurred i n providing capacity: "b" - the operating costs per unit of capacity per period (assumed constant), and "B" - the cost of providing a unit of capacity (assumed independent of the amount of capacity required). If there i s excess capacity the marginal cost of a unit of output i s equal to "b". If new capacity i s required, the marginal cost becomes "b+B". This assumption i s retained throughout Steiner's paper and a l l work subsequent to i t . A more l i m i t i n g q u a l i f i c a t i o n can be found i n the second assumption: "...the product i s to be produced i n two time periods of equal length." A further assumption i s also made: the demand for output i n each period i s independent of demand i n other periods and these independent demands are not i d e n t i c a l : the demand i n one period being everywhere above the demand i n the other period. The number of l i m i t a t i o n s to the analysis i s reduced i n a l a t e r , more general approach, but the elements e s s e n t i a l to the s i m p l i f i e d analysis are retained: each demand curve i s a declining function of the Steiner P.O. Peaks Loads and E f f i c i e n t P r i c i n g , Quarterly Journal of Economics, 1957. 3 . quantity of product i n that period alone and the demand for output (service) i n one period i s independent of demand i n the other period. Steiner's object i s to "determine the prices that w i l l lead buyers to purchase these quantities." He recognizes that the amount of capacity required i s equal to the maximum l e v e l of demand regardless of which period the demand emanates from. Given two equal periods of unequal, independent demand, we may i n f e r the existence of a,peak load problem i f the quantities demanded at any price are unequal. Having established the c r i t e r i a for a peak load problem, i t remains to "specify a schedule of prices which w i l l lead buyers to purchase the quantity of output i n each period that w i l l lead to the s o c i a l optimum ." What then, i s the s o c i a l optimum? Steiner adopts the t r a d i t i o n a l approach to t h i s question. A s o c i a l l y optimum r e s u l t i s obtained by maximizing the "excess of express-ed consumer s a t i s f a c t i o n over the cost of resources devoted to production ." Put more simply, t h i s means that one attempts to maximize the sum of producers' and consumers' surplus. Any d i s t r i b u t i o n a l e f f e c t s are assumed to be equated throughout the economy. The demand for output i n the two periods i s i l l u s t r a t e d i n Figure 1. The demand curves for the two periods meet the Steiner P.O. Peaks Loads and E f f i c i e n t P r i c i n g , Quarterly Journal of Economics, 1957. 3 Ibid. Figure 1 4. Firm Peak Case P2=b X Source: Steiner, P.O. Peak Loads and E f f i c i e n t  P r i c i n g , Quarterly Journal of Economics, 1957. 5 . c r i t e r i a established above. D.^  i s the demand for output i n period 1 and i s the demand for output i n period 2. The operating costs have been subtracted from these curves so they may be viewed as the e f f e c t i v e demands for capacity i n th e i r respective periods. Steiner adds these independent demands v e r t i c a l l y to obtain the t o t a l e f f e c t i v e demand for capacity. Only the po s i t i v e portions of each demand curve are added since i n e f f e c t i v e demand (demand that w i l l not even cover operating costs) i s not relevant to the decision of p r i c i n g . This v e r t i c a l addition i s j u s t i f i e d only i f the two demands are viewed as complementary, not competitive. We now turn to an analysis of Figure 1; Steiner's "firm peak" case. The t o t a l j u s t i f i e d capacity i s X^, (where the t o t a l e f f e c t i v e demand for capacity i s equal to the marginal cost of providing that capacity.) The demand for marginal capacity i s made by period 1 users only, therefore these users can be expected to pay for the marginal cost of (additional) capacity: P^=b+B. Because t h e i r demand for capacity i s much les s , the users of period 2 should be charged only the costs of operation: P 2 = ^ ' T n i - S price w i l l p e r s i s t u n t i l period 2 users demand a l e v e l of output which exceeds i t s cost of production. The prices assigned to the two groups of users are not discriminatory, they merely r e f l e c t the d i f f e r e n t costs of accomodating the users. Steiner then views another applic a t i o n . He asks: What amounts of capacity would be demanded by on-peak and off-peak users i f the prices derived from the firm peak case were applied 6. to the case depicted i n Figure 2? Here the e l a s t i c i t y of demand in both periods d i f f e r s from that observed i n the f i r s t case. Application of P^ and to t h i s case r e s u l t s i n period 1 users demanding and period 2 users demanding x*. This i s c l e a r l y not an optimum solution; period 2 users are only required to pay operating costs (b) but they are the only users placing a demand on capacity. In t h i s s i t u a t i o n x^ units are required but only x^ units of capacity are being paid f o r . I t can be seen that even an average price (eg. b+B =P*) would not be optimum.• Under 2 t h i s scheme, output demanded i n periods 1 and 2 would be x^ and * * ^2 respectively. Capacity equal to x^ units would be required * * at t h i s price but only x^ + would be paid f o r . The marginal 2 unit of capacity would not be j u s t i f i e d by demand for that * capacity. Capacity equal to x^ would not be u t i l i z e d i n period 2. The correct analysis can be understood by reference to Figure 2. Addition of and y i e l d s D^. (the e f f e c t i v e demand for capacity). Intersection of the cost of capacity and t h i s e f f e c t i v e demand curve y i e l d s the amount of capacity j u s t i f i e d by the demand i n 1 and 2. In Figure 2, t h i s capacity i s equal to X q units. At t h i s l e v e l of capacity, the outputs i n each period may be extended to X q because they exceed the costs of operation (b). Steiner outlines the procedure for deriving the optimum l e v e l of capacity and the l e v e l of prices associated with that capacity: "...a unit of capacity i s j u s t f i e d i f and only i f 1. i t i s j u s t i f i e d by the demand i n any period alone or 2. i t i s j u s t i f i e d by the combined demands i n two or more periods. Once the appropriate Figure 2 S h i f t i n g Peak Case 7. Source: Steiner, P.O., Peak Loads and E f f i c i e n t P r i c i n g , Quarterly Journal of Economics, 1957. 8 . capacity i s determined, output i n each period should be extended to that capacity unless additional units of output f a i l to cover the operating costs at an e a r l i e r output. Then given the optimal outputs i n each period and the demand curves, i t i s routine to determine the optimal p r i c e s . " In Figure 2, the demand i n periods 1 and 2 r e s u l t s i n the prices and P^. Steiner maintains that these two prices are discriminatory. (This point w i l l be debated i n succeeding pages). He presents the prices for periods 1 and 2 i n terms of a deviation from the average price B/2: P1 = b+B/2+I^ P 2 = b+B/2+K2 since the sum of the prices i s 2b+B; + = 0. "If the demand curves are d i f f e r e n t at X q , the prices are unequal and since t h i s i s t r u l y a case of j o i n t costs, unequal prices i n the face of equal outputs and j o i n t costs means discriminatory p r i c e s . " The "shifting-peak" case presented by Steiner i l l u s t r a t e s a weakness i n the attempt to charge peak load users a price which includes a contribution to providing capacity while charging o f f -peak users a price which only covers the cost of operation. The scheme f a i l e d because the prices appropriate to peak and o f f -peak periods were assigned to s p e c i f i c periods i n advance. The boundaries of these periods were determined from h i s t o r i c a l demand data. Once the prices were assigned, buyers chose to purchase quantities at those prices that led to a d i f f e r e n t de facto peak. The implications for p o l i c y created by t h i s r e s u l t w i l l be discuss-ed l a t e r i n the thesis. 9. 4 J . H i r s h l e i f e r responded to the work of Steiner i n a comment published by the Quarterly Journal of Economics i n August 1958. H i r s h l e i f e r ' s c r i t i c i s m i s valuable, because i t presents an a l t e r n a t i v e view of marginal cost when capacity has been reached. Steiner adopted the view that marginal cost i s undefined at this point; H i r s h l e i f e r depicts marginal cost as i n f i n i t e . The primary focus of H i r s h l e i f e r 1 s work i s on the description of the prices to peak and off-peak users. As noted above, these prices are d i f f e r e n t , the peak users paying a price which includes the cost of capacity. H i r s h l e i f e r concedes the difference but contends that t h i s difference i s not discriminatory. "...the e f f i c i e n t price differences i n a peak load s i t u a t i o n shown i n Steiner's analysis are not discriminatory because they are equal to the differences i n the marginal cost of serving the classes of customers involved." H i r s h l e i f e r maintained that even though his argument could be dismissed as t r i v i a l , " i t hinges on a semantic i n t e r -pretation of the work discrimination) i t was valuable bacause i t presented the problem i n a more general sense by d i f f e r e n t i a -t i n g between the short-run and the long-run. H i r s h l e i f e r ' s contribution i s presented below. H i r s h l e i f e r d i f f e r e n t i a t e s between the short-run solution and a long-run solution. This i n t e r p r e t a t i o n i s diagrammed i n Figure 3. The demand i n periods 1 and 2 i s shown as two H i r s h l e i f e r J . Peak Loads and E f f i c i e n t P r i c i n g : Comment, Quarterly Journal of Economics, 1958. Figure 3 10 Short-Run and Long-Run Solutions, Discontinuous Cost Function SRMC, SRMC B 2b+B b+B U LRMC-Joint LRMC-Separable Q7 Q B Q Source: H i r s h l e i f e r J . , Peak Loads and E f f i c i e n t P r i c i n g , Quarterly Journal of Economics, 1958. 11. independent curves and Operating costs "b" and capacity costs "B" are assumed constant. I t w i l l be noted that i n t h i s case and are not drawn net of operating costs as was done in Steiner's approach. Capacity cost "B" i s a continuous curve under the assumption of pe r f e c t l y d i v i s i b l e plant. Short-run marginal cost (SRMC) i s discontinuous, being equal to "b" at levels of operation below capacity and undefined thereafter. SRMC i s shown i n Figure 3 as a v e r t i c a l l i n e at capacity l e v e l s of operation. In the short-run, prices are established by equating demand i n each period to the SRMC. Output should be extended to the point where demand equals SRMC. In the present case, output would be extended to capacity i n both periods. This solution i s optimal for the short-run. If a price less than Q^S was charged to period 2 users, demand for output would exceed capacity and a rationing scheme would be necessitated. A price greater than Q^S would, i n the short-run, r e s u l t i n a demand less than capacity. I t i s clear from and D2 that the value placed on an additional unit of "q" through the range "0" to capacity i s greater than the variable cost of supplying i t . The long-run solution i s obtained by equating the relevant, demand curve with the relevant Long Run Marginal Cost (LRMC) curve. The f i r s t step i s the determination of the relevant demand curve. Referring to Figure 3, we can see that i n neither period does demand for capacity exceed "b+B" at the e x i s t i n g capacity l i m i t , therefore an expansion of capacity i s not j u s t i f i e d 12. by either separate demand. If demand i n one period did exceed the cost of capacity, expansion would be j u s t i f i e d and the relevant LRMC curve for comparison with t h i s demand would be LRMC (separable). This long run cost curve indicates the cost of increasing output for one of the periods, output for the other l e v e l being held constant at some lower l e v e l . The marginal cost i s equal to the sum of capacity cost "B" and operating cost "b" for a single period. The combined demand of periods 1 and 2 i s s u f f i c i e n t to j u s t i f y an expansion of capacity. Expansion should continue up to the point where combined demand i s equal to LRMC (j o i n t ) . The j o i n t long run marginal cost of output i s the sum of the operating costs and capacity costs for both periods (2b+B). The optimum l e v e l of capacity given t h i s demand i s Qg. The fore-going discussion i s merely a modification of Steiner's solution. H i r s h l e i f e r compares his solution where demand i n only one period i s high enough to j u s t i f y expansion, (LRMC-separable) with SteinerV s "firm-peak" case. Steiner's "shifting-peak" case i s allowed as being analagous to H i r s h l e i f e r ' s solution where neither period's demand necessitates expansion of capacity but th e i r combined demand does (LRMC-joint). If we accept t h i s i n t e r p r e t a t i o n , H i r s h l e i f e r ' s contention that the prices assigned to output are not discriminatory, seems plaus i b l e . The above analysis i s true for the short-run i n the case where the short-run marginal cost curves are discontinuous. The long-run solution, which involves the v e r t i c a l summation of the independent demands i s only v a l i d i n the r e s t r i c t e d case where the SRMC curves remain discontinuous. 13. If we abandon the assumption of discontinuous SRMC curves, the solution to the long run remains the same but the technique re-quired to derive i t must change. In Figure 4 the SRMC curves are drawn i n a t r a d i t i o n a l shape. Short-run prices are give, as before by the inte r s e c t i o n of and with the applicable SRMC curve. Once again, there i s i n s u f f i c i e n t demand i n either period to j u s t i f y expansion. Expansion i s j u s t i f i e d , however by the combined demands of each period. Since p r i c e i s equivalent to the marginal cost of output, a summation of the demand prices i n each period r e f l e c t s the long-run cost of supplying the t o t a l output demanded S P with e x i s t i n g capacity. i e — t h e sum of Q AS 1 and Q P' i s greater than LRMC ( j o i n t ) . We also note that expansion should continue up to the point where the marginal cost of supplying output to meet the combined demand i s equal to the sum of the in d i v i d u a l period demand prices. (marginal cost of supplying output for each period's demand). Upon reaching optimal capacity, prices are again assigned according to SRMC. With the work of Steiner and H i r s h l e i f e r the theory of peak load p r i c i n g had reached the point where optimal capacity and p r i c i n g decisions could be made, a l b e i t 5 under r e s t r i c t i v e assumptions. O.E. Williamson's paper, publish-ed i n 1966, expanded on the previous work and devised a technique to solve the problem i n a more generalized context. In a r r i v i n g at a s o c i a l welfare function, Williamson Williamson O.E. Peak-Load P r i c i n g and Optimal Capacity  under I n d i v i s i b i l i t y Constraints, American Economic Review, 1966. Figure 4 14. Short-Run and Long-Run Solutions, T r a d i t i o n a l (Continuous) Cost Function Source: H i r s h l e i f e r J. Peak Loads and E f f i c i e n t  P r i c i n g , Quarterly Journal of Economics, 1958. 15. makes e s s e n t i a l l y the same assumptions as Steiner and H i r s h l e i f e r regarding d i s t r i b u t i o n a l e f f e c t . He defines s o c i a l benefit i n the following manner: " . . . t o t a l revenue plus consumer's surplus. (Social cost,) treated as opportunity cost and assuming no technological e x t e r n a l i t i e s , w i l l be separable into t o t a l pecuniary cost less intramarginal rent." If we assume that a l l inputs are available i n completely e l a s t i c supply, intramarginal rents are zero. Like the preceeding assumptions the l a t t e r provides for a s i m p l i f i e d analysis; a l l conclusions reached v i a the analysis must, of course, be regarded i n the l i g h t of these assumptions. Given these d e f i n i t i o n s , Williamson describes his s o c i a l welfare function as follows: (1) W = SB - SC = TR + S - TC where W = net welfare gain, SB = s o c i a l benefit, SC = s o c i a l cost, TR = t o t a l revenue, S = consumers surplus, and TC = t o t a l cost. D i f f e r e n t i a t i n g t h i s expression with respect to output (Q), we obtain the following: (2) dW = _d (TR + S) -_d (TC) = 0 dQ dQ dQ This r e l a t i o n s h i p implies that P = MC where the second derivative of the expression i s less than zero. (3) dfw = dP - d 2 (TC) < 0 dQ 2 dQ dQ 2 That the f i r s t derivative with respect to output of TR + S i s equal to price (P) can be seen from the defination of the deriv-atiave: ' Q 16. TR + S = ^ T P ( Q ) ' dQ1 where P(Q)' i s the demand curve. o (the quantity Q1 demanded at every price P ) . By d i f f e r e n t i a t i n g the l e f t hand side of t h i s expression with respect to Q, we obtain by d e f i n i t i o n : 4) _d (TR + S) = d J P(Q)' dQ1 dQ d~Q o = P(Q) ' These re l a t i o n s f u l f i l l the necessary and s u f f i c i e n t conditions for a maximum. Assuming p e r f e c t l y d i v i s i b l e plant, t o t a l costs are defined as the sum of operating and capacity costs times the quantity of output i n the period under consideration. In t h i s d e f i n i t i o n , Williamson adopts the usual notation of "b" for operating costs and "B" for capacity costs. (5) TC = (b +B) Q Operating costs, "b" are assumed constant per unit of output. Referring to equation (2) we can see that optimal scale of plant i s obtained when P = b + B. If we take the scale of plant as fixed, the optimal price i s determined by maximizing the net welfare gain (w) subject to the capacity constraint (Q): Max. W = (TR + S) - bQ s.t. Q, Q^Q This expression i s set up as Lagrangian: max. L (Q,A) = (TR + S) - bQ - A(Q - Q) D i f f e r e n t i a t i n g p a r t i a l l y with respect to Q and , we obtain: dL = P - b - A dQ dL = -Q + Q 17. equating to 0, we obtain: P - b - A = 0 P = b + A -Q + Q = 0 Q 6 Q (capacity constraint) If the constrint i s not binding, (capacity has not been reached; Q < Q) i s zero and the optimal price i s found by equating the short-run cost of providing output (b) with the output demanded. When capacity i s reached (Q = Q) the value of becomes p o s i t i v e and the optimal price exceeds "b". The rule r e s u l t i n g from t h i s analysis i s , i n essence, a re-statement of the rule derived by H i r s h l e i f e r for expanding and r e t i r i n g capacity. Williamson notes " . . . i f b + A>b = B (and demand i s expected to continue at t h i s l e v e l ) , and expansion of plant i s signalled, whereas i f b +A < b + B, plant should be r e t i r e d . " Williamson now begins to relax the assumptions adhered to i n the previous analysis. I n i t i a l l y he focuses on the e f f e c t of i n d i v i s i b i l i t i e s on the solution to the optimal capacity problem. Plant can be supplied i n d i s t i n c t units of size E. He retains the assumption of non-peaked or uniform loads. Because plant can only be supplied i n d i s t i n c t units the short-run marginal cost of operation i s sharply kinked at the point of capacity and i s undefined beyond th i s point. The i n c l u s i o n of plant i n d i v i s i -b i l i t i e s i n the analysis necessitates the modification of the s o c i a l welfare function to read: W = S + (TR - TC) where S i s consumers surplus and (TR - TC) i s net revenue. Figure 5 General Solution 18. Source: Williamson 0., Peak-Load P r i c i n g , American Economic Review, 1966. 19. Williamson adopts the term "producers surplus" to describe the l a t t e r expression. He also retains the terms "b + B" for operat-ing and capacity costs**. I n i t i a l l y the enterprise i s i n long-run equilibrium where long-run marginal cost, short-run marginal cost and price are a l l equal. Figure 5 depicts the s i t u a t i o n . I f demand s h i f t s from and D^, i s investment i n another unit of capacity j u s t i f i e d . The task at hand i s to devise a technique to determine at what point demand i s s u f f i c i e n t l y large to j u s t i f y expansion. Williamson's solution involves adjusting demand to the point where the enterprise i s i n d i f f e r e n t between the status quo and expan-sion. The enterprise i s assumed to be i n d i f f e r e n t because at thi s point (J i n Figure 5) the net welfare gain associated with either alternative i s the same. Demands greater than would dictate an expansion. Proof: Recalling the d e f i n i t i o n of net welfare gain W, referred to before, we see that at point J , the gain i n consumers surplus S i s just o f f s e t by the loss i n producers surplus (TR - TC). This i s c l a r i f i e d by comparing consumers and producers surplus before and afte r the s h i f t from D^ to D2-When demand equals D-^  consumers surplus i s given by the area UNG. Producers surplus i s zero, therefore the net welfare gain i s equal to UNG. When demand s h i f t s to D 7 and capacity Williamson regards the cost of capacity as the oppor-tunity cost of the resources employed. The foregone alternative i s considered equivalent to an annuity which pays a given amount per period over the useful l i f e of the plant. B, the average capacity cost per period i s equal to ^/z. (where E i s the unit of capacity) plus the average cost of maintenance per period. 20. remains the same, the price or output i s raised to P^ to ra t i o n e x i s t i n g capacity. At t h i s new price, consumers surplus i s equal to VIH and producers surplus i s equal to HING. Net welfare gain i s given by t h e i r sum, VING. The net e f f e c t on the welfare gain r e s u l t i n g from an increase i n capacity can be seen by comparing the increase i n consumers surplus to the loss i n producers surplus. Consumer surplus increases by the amount HING + GJLF + UN. Producers surplus i s reduced by the amount HING + GHLF + JKL. The net gain i s equal to UN - JKL, which by assumption i s zero since the l e v e l of demand was drawn to assure t h i s . We can see that based on the c r i t e r i a of maximizing net welfare gain, any l e v e l of demand greater than w i l l d ictate expansion because expansion would re s u l t i n a po s i t i v e net welfare gain. When expansion i s complete prices are established by equating demand and SRMC. It i s evident from Figure 5 that for any l e v e l of demand intermediate between points N and K, the enterprise w i l l operate at a loss i n the long run. Williamson also notes that i n the r e a l world, demand does not s h i f t "once and for a l l " but instead fluctuates while i t increases over-time. His analysis i s e s s e n t i a l l y correct, however, since by allowing for uncertainty, the rules governing expansion s t i l l apply, "...the counterpart of our previous c r i t e r i o n i s to add capacity whenever E(UN) > E(JKL) where E(.) denotes expectation..." This observation has implications for decision makers i n situations where f a c i l i t y expansion i s often based on forecasts of ex i s t i n g a c t i v i t y . Williamson now attends to the problem of peak loads. It i s i n t h i s analysis that the major contribution of his work can be found. Williamson r e s i s t s the temptation to assume that the peak and off-peak loads are of equal duration. He fe e l s that any conclusions reached as a r e s u l t of t h i s assumption cannot be generalized. Instead he takes a period of a day against which to express costs, and allows the two loads any proportion of t h i s period. By adopting t h i s procedure, Williamson permits convention-a l costing practices normally employed i n uniform load analyses to be applied to situations where the loads are perio d i c . The continuity of t h i s approach merits c r e d i t . Short-run marginal costs and long-run marginal costs are defined as before. The key to thi s approach i s the construction of the demand curves so that they r e f l e c t the r e l a t i v e demands of the i n d i v i d u a l loads. This i s done by weighting each demand according to the proportion of the period for which i t i s e f f e c t i v e "...each demand., (is weighted) by the f r a c t i o n of the cycle over which i t p r e v a i l s . Thus demand i s expressed as D^(w^) where i refers to the subperiod i n question and superscript (w^) to the fr a c t i o n of the cycle during which the demand i n question p r e v a i l s , with each demand curve showing the amount of output per cycle which would be demanded at every price were the demand i n question to pr e v a i l over the entire c y c l e . " It i s also assumed that the periodic demands are independent. This i s a common assumption and was made by Steiner and H i r s h l e i f e r as well. Whether i t i s reason-able i s questionable, p a r t i c u l a r l y i n the case of periodic demands 22. for landing p r i v i l e g e s at an a i r p o r t . Williamson begins the analysis with the assumption of d i v i s i b l e plant and two periodic loads. Neither assumption i s c r i t i c a l to the outcome of the analysis but only serve to simplify i t . The two loads are of eight and sixteen hours length. 1/3 2/3 They are shown i n Figure 6 and are e n t i t l e d D^' and respect-i v e l y . To determine the optimum size of plant, some way must be found to combine the i n d i v i d u a l loads into an "eff e c t i v e demand for capacity curve." It w i l l be r e c a l l e d that Steiner achieved t h i s combination by v e r t i c a l summation of the i n d i v i d u a l demand curves. His summation involved demands for capacity net of operating costs and assumed that these demands were not competitive. This technique cannot be incorporated i n t h i s instance however because the periodic loads are not of equal duration. Williamson's approach to the design of t h i s geometric solution involved the following reasoning: If we consider each periodic load i n d i v i d u a l l y and ignore the other, we must agree that, i n order for net revenue to be zero, the price charged against each load must be b + B/w^ . w^  i s the f r a c t i o n of the entire cycle that load i i s i n e f f e c t . Total revenue from operation of the plant for w^  hours i s given by P^Q^W^' t o t a l cost for t h i s period i s bQ.w. + BQ.. If P.Q.w. - (bQ.w. + BQ. ) i s to equal zero, must equal b + B/w^ . In long-run equilibrium with constant returns to scale and d i v i s i b l e plant TR - TC must be zero. To transform each periodic load curve into a demand for Figure 6 Unequal Demand Solution 23. Source: Williamson 0., Peak-Load P r i c i n g , American Economic Review, 1966. 24. capacity curve, the resultant curve must cut the LRMC curve at a l e v e l of capacity consistent with the price b + B/w^ . Williamson devised an ingenious technique which guaran-teed t h i s r e s u l t . One must take the v e r t i c a l difference between the periodic load curve and the short-run marginal cost curve, multiply t h i s difference by the proportion of the period that the periodic load i s i n e f f e c t (w^) and v e r t i c a l l y add t h i s weighted amount to the short-run marginal cost. This procedure i s repeat-ed for both periodic demands. The resultant curve i s l a b e l l e d i n Figure 6 . The optimal scale of plant for these periodic demands, where capacity cost B = B 1 i s found from the int e r s e c t i o n of the relevant LRMC curve and the e f f e c t i v e demand for capacity curve * D„. This point i s consistent with output equal to Q.. Price i n the off-peak period i s P ^ and P 2^ i s the price i n the peak load period. (the prices are obtained from the in t e r s e c t i o n of the periodic load demand curves and the SRMC curve). It can be seen that the peak demand users pay a higher price for services than do the off-peak users. The amount by which the off-peak users f a i l to meet capacity costs i s just o f f s e t by the amount above t o t a l costs that the peak users are forced to pay. The same * procedure applies when B = B 2. Optimal capacity i s equal to Q2• In t h i s case off-peak users pay only operating costs b and a l l capacity costs are met by the peak loadusers. Williamson also demonstrates a l g e b r a i c a l l y that his p r i c -ing rules are appropriate and not just the r e s u l t of a conveniently arranged diagram. Recalling the s o c i a l welfare funciton introduced i n i t i a l l y W = TR + S - TC, and using the subscripts 1 and 2 to ref e r to peak and off-peak demand, where w^  and w2 are the fractions of the period accounted for by each demand, we obtain: W = (TRX + S 1)w 1 + (TR2 + S 2)w 2 - hQ1 - b Q ^ - BQ2. I f , as i n the f i r s t case i n Figure 6 where capacity i s f u l l y u t i l i z e d during both demand periods, we have = Q 2 . Letting Q = = Q2, and substituting into the welfare function, we obtain: W = (TR1 + S 1)w 1 + (TR2 + S 2)w 2 - bQ(w1 + w2> - B-jQ To obtain the optimum plant s i z e , we d i f f e r e n t i a t e t h i s function with respect to Q, and set i t equal to 0. m= p n w i + p i 2 w 2 - b ( w i + w 2 } - B l = ° P 1 1w 1 + P 1 2w 2 = b(wx + w2) + B x Substituting 1/3 for w-^  and 2/3 for w2 i n the above expression, we obtain: P11 W1 + P12 W2 = b + B l This i s exactly the same r e s u l t obtained i n Figure 6 for the case where B = B^. This solution i s general for any number of periodic demands regardless of the r e l a t i v e time that each demand i s i n e f f e c t during the period. If however, as i n the case where B = B 2, plant i s f u l l y u t i l i z e d only during one demand period, the o r i g i n a l formulation of the welfare function i s retained. Optimal capacity i s found by d i f f e r e n t i a t i n g p a r i t a l l y , 26. f i r s t with respect to Q1, then with respect to Q 2 . W = (TRX + S 1)w 1 + (TR2 + S 2)w 2 - bQ1w1 - b Q ^ - BQ2 dQ± = P21 W1 " b w l = 0 e l , = P22 W2 " b w 2 " B = ° simplifying: P 2 1w 1 = bW± P 2 1 = b and, P22 W2 " b w 2 = B P 2 2 - b = B/w2 once again these r e s u l t s are i d e n t i c a l to those obtained from Figure 6. Summarizing, we can see that i n the off-peak i n t e r v a l , price i s set equal to short-run marginal cost. The price during peak load i s set at incremental operating cost (b) plus the f r a c t i o n of capacity cost a t t r i b u t a b l e to peak load (B 2/w 2). We now turn to a description of the s i t u a t i o n where plant i s not d i v i s i b l e . When capacity can only be added i n discrete units, the method of deriving optimum capacity and prices remains e s s e n t i a l l y the same. Williamson merely combines the technique where plant i s i n d i v i s i b l e and periodic demands are uniform with the technique where plant i s d i v i s i b l e and periodic demands are not equal. Succeeding chapters w i l l be concerned with the applica-tion of t h i s analysis to a i r p o r t landing fee p r i c i n g . I t i s 27. evident that i n the case of a i r p o r t s , expansion of capacity involves the construction of large units (runways) which, because of operational constraints, are not d i v i s i b l e . I t w i l l be r e c a l l e d that when we considered i n d i v i s i b l e plant and uniform periodic demands, we formulated decision rules for expansion by comparing the welfare gain before an expansion and the envisioned gain a f t e r the expansion. This technique i s again used with the addition of d i s s i m i l a r periodic demands. The demands i n the off-peak and peak are seen i n Figure 7. The e f f e c t i v e demand for capacity curve D £ has been constructed by the v e r t i c a l summation of the weighted periodic demands. The diagram depicts the s i t u a t i o n where one i s i n d i f f e r e n t between adding capacity or not, By construction UN = JKL. If we disregard D E and refer to the i n d i v i d u a l demand curves, i t can be seen that the addition to consumers surplus due to expanded capacity and lower prices i s just o f f s e t by the coincident loss of producers surplus. i e . - 2/3(NFG-GKH) i s the amount that the gain i n consumers surplus exceeds the loss i n producers surplus during peak operations; 1/3(MNKO) i s the amount that the additional consumers surplus f a l l s short of the loss i n producers surplus during off-peak operations. Therefore by d e f i n i t i o n : 2/3(NFG-GKH) - 1/3(MNKO) =0. Because plant i s indivisible> long-run equilibrium does not guarantee that long-run marginal costs w i l l be met. Peak load prices w i l l not necessarily exceed LRMC although depending on the r e l a t i v e slopes of the periodic demands and the size of the Figure 7 I n d i v i s i b l e Plant Solution 2 8 . Source: Williamson 0., Peak Load P r i c i n g , American Economic Review, 1966. u n i t of expansion, they may. This chapter has attempted to show how welfare economic theory can be applied to the f i e l d of p r i c i n g , p a r t i c u l a r l y of u t i l i t i e s and transportation services. The l a t t e r areas are notorious for periods of excessive demand as well as very low lev e l s of demand. Application of the theory presented i n t h i s chapter to an actual s i t u a t i o n i s very d i f f i c u l t i f not impossible. Knowledge of short or long-run marginal costs i s very d i f f i c u l t to obtain. Even i f such information was available, equating SRMC to demand would r e s u l t i n a highly variable p r i c e . Some compromise would ultimately be necessary. The next chapter w i l l discuss some recent attempts to reconcile theory and r e a l i t y . 3 0 . Chapter II In both Canada and the United States the growth of a i r t r a f f i c i n the l a s t ten years has been phenomenal. The public has responded e n t h u s i a s t i c a l l y to t h i s f a s t mode of transport, and the demand continues to grow. The capacity of airports to accommodate th i s burgeoning demand has not kept pace. The r e s u l t has been congestion, p a r t i c u l a r l y at airports which serve large, metropolitan areas. T r a d i t i o n a l l y a l l a i r p o r t users have been treated equally - on a " f i r s t come, f i r s t served" basis. Those a i r c r a f t which arrived f i r s t would be accommodated before any successive a r r i v a l s . This philosophy was reasonable at a time when demand was l i g h t , and the resources necessary to meet such demand were r e a d i l y available. But resources are neither p l e n t i f u l nor cheap. Devoting resources to expanding airpor t s leaves less for other uses; expansion of the supply of a i r p o r t f a c i l i t i e s can be accomplished only at a cost. If a i r p o r t capacity i s not s u f f i c i e n t to meet demand i t must be rationed among users i n some manner. At present i t i s allocated to the persons most w i l l i n g to wait. The most common method of rationing goods and services i n "Western" society, i s to l e t people bid for things i n money terms—with goods going to whoever i s w i l l i n g to pay the most. This method, however i s rar e l y used for a i r p o r t s . The r e s u l t i s that e x i s t i n g capacity i s very poorly u t i l i z e d and demand for greater capacity i n t e n s i f i e d . 31. The demand for a i r t r a v e l i s characterized by peaks and troughs. Over a twenty-four hour period, the pattern varies l i t t l e ; peaks i n the early morning and late afternoon when t r a v e l for business i s convenient. T r a f f i c also varies to some extent accord-ing to the day of the week and the season of the year. Since landing fees and t i c k e t prices do not discriminate between any of these factors, demand for service i s greatest during preferred t r a v e l hours. The capacity of the a i r p o r t to accommodate demand i s not only affected by the number and configuration of i t s runways but also by wind d i r e c t i o n and weather. When the weather d e t e r i o r -ates, a i r c r a f t using the a i r p o r t must operate under Instrument Flyi n g Rules (IFR) 1. This s i t u a t i o n requires more spacing between a i r c r a f t , which slows the rate of landing and departures. The demand for a i r p o r t use i s a function of the cost of making a t r i p at a p a r t i c u l a r time, as well as the cost of making the same t r i p at another time. The costs involved i n making the t r i p vary with the amount of congestion present i n the system at the time of the intended t r i p . For a passenger, the largest cost i s the money cost of his fare. For the a i r c r a f t operator, the relevant expenses are the operating costs of the a i r c r a f t plus the landing or departure fee. It i s evident that during delays, the t o t a l cost of t r a v e l w i l l not be uniform across users, nor w i l l costs be consistent with t r a v e l at times of the day when IFR becomes e f f e c t i v e when the cloud base descends below 1000 feet and the horizontal v i s i b i l i t y from the threshold of the runway i s less than three miles. no delays are experienced. The t o t a l cost of t r a v e l i s composed of the out of pocket costs plus the costs of congestion. Because a i r c r a f t operators are not assessed d i f f e r e n t i a l landing fees and passengers are not assessed d i f f e r e n t i a l t i c k e t p r i c e s , there i s no incentive to a l t e r t r a v e l times, and capacity i s rationed by congestion. Those t r a v e l l e r s most w i l l i n g to endure delays continue to t r a v e l at peak demand times, while the others adjust t h e i r t r a v e l plans and use the a i r p o r t when i t i s less congested. Such a system rewards the users who value the service least, while penalizing those who value i t greatest. To date, very l i t t l e progress has been made i n modifying the system of p r i c i n g used at air p o r t s . The major emphasis s t i l l continues to be placed on expansion of capacity. A number of studies have been conducted recently to analyze the p r i n c i p l e s at work i n the production of congestion. The res u l t s of these studies, and the recommendations made from the re s u l t s share a common theme: the c a p i t a l cost of expanding capacity at congested airpor t s far outweighs the benefits that could be derived from such expansion. On the other hand, a change i n the schedule of prices currently used at these airpor t s would rati o n e x i s t i n g capacity e f f i c i e n t l y and provide a useful c r i t e r i o n for ultimate expansion. Three of these studies w i l l be reviewed here. The f i r s t analysis by Michael E. Levine, serves as a synopsis of the problem. When analyzing the role of public p o l i c y toward a i r p o r t s , one inva r i a b l y concludes that airpor t s as a public u t i l i t y should 33. be operated so as to earn "a reasonable return on a prudent 2 investment ." Even though th i s view i s widely held, the basis on which costs should be recovered (cost recovery p r i c i n g based on t o t a l a i r c r a f t weight) does very l i t t l e to achieve this goal. Levine summarizes t h i s dilemma: "For reasons which are never e x p l i c i t l y stated, discussions of p u b l i c - u t i l i t y - t y p e , 'cost-recovery' p r i c i n g of a i r p o r t services always center on the revenue generating function of prices and never on the a l l o c a t i o n and investment regulating functions. The emphasis i s on paying for a known l e v e l of capacity, and l i t t l e attention i s devoted to questions of maximizing the value of use of e x i s t i n g f a c i l i t i e s and determining the amount of capacity which ought to be provided. Capacity i s always matched to "need", and need i s determined independently of p r i c e . " In the United States, landing fees are established through negotiation between the major c a r r i e r s and the a i r p o r t operator. Fees for General Aviation users are usually set at a s p e c i f i c amount (regardless of a i r c r a f t weight) and are often waived i n l i e u of f u e l purchases. On the other hand fees for terminal f a c i l i t y concessions are sold to the highest bidder. Unfortunately, t h i s procedure r e s u l t s i n the highest bidder.acquir-ing a monopoly position as the sole provider of a service. The problems of higher than optimum prices and r e s t r i c t e d output Levine M.E. Landing Fees and the Airport Congestion  Problem, The Journal of Law and Economics, 1969. usually associated with monopolistic enterprises apply i n t h i s case as well. M. Levine i l l u s t r a t e s the procedure adopted at many large American airports for p r i c i n g landing fees. Because of a fear that the concessionaires i n the a i r p o r t terminal building w i l l abuse t h e i r p o s i t i o n , the a i r p o r t operators impose monopoly r e s t r i c t i o n s on output. The large p r o f i t s , received from the concessionaires as rent, are then used to subsidize users of the landing area. The resultant very low landing fees further encourage the use of these f a c i l i t i e s , compounding the problem. The follow-ing agreement i s extracted from Levine's a r t i c l e and i s included here to i l l u s t r a t e very c l e a r l y , the process by which landing fees are calculated. The major airports of the United States use e s s e n t i a l l y the same methods i n setting landing fees: A i r l i n e Parties F l i g h t Fee Requirement Chicago -0'Hare International A i r p o r t for the six months ending June 30 , 1968. Estimated Total A i r p o r t Expenses $ 1 6 , 1 9 4 , 6 0 2 F i r s t 6 months of 1968. Estimated Total A i r p o r t Revenues Excluding 8 , 4 3 7 , 2 0 0 F l i g h t fees, f i r s t 6 months of 1968. Estimated Total F l i g h t Fee Revenue Requirement 7 , 7 5 7 , 4 0 2 F i r s t 6 months of 1968. Estimated F l i g h t Fees from other (Non-Parties) 104,556 A i r l i n e , F i r s t 6 months of 1968. Estimated Total F l i g h t Fee Revenue Requirement 7 , 6 5 2 , 8 3 6 A i r l i n e Parties, F i r s t 6 months of 1968. Estimated Total Landing Weight, A i r l i n e Parties, 1 8 , 6 5 9 , 1 3 7 F i r s t 6 months of 1968. (000 lbs.) Estimated F l i g h t Fee per thousand pounds, A i r l i n e $ .410 Parties, F i r s t 6 months of 1968. 35. The a i r l i n e s support t h i s method of c a l c u l a t i o n as do the air p o r t operators. "That the a i r l i n e s should take t h i s view i s hardly surprising, since i t treats t h e i r primary a c t i v i t i e s as a 'la s t resort' for revenues, and then assesses charges against them only to the extent necessary to cover costs. That the a i r p o r t operators should regard t h i s as an appropriate formula i s odd since i t i s a p r i n c i p l e cause of th e i r present problems." This procedure i s not followed i n Canada, however. Concessions are awarded to the highest bidder, and revenues are col l e c t e d from the contract winner, but these revenues are not applied against landing fees. Landing fees were set by the federal government i n 1967. General Aviation and A i r Carriers have r e s i s t e d any attempts to revise these rates i n recent years. Appendix i l l u s t r a t e s the e x i s t i n g rate structure as well as a breakdown of operating costs and revenues associated with current leve l s of ai r p o r t use. Under the present system of landing fees, there i s no d i f f e r e n t i a t i o n with respect to a i r c r a f t type or the time of day that the landing takes place. Even though the landing f i e l d i s not subsidized by the terminal users, the fees currently imposed 3 are low enough to encourage i t s use by many low value users. The landing fees currently i n e f f e c t i n Canada are among the lowest i n the world. By a low value user i s meant an i n d i v i d u a l who places l i t t l e value on the privi l e d g e of landing at a p a r t i c u l a r a i r p o r t at a given time. Many General Aviation f l i g h t s come under t h i s category. 36. Despite some differences i n the technique by which landing fees are established, the rationale behind the provision of landing access i s the same i n both Canada and the United States. A l l a i r p o r t users are considered equal and are e n t i t l e d ' t o the same service regardless of t h e i r size or the value of t h e i r oper-ation. Users are served on a "first-come, f i r s t - s e r v e d " basis. It i s t h i s basis that i s the subject of the next section. Under the present basis for a l l o c a t i n g landing r i g h t s , users are treated i n a uniform manner. During peak-hour periods, when congestion occurs, a l l a i r c r a f t wishing to land suffer delays. Light a i r c r a f t , (which often carry fewer than six people) impose delays and are the recepients of delay. The costs that these a i r c r a f t impose on other larger a i r c r a f t are far greater than the costs that are imposed on them by these same a i r c r a f t . Regardless of the difference i n operating costs between these two classes of a i r c r a f t , the a i r c r a f t enduring greater hardship (in terms of cost) i s not given any p r i o r i t y over the smaller a i r c r a f t . Further-more, the larger a i r c r a f t does not even have the opportunity to express his willingness to s k i r t the queue by paying a higher landing fee. It i s t h i s l a s t point that i s d i r e c t l y responsible for the d i s t o r t i o n i n the amount of monies allocated to a i r p o r t con-struction and expansion. Having presumed that a i r p o r t users are equal, one i s obliged to service t h e i r demands without hesitation even i f such service necessitates continued expansion of f a c i l i t i e s . If how-ever, we observe that d i f f e r e n t users place d i f f e r e n t values on 3 7 . the r i g h t to land an a i r c r a f t , we can extract the economic rent associated with that desire by p r i c i n g landing fees d i f f e r e n t i a l l y . At present, those users who are the most w i l l i n g to tolerate delay (due to congestion) are the ones who are being served. If we assume that greater delay means greater cost, (both i n operating costs and opportunity cost to the t r a v e l l e r ) then i t i s apparent that those users enduring equal delays are not suffering i d e n t i c a l costs. Each a i r c r a f t operating i n a period of congestion experi-ences only the average delay of a l l the a i r c r a f t operating at that time. The marginal cost of delay due to an additional a i r c r a f t can conceivably be much greater than the average cost. This i s evident i n a s i t u a t i o n where both a i r c a r r i e r s and general aviation share an a i r p o r t . Because of slower approach speeds, the dangers of wake turbulence from larger a i r c r a f t , and the limited a v a i l a b i l i t y of special runways and procedures, a l i g h t a i r c r a f t may cause even more delay than an additional a i r l i n e r . The example c i t e d by the most adamant of the a i r l i n e interests involves a large commercial j e t (et. - DC-8) being compelled to lose his landing sequence to avoid overtaking a smaller, slower general aviation a i r c r a f t which i s landing. The obvious comparison i s made between the r e l a t i v e operating costs of the two a i r c r a f t , with the DC-8 being the most expensive. Levine describes some other aberrations from economic e f f i c i e n c y which can be traced to the f l a t - r a t e system of landing fees : I. The current system of landing fees discourages a i r l i n e s from scheduling t h e i r equipment t i g h t l y and thereby increasing u t i l i z a t i o n . There i s also no incentive to reduce 38. schedules; any company that removes an a i r c r a f t from the schedule i s disadvantaged by a competitor who simply substitutes one of his a i r c r a f t into the vacancy. I I . The current system of landing fees also d i s t o r t s a l l o c a t i o n s between modes of transport. The system delays equally, short haul passengers who have many substitutes for a i r t r a v e l and long haul passengers, who have few substitutes. In consequence, long haul passengers are prevented from out-bidding short haul passengers (for the r i g h t to f l y and of course, to land) who might otherwise use t r a i n s , buses or private automobiles. I I I . The present p r i c i n g system also discourages the development of smaller f a c i l i t i e s i n metropolitan areas. Most of the airports which cater to general aviation t r a f f i c e xculsively, are not located i n as convenient an area as the major a i r p o r t s . In addition, these a i r p o r t s are not as sophisticated i n terms of navigation and landing assistance equipment. Because landing fees are not discriminatory, any general aviation a i r c r a f t w i l l i n g to endure some congestion may use the major a i r p o r t . Adjustment of the schedule of landing fees could make these a n c i l l i a r y a i r -ports more a t t r a c t i v e to general aviation a i r c r a f t and further a l l e v i a t e congestion at the hubs. As a concluding objection to a system of weight based landing fees, Levine challenges the incentives that such a system creates. As mentioned above, weight based landing fees encourage high frequency (low load factor) scheduling of a i r c r a f t . This i s es p e c i a l l y true i n the case of l i g h t e r a i r c r a f t . Smaller a i r c r a f t can be scheduled at r e l a t i v e l y high frequency during peak hours and w i l l incur the same a i r p o r t charges as would be incurred by fewer larger a i r c r a f t carrying the same number of passengers. The t o t a l weight of an a i r c r a f t , which i s used to assess landing charges does not r e f l e c t the variable cost of runway use i n terms of wear and tear of the run-way surface. This wear i s a function of "footprint pressure" of the a i r c r a f t landing gear. The size , number and arrangement of the gear determines how the t o t a l weight of the a i r c r a f t i s d i s t r i b u t e d on to the bearing surface. Many smaller j e t s , with simple landing gear arrangements, place heavier loads on the runways than do the la t e s t generation of large, wide-bodied j e t s . Undoubtedly, aprons and taxi-ways must be enlargened to accommodate the larger c r a f t and such additional investment must be noted, but at present the landing fee schedules provide dis-incentives to the designers of a i r c r a f t insofar as the provision of landing gear which conserves runways. At most large a i r p o r t s , general aviation a i r c r a f t pay either a f l a t fee for landing or substitute the purchase of f u e l . A i r c a r r i e r a i r c r a f t pay both the landing fee and the f u e l flowage fee. The rationale behind a f u e l flowage fee w i l l be discussed at length elsewhere i n t h i s chapter, so only a b r i e f mention w i l l be made of i t here. B a s i c a l l y , heavier, (faster) a i r c r a f t are charged more than l i g h t e r (slower) a i r c r a f t . The higher charge i s a function of the larger volumes of f u e l sold to the larger a i r c r a f t . Aside from the debate over the equity of t h i s scheme, one must observe what incentives are created by i t s use. A i r 40. c a r r i e r equipment i s scheduled with scant consideration to the price of f u e l at each successive stop. (This has t r a d i t i o n a l l y been the case when f u e l was p l e n t i f u l and cheap, i t s relevance may have changed dramatically since the Middle-East war and the Arab o i l embargo.) The amount of f u e l purchased i s usually related only to the stage length just flown, the speed and a l t i t u d e of the f l i g h t and the- anticipated payload for the next stage length. General aviation a i r c r a f t , p a r t i c u l a r l y the very l i g h t variety, consume far less f u e l than t h e i r a i r c a r r i e r counterparts. This low rate of consumption, combined with the waiving of landing fees often encourages use of the a i r p o r t for fr i v o l o u s purposes. Levine mentions the recreational f l i g h t for a cup of coffee or the student p i l o t f a m i l i a r i z a t i o n f l i g h t as examples of such use. The f r i v o l i t y of such f l i g h t s can be debated but the major thrust of the c r i t i c i s m of f u e l flowage fees remains v a l i d : the c o l l e c t i o n of fees for the purchase of f u e l at airpor t s encourages t h e i r use by l i g h t weight, economical a i r c r a f t with low value missions while simulta-4 neously penalizing heavier a i r c r a f t which consume more f u e l . In summarizing his argument, Levine develops a p a r a l l e l comparison between free enterprise market a c t i v i t y and the sort of a c t i v i t y we observe at a i r p o r t s . The question of resource supply and a l l o c a t i o n at airpor t s i s presented i n the l i g h t of economic j u s t i f i c a t i o n . Economic p r i n c i p l e s have been abandoned i n The f a c t that a p a r t i c u l a r a i r c r a f t consumes more f u e l to f l y a given route than does another a i r c r a f t cannot be construed (necessarily) to mean that the " t h i r s t i e r " a i r c r a f t i s less economical. Consideration must be had, amoung other things, of the number of persons accomodated by each a i r c r a f t . 4 1 . establishing prices for a i r p o r t services and i n determining the timing for further investment. The following quote from Levine 1s work summarizes th i s f a i l i n g and sets the stage for the ensuing discussion: "Most goods and services are supplied and allocated according to a system of market prices . These prices serve two primary functions: they d i s t r i b u t e the stock of goods and services i n existence at any given time to those uses i n which they can be employed to maximum consumer s a t i s f a c t i o n ; and they determine over time the pattern of investment i n production ensuring a mixture of production best adapted to consumer wants... ( i t has been) seen that the e x i s t i n g price system for a i r p o r t services f a i l s to a l l o c a t e the e x i s t i n g capacity so as to maximize i t ' s value. It f a i l s also to guide investment i n airpor t s so as to achieve the appropriate mix and l e v e l of output with a minimum investment of resources. This f a i l u r e i s s o c i a l l y wasteful i n two ways—through congestion and inappropriate f a c i l i t i e s i t prevents the a i r transport industry from maximizing consumer s a t i s f a c t i o n , and by f a i l i n g to appropriate-l y match investment to output i t wastes resources which could be used to s a t i s f y wants elsewhere i n the economy." In the market place, production of goods and services i s c a l l e d forth by the demands of consumers. Excessive demand (over available supply) increases the price over production costs and at t r a c t s investment i n expectation of a p r o f i t . The resultant increase i n production, reduces prices u n t i l an equilibrium i s reached where further investment stops and the price s t a b i l i z e s at a l e v e l commensurate with a normal rate of return. This process continues however as entrepreneurs seek to d i v e r s i f y t h e i r products and f i n d a market. D i f f e r e n t i a t i o n of products w i l l continue up u n t i l the point where the cost to the producer of seeking a market for and producing a d i f f e r e n t i a t e d product exceeds the value to the consumer of the d i f f e r e n t i a t i o n . By understanding why entrepreneurs seek to d i f f e r e n t i a t e t h e i r products within a free market environment, i t becomes easier to apply t h i s reasoning to the a i r transportation industry. Transportation may be characterized as a service. Demand for t h i s service t y p i c a l l y varies c y c l i c a l l y over time, being very heavy during some periods and very l i g h t during others. The production of a i r transportation employs some resources for consider-able periods of time. These fixed costs are incurred regardless of demand. F a c i l i t i e s which were constructed to produce a service available to consumers during periods of high demand are automat-i c a l l y a vailable without additional cost to production i n other periods. In periods of low demand the only additional cost of producing the service i s the cost attributable to each unit of the variable cost. With fixed costs of production treated as j o i n t between periods of high and low demand, i t i s i n the best i n t e r e s t s of the entrepreneur to stimulate demand for his product at other-than-peak periods. This i s often done by price d i f f e r e n t i a l s which a t t r a c t consumers not i n the market at peak demand pr i c e s . Some consumers also s h i f t from using the service at peak times to using i t at a reduced price during off-peak times. Because a weight based landing fee i s assessed the users of a i r transportation services, there i s no incentive for a i r p o r t managers to seek out users with d i f f e r e n t needs and develop d i f f e r e n t i a t e d f a c i l i t i e s for them. I t i s evident that the users of a i r p o r t s are not homogeneous. Different categories of a i r c r a f t d i f f e r greatly i n t h e i r demands for a i r p o r t services. Light a i r c r a f t require less elaborate landing aids and can be accomodated by short runways of low strength. As a i r c r a f t s i z e , weight and speed increase and a l l weather operation consistency becomes es s e n t i a l , more sophistication i n instrument landing systems are required to ensure safe operations. The use of sophisticated a i r c r a f t also necessitates provision of long runways capable of supporting high loads. A i r c r a f t operators are compelled to pay a landing fee which (to some degree varies with the type of a i r -craft) r e f l e c t s the weight of t h e i r machine. Because they pay a f l a t rate, regardless of the c h a r a c t e r i s t i c s of the runway they use, a i r c r a f t operators are not i n c l i n e d to use the simplest f a c i l i t y consistent with t h e i r needs. Predictably, because of the lack of demand for such f a c i l i t i e s , they are not supplied. The mechanism through which demand may be directed, i s missing here. The weight based landing fee does not permit the a i r c r a f t operator the opportunity to signal his preference. The same reasoning applies i n the case of e l e c t r o n i c landing approach aids. Such devices are invaluable to the p i l o t and provide assistance i n approaching the a i r p o r t as well as descending on the i d e a l g l i d e slope to a safe touchdown. The complexity of these instruments varies widely. The more precise the guidance system, the more costly i t i s to manufacture and i n s t a l l . Despite opinions to the contrary, the degree of precision required to guide an a i r c r a f t approaching a runway at speeds less than 12 0 miles per hour, i s not great. The approach guidance equipment at airp o r t s frequented by both general aviation and a i r c a r r i e r a i r c r a f t i s often i d e a l for the faster commercial a i r c r a f t but superfluous for the slower, l i g h t e r a i r -c r a f t . Both the Federal Aviation Administration (FAA) i n the 4 4 . United States and the Ministry of Transport (MOT) i n Canada i n s i s t on the i n s t a l l a t i o n of the ultimate i n guidance equipment regardless of i t ' s s u i t a b i l i t y . The a i r c r a f t operator, because he i s not charged (directly) for the use of instrument aids, does not economize i n his use of them. Levine f e e l s that much of the equipment i s supplied to U.S. a i r p o r t s without consideration of need, "...and the FAA whose existence and annual appropriation depends i n part on i t s i d e n t i f y i n g and s a t i s f y i n g a 'need' for i t s services, encourages operators to expect and demand sophistica-ted e l e c t r o n i c assistance needed or not." The previous discussion has shown how the system of weight based landing charges d i s t o r t s the a l l o c a t i o n of resources at a i r p o r t s . For the most part, t h i s discussion centred on design aspects of the a i r p o r t and the consequences of not d i f f e r e n t i a t i n g between users. The following deliberations w i l l be concerned with the e f f e c t that the present system of landing fees has had on decisions to invest i n the a i r p o r t . Landing fees which are not time dependent nor which vary between seasons, encourage overinvestment to accommodate peak demands. As mentioned before, the value of a delay-free schedule varies among a i r c r a f t operators. At one extreme we have a i r c a r r i e r s which r e l y heavily for patronage on t h e i r a b i l i t y to f l y under most weather conditions as well as schedule f l i g h t s at times convenient to the t r a v e l l e r and ensure that the f l i g h t w i l l be punctual. At the other extreme, we have a general aviation a i r c r a f t , whose operator f l i e s for recreation and to whom time i s of l i t t l e consequence. The capacity of the a i r p o r t i s competed for by a l l users but the terms of thi s competition-delays due to congestion, favor the operators who value time l e a s t . The net e f f e c t of large volumes of t r a f f i c and competition for capacity i s strong pressure to expand landing f a c i l i t i e s . This pressure i s invari a b l y i n i t i a t e d by those operators who value time highly. In the United States, at least, an expansion of the a i r p o r t f a c i l i t i e s i s financed (to some degree) by those users who place l i t t l e value on time and would otherwise be content to endure congestion. A i r c r a f t operators contribute to expansion through higher landing fees. This compulsory contribution "encourages greater peak-hour use by low value users who are e n t i t l e d to use the peak-hour f a c i l i t i e s they pay for and who accomodate themselves to reduced congestion by increasing t h e i r operations. The r e s u l t i s s t i l l more investment, higher fees and 5 no reduction i n congestion. The low l e v e l of the landing fees i s not the only problem however. Combined with t h i s i s the lack of exclusive possession of landing rights for a i r c r a f t operators. Without some guarantee of access to the landing area, an a i r c r a f t operator w i l l be reluctant to contract his schedule. Any reduction i n schedule frequency that he makes w i l l be matched by an increase i n a c t i v i t y by another user. This phenomenon was mentioned before but here i t w i l l be embellished. To allow the a i r c r a f t operator the oppor-tunity to maximize his u t i l i t y , he must be permitted to express Levine M.E. Landing Fees and the Airport Congestion  Problem, The Journal of Law and Economics, 1969. his willingness to obtain exclusive r i g h t s to the landing area. Such an expression could be r e f l e c t e d i n a bid registered by the a i r c r a f t operator or the acceptance by him of a peak-hour surcharge established by the ai r p o r t manager. The extraction of greater revenue from e x i s t i n g resources would benefit society as a whole. As we have seen, the l e v e l of landing fees i n Canada and the United States, i s very low. This low rate i n e v i t a b l y a t t r a c t s many users, with congestion occuring at popular times of the day. We have observed the e f f e c t that the low-level, f l a t - r a t e landing fees have had on investment decisions. In the following sections, The rationale behind the current p r i c i n g scheme w i l l be examined and the equity debate surrounding the proposed revisions w i l l be described. The scheme currently used to assess the charges made for air p o r t services i s a compromise between a r b i t r a r y rationing and d i r e c t charging. By d i r e c t charging i s meant a price which i s related d i r e c t l y to the cost of providing a service. It i s generally agreed that rationing by physical or administrative means i s unsatisfactory as a permanent po l i c y for the outputs of public u t i l i t i e s . Physical rationing i s necessarily a r b i t r a r y and i s only r a r e l y successful i n dispensing services so that the benefits derived are equivalent to the costs of supply. I t also offers no guidance for investment decisions. Direct charging techniques are ide a l expressions of marginal cost p r i c i n g rules. A i r p o r t admin-i s t r a t o r s , for unheard of reasons, choose to charge for a i r p o r t services, using c r i t e r i a that are not d i r e c t . As substitutes for 47. d i r e c t charges, the prices derived depart from the i d e a l . This departure i s inevitable for p r a c t i c a l considerations often make the r e a l i z a t i o n of an i d e a l , impossible. Unfortunately, because the c r i t e r i a selected for charging (landing weight and f u e l consumption) departs so dramatically from marginal cost rules, we are l e f t with l i t t l e more than a convenient device with which to c o l l e c t revenue. Guided by the e x i s t i n g p r i c i n g system, decision makers automatically increase capacity when e x i s t i n g capacity approaches f u l l u t i l i z a t i o n . In other words, at t h i s point more capacity i s deemed to be "required." C l e a r l y , i n the absence of a signal to invest of the kind described i n the previous section, i t can r a r e l y be c e r t a i n that the value of the a d d i t i o n a l consump-tio n made possible by the investment w i l l exceed the costs thereby incurred. Even i f the investment w i l l ultimately be required, using the e x i s t i n g p r i c i n g scheme almost guarantees that such investment w i l l be made prematurely. J . Warford, i n his book, g "Public Policy Toward General Aviation ," has developed a decision framework within which one may evaluate a p a r t i c u l a r approach to p r i c i n g . I t i s recognized that t h i s framework i s very t h e o r e t i c a l and would not l i k e l y be used by policymakers as they debate the merits of various prices. Despite t h i s weakness, i t provides a good basis from which to work. Having been exposed to the i d e a l s i t u a t i o n , we are put i n a better position to c r i t i c a l l y analyse the reasoning behind the current p r i c i n g scheme. Warford has Warford J . J . Public Policy Toward General Aviation, The Brookings I n s t i t u t i o n , 1971. 48. selected three c r i t e r i a against which a p r i c i n g scheme i s evaluated. He describes these c r i t e r i a as "influences (which determine) the attitude of a public authority toward charging a pr i c e for services supplied." The f i r s t of these influences i s : 1. Presence of technological external economies— "If the consumption of a commodity re s u l t s i n a net r e a l gain to society over and above that accruing d i r e c t l y to the purchasers, so that the marginal cost of consumption i s less than i t s marginal s o c i a l cost (that i s , net of any external marginal b e n e f i t s ) , the case for p r i c i n g that commodity i s correspondingly weakened. Although theory states that price whould equal marginal s o c i a l cost, the extent of the divergence between marginal cost and marginal s o c i a l cost i s ra r e l y known with any accuracy. To the extent that t h i s i s so, price becomes less useful i n aiding the investment decision or a l l o c a t i n g resources i n the short run." A i r c r a f t operators argue that there are technological e x t e r n a l i t i e s associated with t h e i r a c t i v i t y at an a i r p o r t . In many cases i t i s attested that the economic benefits which r e s u l t from t h i s a c t i v i t y , and which accrue to the remainder of society, exceed the costs which are incurred to maintain i t . Such a s i t u a t i o n would q u a l i f y for subsidy, i n t h i s case the maintenance of low landing fees. 2. Intangible f a c t o r s : p o l i c y makers may consider the maintenance of high safety standards, and the concurrent preser-vation of human l i f e as reasonable j u s t i f i c a t i o n for low landing fees. The value of human l i f e can be measured to some degree i n monetary terms (ie. - costs of hospital treatment, l o s t productiv-i t y etc.) but the cost of suffering associated with injury or death cannot be quantified with consensus. It may be thought that a re v i s i o n of landing fees would.effect safety standards adversely and would cost more than would be gained from additional revenues. 3. Excessive cost of the price mechanism i t s e l f : In many cases, the costs of introducing a p r i c i n g mechanism are too great r e l a t i v e to the benefits provided. This argument i s often heard i n r e l a t i o n to charging for the use of enroute navigation aids. These 7 aids usually consist of a VORTAC f a c i l i t y . Charging for the use of a i r p o r t instrument guidance equipment has also been considered. The d i f f i c u l t y inherent i n the monitoring of usage as well as the b i l l i n g for usage appears (with present technology) to outweigh the benefits. I t has been suggested that where the marginal cost g of output i s close to zero, p r i c i n g i s invariably i n e f f i c i e n t . This may be the si t u a t i o n with regard to runways, at lea s t i n the short-run. However, a necessary condition i s that long-run marginal cost also be zero. The decision maker i s then confronted with the choice of implementing d i r e c t charge p r i c i n g system. His decision must consider both the costs and the benefits associated Very High Frequency Omni-Directional receiver used i n conjunction with DME (distance measuring equipment). Monitoring of t h i s f a c i l i t y enables a p i l o t to navigate very accurately with v i r t u a l l y no reference to the physical features of his course. 8 J.G. Head, "Public Goods & Public P o l i c y , " Public Finance, Vol. 17 #3, 1962. 50. with the system; i n essence he must conduct a type of cost-benefit analysis. "The benefits of obtaining an optimal investment decision may alone warrant the introduction of p r i c i n g ; the fac t that short-run marginal cost i s zero i s not a s u f f i c i e n t condition for i t s r e j e c t i o n . The costs of extending capacity may be substantial; consequently so would be the benefits of deferring or obviating that investment by charging a price and thereby providing decision makers with r e a l i s t i c data about demand." The system of charges i n e f f e c t at North American airport s represents a tradeoff between monetary and non-monetary costs and benefits. The degree to which th i s tradeoff departs from the i d e a l outlined i n the second chapter depends on the p r i o r i t i e s e s t a b l i s h -ed by the policymakers. The following section w i l l discuss some elements of the equity debate surrounding suggested changes i n these p r i o r i t i e s . T r a d i t i o n a l l y , a i r c r a f t operators have been levied fees for the use of airports and airways which supposedly r e f l e c t e d the value of t h e i r use. This goal of charging according to the presumed value of f a c i l i t i e s has not been r e a l i z e d . To achieve such a goal would have involved charging a fee d i r e c t l y related to the use of f a c i l i t y . Direct charging was applied i n the case of landing fees but as we ahave seen, the schedule of fees although d i r e c t , was not designed to permit the operators to indicate t h e i r perception of the value of the services. This value was construed by the a i r p o r t operators and applied independently. Indirect charging i s used to c o l l e c t revenue for the use of the en route navigation services. Aside from the structure of landing fees, (which w i l l be the subject of another chapter) most of the controversy surrounding p r i c i n g i s i n the proxy selected for i n d i r e c t charging as well as the concept of i n d i r e c t charging i t s e l f . The Ministry of Transport (Canada) and the FAA (USA) use the same system i n c o l l e c t i n g revenue for the use of en route navigation systems. As we have seen, i n the United States, the rate charged may d i f f e r from that charged i n Canada, but the p r i n c i p l e remains the same. E s s e n t i a l l y , a f u e l tax i s charged and a fee i s c o l l e c t e d from the a i r c a r r i e r s for each passenger on board the a i r c r a f t . In Canada, the passenger tax i s a function of the capacity of the a i r c r a f t , and does not r e f l e c t load factors on any p a r t i c u l a r day. In recent years, pressure has been exerted on these two governmental bodies to amend the i n d i r e c t charge approach i n p r i c i n g the services of the airway system. The FAA responded to th i s c r i t i c i s m with a statement which to i t s s a t i s f a c -t i o n , j u s t i f i e d the p o l i c y : "A system of d i r e c t charges, under which a s p e c i f i c d o l l a r charge would be levied for each use of a component or service of the airway system, would meet the requirement of an equitable program of user charges i f the d i r e c t charges were related both to the use made of and the benefits derived from i n d i v i d u a l f a c i l i t i e s and services. However, the operational and administrative problems inherent i n d i r e c t charging (eg. - charging for each f l i g h t plan f i l e d , each radio contact made, etc.) appear to preclude i t s consideration for the domestic Federal Airway System i n the aggregate. The large variety of 52. f a c i l i t i e s and services i n use would require a complex schedule of fees that would have to be extensively planned before i n s t a l l a t i o n . A vast and expensive administrative establishment would undoubtedly be required to administer and to c o l l e c t such fees throughout the United States. A further objection to d i r e c t charges i s that t h e i r imposition could adversely a f f e c t the safety of f l y i n g by decreas-ing the readiness of some c i v i l users to a v a i l themselves of a l l 9 appropriate f a c i l i t i e s and services." Although no equivalent po l i c y statement was available from the Ministry of Transport at the time of t h i s writing, the author was assured by a MOT spokesman that the Ministry concurs with the stance of the FAA. Having observed the position adopted by government, i t remains now to reconcile t h i s p o s i t i o n with that of the users. Ideally, charges for use of a i r services should r e f l e c t the costs involved as a r e s u l t of d i f f e r e n t types of a c t i v i t y . Users vary as to the demands that they place on the system. Bearing i n mind the costs of distinguishing between users, the a i r p o r t operator should attempt to associate p a r t i c u l a r users with p a r t i c u l a r costs. As user d i s t i n c t i o n becomes f i n e r , so does the cost of i s o l a t i n g and assigning costs. The temptation to d i s t i n g u i s h a r b i t r a r i l y between d i f f e r e n t users for the purpose of simplifying the adminis-t r a t i o n of prices must be overcome i f any degree of equity i s to be achieved. The o f t - r e f e r r e d to example of a r b i t r a r y d i s t i n c t i o n Administrations Proposals on Airway User Charges, Hearings before the House Committee on Ways & Means, 89 Cong. 2 sess. (1966). concerns the d i f f e r e n t treatment of t r a f f i c f l y i n g under instrument f l i g h t rules (IFR) and v i s u a l f l i g h t rules (VFR). To charge IFR t r a f f i c a higher fee than VFR t r a f f i c regardless of the p r e v a i l -ing conditions i s to discriminate i n favor of VFR users. This i s acceptable except when both users are operating simultaneously. Under such conditions, IFR t r a f f i c being p o s i t i v e l y controlled, provides greater safety for VFR t r a f f i c which i s not so controlled. Equitable treatment would r e s u l t i n no d i s t i n c t i o n being made between these two classes of t r a f f i c when v i s u a l f l i g h t rules are in e f f e c t . I t i s recognized that any form of i n d i r e c t charging i s necessarily imperfect from the aspect of e f f i c i e n c y i n resource a l l o c a t i o n and of equity. The o f f i c i a l stance on d i r e c t charging for airway services has already been noted. With the present state of technology, i t i s generally agreed that the cost of detecting each i n d i v i d u a l use of thi s system and tabulating these uses would exceed the resultant benefits. The concomitant hazard to safety which could r e s u l t from a d i r e c t charge to instrument regulated f l i g h t s i s also j u s t i f i c a t i o n for i n d i r e c t charging. In practice, therefore, the demands of equity and e f f i c i e n c y can probably best be s a t i s f i e d by levying an i n d i r e c t charge. The proxy for assess-ment should r e l a t e as c l o s e l y as possible to the use made of airway services. At present, the f u e l flowage fee i s the system under use. The f u e l consumed by an a i r c r a f t i s d i r e c t l y related to that a i r c r a f t ' s weight and payload as well as to the distance flown. It may also be true that to an in d i v i d u a l a i r c r a f t operator, the net monetary benefit r e s u l t i n g from each mile flown i s greater, the greater the gross weight of his a i r c r a f t . Given these assumptions, f u e l consumption may be used to r e f l e c t the use made of the airway systems and the benefits derived from t h i s use. Cost recovery of t h i s kind discriminates i n favor of l i g h t weight, slow a i r c r a f t . Recalling that the intention of p r i c i n g airway services was to e f f i c i e n t l y a l l o c a t e resources i n addition to ensuring equity, we see that a p r i c i n g scheme based only on f u e l consumption rates would have perverse e f f e c t s . This type of scheme would invariably encourage greater than optimum use of smaller a i r c r a f t and less than optimum use of larger a i r c r a f t . Warford discusses the r e l a t i v e merits of the f u e l tax as i t af f e c t s operators of large a i r c r a f t : The use of f u e l consumption as a proxy for taxation w i l l , on occasion, work to the detriment of larger a i r c r a f t . As a r u l e , larger heavier a i r c r a f t are faster and consequently spend less time i n the airways. This fact i s not recognized by a f u e l tax. Lighter, slower a i r c r a f t , while consuming less f u e l for a given t r i p , take more time to complete i t . Distance has been suggested as an alt e r n a t i v e proxy for the assessment of the f u e l tax. This too has disadvantages. The area over which the distance i s flown w i l l r e f l e c t the cost incurred to provide navigation aids. Obviously a f l i g h t over a remote part of the Yukon i s not comparable to a f l i g h t of si m i l a r distance i n a very congested airspace. The resolution of the problem of proxy selection has been l e f t to default. Neither distance nor f u e l consumption i s an i d e a l proxy, both have disadvantages i n cert a i n applications. Fuel consumption i s used primarily because of the 5 5 . ease of c o l l e c t i n g the tax. The machinery of c o l l e c t i o n already exists and c o l l e c t i o n does not necessitate a complex c a l c u l a t i o n to equate the tax burden to amount of use. This section has shown how weight based landing fees and indiscriminant f u e l flowage fees can lead to congestion on the one hand and a d i s t o r t i o n of e f f i c i e n t equipment u t i l i z a t i o n on the other hand. The following chapter describes the work done for the Port of New York Authority by the Rand Corporation. This author understands that t h i s work represents the most extensive research done i n thi s f i e l d i n recent years. The report develops a model for p r i c i n g a i r p o r t runway capacity which i s economically e f f i c i e n t and resolves many of the problems of equity alluded to above. The data for the model was co l l e c t e d from observations made at . Kennedy International A i r p o r t . The presentation i n t h i s chapter follows the same sequence as the o r i g i n a l paper. There are four sections: Section I — the th e o r e t i c a l formulation of the model. Section II — the development of empirical estimates of t r a f f i c and delays that are required to c a l i b r a t e the model. Section III — the c a l i b r a t i o n of the model i s outlined. Section IV — delay reductions r e s u l t i n g from . t r a f f i c volume reduction are estimated and summarized. Chapter III I Theoretical Model Airp o r t capacity studies have usually used a steady state queueing model i n which average delays are related to the number of operations. As the figure below depicts, as the number of operations per unit of time increases, so does the average delay per operation. A steady state solution can be found at low rates of a r r i v a l . However as the a r r i v a l rate approaches the rate at which the a i r c r a f t can be accommodated, average delay approaches i n f i n i t y and no steady state solution e x i s t s . Figure 1 i s adopted from studies conducted by the Airbourne Instruments Laboratory (AIL) It can be seen that misleading r e s u l t s could obtain from the use of such a model i n a s i t u a t i o n where the a r r i v a l rate frequently exceed the acceptance rate. C a r l i n and Park elected to use a deterministic queueing model. The model i s deterministic i n that a r r i v a l and departure frequencies are not time invariant; they are related to the time of day as well as the season of the year. (The day of the week i s also a determinant). In t h i s model the a r r i v a l rate varies throughout the day and exceeds the service rate for substantial periods of time. The a r r i v a l rate A(t) i s defined as the rate at which a r r i v a l s or departures would land or take o f f i f there were unlimit-ed capacity to accommodate them. This i s the pattern of t r a f f i c that would ensue i f there were no delays. The acceptance rate, c, i s defined as the maximum number of operations that an a i r p o r t can Figure 1 Average Delay as a function of Operational Frequency Operations Per Unit of Time Source: C a r l i n & Park "Model of Long Delays At A i r p o r t s , " Journal of Transport Economics and Policy, 1970. 58. accept during a given period of time. This rate r e s u l t s i n a higher capacity than that predicted by AIL model. 1 The acceptance rate i s the number of operations at which the average delay curve becomes v e r t i c a l . Reference to Figure 1 w i l l elucidate t h i s point. This rate i s dependent on weather conditions and the runway i n use among other things. While considering these d e f i n i t i o n s i t becomes easy to v i s u a l i z e the sequence of events which take place when the a r r i v a l rate A(t) exceeds the acceptance rate c, during the course of a day. Figure 2 i s an i l l u s t r a t i o n of the hypothesized r e l a t i o n s h i p between A(t) and c when A(t) i s very smooth and c i s unvarying. Neither of these assumptions i s r e a l i z e d under normal conditions but relaxing the standard of rigour f a c i l i t a t e s the treatment of the variables without much loss of precision. When the a r r i v a l rate r i s e s above the acceptance rate at time t ^ not a l l a i r c r a f t can be accommodated and backlog or queue begins to develop. This queue eventually equals the number of a i r c r a f t represented by the shaded area under the A(t) curve and above the acceptance rate curve c. Put more s p e c i f i c a l l y , the length of the queue i n aeroplanes at any time t, for t f t =^ t ^= t^, equals: 1. Q(t) = J (A(t) - cj dt to where t Q i s the i n i t i a l point that the queue begins to develop. The delay to an a i r c r a f t which arrives at the a i r p o r t at time t The AIL c r i t e r i o n for capacity i s the experience of an average delay of four minutes to a l l a i r c r a f t requiring accommo-dation. This c r i t e r i o n and i t s application i n the AIL model w i l l be examined i n d e t a i l i n the next chapter. Figure 2 59. A r r i v a l Rate as a Function of Acceptance Rate 60. i s equal to the length of time required to work through the queue i n existence at that time. 2. W(t) = Q(t) c Substituting for Q(t), we obtain: W(t) = 1 /'[A(t) - cj dt 3. c Total delay D i s simply the summation of each of the delays experienced by the i n d i v i d u a l a i r c r a f t : 4. D = J' A(t) . W(t) dt Delay W(t) reaches a maximum at t ^ where the a r r i v a l rate once again equals the acceptance rate. Delays w i l l return to zero at time t 2 . At t h i s point, the queue which developed as a r e s u l t of excess demand w i l l have dissipated. This f a c t i s portrayed by the eq u l i t y of the two shaded areas between times t^ and t ^ (when the queue begins and reached a maximum) and times t ^ and t 2 (when the queue i s at maximum to when i t dissipates completely). I t i s evident from t h i s model that there i s no simple r e l a t i o n between a r r i v a l rate and average delay during a p a r t i c u l a r hour. Rather, the average delay depands upon the pattern of demand as well as the acceptance rate, both which are variable. C a r l i n and Park recognize that the above model i s too simple to be used i n explaining actual observed data. If the model i s to be used for data explanation, some complicating factors must be considered. The smooth a r r i v a l rate pictured i n Figure 2 i s an i d e a l . In r e a l i t y there are major intra-hourly variations i n a r r i v a l rates. A more accurate characterization would be a trend l i n e with many sharp peaks and troughs on eit h e r 61. side of i t . The peaks w i l l contribute to periodic queues even though the average a r r i v a l rate does not exceed the acceptance rate. A further unresolved complication i s the r e l a t i o n s h i p between a r r i v a l s for landing and a r r i v a l s for takeoff. Obviously these two competing a c t i v i t i e s a f f e c t each other. The degree to which each a f f e c t s the other i s dependent on such things as the configuration of the runways i n use as well as any r e s t r i c t i o n s on the airspace around the a i r p o r t . The amount of interdependence between these a r r i v a l s w i l l determine t h e i r net e f f e c t on the usefulness of the model. The f i n a l caveat concerns the range of v a l i d i t y for the model. "The model holds s t r i c t l y only for i n d i v i d u a l days. An attempt to test i t or apply i t on the basis of average data may be misleading. The greater the day to day v a r i a t i o n i n the elements of the model, the more important i s t h i s q u a l i f i c a -2 t i o n . " In the succeeding sections, t h i s l a s t reservation i s incorporated into the model, II The variables described i n the above section are now estimated from data c o l l e c t e d at Kennedy International Ai r p o r t . Recalling the f i n a l q u a l i f i c a t i o n to u t i l i z a t i o n of the model, a l l estimates are disaggregated by weather and season. The authors experienced considerable d i f f i c u l t y i n obtaining records of delays to i n d i v i d u a l f l i g h t s . The scheduled c a r r i e r s kept records of delays r e l a t i v e to scheduled times but C a r l i n , A. & Park, R.E. The E f f i c i e n t Use of A i r p o r t  Runway Capacity i n a Time of Scarcity, The Rand Corporation, 1969. since schedules have a substantial allowance for delay b u i l t into them, the estimates for delay would have been downward biased. The same c a r r i e r s also recorded f l i g h t - p l a n time for each f l i g h t . These times were used as estimates of undelayed f l i g h t time. Subtracting f l i g h t - p l a n time from actual time elapsed i n f l i g h t would y i e l d a f a i r l y r e l i a b l e estimate of a r r i v a l delays. The r e s u l t i n g estimates would have been s l i g h t l y biased upward since the f l i g h t - p l a n times assume optimal a l t i t u d e s and routings that are not always r e a l i z e d . Because of these problems as well as the problems inherent i n c o l l e c t i n g data from d i f f e r e n t sources while presuming homogeneity of variance both within and between sources, the authors elected to use an i n d i r e c t s t a t i s t i c a l estimating technique. This technique has the following properites: F l i g h t times are asssumed to be the sum of three elements; 1. an average undelayed f l i g h t time T (which depends only on the route flown and the type of a i r c r a f t used. 2. an average delay time D (which depends i n i t i a l l y only on the time of day). 3. a random error term U (this term represents a l l of the influences which cause the actual f l i g h t time to deviate from 3 the average f l i g h t time). Formally stated, the expression i s : 0.., = T. + D. + U. 1 3 k 1 j 1 3 k The actual time spent i n f l i g h t w i l l now be referred to as the actual off-to-on time where o f f refers to the takeoff and on refers to the subsequent landing of an a i r c r a f t . 0. ., i s the actual off-to-on time for a p a r t i c u l a r f l i g h t . T. 1JK 1 i s the average undelayed f l i g h t time for the i t h route segment and equipment combination. To c l a r i f y the expression, we refe r to the text of the o r i g i n a l a r t i c l e : "For example, i f CKj^ i s the actual off-to-on time for a 727 f l i g h t from O'Hare to Kennedy, T^ i s the average undelayed j e t f l i g h t time form O'Hare. D.. i s the average delay during the j t h period, which for the moment we s h a l l t r e a t as though i t were a function only of the time of day when the f l i g h t i s scheduled to a r r i v e . If our f l i g h t i s scheduled to arri v e at 1643, D.. i s the average delay to f l i g h t s scheduled to ar r i v e at Kennedy between 1600 and 1659 (hours). U.., i s the ramdon error term." 1JK The data used i n thi s i n d i r e c t estimating technique was supplied by American A i r l i n e s and United A i r Lines. I t consisted of complete and accurate records of the actual off-to-on times of a i r c r a f t using Kennedy International A i r p o r t . The computational procedure consisted of the regression of these data, 0^^ on two sets of dummy variables. The f i r s t set of dummy variables repre-sented the ai r p o r t of o r i g i n and the type of a i r c r a f t making the f l i g h t . Recalling the above example, the f i r s t set of dummy variables would equal zero except the one variable representing je t f l i g h t from O'Hare, which would equal one. The second set of dummy v a r i a b l e l represented scheduled a r r i v a l time. By r e f e r r i n g to the example once more, we can see that the second set of dummy C a r l i n , A & Park, R.E. A Model of Long Delays at  Busy Airports, Journal of Transportation Economies and Policy, 1970. variables would equal zero except the one that represents a r r i v a l s between 1600 and 1659 hours, which equal one. The regression program used, omitted the constant term which usually appears i n regression equations. The regression of o n t n e dummy variables yielded estimates of T^ as c o e f f i c i e n t s of the f i r s t set and D.. as c o e f f i c i e n t s of the second set. Unfortunately, estimating techniques of the sort just described do not produce unique c o e f f i c i e n t s . The mutual addition and subtraction of constant amounts of time from each of the T. and I D. estimates would not a f f e c t the value of O. .. . To enable the estimates to be uniquely determined, the authors a r b i t r a r i l y removed a degree of freedom from the D.. estimates. They chose a reference point during the early morning hours and sp e c i f i e d zero delays during that period. Having done t h i s , the interp r e t a t i o n of delay i s changed. A delay of any length of time could no longer be regarded as absolute but only r e l a t i v e to delays i n the r e f e r -ence period. The reference period selected was the hours between 0200 - 0700. Because of the exceptionally low volumes of t r a f f i c using Kennedy International at that time, i t was f e l t that a reference delay of nearly zero would not invalidate subsequent estimates. Table I shows the re s u l t s of the two regressions for a i r c r a f t a r r i v i n g at Kennedy International. In the f i r s t regression dummy variables were assigned to r e f l e c t only the hour of scheduled a r r i v a l . The c o e f f i c i e n t s r e s u l t i n g from th i s regression are therefore estimates of o v e r a l l average delays by time of day. 65. Table I Average Delays, W(t), to Kennedy A r r i v a l s , A p r i l 1967 through March 1968 (minutes) Hour Overall Summer Summer Winter Winter of Average G • W.* B.W. ** B.W. B.W. AD SE AD SE AD SE AD SE AD SE 00-01 2.6 .8 6.1 1.2 '7.2 2.0 .4 1.2 .8 2.3 01-02 1.1 .8 2.5 1.2 4.9 2.1 1.4 1.1 3.6 2.4 02-06 0.0 0.0 5.5 1.9 0.0 .9 1.8 06-07 0.0 0.0 5.2 1.1 0.0 2.1 1.1 07-08 5.1 .9 4.5 1.7 8.0 2.2 3.1 1.6 16.2 3.1 08-09 3.0 .7 .7 1.0 6.2 1.2 .6 1.4 13.0 2.4 09-10 2.5 .7 2.6 1.0 6.3 1.3 .2 1.2 6.6 1.9 10-11 3.4 .7 2.7 1.2 8.3 1.8 1.0 .8 15.1 1.5 11-12 4.5 .7 3.8 .9 8.7 1.2 3.0 .9 14.3 1.6 12-13 3.9 .6 4.3 .8 8.8 1.1 1.3 1.7 15.0 1.4 13-14 2.5 .7 2.0 .9 8.4 1.5 1.1 .8 13.4 1.5 14-15 4.5 .6 3.9 .7 12.0 1.1 1.8 .7 12.6 1.4 15-16 11.0 1.3 9.4 1.5 15.7 2.5 4.3 2.5 28.0 5.6 16-17 13.7 .5 13.7 .7 31.7 1.2 8.0 .6 37.5 1.1 17-18 19. 7 .5 20.9 .6 43.5 1.0 9.6 .6 45.5 1.2 18-19 24.9 .5 25.6 .6 56.8 1.0 8.9 .7 51.4 1.3 19-20 17.2 .6 19.0 .7 47.2 1.2 5.5 .7 34. 7 1.5 20-21 14.4 .5 13.9 . 7 42.7 1.1 5.7 .7 34.9 1.2 21-22 11.8 .6 10.6 .7 35.2 1.3 3.3 .9 25.6 1.7 22-23 6.7 .6 7.9 .8 21.1 1.2 2.6 .7 13.4 1.4 23-24 2.3 .5 5.8 .7 11.4 1.2 2.2 .7 1.8 1.4 Source: C a r l i n , A & Park, R., A Model of Long Delays at Busy Airport s , Journal of Transport Economics and PoTicy, 1970. *Good Weather **Bad Weather AD—Average Delay SE--Standard Error 66. In the second regression, the variables were assigned to r e f l e c t season and weather i n addition to time of day. The resultant regression c o e f f i c i e n t s r e f l e c t average delay i n a r r i v a l by the time of day as well as the weather and season i n e f f e c t at the time of a r r i v a l . The estimates i n Table I are based on 31,890 observations recorded by American A i r l i n e s and United A i r l i n e s during the period A p r i l 1 , 196 7 through March 31 , 1968. The nineteen most frequently served c i t i e s were used as or i g i n a t i n g points for a i r c r a f t a r r i v i n g at Kennedy. The d e f i n i t i o n of weather and season as used i n the study i s as follows: a) good weather—ceilings of at least 2000 feet and v i s i b i l i t i e s of at least f i v e miles. b) bad weather—the weather i s considered bad i f l i m i t s f a l l below those associated with good weather. In t h e i r o r i g i n a l work for the Rand Corporation, C a r l i n and Park selected a d i f f e r -ent c r i t e r i a for weather categories: C e i l i n g s of at least 2000 feet accompanied by v i s i b i l i t i e s of at least 5 miles were classed as "good VFR". VFR weather conditions, that i s , c e i l i n g s of at least 1000 feet and v i s i b i l i t i e s of at least three miles, that did not q u a l i f y as good VFR f e l l i n to the "marginal VFR" category. Below t h i s , with c e i l i n g s down to 500 feet and v i s i b i l i t i e s down to one mile, comes a "marginal IFR" category. The worst category with c e i l i n g s less than 500 feet or v i s i b i l i t y less than one mile was c a l l e d "bad IFR." The regressions using these weather categories suggested strongly that the r e l a t i o n of delays to weather conditions i s continous rather than dichotomous. Stated simply, the worse the more pronounced the delays. In t h e i r l a t e r work, the authors chose to use a dichotomous re l a t i o n s h i p however. Based on the re s u l t s of the Rand study, C a r l i n and Park f e l t that the dichotomous d i s t i n c t i o n i n weather that they had selected, (good and bad weather) f i t t e d the observed delay patterns much better than the standard VFR/IFR dichotomy. The seasonal dichotomy used i n c a l -culating delay pattern was as follows: c) Summer — the f i r s t half of the year i n which day-l i g h t savings i s i n e f f e c t . In the sample period used, th i s was from A p r i l 30, 1967 through October 28, 1967. d) Winter — the balance of the period studied. Returning to Table I, we can observe the pattern of delays to a r r i v i n g a i r c r a f t at Kennedy a i r p o r t . The r e s u l t s show that the longest average delays were experienced by f l i g h t s scheduled to arrive between 1800 and 1900 hours, regardless of the season or the weather. The f i r s t column, e n t i t l e d "Overall Average" (delay) shows the average delay during t h i s period to be 24.9 minutes. The standard error associated with t h i s estimate i s .5 i n d i c a t i n g the range of accuracy of the estimate to be 24.9 + 1 minute. The confidence l i m i t of t h i s estimate i s approximately 95 percent. The standard error of estimate i s probably biased s l i g h t l y downward because the variance of the error term U . a s s o c i a t e d with each estimate, i s not constant. Least squares regression assumes that error i s randomly d i s t r i b u t e d wi.th a zero mean and constant variance. Almost c e r t a i n l y , the variance surrounding the a r r i v a l delay estimates, i s not constant, varying with each a i r p o r t of 6 8 . a i r c r a f t o r i g i n . The size of the standard error depends on the v a r i a b i l i t y of delay times within a p a r t i c u l a r time category as well as on the number of observations that f a l l i n that category and the number of observations i n the reference period (0200-0700 hrs) . Thus at higher lev e l s of delay, when there are generally more operations and hence more observations during each period, the size of the standard error tends to decline not only r e l a t i v e to the size of the estimated delay, but also absolutely. This can be seen from Table I. Considering t h i s caveat, we can better in t e r p r e t the table's r e s u l t s . Estimates were also made of the pattern of a r r i v a l s for landing. These patterns of a r r i v a l s are not the actual rates at which a i r c r a f t land or takeoff. As described i n the introduction to t h i s chapter, a r r i v a l rates A(t) are the rates at which a i r c r a f t are ready to land or takeoff. i e - the rate at which the present t o t a l number of landings and takeoffs would occur i f there were no delays. As above, d i r e c t observations of A(t) are not made. The nature of A(t) i n the absence of delay i s something which may be estimated but because delays currently e x i s t , cannot be observed. Two sources of data were used to make these estimates: A i r l i n e schedules and observations on actual landings by general aviation a i r c r a f t . It was evident to C a r l i n and Park, that a i r l i n e schedules as published, contain an allowance for t a x i times and are usually expressed i n terms of gate a r r i v a l instead of actual touchdown on the runway. They chose to accept these schedules verbatim however, because the use of scheduled a r r i v a l times ensured comparability with W(t) estimates (the delay to an a i r c r a f t landing at time t ) . Having sc r u t i n i z e d the a i r l i n e schedules, the average schedules for a i r l i n e s operating at Kennedy during the f i r s t week of September 1967 were selected as t y p i c a l of the summer half of the year. Similar schedules for the f i r s t week of February 1968 were selected as t y p i c a l of winter. Along with other data, these a r r i v a l rates are shown i n Table I I . The general aviation compon-ent of A(t) posed a more d i f f i c u l t problem. Other than a i r t a x i s , general aviation t r a f f i c does not operate on a scheduled basis. 5 Because of the nature of the a i r c r a f t composing t h i s category any estimates of a r r i v a l rates must be based on d i r e c t observations Rather than observe the a c t i v i t y f i r s t hand, the authors used the records of the Federal Aviation Administration. These documents, c a l l e d Runway Use Logs, contain records of both a i r c a r r i e r and general aviation t r a f f i c by runway used and time of day. A random sample of days from January 15, 1968 to July 31, 196 8 was selected. Two additional adjustments were necessary before the general aviation estimates could be added to the a i r c a r r i e r schedules to give a t o t a l A ( t ) . The primary i n t e r e s t of the study was i n the demands placed on a i r c a r r i e r duty runways. The f i r s t adjustment therefore, was to subtract general aviation t r a f f i c that did not use duty runways. Subtracting general aviation t r a f f i c that did General aviation i s a category that includes a l l t r a f f i c other than a i r c a r r i e r and m i l i t a r y operations. I t include a i r t a x i , business and private a i r c r a f t . Many private a i r c r a f t are used for i n s t r u c t i o n a l or recreational purposes. 70. Table II A r r i v a l Rates, A ( t ) , for Kennedy A r r i v a l s , A p r i l 1967 through March 1968 (air c a r r i e r equivalents) Hour General Aviation C a r r i e r Schedules A(t) of on Day Duty Runway Summer Winter Summer Winter Av. 00-01 .4 14.7 15.0 15.0 15.3 15.2 01-02 .1 8.6 10.1 8.7 10.2 9.6 02-03 .2 4.9 5.7 5.1 5.9 5.5 03-04 .4 4.4 5.3 4.7 5.6 5.2 04-05 .2 2.4 3.8 2.6 4.0 3.3 05-06 .2 5.4 5.0 5.6 5.2 5.4 06-07 .8 15.1 19.4 15.8 20.1 18.0 07-08 2.9 11.6 8.4 14.1 10.9 12.5 08-09 3.8 17.6 18.3 20.9 21.6 21.3 09-10 2.4 17.3 12.8 19.4 14.9 17.2 10-11 2.6 18.4 22.1 20.7 24.4 22.6 11-12 2.8 21.6 12.8 24.0 15.2 19.6 12-13 2.1 24.4 25.1 26.2 26.9 26.6 13-14 3.8 20.0 22.7 23.3 26.0 24.7 14-15 3.8 28.0 30.5 31.3 33.8 32.6 15-16 3.0 30.7 34.0 33.3 36.6 35.0 16-17 2.7 48.6 49.2 50.9 51.5 51.2 17-18 3.5 42.7 37.1 45.7 40.1 42.9 18-19 2.2 40.3 34.2 42.2 36.1 39.2 19-20 2.4 32.0 24.5 34.1 26.6 30.4 20-21 2.2 34.7 34.1 36.6 36.0 36.3 21-22 1.5 30.7 18.7 32.0 20.0 26.0 22-23 1.8 17.7 17.0 19.3 18.6 19.0 23-24 .7 13.6 13.8 14.2 14.4 14.3 Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Airport s , Journal of Transport Economics and Policy, 1970 71. not use duty runways was j u s t i f i e d i t , i n actual fact, those a i r c r a f t landing on non duty runways had no e f f e c t on a i r c r a f t landing on duty runways. While t h i s assumption may not be abso-l u t e l y correct, i t seems reasonable. The second adjustment to be made to the general aviation component of A ( t ) , concerns the equating of demand for capacity between a i r c a r r i e r and general aviation t r a f f i c . Not a l l kinds of operations place the same demands on the runways; general aviation t r a f f i c , composed of r e l a t i v e l y small a i r c r a f t , requires less service time than the larger machine of the a i r c a r r i e r s . Using the AIL Airport Capacity Handbook, C a r l i n and Park estimated r e l a t i v e service times for the two classes of a i r c r a f t . I t was found that at Kennedy International, an average general aviation landing requires 0 .87 times the service time of the average a i r c a r r i e r landing. This factor was then used to weight general aviation landings so that they could be added to the a i r c a r r i e r component to produce a f i n a l A ( t ) . Having ascertained estimates of delay and t r a f f f i c volumes at Kennedy International during the year A p r i l 1967 to March 1968, and estimate of t o t a l delay to a i r c r a f t a r r i v i n g during that period could be made. During each hour of operation, an average of N a i r c r a f t were delayed an average of W minutes. Total delays per day could then be estimated by use of the rela t i o n s h i p introduced e a r l i e r : z* D = J> N(t) . W(t) This r e l a t i o n s h i p was applied separately to general aviation (on 72. duty runways) and a i r c a r r i e r s (average of winter and summer schedules of a r r i v a l s ) . Average delay data from Table I was substituted into the expression for W(t) and a r r i v a l rates from Table II were substituted for N(t). Estimates were mult i p l i e d by 366 to determine t o t a l annual delay. Delay to a i r c a r r i e r s for the period chosen was estimated at 1.74 m i l l i o n minutes; general aviation a i r c r a f t were delayed 0.14 m i l l i o n minutes. Discussion: The drawbacks usually associated with averaging of data and the use of data under debatable assumptions apply i n thi s study. Because the data i s not i d e a l , one would not expect i t to f i t the proposed model very well. Despite these obvious f a i l i n g s , the model as presented does account for much of the observed delay. Figure 3 i s a plot of the average a r r i v a l and delay data found i n Tables I and I I . The resemblance between the t h e o r e t i c a l Figure 2 and the actual Figure 3 i s s t a r t l i n g , p a r t i c u l a r l y the position of the delay peak r e l a t i v e to the a r r i v a l peak. The a r r i v a l peak i s found between 1600 and 1700 hours; the delay peak occurs two hours l a t e r . I l l The "Schedule Evaluator" The f i r s t two sections dealt with observed a r r i v a l patterns and average delays. These estimates, taken together, enabled t o t a l delay to be calculated. C a r l i n and Park have also constructed a model to evaluate the e f f e c t on delay of d i f f e r e n t patterns of a r r i v a l s . The int e g r a l s , introduced i n the f i r s t section, are replaced with corresponding summations so that hourly data may Figure 3 Average Delay as a Function of Average A r r i v a l Rate 60 ^ U 50 -o 2 4 6 8 10 12 14 16 18 20 22 24 Time of day Source: C a r l i n & Park, A Model of Long Delays at  Busy Airports, Journal of Transport Economics and Policy, 1970 74. be used instead of continuous data. To produce a model capable of predicting delay as a function of a r r i v a l rate, c a l i b r a t i o n i s necessary. The rationale behind t h i s statement i s best understood by reference to C a r l i n and Park: "The schedule evaluator takes a r r i v a l rates A(t) and acceptance rates c as input, and calculates delays W(t) as output. We have data on average A(t) and W(t), but none on average accept-ance rates; that i s , data on one of the required inputs i s missing. C a l i b r a t i o n consists of trying d i f f e r e n t values of c together with observed A ( t ) , to see which most cl o s e l y reproduces observed W(t). The values of c that produce the best f i t are accepted as being average acceptance rates. These same values of c can then be used as input with "other a r r i v a l patterns of in t e r e s t i n order to calculate the delay pattern W(t) that would r e s u l t from the other A(t) . " 6 In section I, a number of caveats were issued to prepare the reader i n evaluating the long delay model as applied to r e a l s i t u a t i o n s : short period fluctuations i n the a r r i v a l rate, i n t e r -dependence of landings and takeoffs and the problem i n the averag-ing of data. Predictably, these same li m i t a t i o n s must be considered when working with the schedule evaluator. Ideally, data would be available for very short time periods, for instance, f i v e minute i n t e r v a l s . An a b i l i t y to gather data i n such small increments would dampen intra-hourly variations i n a r r i v a l rates. Unfortunately, the data used i n the model represents the average of hourly a r r i v a l rates. As such, the model i s incapable of predicting delays during periods when the a r r i v a l rate A(t) i s below the acceptance rate and a queue c a r r i e s over from one hour to the next. Obviously, because of high intra-hourly v a r i a t i o n i n a r r i v a l rates, delays D C a r l i n , A. & Park, R.E. A Model of Long Delays at  Busy Airpor t s, Journal of Transport Economics & po l i c y , 1970. 75. could be experienced within the hour period. On the basis of average hourly a r r i v a l rates and average acceptance rates, however, no delays may be predicted. Because of thi s l i m i t a t i o n , the model was f i t t e d to a r r i v a l s at Kennedy between 1600 and 2100 hours, when the a r r i v a l rate consistently exceeds the acceptance rate and queues ex i s t . Given the resultant c a l i b r a t i o n , the model predicts delays of up to f i v e minutes for periods of very l i g h t t r a f f i c , whereas the long delay model predicted zero delay for the same period. The dilemma of interdependence between landings and take-o f f s was resolved i n exactly the same fasshion for t h i s model as for the unmodified long-delay model. Even though t r a f f i c at Kennedy uses two, independent, non-intersecting runways, there i s mutual influence from the a i r c r a f t using the runways. Neither runway i s used exclusively for takeoffs or landings. Departures sometimes use the landing runway and a r r i v a l s sometimes land on the takeoff runway. An assumption of independence between a c t i v i t y on each runway was made. The j u s t i f i c a t i o n for t h i s assumption i s debat-able but i t s acceptance f a c i l i t a t e d the development of the model. To provide greater d e t a i l and reduce averaging error, the data was disaggregated into four c l a s s i f i c a t i o n s . The categories used i n the development of the long-delay model were retained: 1. Summer, good weather 2. Summer, bad weather 3. Winter, good weather 4. Winter, bad weather In the f i r s t two categories, a high and low acceptance figure i s used with a r r i v a l rates A(t) from Table I I . Numbers 3 and 4 are obtained i n e s s e n t i a l l y the same manner, except that winter A(t) data from Table II i s used i n conjunction with high and low acceptance rates. C a l i b r a t i o n i s accomplished by adjusting the capacity figures used so that the calculated delays match observed delays (from Table I) as c l o s e l y as possible i n each of the four cases. The c r i t e r i o n selected for matching calculated to observed delays was: 1 t = /7 3-calculated W(t) - observed W(t) standard error (t) This sum of squared normalized deviations i n minimized. The average capacities that resulted i n the best f i t are: 1. Summer, good weather - 40.8 2. Summer, bad weather - 36.1 3. Winter, good weather - 43.3 4. Winter, bad weather - 34.5 Using the capacity figures above, the associated delay patterns 7 were averaged to obtain an o v e r a l l average delay pattern. Table I I I , which i s presented below, shows the delays calculated by the schedule evaluator for each of the disaggregated cases as well as the observed delays. Comparison shows the f i t to be consistently good. Each delay sample was weighted by the f r a c t i o n of t o t a l observations that "belonged" to i t . 77. Hour of Day Table III Delay Calculation—Schedule Evaluator Technique Overall Summer Summer Winter Average G.W. B.W. G.W. Winter B.W. Cal Obs Cal Obs Cal Obs Cal Obs Cal Obs Average delay i n minutes: 16-17 13 14 10 14 27 32 8 8 37 37 17-18 22 20 21 21 42 43 12 10 46 46 18-19 23 25 25 26 52 57 49 51 19-20 18 17 21 19 48 47 35 35 20-21 15 14 13 14 48 43 37 35 G.W. Good Weather B.W. Bad Weather Cal Calculated Obs Observed Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Airport s , Journal of Transport Economics and Policy, 1970 78. The schedule evaluator i s p o t e n t i a l l y valuable as a predictor of the effectiveness of schemes designed to ra t i o n the capacity of an a i r p o r t . Throughout t h i s thesis, a path has been sketched from t h e o r e t i c a l discussion. The schedule evaluator represents the f i r s t successful attempt to produce a tool capable of monitoring the e f f e c t of changes i n policy . Admittedly, the tool i s rudimentary, but i t i s nonetheless valuable. The application of the schedule evaluator i s very simple. F i r s t , the a r r i v a l patterns are altered. (Usually to remove some portion of the o r i g i n a l t r a f f i c . ) The modified a r r i v a l s are then evaluated using the acceptance rates derived before. To t e s t the e f f e c t on delays of a reduction i n a r r i v a l s , C a r l i n and Park reduced A(t) (the general aviation component) by f i f t y percent, leaving the a i r c a r r i e r component untouched. This reduction i n anticipated general aviation t r a f f i c was due to an ar b i t r a r y twenty-five d o l l a r minimum landing fee established i n August, 1968. After the introduction of th i s minimum fee, approximately 50% of general aviation t r a f f i c o r i g i n a l l y using the f a c i l i t y , diverted to other airpor t s or sh i f t e d from duty to non-duty runways. Being cognizant of t h i s s h i f t , C a r l i n and Park sought to anticipate the reduction i n delays and compare th i s to observed delays. The schedule evaluator calculated a peak average delay of 18 minutes whereas the delay associated with the then current a r r i v a l pattern, was 23 minutes. Table IV shows these figures. For a i r c r a f t a r r i v i n g at Kennedy International between 1600 and 2100 hours, t o t a l delays were calculated to drop from 79. Hour of Day Table IV Peak Average Delay 50% of Actual General Actual Aviation 50% of Actual No General General Aviation and 47 Aviation Schedule Limit Average delay i n minutes: 16-17 13 12 11 10 17-18 22 18 15 16 18- 19 19- 20 20- 21 23 18 15 18 13 10 14 16 12 Total yearly delay to c a r r i e r planes i n m i l l i o n s of minutes: 16-21 1.27 1.01 0.80 0.88 Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Airport s, Journal of Transport Economics and P o l i c y , 1970 80. 1.27 m i l l i o n minutes per year to 1 .01 m i l l i o n minutes per year. A second suggestion for the a l l e v i a t i o n of congestion was the, banning from duty runways of a l l general aviation a i r c r a f t . With no general aviation t r a f f i c and with unchanged c a r r i e r schedules, the schedule evaluator estimated an eight minute reduction i n peak 8 average delay, and a 0 .47 m i l l i o n minute reduction i n t o t a l yearly a i r c a r r i e r delay for the period from 1600-2100 hours. The l a s t p o l i c y evaluated was the inc l u s i o n of $25 minimum fee and a l i m i t on planned operations during bad weather. The authors anticipated a reduction i n general aviation a c t i v i t y equal to the case where only the minimum fee was i n e f f e c t . A i r c a r r i e r s would be r e s t r i c t -ed to eighty movements per hour between 1700 and 2000 hours and seventy movements per hour for the r e s t of the day. Anticipated l i m i t for a i r c a r r i e r a c t i v i t y was set at forty-seven per hour i f bad weather persisted for the f i v e hour period. The pattern of calculated delays for t h i s reduced a r r i v a l pattern f a l l s approxi-mately between the f i r s t two. Peak average delays would be reduced by eight minutes and t o t a l delays during the f i v e hour period by about 0 .39 m i l l i o n minutes annually. The model that was described i n t h i s section was develop-ed from data gathered at Kennedy International A i r p o r t . It sought to r e l a t e the pattern of a r r i v a l s to the acceptance c a p a b i l i t y of the f a c i l i t y . This r e l a t i o n was then described i n terms of delay The peak average delay i n actual conditions was found to be 23 minutes for the period 1800-1900 hours. The peak average delay for the condition of banishment for general aviation a i r c r a f t was found to be 15 minutes for period 1700-1800 hours. 81. to a r r i v i n g a i r c r a f t . The pattern of a r r i v a l s , given an acceptance rate, was shown to determine the pattern of delay. The p o l i c y changes investigated modified a r r i v a l patterns through enforce-ment of a r b i t r a r y minimum landing fees or exclusion of a l l general aviation t r a f f i c from duty runways. The next work reviewed, also by C a r l i n and Park, r e s u l t s from an extension of the study which produced the schedule evaluator. Here we once again encounter marginal cost p r i c i n g of services; the marginal cost of delay i s estimated and t h i s cost i s included i n a proposed price to ration landing capacity. Marginal Cost P r i c i n g of A i r p o r t Runway Capacity-The s i t u a t i o n repeatedly queried throughout this study i s the congestion costs that an additional user (of the airport) imposes on the a i r c r a f t using the f a c i l i t y at the time of his a r r i v a l . If an a i r c r a f t lands or takes o f f at a time such that i t causes another' a i r c r a f t to wait, i t delays the other a i r c r a f t and i t s passengers with resultant costs to both. During times of congestion, queues develop, and each user imposes some delay on a l l following users u n t i l the end of the busy period. The busy period ends when the queue dissipates. The e f f e c t that an additional a i r c r a f t has on the a i r c r a f t already i n the queue can be i l l u s t r a t e d quite well by r e f e r r i n g to a discussion found i n the o r i g i n a l Rand Report prepared for the Port of New York Authority: 82. "... the length of queue and delays on a p a r t i c u l a r day at a congested a i r p o r t , by time of day (are) shown by the heavy l i n e i n Figure 4. In t h i s i l l u s t r a t i o n , the addition of the one more a i r c r a f t d e siring service at, say, time 04 would r e s u l t i n the queueing pattern indicated by the enclosed area plus the single cross-hatched area. Note that although the add i t i o n a l airplane would be serviced during minute 07, the e f f e c t s on other a i r c r a f t would be much longer l a s t i n g . In t h i s case, a l l a i r c r a f t a r r i v i n g a f t e r the additional one would be delayed by one minute u n t i l minute 18. The t o t a l delay imposed on the other airplanes can be seen to be equal to the single cross-hatched area, or 13 minutes." The model developed i n t h i s study, was designed to deter-mine the "cost of delays imposed by users of type i at a time t when the remaining busy period equal B minutes". Use i s defined with reference to the type of a i r c r a f t and by s p e c i f i c a t i o n as to whether the a i r c r a f t i s landing or taking o f f . The time re-quired to service each type of operation i s designated S^. The number of operations of each type that would occur from time t u n t i l the end of the busy period i s designated N^. The cost per minute of operation i s defined as c^. If a l l of these parameters were known with certainty, i t would be quite simple to calculate the marginal cost of an addition-a l user of type i i n terms of imposed delay. 1. C. = S. S N.c. l l 4~~ l l The additional operation delays each of the N =^N. operations for S. minutes at a cost to each of c. per minute. But absolute service times S^,, and numbers of type i operations N^ are d i f f i c u l t to estimate. With the a v a i l a b i l i t y of data, i t i s somewhat easier Figure 4 Queue Length 22. 1 1^ 1 10 15 Minute of Hour 20 25 Additional position i n queue occupied as a r e s u l t Qy\ of an additional plane Position i n queue occupied by additional plane Position i n queue occupied without additional plane C a r l i n A. & Park R.E., The E f f i c i e n t Use of Airport Runway Capacity _in a Time of Sclr~city, The Ra^d" Corporation7l^e7 84. 9 to estimate r e l a t i v e s e r v i times, s^ = S^/s, and proportions of various types of operations, 1^ n^ = 1SL/N. The above r e l a t i o n -ship was transformed into a more usable form by f i r s t defining a second r e l a t i o n s h i p : "The length of the remaining busy period must just equal the sum of the time necessary to service each of the airplanes that lands or takes o f f before i t (the remaining busy period) ends." no 2. B = 2 N.S. Dividing by B, we obtain: 3. C. S. $ N.c. B £ N, S Simplifying, we obtain further, (both the numerator and the denominator of the above expression are divided by S^N) no 4. C. s. 5 n.c. i _ i & i i B £ n. s . <.=/ In t h i s r e l a t i o n s h i p we have the marginal cost per minute of the remaining busy period (C^) expressed i n terms of use proportions ~~B (n^), r e l a t i v e service times (s^) and the cost to i n d i v i d u a l a i r c r a f t per minute (of delay), c^. Four kinds of operations were selected as a description 9 The method for estimating the s*s evolved using the Ai r p o r t Capacity estimates made several years ago by the Airborne Instruments Laboratory. The AIL capacity figures vary according to the mix of large and small planes and the mix of landing and takeoffs, making i t possible to estimate service time. Estimates of the n's were obtained from aggregate t r a f f i c s t a t i s t i c s , corrected to eliminate that f r a c t i o n of general aviation t r a f f i c that used non-duty runways. 85. of a c t i v i t y at LaGuardia A i r p o r t : 1. a i r c a r r i e r landings 2. a i r c a r r i e r takeoffs 3. general aviation landings 4. general aviation takeoffs For the case of an a i r c a r r i e r landing, s.^  = 1. Therefore the marginal delay cost due to an a i r c a r r i e r landing at time t i s equal to: C l = S l & n i C i B i n i s i 5. C± = (1) n l C + n 2 c 2 + n 3 c 3 + n 4 c 4 B ( t ) n l 1 ) + n2 S2 + n 3 S 3 + n4 S4 From the above c a l c u l a t i o n , i t i s evident that to calculate the marginal delay costs attributed to any other operation, one need only f i n d the product of and the r e l a t i v e service time of the selected operation s^. The value of each term i n the above expression changes over time. As mentioned e a r l i e r , r e l a t i v e service time s., varies I as a function of a i r c r a f t mix and runway configuration. The cost of operation varies as a r e s u l t of changing load factors. The r e l a t i v e proportions of a i r c a r r i e r and general aviation a i r c r a f t also changes hourly. The cost of dealing e x p l i c i t l y with each of these complexities i s very large. Therefore yearly average values were used i n l i e u of empirical estimates (transformed by allowance for changing conditions). The value of B(t ) , the remaining busy 86. period i s averaged as well, but each average accounts for one hour of the day. Table V shows the estimates of these parameters for LaGuardia A i r p o r t . T r a f f i c proportions n ^ were obtained from t r a f f i c s t a t i s t i c s aggregated for the year 1967. To maintain consistency, these data were corrected to eliminate the f r a c t i o n of general aviation a i r c r a f t not using duty runways. Relative service times were estimated using a previously mentioned technique: The Airborne Instrument Laboratory a i r p o r t capacity manual was used to derive service time r a t i o s for various mixes of a i r c r a f t . Line three i n Table V i l l u s t r a t e s the cost of operation, i n d o l l a r s per minute to a i r c r a f t owners. Each figure contains i n addition to d i r e c t variable costs of f u e l , o i l and crew time, some allowance for i n d i r e c t variable costs such as maintenance and depreciation. The value of passenger time i s also included i n Table V. Despite the controversy surrounding any estimate of the value of time of various i n d i v i d u a l s , C a r l i n and Park have included t h i s estimate. The marginal cost of delay i s sensitive to estimates of the value of time. A s e n s i t i v i t y analysis was performed using time values of $3 and $6 for a i r c a r r i e r and general aviation passenger time respectively. The costs shown i n Table V would be reduced by approximately 25%. If the estimates of passenger time were increased to $12 and $24 per hour, the costs would be increased by $49. Line four i n Table V represents the marginal delay costs per minute of remaining busy period. These figures are obtained by substituting into expression 5, the values estimated for n.. 87. Table V Cost of Delay A.C. A.C. G.A. G.A. Land. T.O. Land. T.O. Proportion of t o t a l t r a f f i c on duty runways, n^ .32 .32 .18 .18 Service time r e l a t i v e to a i r c a r r i e r landings, s^ 1.00 .86 .54 .46 Cost to a i r c r a f t owners (dollars per minute) 6.50 2.60 1.00 .50 Passengers per operation 46.80 46.80 1.80 1.80 Cost of passenger time (dollars per minute) 4.68 4.68 .36 .36 Marginal cost of delays (dollars per minute), 11.18 7.28 1.36 .86 Marginal cost of delays per minute of remaining busy period ( d o l l a r s ) , C. /B(t) 8.15 7.01 4.40 3.75 l A.C. A i r Car r i e r Land. Landing T.O. Takeoff G.A. General Aviation Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Airport s, Journal of Transport Economics and Policy, 1970 8 8 . s . and c.. 1 1 Average remaining busy period, B (t): The c a l c u l a t i o n of the average remaining busy period was based on data supplied by American A i r l i n e s and United A i r Lines. The data was used to di s t i n g u i s h times during the day when the a i r p o r t was busy. (ie- a i r c r a f t attempting to use the a i r p o r t encountered delays). B r i e f l y , the method used to calculate the remaining busy period i s as follows: For some f l i g h t s , p a r t i c u l a r -l y American A i r l i n e s , p i l o t reports of delays enroute and i n the New York terminal area were used. In some cases, the p i l o t reports were missing, and delay estimates were based on the excess of actual over planned f l i g h t time. Unfortunately, t h i s type of estimate r e f l e c t s other influences, notably enroute wind and weather fore-cast errors. For departure delays, the difference between gate departure and takeoff, less a standard taxi-time was calculated. On some occasions, data was not available from the A i r l i n e s and use was made of the FAA Runway Use Logs which record the time of landing or takeoff to the nearest minute. After obtaining the data on delays, the information was tabulated at ten minute in t e r v a l s from 0100 to 2400 hours for fourteen sample days. In addition, the six busiest hours of ai r p o r t operation were c r i t i c a l l y examined for each of fourteen extra days. A l l of these values were then averaged over the sample days to estimate the average expected busy period remaining by time of day. Table VI shows the hourly average of the ten minute estimates of the expect-ed remaining busy period. Table VI also shows estimates of the 89 Table VI Hourly Average of Expected Remaining Busy Period F u l l Marginal Delay Costs ($/incremental op.) H o f r Busy^Period A I R C A R R I E R S GENERAL AVIATION Day (minutes) A r r i v a l s Departures A r r i v a l s Departures 0000-0700 0.0 0 0 0 0 0700-0800 7.4 60 52 32 28 0800-0900 33.1 270 232 146 124 0900-1000 33.2 271 233 146 125 1000-1100 19.9 162 140 88 75 1100-1200 11.4 93 80 50 43 1200-1300 30.1 245 211 132 113 1300-1400 72.9 594 511 321 173 1400-1500 85.2 694 597 375 319 1500-1600 133.7 1094 937 588 501 1600-1700 118.2 963 829 520 443 1700-1800 96.4 786 676 424 361 1800-1900 74.5 607 522 328 279 1900-2000 44.6 364 313 196 167 2000-2100 19.5 159 137 86 73 2100-2200 7.2 59 50 32 27 2200-2300 1.7 14 12 8 7 2300-2400 .4 3 3 2 2 Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Air p o r t s , Journal of Transport Economics and Policy, 1970 9 0 . f u l l marginal cost of an additional operation for each hour of the day. Columns 2 through 5 i n t h i s table are average values of the delay costs imposed on other users by the incremental user. The magnitude of these costs must, of course, be interpreted i n the l i g h t of the assumptions underlying t h e i r estimation. The s e n s i t i v i t y of these costs to changes i n the assumptions regarding the value of time i s the same as that mentioned e a r l i e r . Thus fa r , t h i s study has shown i n a very unique manner, estimates of the delay costs attributable to a i r c r a f t using the a i r p o r t at a time of severe congestion. Despite the debate surrounding the value of time component of these costs, the i n e f f i c i e n t use of runways under the current weight based schedule of landing fees i s evident. The question s t i l l remains however, of what sort of p r i c i n g scheme to implement so that e f f i c i e n c y w i l l p r e v a i l and the airports w i l l continue to be used. The l a t t e r q u a l i f i c a t i o n i s not as facetious as i t f i r s t appears. For instance; what i s an obvious outcome i f the marginal costs of an incremental operation were charged as landing fees? The numbers of a i r c r a f t using the a i r p o r t would be d r a s t i c a l l y reduced. This reduction i n the number of users would reduce the marginal cost of operation and thereby force a reduction i n the price of land-ing p r i v i l e g e s . If the reaction to the f u l l marginal cost price was dramatic enough, subsequent user charges could conceivably be lower than the current l e v e l of charges. Under these lower charges, t r a f f i c volumes would exceed the current l e v e l . Allowed to continue, t h i s s i t u a t i o n would never converge to an equilibrium. Faced with t h i s p o s s i b i l i t y , the problem of improving e f f i c i e n c y i n runway use becomes one of introducing a p r i c i n g system which i s d i r e c t l y related to the marginal cost of operation but which i s p r a c t i c a l . Ideally, such a system would r e f l e c t the e l a s t i c i t y of demand for landing. In other word, the p r i c i n g analyst would know beforehand what the pattern of t r a f f i c would be under d i f f e r e n t sets of prices. Obviously such knowledge i s not a v a i l -able. An a l t e r n a t i v e to either f u l l marginal cost p r i c i n g or the optimum system mentioned above i s a scheme whereby an increasing percentage of the f u l l marginal cost i s charged as recomputed aft e r each successive increase. C a r l i n and Park considered t h i s and other a l t e r n a t i v e s . The major drawback, they f e l t , to p r i c i n g schemes based on recovery of delay costs, was the resistence to implementation by the a i r l i n e s . The authors f e l t that because of commitments for additional a i r c r a f t and the size of e x i s t i n g f l e e t s of a i r c r a f t , the a i r l i n e s would not accept higher landing charges. The net e f f e c t of the higher charges would be f e l t i n reduced f l e e t sizes and higher load factors thus assuring more e f f i c i e n t operations for the a i r l i n e s . However these adjustments to f l e e t size and the improvement i n load factors are long run e f f e c t s ; even though the a i r l i n e s could appreciate these benefits i n the long run, t h e i r resistance to the p o l i c y (higher landing charges) that would generate the benefits would be based almost exclusively on the short term problems that the p o l i c y would create. The i n i t i a l step toward the ultimate solution of e f f i c i e n t use of the runways i s proposed by C a r l i n and Park. This 9 2 . solution combines aspects of marginal cost p r i c i n g with p r a c t i c a l constraints to assure acceptance by the users. The approach described below l i m i t s t o t a l a i r l i n e runway use payments to what they would be under agreements currently i n e f f e c t . However the basis on which fees are levied i s changed so that fees during any (one) hour are proportional to those that would p r e v a i l under f u l l marginal cost p r i c i n g . The proportion of marginal cost charges and the rationale underlying i t s c a l c u l a t i o n are as follows: As mentioned above, the t o t a l of a l l fees paid by a i r -l i n e s i s assumed to remain constant. To determine the proportion-a l adjustment of the i n d i v i d u a l a i r l i n e payments, the hypothetical amount due under f u l l marginal cost p r i c i n g was f i r s t computed. This was done by using the average of September 1 9 6 7 and February 1 9 6 8 A i r l i n e schedules for an a c t i v i t y estimate and then c a l c u l a t i n g the r e s u l t i n g charges from the f u l l marginal delay costs i n Table VI. Data on actual charges was also available for runway use during the period March 1 9 6 7 to February 1 9 6 8 . By d i v i d i n g the actual charges by the hypothetical charges, a percentage was determined. Applying t h i s percentage against the t o t a l of actual fees c o l l e c t e d resulted i n the "proportional cost" fees shown i n Table VII. To answer the question of acceptance by the a i r l i n e industry, C a r l i n and Park compared what a i r l i n e payments would have been using the prices from Table VII with what payments act u a l l y were for the period studied. The r e s u l t s were encourag-ing: without exception the major c a r r i e r s were not adversely affected but the l o c a l service a i r l i n e s were. This was undoubtedly Table VII Proportional Marginal Cost Prices for LaGuardia A i r p o r t Hour of AIR CARRIER GENERAL AVIATION POST-AUGUST 1968 ACTUAL MINIMUMS Day Arr. Dep. Arr Dep. Dep. Either OOOOt- 0700 0 0 0 0 5 0 7 0 0 - 0 8 0 0 7 6 3 3 5 0 8 0 0 - 0 9 0 0 30 26 16 14 25 0 9 0 0 - 1 0 0 0 31 26 17 14 25 1 0 0 0 - 1 1 0 0 18 16 10 9 5 1 1 0 0 - 1 2 0 0 11 9 6 5 5 1 2 0 0 - 1 3 0 0 28 24 15 13 5 1 3 0 0 - 1 4 0 0 67 58 36 31 5 1 4 0 0 - 1 5 0 0 78 67 42 36 5 1 5 0 0 - 1 6 0 0 123 106 66 57 25 1 6 0 0 - 1 7 0 0 109 94 59 51 25 1 7 0 0 - 1 8 0 0 89 76 48 41 25 1 8 0 0 - 1 9 0 0 69 59 37 32 25 1 9 0 0 - 2 0 0 0 41 35 22 19 25 2 0 0 0 - 2 1 0 0 18 15 10 8 5 2 1 0 0 - 2 2 0 0 7 6 4 3 5 2 2 0 0 - 2 3 0 0 2 1 1 1 5 2 3 0 0 - 2 4 0 0 0 0 0 0 5 Proportional Marginal Cost Prices for LaGuardia ($ per operation) Arr. Dep. A r r i v a l s Departures Source: C a r l i n , A. & Park, R. A Model of Long Delays at Busy Air p o r t s , Journal of Transport Economics and Policy, 1970 94. due to the types and frequency of operation of the a i r c r a f t used by these firms. Considering the e f f e c t that the $25 minimum fee had on general aviation a c t i v i t y at major New York a i r p o r t s , (an average of 40% reduction i n general aviation movements) the proportionately higher fees for operations between 1300 and 1900 hours would have a very large e f f e c t . In t h i s l a s t section, we have seen another approach to improving the e f f i c i e n c y of use of a i r p o r t runways. We observed the attempts to quantify the marginal cost of delay a t t r i b u t a b l e to incremental operations during times of congestion. We also observed the p r a c t i c a l constraints on introducing p r i c i n g schemes based exclusively on t h e o r e t i c a l p r i n c i p l e s . C a r l i n and Park have made a major contribution to t h i s f i e l d of endeavor by successfully aligning economic theory with p r a c t i c a l considerations for p o l i c y . In the next chapter, we begin the analysis of the s i t u a t i o n at Vancouver International A i r p o r t . The problem w i l l be approached, i n a sense, from behind. The proposals for expansion w i l l be outlined and the techniques which resolve the issue w i l l be introduced. After a thorough explanation of the analysis, the data from Vancouver Airport w i l l be presented and subjected to scrutiny. Chapter IV There has been discussion among Minsitry of Transport O f f i c i a l s for the l a s t f i f t e e n years, of the need for an additional runway p a r a l l e l to the 08-26 f a c i l i t y . At present, Vancouver ai r p o r t has two i n t e r s e c t i o n runways: 08-26 and 12-30. The runways are l a b e l l e d as such because of t h e i r alignment with compass headings. The general layout of these runways i n r e l a t i o n to Vancouver c i t y , Richmond, and the adjoining water can be seen by reference to Figure 1. The proposed runway i s shown to the north of the current 08-26 f a c i l i t y . Complete with connecting taxiways, t h i s runway has been shaded i n grey. The following i s a detailed description of the runway as envisaged by the Aviation Planning and Research D i v i s i o n of the Ministry of Transport. Runway— Class 'A', 11,000 feet x 200 feet concrete Taxiways — High speed e x i t type positioned at 4500 feet, 6500 feet, and 7500, feet from each end of the runway. Each taxiway i s 75 feet wide and i s constructed of concrete. Lighting: Runway— 1. F u l l Category II standard with high speed and end e x i t marking. 2. Approach; high i n t e n s i t y Category II standard 08L, Category I standard 26R. Taxiway— Medium i n t e n s i t y taxi-edge l i g h t i n g . 97. Navigational Aids - Category II Instrument Landing System (ILS)-08L - non-categorized ILS-26R - middle marker (MM) 08L,26R - outer marker (OM) 26R - Non-directional beacon (NDB) at MM 08L and at OM 26R Transmissometers - Three units; each touchdown zone and r o l l o u t Additional - Runway and t a x i way pointing, signs, windsock etc. as required. The l a t e s t resurgence of i n t e r e s t i n t h i s project occurred i n the f a l l of 1971 when the Aviation Planning and Research D i v i s i o n of the MOT completed a report e n t i t l e d "Vancouver International Airport Capacity/Demand analysis for selected Runway configurations." Despite the recommendations of the report, which concluded that the construction of a p a r a l l e l runway would be the most expensive solution i n the short term, the MOT decided to i n i t i a t e expro-p r i a t i o n proceedings to purchase the land on Sea Island required for construction of the runway. The Ministry j u s t i f i e d i t s decision to construct the additional runway by presenting data on forecast demand at the a i r p o r t and the requirement to close the 08-26 runway for r e h a b i l i t a t i o n . This section w i l l not be concerned with the debate surrounding the claim for immediate reconstruction of runway 08-26. Instead i t w i l l concentrate on the requirement for expansion based on predictions of t r a f f i c volumes and the resultant lack of future capacity. In t h e i r analysis of the requirement for a runway p a r a l l e l 98. to 08-25, the Ministry of Transport assumed a growth trend for the years 1971-1975 of 12-15% for domestic t r a f f i c and 8-10% for International t r a f f i c . These analysts maintained that even though the growth i n domestic a i r c r a f t movements was moderated by the use of large wide-bodied a i r c r a f t , (capable of handling up to 400 passengers) the increasing incidence of international charters would o f f s e t t h i s growth reduction and produce an o v e r a l l growth rate of 10%. General Aviation a c t i v i t y was expected to taper o f f i n the same period. A growth rate of 11%% was given for General Aviation for the period 1971-1975. The following figure depicts t h i s projected increase for both a i r c r a f t groups. Since the MOT report was compiled, s i g n i f i c a n t changes have taken place i n the supply of petroleum products to the world's a i r l i n e s as well as to general aviation a i r c r a f t . The Arab-Israeli c o n f l i c t and the o i l embargo that resulted from i t , severely r e s t r i c t e d the supply of j e t f u e l and aviation gasoline. The price of f u e l has increased by more than 100% since 1973. This dramatic increase i n f u e l costs has p r e c i p i t a t e d a s i g n i f i c a n t reduction i n the frequency of f l i g h t s offered by the c a r r i e r s . This reduction has been moderated to some extent since the removal of the Arab o i l embargo, but f u e l prices have not f a l l e n measure-ably and could conceivably go up again. With a i r l i n e p r o f i t s often very tenuous, a further shrinkage of the p r o f i t margin with higher f u e l costs w i l l , i n a l l l i k e l i h o o d , cause future reductions i n f l i g h t s . I t remains to be seen exactly what the e f f e c t on a i r c a r r i e r s w i l l be from higher f u e l costs, but i t seems very conser-vative to suppose that the MOT projections of future t r a f f i c flows Figure 2 A i r Movement Forecast 99. 160 150 140 130 120 110 100 90 80 70 60 50 40 30 Vancouver International Airport, Actual and Forecast; General Aviation and A i r Carrier Movements. General Aviation-1971-1975 @ll3s% 1975-1980 @8% / Ai r Carrier-1971-1975 @10% / 1975-1980 @8% / Ge: iera! L Av Lati on / / Act\ l a l - -Fo recai 5t / / / / / 7* •/-/ y y Air Can l e r / / 1966 1968 1970 1972 1974 1976 1978 1980 Year Source: Aviation Planning & Research D i v i s i o n , Ministry of Transport, Vancouver International Airport-Capacity/Demand Analysis For Selected Runway Configurations, 1971. 100. are optomistic. The above comments are admittedly, conjecture based on an attempt to r e l a t e MOT t r a f f i c predictions to a since increased price of f u e l . In the absence of factual data, no meaningful statement can be made about future t r a f f i c flows. The same cannot be said however about the " a b i l i t y " of the Vancouver Airport to accommodate t r a f f i c . There has been considerable work done i n the f i e l d of a i r p o r t design and a i r p o r t capacity. The majority of t h i s work was done by the Airborne Instruments Laboratory, of New York. This group produced a handbook i n 1963 designed for use i n deter-mining the a b i l i t y of an a i r p o r t to accommodate t r a f f i c . The book was updated into a second e d i t i o n , published i n 1969. I t i s the second editon that w i l l be referred to hereafter. The handbook was also used by the MOT i n the preparation of i t s report about the capacity of the Vancouver Ai r p o r t . Calculations derived using techniques outline i n the handbook w i l l be presented i n the f i n a l section of t h i s chapter. Because of the reliance placed on the handbook i n the remainder of t h i s thesis, i t i s e s s e n t i a l that the reader be very f a m i l i a r with the rationale behind i t and the techniques and procedures followed i n the c a l c u l a t i o n and under-standing of a i r p o r t capacity. The following section i s a b r i e f description of the techniques used i n c a l c u l a t i n g a i r p o r t capacity. Reference to Appendix B, at the end of the thesis w i l l f a c i l i t a t e understanding of the terms used throughout the description. The capacity of an a i r p o r t i s the number of operations that the f a c i l i t y can process when delays to the a i r c r a f t using i t 101. has reached an a r b i t r a r y maximum. I t i s apparent that i f two a i r c r a f t wish to use a runway simultaneously, one of the two w i l l be delayed i n his use. In other words, a l l a i r c r a f t compete for the use of runways; those which a r r i v e subsequent to others are compelled to queue up for the use of the runway. The length of time that an a i r c r a f t spends waiting i s equivalent to the time that i t i s delayed. Delay i s dependent upon a number of factors. One factor governing delay i s the number of a i r c r a f t using the a i r p o r t . The higher the "movement rate," the longer the delays per a i r c r a f t . The parameters that a f f e c t the service time of a i r c r a f t are diverse yet related. Each contributes something to the determination of delay and each i s present i n the a i r p o r t environment. The goal of the AIL group was to develop, v i a computer programs, a technique whereby these parameters are compared and a l i m i t of capacity determined, (for any given a i r p o r t ) . A four minute average delay c r i t e r i o n was selected for a number of reasons: Observations i n the f i e l d indicated that beyond a four minute average delay point, small increases i n the movement rate resulted i n a very marked increase i n average delay. The following figure has been extracted from the AIL Handbook and represents a t y p i c a l average delay curve. The d i s t r i b u t i o n of delays under a four minute average was such that maximum delays did not exceed twenty minutes while minimum delays were of a few seconds duration. At airpor t s where departures and a r r i v a l s use the same runway, a r r i v a l s are given p r i o r i t y over departures. Both types Figure 3 AIL Delay as a Function of Movement Rate 102. 10 20 30 40 50 60 Movement Rate Source: Airborne Instruments Laboratory, Airport  Capacity Handbook-Second E d i t i o n , New York 19 69. 103. of t r a f f i c are handled on a first-come, f i r s t - s e r v e d basis. Having established t r a f f i c p r i o r i t i e s , a l l that remains to a f f e c t a i r p o r t capacity i s the spacing or i n t e r v a l s between a i r c r a f t movements. A i r c r a f t service times are affected by six factors. The e f f e c t that any factor has in determining service time (and subsequently determining capacity) hinges on other elements. These elements w i l l be discussed i n the succeeding section. Service time i s d i r e c t l y proportional to the following factors: 1. Weather (ie.-IFR, VFR) and i t s e f f e c t on procedures o 2. Runway configuration (single runway, int e r s e c t i n g runway) 3. A i r c r a f t population (the mix of a i r c r a f t types) 4. Individual runway design (length and number of runways, type and location of turnoffs) 5. Runway use (mixed operations, a r r i v a l s only, departures only) 6. Airspace considerations (departure routings d i r e c t l y a f t e r takeoff) The number of operations that can take place varies with the weather. When weather deteriorates, so does the number of oper-ations that can be safely accommodated. Normally, weather con-ditions are categorized according to the location of the cloud base and the runway v i s i b i l i t y . V i s u a l F l y i n g Rules and Instrument Fl y i n g Rules are the t r a d i t i o n a l d i v i s i o n s for i d e a l and marginal weather. The AIL research group found a poor 104. c o r r e l a t i o n between capacity and weather when these accepted weather c l a s s i f i c a t i o n s were used. They altered the c l a s s i f i c a -t i o n , changing the l i m i t s for each, and found that a i r p o r t capacity was more s i g n i f i c a n t l y affected by the change i n c r i t e r i a . The new c r i t e r i a were labeled VAW or Vi s u a l A i r p o r t Weather — cloud base of 700 feet and v i s i b i l i t y of 2 miles, and IAW or Instrument Airport Weather — cloud base and v i s i b i l i t y equal to VAW minimums or lower. Runway configuration and design, as mentioned above, aff e c t s the capacity of the a i r p o r t . The exact influence that each factor has on a i r p o r t capacity i s d i f f i c u l t to ascertain, but estimates have been made with the computer available to the AIL. These estimates, have i n turn been v e r i f i e d by observations. Feed-back from f i e l d observations has been applied to the computer program, r e s u l t i n g i n a t o o l which has v a l i d i t y . The factors which influence runway capacity under VAW and IAW are respect-l v e l y : VAW - the use of runways by a r r i v a l s w i l l be influenced by: - wind d i r e c t i o n and strength - length of runway - runway occupancy (runway r a t i n g ) . Poor turnoffs on an inte r s e c t i n g system of runways w i l l encourage p i l o t s and c o n t r o l l e r s to use the one-approach system, but Excerpted from the AIL Ai r p o r t Capacity Handbook, 2nd ed. June, 1969. 105. then to "break-off" some a r r i v a l s at close ranges to use a second runway, to avoid wave-offs due,to excessive occupancy of preceding a i r c r a f t on the main runway. - l o c a l noise regulations - p r e f e r e n t i a l runways. IAW - In IAW for any configurations, the number of approach paths i s r e s t r i c t e d to the number of ILS i n s t a l l a t i o n s or VORTAC approaches Therefore although a configuration might have three runways, only one w i l l be used for a r r i v a l s i f only one runway has an instrument approach c a p a b i l i t y . IAW or VAW - the use of runways by departures w i l l be influenced by: - r e l a t i v e closeness of runway to departure gate or parking area - d i r e c t i o n of departure once airborne - runway length - wind d i r e c t i o n and strength - l o c a l noise regulations - p r e f e r e n t i a l runways - a i r c r a f t population Another factor that can greatly influence runway use by a r r i v a l s and departures i s the r e l a t i v e positions of the runways to each other and to the terminal and parking areas. For example, i t i s a more complicated t r a f f i c control task to cross t a x i i n g a i r c r a f t across a landing runway than a takeoff runway. Therefore, on two close p a r a l l e l runways with the terminal on one side, the inner runway can be used primarily for departures, and the outer runway for a r r i v a l s . Exception to t h i s use could r e s u l t from runway length considerations (one may have to be used by large 106. a i r c r a f t ) or noise problems. Having f a m i l i a r i z e d himself with the c r i t e r i a a f f e c t i n g a i r c r a f t service times, the reader may now apply these c r i t e r i a i n the determination of a i r p o r t capacity. The following paragraphs are an explanation of the actual technique used for c a l c u l a t i n g a i r p o r t capacity: I n i t i a l l y , the ai r p o r t i s c l a s s i f i e d according to the configuration of i t s runways. The runway configuration may consist of one, two or p e r i o d i c a l l y three i n d i v i d u a l s t r i p s . The orientation of the runways, one to the other(s), i s also included i n the configuration. Typical configurations include: p a r a l l e l , i n t e r s e c t i n g and open V. The p a r a l l e l arrangement consists of two runways located beside each other i n a p a r a l l e l fashion. The in t e r s e c t i n g arrangement i s s e l f -evident. The open-V configuration consists of two runways separat-ed from each other by more distance at one end than at the other. Figure 4 presents an example of each type of arrangement. Having c l a s s i f i e d the a i r p o r t according to the number and configution of i t s runways, one must then determine the composition of the population of a i r c r a f t using the a i r p o r t . The AIL Handbook c l a s s i f i e s a i r p o r t population according to runway requirements. The normal loaded weight of the a i r c r a f t i s included i n these requirements; for class A a i r c r a f t , the length of runway required for takeoff or landing i s an additional requirement. AIL designations referred to i n succeeding a i r p o r t population discussions can be 107. Figure 4 Runway Configurations P a r a l l e l Open - V Intersecting 108. 2 found i n the following l i s t of a i r c r a f t c l a s s i f i c a t i o n s : Class A a i r c r a f t — A l l j e t a i r c r a f t normally requiring runway lengths exceeding 6000 feet (corrected to sea level) for takeoff and/or landing. BAC (Vickers) VC10 Convair 880 990 Boeing 707 Douglas DC8 720 DC10 747 DeHavilland (H.S.) Comet Sud Carvelle Lockheed 1011 Class B a i r c r a f t — 1. Piston and turboprop a i r c r a f t having a normal loaded weight i n excess of 36,000 pounds. 2. Jet a i r c r a f t not included i n Class A but having a normal loaded weight i n excess of 25,000 pounds. BAC 111 Lockheed Constellation E l e c t r a Jetstar Boeing 727 Martin 404 737 Canadair CL-444 Vickers Viscount Vanquard Convair 240/340/440 58/600 Curtiss C-46 Douglas DC-4 DC-6 DC-7 DC-9 AIL Airport Capacity Handbook, 2nd ed. New York, June 1969. 109. Class C a i r c r a f t — 1. Piston and turboprop a i r c r a f t having a normal loaded weight greater than 800 pounds and less than 36,000 pounds. 2. Jet a i r c r a f t having a normal loaded weight greater than 8000 pounds but less that 25,000 pounds. Aero Commander Jet Commander Beech 18 PACAIR RAUSCH VOLPAR Beech King A i r Dassault Fan Jet Falcon Douglas B-26 DC-3 F a i r c h i l d F-27/F-227 Grumman Gulfstream I Gulfstream II H.S. 125 Lear Jet 23 24 Lockheed 18 Lodestar Lockheed PV-2 Oakland Pacaero Nord 262 North American Sabreliner Class D a i r c r a f t — A l l l i g h t twin-engined piston and turbo-prop a i r c r a f t having a normal loaded weight less than 8000 pounds, and some high-performance single-engine l i g h t a i r c r a f t . They are small, l i g h t , twin-engined a i r c r a f t with the exception of those marked with an asterisk (*). 110. Aero Commander (500, 600, 700 series Cessna 310 Grand and Turbo) 320 411 336/337 Beech Bonanza* Debonair* H.S. Dove Beech Baron Travel A i r Navion-Camair 480 and Queen A i r Temco-Riley Twin Twin Bonanza Piper Apache Aztec Twin Comanche Class E a i r c r a f t — A l l single engine a i r c r a f t with the exception of the Mustang (C) Bonanza (D), and Debonair (D) and small STOL a i r c r a f t . The most common types of class E a i r c r a f t are: Cessna series 150 through 210 Mooney 20 series Piper series, Colt, Tri-Pacer, Cherokee and Comanche Beech Muskateer, D.H. Beaver, Bellanca, Helio Courier, Luscombe, Navion, and Stinson. In addition to the aforementioned information, one also requires data on the r a t i o of a r r i v a l s to departures at the a i r -port as well as knowledge of the type and amount of control and approach aids. With t h i s information, the P r a c t i c a l Hourly Capacity (PHOCAP) of the a i r p o r t can be calculated. Procedure: The method used i n the AIL A i r p o r t Capacity Handbook involves segregating a c t i v i t i e s into two categories - those which take place during V i s u a l A i r p o r t Weather and those which take place during Instrument Airport Weather. Computer derived nomograms 111. are used to determine the hourly a r r i v a l and departure capacities under both weather conditions. The PHOCAP f o r VAW conditions i s i n i t i a l l y taken as the sum of the hourly a r r i v a l capacity (HAC) and the hourly departure capacity (HDC) or twice the HDC, which ever i s less. The same procedure i s used i n c a l c u l a t i n g PHOCAP under IAW conditions except that consideration i s given to the sophistication of A i r T r a f f i c Control devices at the a i r p o r t i n question. In addition to the PHOCAP, the AIL A i r p o r t Capacity Handbook provides a means through which to calculate the P r a c t i c a l Annual Capacity (PANCAP) of an a i r p o r t . PANCAP refers to the number of movements that an a i r p o r t can process before delays exceed some index l e v e l . The index used i n the handbook allows f i v e minute delays to occur for 8 percent of the year (541 hours). A ten minute average delay i s permitted to occur 4 percent of the year. E s p e c i a l l y poor weather may cause average delays of 40 minutes. The c r i t e r i o n incorporated into the index permits delays of t h i s duration to occur for 1 percent of the year. The PANCAP of an a i r p o r t i s dependent on the types of a i r c r a f t seeking accomodation and the f a c i l i t i e s available at the a i r p o r t to service these a i r c r a f t . Apart from approach and navigation aids, the primary f a c i l i t y at an a i r p o r t i s the runway The length of the runway and the number and nature of the e x i t ramps and taxi-ways determine capacity. I f there i s more than one runway, the p o s i t i o n of each runway, r e l a t i v e to the others i s a determinent of capacity. Weather conditions, e s p e c i a l l y the wind 112. strength and d i r e c t i o n influence PANCAP as well. Procedure: Using the technique outlined i n the handbook, one determines the index figure for overload comparison. An hourly test demand i s compared with the hourly capacity and an i n d i c a t i o n of overloading ( i f the test demand exceeds the hourly capacity) i s produced. This overload c r i t e r i o n i s then weighted by the annual percentage of such demand situations and the product i s compared with the index figure. Because the index figure has been calculated to ensure only a c e r t a i n amount of overloading, i t s comparison with the overload-criteria-annual-use product i s the test of completion for the PANCAP c a l c u l a t i o n . Usually successive attempts to recalculate the test demand must be made before an equality between the index figure and the test demand can be reach-ed. Once equality i s attained, the t e s t demand i s m u l t i p l i e d by annual u t i l i z a t i o n to a t t a i n PANCAP. The Ministry of Transport (Canada) has used the AIL Hand-book to calculate the PHOCAP and PANCAP of Vancouver International A i r p o r t . The next section w i l l show how t h i s c a l c u l a t i o n was made, some of the l i m i t a t i o n s to i t s conclusions as well as a b r i e f analysis of the data u t i l i z e d . The f i r s t step taken i n the c a l c u l a t i o n of capacity at Vancouver International Airport was an inspection of the configura-t i o n of runways. Figure 1 depicts the organization of runways and taxiways at Vancouver. The two runways in t e r s e c t each other at point A. This point i s 57 00 feet from the threshold of runway 12 113. 1600 feet from the threshold of runway 30. The point of i n t e r -section i s 4800 feet from the threshold of runway 08 and 5800 feet from the threshold of runway 30. Each runway i s l a b e l l e d according to the d i r e c t i o n i n which i t i s oriented. Next, data were assembled to determine the d i s t r i b u t i o n of the classes of a i r c r a f t using the a i r p o r t . C l a s s i f i c a t i o n of a i r c r a f t types was accomplished using the c r i t e r i a established by the AIL (see pp 103 - 105, t h i s paper). The population d i s t r i -bution appears i n Table I. Two assumptions were made by the MOT study group: 1. There are no r e s t r i c t i o n s on the use of airspace around the a i r p o r t . 2. The r a t i o of a r r i v a l s to departures i s one. The calculations performed by the MOT are i l l u s t r a t e d i n Tables II and I I I . I t can be seen that t o t a l capacity under both VAW and IAW i s at the least, double the departure capacity. The f i n a l column i n Table III represents the percentage of t o t a l annual use that the p a r t i c u l a r runway combination was i n use. The figures i n t h i s column, as well as the PHOCAP figures were used i n the c a l c u l a t i o n of PANCAP. Table IV represents the f i r s t i t e r a t i o n of the process through which the annual capacity of the a i r p o r t i s determined. Annual u t i l i z a t i o n and annual capacity figures are given for both "public-desire" and "off-peak use" categories. The public desire capacity figure may be interpreted to mean the capacity of the air p o r t when the d i s t r i b u t i o n of t r a f f i c i s a function of public demand for transportation. A d i s t r i b u t i o n t y p i c a l of public desire would have two d i s t i n c t peaks, one i n the morning and the other i n Table I Vancouver International A i r p o r t POPULATION DISTRIBUTION - JUNE-JULY 1970 A i r c r a f t Population D i s t r i b u t i o n C l a s s VAW IAW A 10% 20% B 24% 51% C 8% 11% D 19% 10% E 39% 8% Source: Vancouver International Airport - Capacity/Demand Analysis for Selected Runway Configurations, #R-71-8, MOT, 1971 115, Table II Calculation of Multiple Runway Capacities (movements per hour) Runway Configurations V A W Arr. Dep. Total C a p a c i t y I A W Arr. Dep. Total C a p a c i t y Takeoff 26 Land 30 Takeoff 30 Land 26 Takeoff 12 Land 08 Takeoff 08 Land 12 40 40 40 40 40 37 33 35 80 74 66 70 38 38 38 38 27 54 25.5 51 25.5 51 26 52 IAW Instrument Ai r p o r t Weather VAW Vi s u a l A i r p o r t Weather Source: Vancouver International A i r p o r t - Capacity/Demand Analysis for Selected Runway Configurations, #R-71-8, MOT, 1971 116. Table III Percent Annual Runway Use % of Weather RUNWAY CONFIGURATION % Time Condition Description Capacity Used Applicable Below IAW — — - 3.36 IAW 8.9% 11 12 08 12 45 44 50 50 4.47 4.47 VAW 87.71% VI TO-2 6 L-30 80 3 2.63 V2 TO-30 L-26 74 9 7.89 V3 TO-12 L-08 66 9 7.89 V4 TO-08 L-12 70 9 7.89 V5 08 58 35 30.70 V6 26 58 35 30.70 Source: Vancouver International A i r p o r t - Capacity/Demand Analysis for Selected Runway Configurations, #R-71-8 MOT, 1971 117. the late afternoon. Off-peak capacity i s always greater than public desire; i t allows for a modification i n public demand so that otherwise quiet times of day become busy as demand " s p i l l s over" from peak periods. It i s assumed that the t r a v e l l i n g public would not use the off-peak periods i f capacity at peak periods was greater. In Table IV column 7, the test demand figure i s determined from reference to a nomogram. Column 8's derivation i s described i n the table, as are columns 9 and 10. I t can be seen that the resultant annual overload of 14.02 i s not equal to the capacity index of 23. Successive i t e r a t i o n s were performed r e s u l t i n g i n a f i n a l overload c r i t e r i a of 24.02. Annual capacity figures under both public desire and off-peak curves were deter-mined using the f i n a l overload c r i t e r i a . Limitations of the Study-The VAW and IAW population d i s t r i b u t i o n i n Table I i s , in a c t u a l i t y , the d i s t r i b u t i o n associated with IFR and VFR weather. Because of the mild nature of Vancouver's weather, l i t t l e difference seems to e x i s t between the t h e o r e t i c a l VAW-IAW a i r c r a f t population d i s t r i b u t i o n and the d i s t r i b u t i o n found i n the MOT study. This same d i s t r i b u t i o n i s applicable only for the peak period of June, and July 1970. This author attempted to audit the technique used by the MOT study group i n t h e i r c a l c u l a t i o n of the P r a c t i c a l Annual Capacity of Vancouver Ai r p o r t . (Reference to Table IV w i l l resolve any confusion a r i s i n g from the following discussion.) It w i l l be r e c a l l e d that one step i n the c a l c u l a t i o n of 118. Table IV Capacity Calculation % Annual Annual Overload Code Configuration HDC HAC Use TD OF OC C r i t e r i a VI TO-2 6 40 X 2.63 36 - - -L-30 X 40 36 - - -V2 TO-30 37 X 7.89 36 - - -L-26 X 37 36 - - -V3 TO-12 33 X 7.89 36 1.09 .09 .71 L-08 X 33 36 1.09 .09 .71 V4 TO-08 35 X 7.89 36 1.03 .03 .24 L-12 X 35 36 1.03 .03 .24 V5 TO-08 29 X 30.70 36 1.24 .18 5.53 L-08 X 29 36 1.24 .18 5.53 V6 TO-2 6 29 X 30.70 36 1.24 .18 5.53 L-26 X 29 36 1.24 .18 5.53 11 TO-08 22.5 X 4.47 21 - - -L-08 X 22.5 21 - - -12 TO-2 6 22 X 4.47 21 - - -L-26 X 22 21 - - -(1) (2) (3) (4) (5) (6) (7) (8) (9) TD Test Demand OF Overload Factor; Column 7 Column 3; Column 7 T Column 4 OC Overlad C r i t e r i a ; From Table 13-1, AIL Handbook Capacity Indiex = 23 F i n a l Annual Overload C r i t e r i a =24.02 IAW Demand Factor =58% VAW Peak Hour Demand - 3 6 x 2 = 7 2 movements per hour Approximate Annual U t i l i z a t i o n - Public Desire = 3160 hours Approximate Annual U t i l i z a t i o n - Off-peak = 3740 hours Annual Capacity - Public Desire = 3160 x 72 = 227,520 movements Annual Capacity - Off-peak = 3740 x 72 = 269,280 movements Source: Vancouver International A i r p o r t - Capacity/Demand Analysis J? / - l I • "I -r-» y-» _• l J il T I <-7 1 r» H I I A m 1 f » T l 119. P r a c t i c a l Hourly Capacity involved the determination of departure capacity, (in addition to a r r i v a l capacity) for a p a r t i c u l a r combination of runways. Once the departure capacity was available, the t o t a l capacity of the runway(s) could be ascertained. Table II depicts the values of a r r i v a l , departure and t o t a l capacity for four runway combinations. In three cases, the departure capacity i s less than the a r r i v a l capacity. AIL instructions s t i p u l a t e that t o t a l capacity i s determined by the doubling of either the a r r i v a l or departure capacity, which ever i s less. This has been done i n the PHOCAP c a l c u l a t i o n . When we address the c a l c u l a t i o n of PANCAP, however, AIL instructions provide for i n c l u s i o n of the o r i g i n a l PHOCAP a r r i v a l and departure capacities. In e f f e c t , each i n d i v i d u a l capacity, as determined from the AIL Handbook should be entered into i t s respective place i n columns three and four of Table IV. However, we f i n d that the figures located i n these positions have been obtained by halving the t o t a l capacity figures obtained from Table I I . This i s only acceptable when, by c o i n c i -dence, a r r i v a l and departure capacities are i d e n t i c a l . The o v e r a l l e f f e c t of t h i s oversight i s s l i g h t . P r a c t i c a l Annual Capacity figures are only very s l i g h t l y affected. The p r a c t i c a l capacity of the a i r p o r t using the modified procedure i s 243,320 movements annually under the "Public Desire" c r i t e r i o n and 286,440 movements annually under the "Off-Peak Use" c r i t e r i o n — a 6.5% difference. Table V and VI show the difference i n the capacity data selected as well as the eventual annual capacity figure. If one accepts the MOT forecasts of t r a f f i c at Vancouver Airport, i t i s r e a d i l y apparent 120. Table V Capacity C a l c u l a t i o n — D a t a Revision % Annual Annual Overload Code Configuration HDC HAC Use TD OF OC C r i t e r i a VI TO-2 6 L-30 40 X 2.63 38 - - -X 40 38 V2 TO-30 L-26 40 X 7.89 38 1.03 .03 .24 X 37 38 V3 TO-12 L-08 40 X 7.89 38 1.15 .13 1.03 X 33 38 V4 TO- 08 L-12 40 X 7.89 38 1.09 .09 .71 X 35 38 V5 TO-08 L-08 29 X 30.70 38 1.31 .30 9.21 X 40 38 V6 TO-2 6 L-26 29 X 30.70 38 1.31 .30 9.21 X 40 38 11 TO-08 L-08 22.5 X 4.47 22 - — — X 38 22 12 TO-2 6 L-26 22 X 4.47 22 — -— X 38 22 (1) (2) (3) (4) Ai (5) mual (6) Overl (7) oad — (8) 20.40 (9) TD Test Demand OF Overload Factor; Column 7 -f Column 3; Column 7 -f Column 4 OC Overload C r i t e r i a ; From Table 13-1, AIL Handbook Capacity Index = 23 I n i t i a l Annual Overload C r i t e r i a = 20.40 IAW Demand Factor = 58% I n i t i a l Test Demand = 1.3 x 29 = 38 (VAW) I n i t i a l Test Demand = .58 x 38 = 22 (IAW) Table VI 121. Capacity C a l c u l a t i o n — F i n a l Iteration % Annual Annual Overload Code Configuration HDC HAC Use TD OF OC C r i t e r i a VI TO-2 6 L-30 40 X 2.63 38.5 _ _ -X 40 38.5 V2 TO-3 0 L-26 40 X 7.89 38.5 1.04 .04 .32 X 37 38.5 V3 TO-12 L-08 40 X 7.89 38.5 1.17 .14 1.10 X 33 38.5 V4 TO-08 L-12 40 X 7.89 38.5 1.10 .10 .79 X 35 38.5 V5 TO-08 L-08 29 X 30.70 38.5 1.33 .34 10.44 X 40 38.5 — V6 TO-2 6 L-26 29 X 30.70 38.5 1.33 .34 10.44 X 40 38.5 11 TO-08 L-08 22.5 X 4.47 22.3 - -— X 38 22.3 12 TO-2 6 L-26 22 X 4.47 22.3 — — -X 38 22. 3 (1) (2) (3) (4) (5) Annual (6) Overl (7) oad — (8) • 23.09 (9) TD Test Demand OF Overload Factor; Column 7 T Column 3; Column 7 4- Column 4 OC Overload C r i t e r i a ; From Table 13.1, AIL Handbook Capacity Index = 2 3 F i n a l Annual Overload C r i t e r i a - 23.09 IAW Demand Factor = 58% F i n a l Test Demand =• 38.5 (VAW) F i n a l Test Demand = .58 x 38.5 = 22.3 (IAW) Approximate annual u t i l i z a t i o n - public desire = 3160 hours Approximate annual u t i l i z a t i o n - off-peak = 3720 hours Annual capacity - public desire = 3160 x 77 = 243,320 movements Annual capacity - off-peak = 3720 x 77 = 286,440 movements VAW peak hour demand = 38.5 x 2 = 77 movements per hour 122. that e x i s t i n g capacity rationed at e x i s t i n g prices i s s u f f i c i e n t to meet demands u n t i l 1980. Based on an analysis of the procedure adopted by the Ministry of Transport, i t i s reasonable to conclude that Vancouver International A i r p o r t has s u f f i c i e n t f a c i l i t i e s to accommodate the public demand for a i r t r a v e l . The question s t i l l remains however, of whether the rationale behind the schedule of prices, which rations t h i s capacity, i s e f f i c i e n t or even equitable. When the MOT forecasts demand, i t does not provide for the e f f e c t on demand that a price change p r e c i p i t a t e s . The following chapter w i l l examine one approach to p r i c i n g a i r p o r t capacity that t h i s author considers exemplary. I n i t i a l l y , the approach w i l l be described generally; the l a t t e r part of the chapter w i l l be an application of the approach to Vancouver Air p o r t . 123. Chapter V Throughout th i s thesis, the rationale behind the p r i c i n g of transportation has been queried. We have seen how poorly the present weight based system of landing fees serves as an i n s t r u -ment for e f f i c i e n t l y rationing runway capacity. The gross take of f weight of an a i r c r a f t i s , at best, a poor barometer of the cost of landing or taking o f f . Joseph Yance, i n his a r t i c l e "Movement Time as a Cost i n A i r p o r t Operations" has proposed a method to determine landing fees which r e f l e c t s , very well, the r e l a t i v e cost of operating an a i r c r a f t at a congested a i r p o r t . The variable under study i n t h i s proposal i s the length of time an a i r c r a f t movement takes r e l a t i v e to other a i r c r a f t . Yance used a technique developed by the AIL to determine what the r e l a t i v e demands of the classes of a i r c r a f t were. A i r c r a f t were grouped according to the population c l a s s i f i c a t i o n s outlined by the AIL Handbook. Yance calculated the capacity for the a i r p o r t (Washington National) when the proportion of the t o t a l a i r c r a f t population represented by class A and B a i r c r a f t was as low as 0 to where i t was as high as 100. This study has been re p l i c a t e d using data available from Vancouver International A i r p o r t and the Meteorological Branch of the Ministry of Transport. Table I was produced from the AIL Airport Capacity Handbook. Certain adjustments were made to the technique used by Yance i n the construction of a si m i l a r table found i n his study: 124. 1. Because the second ed i t i o n of the AIL handbook was used, a r r i v a l and departure capacities were interpolated from a figure which (under the "A" a i r p o r t c l a s s i f i c a t i o n ) was limited to and A+B population percentage of 11. To determine the capacity of the a i r p o r t (Vancouver International) when the A+B population percentage was less than 11, nomographs r e l a t i n g to a general-aviation-type a i r p o r t were used. Because of t h i s l i m i t a t i o n , the reader i s cautioned when int e r p r e t i n g the capacity figures for A+B populations less than 11 percent. 2. In the c a l c u l a t i o n of a r r i v a l capacity at a general aviation a i r p o r t , an accurate estimate of touch and go operations i s required. Since a precise figure was not available, the following technique was adopted: The data for a i r c r a f t movements fo r the peak of months of June, July and August, 1973 was examined. The 1 . 2 t o t a l s for l o c a l and i t i n e r a n t f l i g h t s under V i s u a l F l y i n g Rules were extracted. Local operations were then compared to the Total Movements which occurred under V i s u a l F l y i n g Rules. The average of each month's calculated proportion was used as the percentage of Touch and Go operations taking place at Vancouver International A i r p o r t . 3. As i n other references to AIL work, VFR c r i t e r i a have x A l o c a l f l i g h t i s defined as a movement i n which the a i r c r a f t remains at a l l times under tower control, such as i n c i r c u i t s around the a i r p o r t for practice landings and take o f f s . Each touch and go operation i s counted as one landing and one takeoff and hence as two movements. 2 An i t i n e r a n t movement i s one i n which the a i r c r a f t enters or leaves tower control. 125. been displaced by VAW c r i t e r i a . Because of data l i m i t a t i o n s , a precise t a l l y of movements taking place under VAW could not be obtained. However, data was available from the MOT Meteorological Branch and a i r c r a f t movements could be matched to p r e v a i l i n g weather with reasonable accuracy. Because the proportion of time that weather conditions were below VAW c r i t e r i a was so small (June - .8%, July - .3%, August - 3.8%) l i t t l e d e t a i l was l o s t by overlooking the discrepancy. The t o t a l capacity figures seen i n Table I were obtained i n the following manner: The runway combina-tions from Table II of the l a s t chapter were selected as represent-ative examples of runway use at Vancouver International. The Hourly Departure Capacity and Hourly A r r i v a l Capacity was calculated for each configuration and the t o t a l capacities determined. Each t o t a l 3 capacity was then weighted and the resultant products averaged to determine an average p r a c t i c a l hourly capacity. The figures i n columns three and f i v e of Table I were obtained as follows. With a l l movements consisting of general aviation a i r c r a f t , capacity i s reached at 113 movements per hour. If the population mix becomes 89 percent general aviation, 11 percent a i r c a r r i e r , t o t a l capacity f a l l s to 90 movements per hour. This capacity i s equivalent to 9.9 a i r c a r r i e r a i r c r a f t (.11 X 90) and 80.1 general aviation a i r c r a f t (.89 X 90) per hour. The remainder of the columns are derived i n a si m i l a r manner. I n i t i a l l y , an increase i n the movement rate of a i r The weights used were the percentage annual use made of each runway combination. 126. c a r r i e r a i r c r a f t of 9.9 requires a reduction of general aviation movements by 32.9. The trade o f f i n terms of the time demand of the two classes of a i r c r a f t i s therefore = -1^1 = o 30 A G 32.9 U , J U Table II gives the r e l a t i v e time demands of general aviation and a i r c a r r i e r a i r c r a f t . For the most part, the r a t i o increases as the proportion of c a r r i e r a i r c r a f t i n the population increases. There i s a curious "bump" i n the data for a i r c a r r i e r population proportion of 11 - 20 percent as well as a reduction i n the r a t i o for a i r c a r r i e r populations exceeding 70 percent. The reasons behind these aberrations were not f u l l y explored. Some of the causes that suggested themselves included: 1. The technique inherent i n the i n i t i a l c a l c u l a t i o n of t o t a l capacities; because the AIL Airport Capacity Handbook requires data on the i n d i v i d u a l proportions of A and B a i r c r a f t i n order to calculate HAC, an estimate was made of the respective proportions of A and B a i r c r a f t (theoretical) i n a i r p o r t populations where the A + B population exceeded that encountered at Vancouver. With present t r a f f i c , Vancouver a i r p o r t consists of 10 percent A a i r c r a f t , 24 percent B a i r c r a f t and 66 percent C + D + E a i r c r a f t . The r a t i o of A to B a i r c r a f t currently i n evidence at Vancouver was assumed to p e r s i s t at higher A + B populations. This assump-tion has a major e f f e c t on the ultimate determination of t o t a l capacity. 2. The t o t a l capacities were derived using a weighted average. The AIL Handbook has no provision for the averaging of Table I 127. Capacity for Two Intersecting Runways for Various Mixes of Class A, B and Class C, D, E A i r c r a f t at Vancouver International A i r p o r t Total Capacity CLASS A + B No. Ai r c r a f t / H r CLASS C,D,E No. A i r c r a f t / H r 113 0 0 100 113.00 90 11 9.90 89 80.10 ,88 20 17.60 80 70.40 81 30 24.60 70 56.70 77.5 40 31.00 60 46.50 75 50 37.50 50 37.50 73 60 43.80 40 29.20 71.5 70 50.05 30 21.45 67 80 53.60 20 13.40 59 100 59.00 0 0 (1) (2) (3) (4) (5) Table II Trade-off between C a r r i e r and General Aviation A i r c r a f t at Vancouver International A i r p o r t Carriers A C A G Relative Demands G.A. to A i r Ca r r i e r 0-11 9.90/32.90 0.30 11-20 7.70/9.70 0.79 20-30 6.70/13.70 0.49 30-40 6.70/10.20 0.65 40-50 6.50/9£00 0.72 50-60 6.30/8.30 0.76 60-70 6.25/7.75 0.83 70-80 3.55/8.05 0.44 80-100 6.60/13.40 0.49 1 2 8 . capacities associated with i n d i v i d u a l runway configurations. Normally, the P r a c t i c a l Hourly Capacity of a runway configuration i s incorporated into the P r a c t i c a l Annual Capacity of the Airport, given data on p r e v a i l i n g runway use proportions. The attempt, i n t h i s instance, to condense i n d i v i d u a l PHOCAPs into an average PHOCAP represents a new u t i l i z a t i o n of the AIL methodology. Refinements to the above technique would undoubtedly improve the progression of r a t i o s found i n Table I I . Having derived trade-off r a t i o s between a i r c a r r i e r and general aviation a i r c r a f t i t now remains to apply these r a t i o s to observed movement rates. T r a d i t i o n a l l y , movement rates at Vancouver International Airport are at a maximum during the warm summer months of June, July and August. I t i s during t h i s period that congestion, i f any, occurs. Referring to the Monthly Report on A i r c r a f t Movements for Vancouver International A i r p o r t , we can see that movements during August 1973 reached a maximum of 1006 d a i l y on the 18th of t h i s month. The t o t a l number of move-ments for August 1973 reached 21,115. This t o t a l translates to peak-hour t o t a l s of 92, 91, 88 and 87 for 1600, 1 2 0 0 , 1900 and 1300 hours respectively for peak days during the month. Average hourly t o t a l s are considerably lower however, (see Table I I I ) . A i r c a r r i e r s accounted for as high as 30.4 percent of t o t a l move-ments during the month of June 1973, and as high as 28.0% during the month of July 1973. Reference to Table II indicates that an a i r c a r r i e r population of 2 8 percent i s i n the range where the trade o f f between r e l a t i v e demands of a i r c a r r i e r and general aviation i s .49. 129. Table III Vancouver International A i r p o r t August 1973; Peak Number of Total A i r c r a f t Movements Total A/C Movements Hour Peak Total Average 00 25 202 6.5 01 10 57 1.8 02 2 13 .4 03 4 20 .6 04 2 17 .5 05 7 65 2.1 06 12 178 5.7 07 44 770 24.8 08 61 1077 34.7 09 75 1320 42.6 10 84 1296 41.8 11 80 1349 43.5 12 91 1472 47.5 13 87 1512 48.8 14 82 1541 49.7 15 76 1371 44.2 16 92 1623 52.4 17 85 1736 56.0 18 74 1590 51.3 19 88 1417 45.7 20 54 1052 33.9 21 42 576 18.6 22 37 490 15.8 23 27 371 12.0 Source: Monthly Report on A i r c r a f t Movements for Vancouver  International A i r p o r t , Aviation S t a t i s t i c s Centre, August, 1973 130. Relative Landing Fees: The time that a movement takes has an "opportunity cost" associated with i t . This opportunity cost can be viewed i n two ways. If an additional movement takes place during peak times when the a i r p o r t i s operating at capacity, the average delay to a l l a i r c r a f t i s increased. If average delay i s to be kept constant, an additional movement by one class of a i r c r a f t must be accompanied by a decrease i n the movement rate of another cl a s s . Yance concentrated on the l a t t e r d e f i n i t i o n of opportunity cost because i t referred to the r e l a t i v e l e v e l of landing fees for d i f f e r e n t classes of a i r c r a f t . The same view i s adopted here. The previous chapter i l l u s t r a t e d that under the 4 minute average delay c r i t e r i a , Vancouver International A i r p o r t i s not operating at i t s p o t e n t i a l capacity. The above technique was developed by Yance for application to Washington National A i r p o r t which, i n 1965, was operating at capacity and was p e r i o d i c a l l y experiencing very high delays to departures. The f a c t that Vancouver a i r p o r t i s currently not experiencing these problems should not detract from the p o t e n t i a l usefulness of such a technique in determining a landing fee schedule which would meet e f f i c i e n c y c r i t e r i a . The example which i s used to i l l u s t r a t e the a p p l i c a t i o n of Yance's technique i s not representative of normal a c t i v i t y at Vancouver. I t does however focus on a l i k e l y solution to the inevitable increase i n demand for service at Vancouver International. In a previous paragraph, we saw that a i r movements at Vancouver reached a l e v e l of 1,006 on August 18, 1973. Of these movements, 159 were a i r c a r r i e r . This proportion of a i r c a r r i e r a i r c r a f t (16%) f a l l s into the range of trade-off of 0.79. Because of the uncertainty surrounding t h i s r a t i o , we w i l l instead use the next r a t i o of 0.49. From the d e f i n i t i o n of opportunity cost adopted above, we see that to increase the movement rate of general aviation a i r c r a f t by one movement per hour, keeping the average delay constant, the movement rate of c a r r i e r a i r c r a f t would have to be reduced by 0.49 per hour. The opportunity cost of accommodating a general aviation a i r c r a f t i s 0.49 as much as that of an a i r c a r r i e r a i r c r a f t . However, the landing fees paid by general aviation are i n a much lower r a t i o than t h i s to those paid by a i r c a r r i e r s . ^ In money terms, a general aviation a i r c r a f t weighing 10,000 lbs. landing at Vancouver a f t e r a domestic f l i g h t would pay $2.50 whereas an a i r c a r r i e r weighing 100,000 l b s . would pay $25.00 for landing. If we view landing charges from an opportunity cost standpoint, we see that during peak periods the general aviation a i r c r a f t pays a fee of $2.50 compared with an opportunity cost of (0.49 x $25.00) $12.25. This example assumes that the a i r c a r r i e r a i r c r a f t displaced from landing i s domestic; i f i t was i n fact a trans-oceanic f l i g h t the opportunity cost of landing the general aviation a i r c r a f t would have been (0.49 x 140) $68.60. It i s recognized that the marginal cost of a landing For the schedule of fees assessed the users of a i r p o r t f a c i l i t i e s , see Appendix A. 132. at Vancouver a i r p o r t i s composed of factors other than the opportunity cost of a i r c r a f t "displaced" from the landing queue. It i s suggested however that (assuming that the current l e v e l of landing fees for a i r c a r r i e r a i r c r a f t i s appropriate) r e v i s i o n of general aviation landing fees would a l l e v i a t e congestion at peak hours as well as provide a c r i t e r i a against which to evaluate expansion. Conclusion When one i n i t i a l l y addresses the topic of p r i c i n g , one perceives a seemingly well-ordered world of l o g i c a l rules which, i f pursued, conclude i n a precise figure to be charged. Unfort-unately, as we have seen, e x t e r n a l i t i e s impose on t h i s i d y l l i c s e t ting and compel the analyst to adopt p r i c i n g techniques which can only approximate the t h e o r e t i c a l i d e a l . In the f i e l d of a i r transportation, e x t e r n a l i t i e s are composed of government i n t e r -ference i n what could otherwise be a free enterprise market. In Canada, because of i t s extreme size and geographic nature, a i r transportation i s a necessity i f people and goods are to be transported quickly over great distances. Perhaps i t i s t h i s aspect of a i r transportation that separates i t from other modes and entices governments to l a v i s h hugh sums of money on i t s provision. Whatever the reason, large amounts of money are spent annually on the construction of new airports or the main-tenance and expansion of e x i s t i n g ones. St. Scholastique i n Montreal, and Pickering A i r p o r t i n Toronto are excellent examples of new construction necessitated by the burgeoning demand for a i r transportation. The recent history of a i r transportation i n Canada i s replete with examples of government spending unmatched by government c o l l e c t i o n s . The Ministry of Transport c o l l e c t s fees from the users of a l l a i r p o r t f a c i l i t i e s . This thesis has concentrated on landing fees but a b r i e f mention of other f a c i l -i t i e s serves to i l l u s t r a t e the ever widening gap between revenues 134. and costs. Costs accumulate as a r e s u l t of a c t i v i t y i n the following areas: Airports A i r T r a f f i c Control & Telecommunications Control of C i v i l Aviation A i r Services Administration Construction Branch Meteorology, C i v i l Aviation Search & Rescue, C i v i l Aviation A i r Transport Committee - CTC Revenues are c o l l e c t e d from users of the following f a c i l i t i e s : Terminal: Space ren t a l Concession Shops and P r i v i l e g e s Joint User Terminal F a c i l i t i e s Charge Observational Turnstiles Sale of U t i l i t i e s Miscellaneous F i e l d : Landing Fees Gas and O i l Fees A i r c r a f t Parking Mobile Equipment Registration Fees Terminal Building Area Telecommunications Control of C i v i l Aviation: Aviation Personnel Licences A i r c r a f t Registration C e r t i f i c a t e s A i r p o r t Licence Fees Airworthiness C e r t i f i c a t e s Meteorology P r o v i n c i a l Aviation Fuel Tax 135. Depending on the cost of c a p i t a l figure used, costs have exceeded revenues at an increasing annual rate since 1954 when comparisons were f i r s t published. Figure 1 depicts t h i s s i t u a t i o n ; a l l figures shown are i n 1968 d o l l a r s . At the time of writing, t h i s represented the most recent data a v a i l a b l e . Ine f f i c i e n c y of any sort should be removed from a i r p o r t f a c i l i t y p r i c i n g i f the gap depicted i n Figure 1 i s to be closed or prevented from enlarging. It i s apparent from the work described i n the f i r s t three chapters of t h i s thesis that the derivation of a landing fee schedule which s a t i s f i e s economic e f f i c i e n c y c r i t e r i a and i s sim-ultaneously applicable, i s not a simple task. Once the work of Williamson i s understood, the p r i c i n g of landing fees under vary-ing l e v e l s of demand becomes straight forward. I t i s the a p p l i c -ation of t h i s work that comprises the major hurdle. C a r l i n & Park are responsible for the most comprehensive attempt to determine a schedule of landing fees which conforms to economic p r i n c i p l e s . J. Yance, whose work was r e p l i c a t e d i n the l a s t chapter also was successful i n devising a technique which can be used i n establishing landing fees. Ultimately, even the most tenable of arguments must be evaluated i n the p o l i t i c a l arena. The rationale suggested for use at Vancouver International A i r p o r t (and indeed at any federal a i r p o r t i n Canada) i s the model developed by Yance. The example of a peak-hour landing fee (where the mix of a i r c a r r i e r to general aviation a i r c r a f t i s .16) of $12.25 for a 10,000 l b . general aviation a i r c r a f t would undoubtedly be characterized by general Figure 1 136. Annual Costs and Revenues Canada 1954-68 C i v i l Aviation Infrastructure (In M i l l i o n s of 1968 Constant Dollars) 240 J 220 200 M i l l i o n s Gross Revenues (includes Provinc Aviation Fuel Tax) Net Revenues Cost of Capital 9% 7% 1954 1956 1958 1960 1962 1964 1966 1968 Year Source:. Haritos Z., Gibberd J.D. C i v i l Aviation Infrastructure  Annual Costs and Revenues, 1954-1968. CTC. 1972. 137. aviation as discriminatory and not i n keeping with the tenets of the law. I t i s un l i k e l y that any upward adjustment of landing fees w i l l meet with the approval of a i r p o r t users. The Yance approach to peak-hour p r i c i n g i s not unique; there are many other approaches which ultimately would achieve the same end — economic e f f i c i e n c y . This approach was selected for i t s i n t r i n s i c appeal and i n i t i a l ease of applica t i o n . There i s nothing sacred about the r e l a t i v e time demand r a t i o s and the resultant demand-related landing fees. The l a t t e r i s completely dependent upon the e x i s t -ing rate structure. I f , upon adoption of th i s technique, demand f e l l o f f dramatically at peak times and was not simply r e d i s t r i -buted over the remaining hours, the schedule of prices could be revised. The strength of the suggested fee schedule i s found i n the rationale behind i t , not i n i t s r e l e n t l e s s a p p l i c a t i o n . U t i l i z i n g the demand r a t i o s from Table II of the l a s t chapter, i t i s possible to construct a schedule of landing fees which r e f l e c t s the time required to process d i f f e r e n t a i r c r a f t under d i f f e r e n t conditions. Because of the uncertainty of the general a v i a t i o n - a i r c a r r i e r demand r a t i o s at either end of the ai r p o r t population scale, only the r a t i o s related to an a i r c a r r i e r population of 30% - 70% w i l l be used. The following table has been constructed by applying the aforementioned demand ra t i o s to current lev e l s of landing fees. This c a l c u l a t i o n assumes that the e x i s t i n g structure of fees for a i r c a r r i e r a i r -c r a f t i s appropriate. (A complete description of landing fees at Canadian airpor t s can be seen i n Appendix "A".) Under ex i s t i n g regulations, an a i r c r a f t weighing less 138. than 45,000 l b s . (domestic f l i g h t ) i s assessed a charge of $ .20 per 1 ,000 lbs. of gross takeoff weight. An a i r c r a f t f l y i n g under sim i l a r conditions but weighing i n excess of 100,000 l b s . i s assessed a charge of $ .30 per 1,000 lbs. The amounts payable by a general aviation a i r c r a f t weighing 10,000 l b s . and an a i r c a r r i e r a i r c r a f t weighing 120,000 l b s . would be $2 .00 and $36.00 respectively. Table I Proposed Fee Schedule at Vancouver International A i r p o r t Relative Demands % Carriers G.A. to A.C. G.A. Fee A.C. Fee 20 - 30 .49 30 - 40 .65 40 - 50 .72 50 - 60 .76 60 - 70 .83 $ 17.64 $ 36.00 23.40 36 .00 25.92 36.00 27.36 36 .00 29.88 36.00 I t i s apparent from Table I that the cost to general aviation a i r c r a f t would be s i g n i f i c a n t l y increased i f landing fees were assessed i n t h i s manner. These fees are not completely unfounded; minimum fees of $25.00 for peak-hour use have been i n force at Port of New York Authority airports for f i v e years. It should be stressed however, that the magnitude of 139. these fees i s not beyond debate. In fact, i t would be surprising were i t otherwise. The ultimate success of t h i s approach depends on the manner i n which i t i s implemented. Ideally, t h i s fee schedule would be introduced a f t e r a period of discussion. Debate would determine how accurately the r e l a t i v e demand fee schedule r e f l e c t s the opportunity cost of delays during busy times. Afte r the introduction of the schedule, a c t i v i t y at the a i r p o r t should be c a r e f u l l y monitored to determine the impact of the new l e v e l of p r i c e s . The schedule of fees should be modified based on these observations to ensure that the ai r p o r t continues to be u t i l i z e d e f f i c i e n t l y . 140. Bibliography Airborne Instruments Laboratory, A i r p o r t Capacity Handbook-Second E d i t i o n , New York 1969. Aviation Planning & Research D i v i s i o n , Ministry of Transport, Vancouver International A i r p o r t - Capacity/Demand Analysis  For Selected Runway Configurations, 1971. Aviation Planning & Research D i v i s i o n , Ministry of Transport, An Analysis of the Vancouver International A i r p o r t Runway  System With Reference To Th"e Requirement For P a r a l l e l Runway  08L - 26R, 1972. Buchanan, J.M. Peak Loads and E f f i c i e n t P r i c i n g : Comment, Quarterly Journal of Economics, 1966. C a r l i n , A. & Park, R.E. A Model of Long Delays at Busy Ai r p o r t s , Journal of Transport Economics & Policy, 1970. C a r l i n , A. & Park, R.E. Marginal Cost P r i c i n g of Ai r p o r t  Runway Capacity, The American Economic Review, T970. C a r l i n , A. & Park, R.E. The E f f i c i e n t Use of Ai r p o r t Runway  Capacity i n a Time of Scarcity, The Rand Corporation, 1969. Dyert, R. Some Issues i n Airport P r i c i n g , Report of Economic Session, A i r p o r t Operators Council International Annual Meeting, 1967. Eckert, R.D. Airports and Congestion - a problem of misplaced  subsidies, The American Enterprise I n s t i t u t e for Public Policy Research, 1972. Feldman, D. On the Optimal Use of Airports i n Washington D.C. Socio-Economic Planning Science, 1967. Grampp, W.D. An Economic Remedy for Airport Congestion: The  Case for F l e x i b l e P r i c i n g , Business Horizons, 1968. H i r s h l e i f e r , J . Peak Loads and E f f i c i e n t P r i c i n g : Comment, Quarterly Journal of Economics, 1958. Horonjeff, R. Planning and Design of Airports 1962. Jackson, R. Air p o r t Noise and Congestion; A Peak-Load P r i c i n g  Solution, Applied Economics, 1971. Levine, M.E. Landing Fees and the Air p o r t Congestion Problem, The Journal of Law and Economics, 1969. 141. 16. Minasian, J.R. Ambiguities i n the Theory of Peak-Load P r i c i n g , 1969. 17. Minasian, J.R. & Eckert, R.D. The Economics of Airport Use, Congestion and Safety, C a l i f o r n i a Management Review, 1969. 18. Ministry of Transport, Meteorological Branch, Monthly Summaries  of Operational Weather, Dec. 1972 - Nov. 1973. 19. S t a t i s t i c s Canada, Aviation S t a t i s t i c s Centre, Monthly Report  on A i r c r a f t Movements - Vancouver International Airp o r t , Dec. 1972 - Nov. 1973. 20. Steiner, P.O. Peak Loads and E f f i c i e n t P r i c i n g , Quarterly Journal of Economics^ 1957. 21. Warford, J . J . Public P o l i c y Toward General Aviation, The Brookings I n s t i t u t i o n , 1971. 22. Williamson, O.E. Peak-Load P r i c i n g and Optimal Capacity under  I n d i v i s i b i l i t y Constraints, American Economic Review, 1966. 23. Yance, J.V. Movement Time as a cost i n A i r p o r t Operations, Journal of Transportation Economics and Policy, 1969. 24. Yance, J.V. P r i c i n g to Reduce Airport Congestion, Highway Research Record, T9~69. 142. APPENDIX "A" Fees Regulations 1 - 1 September 23, 1970 14 PART I REGULATIONS RESPECTING FEES AND CHARGES FOR CANADIAN CIVIL AIR SERVICES Short Title These Regulations may be cited as the Air Services Fees Regulations. Interpretation In these Regulations "Assistant Deputy Minister, A i r " means the Assistant Deputy Minister of the Department; "commercial flying school" means a flying school licensed by the Air Transport Board; "Department" means the Department of Transport; "domestic flight" means a flight between points in Canada; "flying club" means a flying club that is a member of the Royal Canadian Flying Clubs Association; "international flight" means a flight between Canada and a place outside of Canada that is not a trans-oceanic flight; "Minister" means the Minister of Transport; "owner" in relation to an aircraft, includes a person operating the aircraft; "state aircraft" means an aircraft, other than a commercial aircraft, owned and operated by the government of any country or the government of a colony, dependency, province, state or territory of any country; "trans-oceanic flight" means a flight between Canada and a place outside of Canada that passes over or is intended to pass over the Atlantic Ocean, except a flight between Canada and Bermuda, St. Pierre and Miquelon, and the United States; and "weight" in relation to an aircraft means the maximum permissible take-off weight specified in its certificate of airworthiness or in a document referred to therein. Application (1) Subject to subsection (2), these Regulations apply to every airport operated by the Department. (2) Sections 7, 8 and 9 do not apply to any part of an airport held under a lease granted By Her Majesty in right of Canada. Landing Fees (1) Every owner of an aircraft that is based at an airport and that is owned and operated by a flying club or commercial flying school shall pay (a) the fees set out in Schedule A for each landing of the aircraft where the aircraft is engaged in flying training at that airport; and (b) the fees referred to in subsection (2) for each landing of the aircraft where the aircraft is engaged in other than flying training. (2) Every owner of an aircraft not mentioned in paragraph (1) (a) shall pay the fee set out in Fees Regulations 2 - 1 September 23, 1970 144. PART 2 SCHEDULE A Flying Club or Commercial Flying School Landing Fees (section 4 (1)) 1. For each hour flown by the aircraft $ .30 SCHEDULE B Domestic Flight Landing Fees (section 4 (2) (a)) 1. For aircraft of not more than 45,000 pounds weight; fee per 1, 000 pounds or fraction thereof. .20 2. For aircraft over 45,000 pounds weight but not over 100,000 pounds weight; fee per 1, 000 pounds or fraction thereof .25 3. For aircraft over 100,000 pounds weight; fee for 1,000 pounds or fraction thereof 30 4. Minimum fee payable regardless of weight 1. 00 SCHEDULE C International Flight Landing Fees (section 4 (2) (b)) For aircraft of not more than 70,000 pounds weight; fee per 1, 000 pounds or fraction thereof 25 For aircraft over 70,000 pounds weight but not over 147,000 pounds weight; fee per 1, 000 pounds or fraction thereof .35 For aircraft over 147,000 pounds weight; fee per 1,000 pounds or fraction thereof .50 Minimum fee payable regardless of weight 1. 00 SCHEDULE D Trans Oceanic Flight Landing Fees (section 4 (2) (c)) 1. For aircraft of not more than 90,000 pounds weight; fee per 1, 000 pounds or fraction thereof 1.33 2. For aircraft over 90,000 pounds weight but not over 125,000 pounds weight; fee per 1,000 pounds or fraction thereof 1.40 3. For aircraft over 125,000 pounds weight but not over 150,000 pounds weight; fee per 1,000 pounds or fraction thereof 1.46 4. For aircraft over 150., 000 pounds weight; fee per 1,000 pounds or fraction thereof 1. 51 145, Fees Regulations 2-2 September 23, 1970 SCHEDULE E Canadian Stations Operating in the International  Aeronautical Telecommunications Service (section 5) Station Churchill, Man,... Edmonton, Alta . . . Frobisher, N.W.T Gander, Nfld Goose Bay, Nfld. . . Moncton, N. B Mont Joli, P.O. Montreal, P.Q Resolute, N. W. t. . Sydney, N.S Vancouver, B. C. . . "Winnipeg, Man. . . . Call Sign VAP VFE VFF VFG VFZ VFX VCF VFN VFR4 VFS VFU VFW5 2. SCHEDULE F General Terminal Charges (section 6) Charge for each unit of five seats seating capacity, calculated to the nearest unit of five seats, of an aircraft on a (a) domestic flight (b) non-domestic flight Minimum charge regardless of seating capacity for an aircraft on a (a) domestic flight. ; (b) non-domestic flight $1. 00 2.00 2.00 4.00 SCHEDULE G Aircraft Parking Charges Elsewhere Than in a Hangar (section 7) For each 10 square foot unit of area or portion thereof (a) Per day (b) Per week (c) Per month $ .01 .06 .20 (d) Per year j _ 2 0 2. Minimum parking charge per day or any part thereof in excess of six hours .• 3. Where an owner of an aircraft elects to pay the monthly charge with respect to the overnight lay-overs of a scheduled flight, only one aircraft of the same type or a smaller type may be over-nighted for each monthly charge paid. Where an aircraft larger than the one for which a monthly charge has been paid is over-nighted at the airport, it shall be charged the daily rate for that type of aircraft. $1.00 Fees Regulations 2 - 3 September 23, 1970 146 SCHEDULE G (Cont'd) Airports at which free parking privileges are available for the first twenty-four hours to an owner of a private aircraft weighing not over five thousand pounds are Calgary International Cartierville Edmonton International Fredericton Frobisher Gander International Goose Bay Halifax International Lakehead London Moncton Montreal International North Bay Ottawa International Quebec Saint John, N. B. Saskatoon Sept-D.es Sydney Toronto International Vancouver International Victoria International Windsor Winnipeg International SCHEDULE H Hangar Storage Charges (section 8) Per day For each 10 square foot unit of area or portion thereof or Portion occupied by an aircraft thereof (a) For heated hangars $ .041 (b) For unheated hangars at Frobisher .038 (c) For unheated hangars at airports other than Frobisher .... . 0223 Minimum charge for storage in a heated hangar during the winter season (November 15 to April 15) •' $5.00 SCHEDULE I Goods Storage Charges (section 9) Per day or Portion For each 10 square foot unit of area or portion thereof thereof (a) In a hangar $ .0164 (b) In a building other than a hangar ,01 (c) Elsewhere than in a building. .0033 Fees Regulations 2-4 September 23, 1970 SCHEDULE J Training Landings (section 4 (3)) Air carriers wishing to carry out training flights must apply to the appropriate Regional Director. A flying training flight is a familiarization flight conducted exclusively for the purpose of improving the skill and knowledge of the aircrew. Subject to paragraphs 4 and 5 training landings will be charged for at 20% of domestic landing fees. Air carriers who prior to July 1, 1969-paid a fixed annual amount for flying training landings at Montreal, Toronto, Winnipeg, Vancouver, Ottawa and Edmonton International Airports and Abbotsford Airport will be charged for training landings at the following rates at those Airports. 147, July 1, April 1, April 1, April 1, April 1, April 1, Year 1969 - March 31, 1970 1970 - March 31, 1971 1971 - March 31, 1972 1972 - March 31, 1973 1973 - March 31, 1974 1974 - March 31, 1975 (and thereafter) Rate 10% of Domestic 12% of Domestic 14% of Domestic 16% of Domestic 18% of Domestic 20% of Domestic Landing Fees Landing Fees Landing Fees Landing Fees Landing Fees Landing Fees The special rate for flying training landings is applicable to Canadian carriers only. Non-Canadian carriers wishing to carry out flying training landings at departmental airports will be charged the appropriate international or trans-oceanic landing fee upon arrival at an airport, and for each flying training landing thereafter theiull domestic landing fee, except that the trans-oceanic landing fee will apply to the last landing prior to a trans-oceanic flight upon departure from Canada. Fees Regulations 1-2 September 23, 1970 (3) (1) (2) (1) (2) 148, (a) Schedule B for each landing of the aircraft that concludes • (i) a domestic flight, or (ii) a planned trans-oceanic flight that was dis-continued at an airport in Canada following the commencement of the flight at another airport in Canada; (b) Schedule C for each landing of the aircraft (i) for a technical purpose at Goose Bay Airport, Gander International Airport or Ottawa Inter-national Airport while on a trans-oceanic flight; and (ii) that concludes an international flight; (c) Schedule D for each landing of the aircraft, other than a landing described in paragraph (b) at an airport that is (i) the last point of landing prior to a trans-oceanic flight, or (ii) the first point of landing after a trans-oceanic flight. Notwithstanding subsections (1) and (2), every air carrier licensed under subsection (1) of Section 15 of the Aeronautics Act shall pay the fee set out in Schedule J for the landing of an aircraft engaged in the training of aircrew person-nel of that air carrier. Telecommunication Service Fee Every owner of an aircraft shall pay a fee of thirty dollars for each flight of the aircraft where the aircraft is engaged on a flight that requires and uses international frequencies and services provided by aeronautical stations listed in Schedule E. For the purposes of this section, a flight means the whole of a journey of an aircraft regardless of the number of intermediate stops. General Terminal Charge Subject to subsection (2), every owner of an aircraft that uses the air terminal building at an airport to which this section applies for the purpose of embarking or disembarking passengers shall pay, on each embarkation or disembarkation of passengers, the terminal charge set out in Schedule F. Where a terminal charge is payable pursuant to subsection (1) for dis-embarking passengers at an air terminal building, a terminal charge is not payable pursuant to that subsection (a) (b) (c) for embarking passengers on the aircraft from the terminal building on a through flight of that aircraft; for embarking passengers on the aircraft from the terminal building for the turn-around flight of that aircraft, irrespective of the flight number, where the aircraft does not have a scheduled lay-over of more than three hours; or for embarking passengers on the aircraft from the terminal building for the onward flight of that aircraft, irrespective of the flight number, if it completes a domestic flight and commences a non-domestic flight Fees Regulations 1 - 3 September 23, 1970 14 or completes a non-domestic flight and commences a domestic flight, where the aircraft does not have a scheduled lay-over of more than three hours. (3) This section applies to Calgary, Edmonton, Montreal, Toronto, Winnipeg and Vancouver International Airports. (4) For the purposes of this section, a "through flight" means a flight by an aircraft that arrives at and departs from an airport under the same flight number as part of the continuous journey of that aircraft. Aircraft Parking Charge (1) Subject to subsection (2), where an aircraft is parked on any part of an airport elsewhere than in a hangar for more than six hours, the owner of the aircraft shall pay to the officer in charge of the airport the parking charge set out in Schedule G. (2) No parking charge is payable, in respect of a private aircraft weighing five thousand pounds or less, (a) for the first twenty-four hour period during which the aircraft is parked at an airport listed in Schedule G; or (b) for parking at an airport not listed in Schedule G when the aircraft is parked in an area set aside and marked by the officer in charge of the airport as a free parking area. (3) The total parking charges for any aircraft parking at an airport shall not exceed (a) in any week, the weekly charge determined in accordance with Schedule G; and (b) in any month, the monthly charge determined in accordance with Schedule G. (4) An owner of an aircraft may, by notifying in writing the officer in charge of an airport, elect to pay (a) for the purpose of schedule flight overnight lay-overs the monthly parking charge set out in Schedule G; and (b) for a private aircraft having a weight of five thousand pounds or less, based at an airport where parking charges are payable in respect of the aircraft, the annual parking charge set out in Schedule G. (5) For the purpose of this section (a) any period of more than six hours but not more than twenty-four hours shall be counted as one day; and (b) the area occupied by an aircraft is deemed to be the area obtained by multiplying the overall length of the aircraft by the overall width, including wings, rotors and undercarriage. Fees Regulations 1 - 4 September 23, 1970 10. 12. (3) Hangar Storage Charge (1) '- Where an aircraft is placed in a hangar, the owner of the aircraft shall pay to the officer in charge of the airport the hangar storage charge set out in Schedule H. (2) Where arrangements are made with the officer in charge of an airport for storage of an aircraft in a hangar for a continuous period of not less than two months and the aircraft remains in the hangar for such period, the storage charge set out in Schedule H shall be reduced by twenty-five per cent. For the purpose of Schedule H, the area occupied by an aircraft is deemed to be the area obtained by multiplying the overall length of the aircraft by the overall width, including wings, rotors and undercarriage. Goods Storage Charge Where goods, other than an aircraft, are placed on any part of an airport, the owner or the person causing the goods to be placed on the airport shall pay to the officer in charge of the airport the storage charge set out in Schedule I. Where goods are stored in a hangar and occupy less than one-quarter of the floor space of the hangar, the storage charge set out in Schedule I shall be increased by twenty-five per cent. Payment of Fees and Charges All fees and charges shall be computed to the nearest five cents. 11. (1) Fees and charges shall be paid at the place and in the manner prescribed by the Assistant Deputy Minister, Air. Notwithstanding subsection (1), the owner of a private aircraft who elects to pay the annual parking charge prescribed by paragraph 7 (4) (b), shall pay the charge annually in advance to the officer in charge of the airport. 150; (1) (2) (2) Removal of Aircraft or Goods The officer in charge of an airport may cause any aircraft or goods in respect of which any charge under section 7, 8 or 9 remains unpaid for three months to be • removed at the expense and risk of the owner to any place on the airport where they will not interfere with the operation or maintenance, of the airport and from the time of that removal no further charge is payable in respect of that aircraft or those goods. Exemptions 13. Notwithstanding anything in these Regulations, no fee or charge is payable (a) under section 4 in respect of the landing at an airport, other than at Toronto, Vancouver or Montreal International Airports, of (i) an aircraft that is not based at the airport and that is owned and operated by a flying club or commercial flying school, if the owner of the aircraft notifies the officer in charge of the airport that the aircraft is engaged in flying training, or (ii) a private aircraft weighing not over five thousand pounds; Fees Regulations 1 - 5 September 23, 1970 151. (b) under paragraph 4 (2) (a) or 4 (2) (b), in respect of the forced landing at any airport of an aircraft in distress when engaged on a domestic or international flight; (c) under paragraph 4 (2) (b) or 4 (2) (c), in respect of the landing of an aircraft at any airport after the discontinuance of a trans-oceanic flight that commenced at another airport in Canada; (d) under subsection 4 (2), in respect of the landing of an aircraft at the airport from which it took off on a trans-oceanic flight after the discontinuance of the flight; or (e) in respect of state aircraft (i) under sections 4 and 5, for any landing or flight (ii) under section 6, for general terminal charges if the aircraft is stationed in a location designated by the officer in charge of the airport, (iii) under section 7, for the first thirty days that the aircraft remains parked in a location designated by the officer in charge of the airport, and (iv) under section 8, for the first forty-eight hours that the aircraft remains in a hangar. 152, APPENDIX "B" Source: A i r p o r t Capacity Handbook - Second E d i t i o n AIL, A D i v i s i o n of Cutler - Hammer, Deer Park, New York June, 1969 153. GLOSSARY "A" a i r p o r t : An a i r p o r t where a i r c r a f t Classes A and B are greater than ten percent of population — p r i n c i p a l l y used by a i r c a r r i e r s . Airspace: Defined for use i n computing capacity for "A" a i r p o r t s . If unlimited airspace exists around an a i r p o r t , departures can be sequenced, one behind the other, at short i n t e r v a l s (low-service times). A slow a i r c r a f t , ahead of a f a s t a i r c r a f t , can be turned away from the a i r p o r t very quickly i n any d i r e c t i o n allowing the f a s t a i r c r a f t to be released i n a short time. However, i n a highly r e s t r i c t e d airspace s i t u a t i o n where noise abatement i s a problem and other airports are nearby, each departure may have to follow others along the same path for some distance. This w i l l r e s u l t i n long-service times, with a corresponding decrease i n departure capacity. The graphs used i n capactiy computations allow for: 1. Highly r e s t r i c t e d airspace: Defined as one common path out of an a i r p o r t where a i r c r a f t must follow each other from l-to-5 miles. This type of airspace i s commonly found at busy airport s where noise abatement i s a problem and when other busy airports are within a ten-mile radius. Also, mountains can cause si m i l a r conditions. 2. Normal airspace: Where a i r c r a f t can be 'fanned 1 out over three basic d i r e c t i o n s . Some noise r e s t r i c t i o n s may be present, but are not severe, and the closest busy a i r p o r t i s more than ten miles away. 154. 3. "Unrestricted" airspace: Self-explanatory, and implies no noise, other busy a i r p o r t , or any geographical r e s t r i c t i o n s nearby. ANDE: The ANnual DElay to a r r i v a l and departures totaled over a one-year period. Annual capacity: The P r a c t i c a l ANnual CAPacity (PANCAP) of an air p o r t i s reached when the delay to operations over a one-year period reaches the c r i t e r i a l e v e l . A r r i v a l capacity: The hourly a r r i v a l movement rate at which an average delay of four minutes occurs. Also, abbreviated as HAC — hourly a r r i v a l capacity. Capacity: The operating l e v e l , expressed as the rate of a i r c r a f t movements, which r e s u l t s i n a given l e v e l of delay. Computer sequencing: A future technique to be used by a i r t r a f f i c control to sequence a r r i v a l s and departures with the a i d of com-puters. Also c a l l e d TIC — terminal i n t e r v a l computer. Crosswind c r i t e r i a : The allowable crosswind for routine landing and takeoff operations. Suggested as 15 knots for PANCAP and ANDE calc u l a t i o n s . Departure capacity: The departure movement rate at which an aver-age delay of four minutes occurs. Also abbreviated as HDC — hourly departure capacity. "G" a i r p o r t : An ai r p o r t where a i r c r a f t Classes A and B are less than or equal to ten percent of the population — p r i n c i p a l l y used by general aviation. HAC: Hourly a r r i v a l capacity. HDC: Hourly departure capacity. Hourly capacity: The movement rate per minute at a selected de-155. lay l e v e l usually four minutes more often c a l l e d P r a c t i c a l HOurly CAPacity — PHOCAP. HTC: Hourly t o t a l capacity — used as a working term i n PHOCAP and PANCAP computations. IAW: Instrument a i r p o r t weather — see "Weather conditions". IAW approach: An instrument approach using ILS, VOR, or other aids during IAW-type weather. IAW control: A i r - t r a f f i c - c o n t r o l procedures used during IAW-type weather and i s based on either radar or non-radar cont r o l . Intersection r a t i o : In the case of two int e r s e c t i n g or open-V runways, the rel a t i o n s h i p between the t o t a l runway lengths and the i n t e r s e c t i o n distances must be expressed as a r a t i o . L a t e r a l separation of p a r a l l e l runways: For IAW conditions i n 1968-75 and both IAW and VAW i n 1975, you w i l l be required to know the separation between the two p a r a l l e l runways. If i t i s 3,500 feet or l e s s , and the runway thresholds are o f f s e t from eachother, a correction factor w i l l be required. MTB: An acronym used to i d e n t i f y a p a r a l l e l runway configuration when the main terminal i s between the runways. MTO: An acronym used to i d e n t i f y a p a r a l l e l runway configuration where the main terminal i s outside the runways. Off-peak'use: A term used to describe the spreading of a i r c r a f t movements outside the peak hour periods. Generally occurs at airports where PANCAP i s exceeded as a means of reducing delay. Used i n PANCAP computations. PANCAP: See annual capacity. PHOCAP: P r a c t i c a l HOurly CAPacity — an abbreviation frequently 156. used as i t i s a key to many capacity computations. I t i s the movement rate which r e s u l t s i n a selected average delay (usually four minutes). Since i t i s delay-related, PHOCAP can be exceeded but at the pr i c e of a higher average delay. Population: For capacity analysis, the population i s defined as the actual mixture of a i r c r a f t classes making up a movement rate. The mixture of a i r c r a f t classes w i l l greatly a f f e c t capacity and delays. For a given runway configuration, a popula-tion of l i g h t a i r c r a f t w i l l produce a much higher capacity than a population of heavy a i r c r a f t , including j e t s . To use the graphs for determining capacity, i t i s neces-sary to state the population i n terms of percentages of classes of a i r c r a f t . P r a c t i c a l HOurly CAPacity: Commonly used as PHOCAP. I t i s the movement rate which re s u l t s i n a selected average delay (usually four minutes). Public desire: Used herein to describe the hourly d i s t r i b u t i o n of t r a f f i c when i t reacts to the public desire for transportation. This normally r e s u l t s i n a major peak period i n the afternoon:and a lesser peak i n the morning. Typical of the d i s t r i b u t i o n at an ai r p o r t operating well below PANCAP. Radar control: Used herein to describe terminal a i r t r a f f i c con-t r o l by use of radar, generally an ASR type. Ratio of a r r i v a l s to departures: This term i s used only i n con-junction with "A" a i r p o r t s . For capacity analysis, r a t i o i s defined as the number of landings per hour divided by the number of takeoffs per hour 157. at a given a i r p o r t or configuration, where = number of landings or a r r i v a l s per hour for a given a i r p o r t or configuration = number of takeoffs or departures per hour f o r a given a i r p o r t or configuration ^ S = t o t a l number of movements per hour for a given a i r p o r t or configuration For the same a i r p o r t or configuration, A S = A L + A T Ratio = ^ L When ca l c u l a t i n g a i r p o r t capacity, i t i s usual to express capacity i n terms of movements per — ^S. I f ratio, i s 1.0, then ^ L =^T. Thus at a S of 40 movements per hour and r a t i o of 1.0, ^ L = 20. However, i f r a t i o i s not 1.0, then A L = A s y t i o = 4 Q .L = 2 Q 1 + Ratio 1 + 1 1 + Ratio Runway c h a r a c t e r i s t i c : In capacity analysis, c e r t a i n runway char-a c t e r i s t i c s must be determined for accurate capacity analysis. For each runway that i s used for landings on any config-uration, the following information i s required: 1. Usable runway length i n feet 2. Number of turnoffs that can be used on each runway 3. Type of turnoffs to be used 4., Location of turnoffs along the runway 158. Usable runway length i s measured from the runway thres-hold to the end of the runway. A runway often has turnoffs on either side of the runway. The use of turnoffs by landing a i r c r a f t i s determined by the u l -timate destination of the a r r i v a l s on the a i r p o r t . Therefore, the number of turnoffs must be l i s t e d by " l e f t " and "r i g h t " with some notation to indicate the location of the a i r c a r r i e r and general aviation terminals. For t h i s analysis, there are:three basic types of turnoffs: 1. Right angle 2. Angled 3. High speed Runway configuration: A runway configuration i s a layout or de-sign of a runway, or runways, where operations are mutually de-pendent on the p a r t i c u l a r runway or runways being used at one given time. Thus, two widely spaced p a r a l l e l runways, with a r r i v a l s and departures on both runways, may be considered a two single runway configurations (with mixed operations on each) at an "A" ai r p o r t . However, two very close p a r a l l e l runways i n bad weather are considered as one runway configuration, since a r r i v a l s on one of the two w i l l a f f e c t departures on the other. Exact d e t a i l s of various configurations are given with PHOCAP computation i n s t r u c t i o n s . Runway ratings: Defined as the average runway occupancy time for 159. a given population of landing a i r c r a f t on a given runway. As each a r r i v a l lands, i t occupies a runway for a cer-t a i n time. The occupancy time depends on: 1. A i r c r a f t type or class 2. Physical properties of runway If departures are using the same runway for takeoff, long a r r i v a l occupancy times w i l l give r i s e to longer departure delays. To simplify the analysis, one f i n a l average occupancy time i s calculated for each a r r i v a l population by runway. This i s c a l l e d the runway rating (R_.) . It i s emphasized that the value of R_. calculated for any runway can change i f : 1. Population i s changed 2. Runway i s altered (length, type of turnoffs, etc.) Runway use: For capacity analysis, "runway use" i s the function of a runway or configuration, with respect to a r r i v a l s and de-partures. That i s : 1. Mixed operations ( a r r i v a l s and departures) 2. A r r i v a l s only, or 3. Departures only Thus, a single runway, whether by i t s e l f or as one of a pair p a r a l l e l runways, can be used for mixed operations; or, i n the case of two p a r a l l e l runways, one can be used for landings only, and the other can be used for takeoffs only. Two intersecting runways may d i f f e r i n t h e i r use. One such configuration may have landings only on one runway, and take-160. o f f s only on the other runway. Another s i m i l a r configuration may have mixed operations on both runways. There are many variations of runway use for the numerous a i r p o r t configurations. Proper selection of runway use i s v i t a l to capacity c a l c u l a t i o n s . Service times: That time required to complete an operation on a runway before another a i r c r a f t can perform an operation on that runway. T and G: An abbreviation for touch and go. Terminal i n t e r v a l computer: A subsystem for precise terminal a i r t r a f f i c c ontrol. Expected to come into use i n 1975 and beyond. W i l l a s s i s t i n more e f f i c i e n t sequencing of a r r i v a l s and departures to maximize capacity. The a v a i l a b i l i t y of t h i s aid i s presumed i n the 1975+ capacity c a l c u l a t i o n s . TIC: An abbreviation for terminal i n t e r v a l computer. Touch and go: Training operations wherein the p i l o t approaches the runway, touches his wheels and goes on for another a e r i a l c i r c u i t . T r a f f i c p r i o r i t y : The r e l a t i v e p r i o r i t y given a r r i v a l s and de-partures. Since a r r i v a l s are currently usually given p r i o r i t y , departure delays are usually greater than a r r i v a l delays and are therefore important to capacity c a l c u l a t i o n s . The PHOCAP computa-tions are based on normal usage. VAW: V i s u a l a i r p o r t weather. Weather conditions: For capacity calculations, i t i s necessary to define s p e c i a l weather categories. The two categories used throughout the handbook (in place of VFR and IFR) are: VAW - v i s u a l a i r p o r t weather 161. IAW = instrument a i r p o r t weather They are defined as follows: "G" Airp o r t : VAW exists when the c e i l i n g and v i s i b i l i t y are greater than 1000 feet and three miles. IAW exists when the c e i l i n g and/or v i s i b i l i t y are equal to, or less than, 1000 feet and three miles. "A" Ai r p o r t : VAW, c e i l i n g , and v i s i b i l i t y are greater than 700 feet and two miles. IAW, c e i l i n g , and/or v i s i b i l i t y are equal to, or less than 700 feet and two miles. 

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