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Criteria for forecasting intercity air travel Oehm, Peter Friedrich 1967

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CRITERIA FOR. FORECASTING INTERCITY AIR TRAVEL by PETER FRIEDRICH OEHM B.A., University of Waterloo, 1962 M.A., University of Cinc i n n a t i , 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Di v i s i o n of COMMUNITY AND REGIONAL PLANNING We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1967 In p r e s e n t i n g 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 o f the r e q u i r e m e n t s f o r an advanced deg ree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g ree t h a t t h a 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 f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depa r tment o r by h i s r e p r e s e n t a t i v e s . . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f Community and Regional Planning The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Da te April 26f 1967.  i i i ABSTRACT Airports, as terminals for a i r transportation, are places for both the movement of passengers and freight. They have a major influence on urban development. The significance of a i r transportation i s often •underestimated by ci v i c o f f i c i a l s and transportation planners. Functionally, airports are no different from the older and well established r a i l or port terminals around which most of our contemporary metropolises have developed. An understanding of the nature of present and future a i r t r a f f i c enables the transportation planner to foresee the urban spatial structure and i t s general relationship to the intercity transportation network. Before the impact of the airport upon the regional urban structure can be ascertained, i t i s necessary to establish the position and function of the airport within the regional transportation infrastructure. In order to determine this, i t i s necessary to know the present and future travel movements emanating from i t and terminating there. Herein an hypothesis i s postulated to determine the relative signigicance of a set of selected factors upon Vancouver's inter-city a i r travel and ultimately their influence upon i t s spatial structure. INTERCITY AIR PASSENGER TRAFFIC IS INFLUENCED BY FOUR MAJOR FACTORS: POPULATION, INTERCITY AIR DISTANCE, INTERCITY LINE TIME, AND INTERCITY LINE PRICE. THIS SET OF INDEPENDENT • VARIABLES CAN BE POSTULATED IN A MATHIMATICAL MODEL TO ADE-QUATELY DESCRIBE AND FORECAST LEVELS OF INTERCITY AIR PAS-SENGER TRAFFIC. A- description and review of current a i r t r a f f i c forecasting methods i s continued out i n Chapter I I . Five methods are-outlined as follows: the market analysis technique, the national income method, the city analysis approach, the econometric model, and the gravity model technique. The gravity model technique i s selected for emphasis i n this thesis. Chapter I I i v presents i n turn a brief history of the evolution of the gravity model as a t r a f f i c predicting device. I t i s shown that the gravity model i s a valid predictive device for forecasting the gross- t r a f f i c movements between two t r a f f i c centres. Chapter III i s devoted to a discussion of the significance of the gravity model to a i r t r a f f i c prediction. As generally conceived, the gravity model relates the influence of urban population and interurban distance to inter-c i t y a i r t r a f f i c movements. This traditional theory of gravitational inter-actance has been modified by a number of a i r transportation researchers. Multiple regression analysis i s the primary method of Investigation i n each of these studies. By means of regression analysis, the variables, as selected for inclusion i n the hypothesis, have been shown to have validity i n some United States c i t i e s , Certain major assumptions are set out i n order that the selected vari-ables can be isolated and studied i n the allotted time period. The lim i t a -tions imposed upon each of the selected variables are outlined i n Chapter IV. In Chapter IV linear regression analysis i s used to obtain the relative significance of each variable as an a i r t r a f f i c determinant. The val i d i t y for inclusion of a variable as a factor of a i r t r a f f i c generation, i s deter-mined by the coefficient of correlation for that variable. The coefficients of correlation for the selected variables ranged from 0.76 to 0.85. This would indicate that the selected variables are valid components of the rela-tionship as postulated i n the hypothesis. Chapter V outlines the basic method of research used. The main tech-niques employed include the gravity model and multiple regression analysis. By this analysis i n an iterative manner, several valid relationships have been established between a i r t r a f f i c volume and the selected variables. V However, while these relationships are considered to be reasonable, their v a l i d i t y i s affected by constraints placed on them i n time, i n space, and i n data as i s presented-in Chapters V and VI. Prom these relationships, certain conclusions are postulated. Gravity models are useful i n examining the relationship between demo-graphic factors, transport factors, and intercity a i r passenger t r a f f i c . Distance proved to be a variably important factor. I t appears to influence a i r t r a f f i c i n a definite manner which depends upon the population of the study c i t i e s . Distance, according to the research, i s less of a restrictive factor for travel involving larger c i t i e s as i s shown i n Table 10. As for intercity travel time, there i s no doubt that i t i s an important factor on some routes. In particular, differences i n time resulting from different types of equipment may affect a traveller's decision. The apparent f r i c t i o n effect of time/distance for travel among smaller c i t i e s may only reflect the fact that slower aircraft are used to serve these small communities. I t i s possible that the introduction of short haul jet aircraft w i l l minimize this difference. The regression equation developed here can only be used as a predictive device i n certain cases, i n particular, on routes connecting large popula-tion centres. On many routes, the standard deviations are low, and, thus predictions are reasonably accurate. That i s , when annual predicted t r a f f i c i s within 20 percent of actual annual t r a f f i c , i t i s accepted as a good projection. However, the relationships, as established, leave much of the ai r t r a f f i c v a r i a b i l i t y unexplained. Consequently, areas for further study are suggested i n the concluding portion of the thesis. The research areas recommended for further study should include several recent developments i n intercity common carrier transportation. These v i technological achievements include: (l) the development of a better short haul aircraft ( i e . D.C. 9 or Boeing 737); (2) the provision of jumbo jets by 1970; (3) the introduction of V.T.O.L. and S.T.O.L. services by 1973; i'U) the provision of a commercial supersonic vehicle by 1975; and, (5) the inauguration of high speed passenger train services on routes of 100 to 500 miles i n length. In Canada and the United States, the degree of success of these new experimental passenger train services places definite limitations on the validity of predicting short haul a i r t r a f f i c over a long time period. v i i TABLE OF CONTENTS Page ABSTRACT i i i LIST OF TABLES ... i x LIST OF ILLUSTRATIONS x LIST OF MAPS -.. x LIST OF APPENDICES x i ACKNOWLEDGEMENTS x i i Chapter I INTRODUCTION 1 A. Introduction 2 (a) Obj ectives and Hypothesis ............ 2 (b) Assumptions .......................... U (c) Thesis Definitions 7 B. A i r Transportation and the GoiMuhity .......... 8 (a) General Discussion ................... 8 (b) Economic Impact 9 (c) A i r Transportation and. Planning ...... 10 I I A REVIEW OF AIR TRAFFIC FORECASTING METHODS ......... H The Market Analysis Technique 15 The National Income Method ....................... 16 The C i t y Analysis Approach.............. 16 The Econometric Model 17 The Gravity Model as an A i r J T r a f f i c Forecasting Method 17 I I I INFLUENCE OF URBAN POPULATION AND DISTANCE ON AIR TRAFFIC 26 IV VARIABLES INFLUENCING INTERCITY AIR PASSENGER TRAFFIC 32 A. A i r Transportation Variables Considered ...... 36 ('1) I n t e r c i t y Travel Price 36 (2) I n t e r c i t y Line Travel Time 36 (3) I n t e r c i t y Linear Distance ............ 38 (A) Population 41 v i i i Chapter Page B. Other Variables Not Considered 41 C. The Relationship Between the Selected Variables , 42 D. Variables Used i n the Model 44 (1) Intercity Line Travel Price 44 (2) Intercity Line Travel Time 45 (3) Intercity Linear Distance , 45 (4) Population 46 (5) Quantity of Travel .. 46 V METHOD OF RESEARCH ;. 48 A. Non-Computerized Research 52 (a) The Gravity^ Model 52 (b) Linear Regression Analysis 57 B. Computerized Research 59 Multiple Linear Regression Analysis 59 C. Research on Future Application of the Model .... 61 VI APPRAISALS AND CONCLUSIONS — RECOMMENDATIONS FOR FURTHER STUDY 67 A. Appraisal of Methodology, 68 (a) Selection of Study Variables and Cities 68 (b) Selection of Gravity Model Approach .... 69 (c) Selection of Linear Multiple Regression Technique 71 B. Validity of Method 73 C. Validity of the Hypothesis 74 (a) Review of the Hypothesis 74 (b) Conclusions 76 D. Recommendations for Further Study 77 BIBLIOGRAPHY 82 APPENDICES 91 i x LIST OF TABLES Table Page 1 Intercity Passenger Travel ...» 3 2 Intercity Traffic Using Linear Distance Variable i n the Gravity Model 53 3 Intercity Traffic Using Intercity Travel-Time • Variable i n the Gravity Model 54 4 Intercity Traffic Using Intercity Travel Price Variable i n the Gravity Model -.- 55 5 Intercity-Traffic Using Non-Computerized Linear Regression Relationship- 56 6 Multiple Regression Analysis Applied to Selected Variables 58 7 The Relative Significance of the Selected Variables as Determined by Multiple Regression Analysis ...... 60 3 Intercity Travel Times, 1966, 1970 and 1975 Between Vancouver and Selected Points 62 9 Intercity Travel Time, 1966 and-1980 Between Vancouver and Selected Points 64 10 _ Predicted Intercity A i r Traffic Usirig Multiple Regression Analysis ... 72 X LIST OF ILLUSTRATIONS Figure Page 1 Regression Line (Yc =• 11.5 - 0.2X) To Explain Relationship Between Tr a f f i c and Intercity-Line Travel Cost 35 2 Regression Line (Yc c 13.2 - 0.7X) To Explain Relationship Between T r a f f i c and Intercity Line Travel Time 37 3 Regression Line (Yc = 8.5 + 0.1X) To Explain Relationship Between Tr a f f i c and Distance 39 4 Regression Line (Yc• = 1.7 +• 3.3X) To Explain Relationship Between Tr a f f i c and Population 4-0 LIST OF MAPS Map Page 1- United States — 194-0 Potentials of Population 23 2 Major Traff i c Centres i n Canada 50 3 Major Traffic Centres i n B r i t i s h Columbia 51 x i LIST OF APPENDICES Appendix Page A Correlation Between Intercity Travel Price and A i r Passenger Traffic . . 92 B Correlation Between Intercity A i r l i n e Time and A i r Passenger Traffic 95 C Correlation Between Linear Distance and A i r Passenger T r a f f i c 98 D Correlation Between Gity Population and A i r Passenger T r a f f i c . 100 E Correlation Between City Population and A i r Passenger Tr a f f i c 103 F Distribution of Labour Force,and Business Trips Per Employee by Industry Category 1950 and I960 105 G R a i l Competition Provided by Canadian National Railways and Canadian Pacific Railway Between Vancouver and Selected Points (May 1, 1967) 107 H Derivation of Equation Yc = 6.4 -»- 4.7X - 0.071 - 0.2Z 109 x i i ACKNOWLEDGEMENTS I t i s v i r t u a l l y impossible to try to acknowledge a l l the help, guidance, and inspiration received during the preparation of this thesis. However, I w i l l endeavour to thank those who have helped directly i n i t s preparation. Grateful appreciation i s extended to Dr. H. Peter Oberlander, Dr. T. Heaver, and Professor G. Rosenberg for their inspiring guidance during my year at the University of B r i t i s h Columbia; to Professor R. Collier and Dr. S. Pendakur for their constructive criticism during the preparation of this thesis; and to the Central Mortgage and Housing Cor-poration for their financial assistance. I am also indebted to a number of people who contributed much of the data necessary for the preparation of the thesis; namely, Miss Marjorie Windeler, A i r Canada, Montreal; Mrs. Velma Rust, A i r Transport Board, Ottawa; Mr. W. B. Statton, Canadian Pacific Airlines, Vancouver; and Mr. J. M. Robbins, Pacific Western Airlines, Vancouver. Final thanks are due to the typist and cartographer, Mrs. Ronald Mann and Mr. Gary Thorsteinson respectively. Vancouver, B.C. May 5, 1967. Peter F. Oehm. CHAPTER I 2 A. Introduction (a) Objectives and Hypothesis The past 20 years have seen staggering changes i n the means of transporting people from one geographic location to another. The a i r industry which i n 1951 logged only 16 percent of intercity common carrier passenger miles, i s now carrying i n excess of 50 percent of the passenger mile total>in the United States and Canada1. In I960 more than 492,000 passengers were handled at the Vancouver International Airport. In 1965 2 the corresponding figure was 591,000 passengers . By 1975 the number of domestic a i r travellers i s expected to-exceed 3.7 million at Vancouver 3 International Airport . I t i s generally conceded that significant improve-ments, Including increased passenger comfort (services), speed, r e l i a b i l i t y , and decreasing costs are the factors that have attracted people to a i r trans-portation i n record numbers. An understanding of the-nature of present and future a i r t r a f f i c en-ables the transportation planner to foresee the urban spatial structure and i t s general relationship to the intercity transport network. A comparison can be drawn between airports and other terminals, such as those used for Intercity r a i l operations. In the same manner that these terminals have influenced urban development i n the past, the airport i s and can be expected to do so to a greater degree i n the future. Before the impact of the a i r -port upon the regional urban structure can be ascertained, the position and function of the airport within the regional transportation infrastructure must be understood. In order to do this, i t i s necessary to know the pre-sent and future travel movements emanating from i t and terminating at i t . Therefore, to determine the relative significance of selected factors upon 3 TABLE 1 INTERCITY PASSENGER TRAVEL IN THE UNITED STATES (a) (Passenger Miles i n M i l l i o n s ) COMMON CARRIERS 1953 1958 1959 1961 1962 1963 A i r l i n e s Railroads Motor Bus 14,794 26,905 28,400 25,375 18,474 20,800 29,308 17,502 20,400 31,062 16,154 19,700 33,623 15,859 21,000 38,456 14,527 21,400 Total 70,099 64,649 67,210 66,916 70,482 74,383 A i r Share (%) 21.1 39.3 43.6 46.4 47.7 51.7 Private Auto 529,200 629,946 659,435. 692;000 713*000 723,000 Total (Common Carri e r and Auto) 599,299 694,145 726,645 758,916 783,482 797,383 Common Carrier Share (%) A i r Share (%) Auto Share (%) 11.7 2.5 88.3 9.3 3.7 90.7 9.2 4.0 90.8 8.8 4.1 91.2 9.0 4.3 91.0 9.3 4.8 90.7 (a) SOURCE: A i r Transport Association, A i r Transport Facts and Figures 1964. Vancouver's i n t e r c i t y a i r t r a v e l and ultimately t h e i r influence upon i t s s p a t i a l structure, a hypothesis i s formulated. INTERCITY AIR PASSENGER TRAFFIC IS INFLUENCED BY FOUR MAJOR FACTORS: POPULATION, INTERCITY AIR DISTANCE, INTERCITY LINE TIME, AND INTERCITY LINE PRICE. THIS SET OF INDEPENDENT VARIABLES CAN BE POSTULATED -IN A MATHEMATICAL MODEL TO ADE-QUATELY DESCRIBE AND FORECAST LEVELS OF INTERCITY AIR PAS-.. .. SENGER TRAFFIC. Growth and change of a i r t r a v e l patterns are determined by factors which change over time. I t i s assumed that the most s i g n i f i c a n t deter-minants of i n t e r c i t y a i r t r a v e l are the t o t a l population of interacting c i t i e s , the l i n e t r a v e l p r i c e , and the l i n e time between these t r a f f i c centres as w e l l as the a i r distance between these two c i t i e s . The measu re s e l e c t e d a s t h e dependen t v a r i a b l e i s t h e number o f one way a i r t r i p s f o r b u s i n e s s o r non b u s i n e s s p u r p o s e s f o r a s e l e c t e d c i t y p a i r . V a n c o u v e r ' s 25 p r i m e t r a f f i c c e n t r e s were a r b i t r a r i l y c h o s e n f o r s amp le a n a l y s i s f r o m s t a t i s t i c s made a v a i l a b l e , b y t h e A i r T r a n s p o r t Board^ " . R e g r e s s i o n a n a l y s i s i s " u s e d t o f i n d t h e " b e s t " e q u a t i o n r e l a t i n g t h e dependen t v a r i a b l e ( t c ) t o a n y number o f i n d e p e n d e n t v a r i a b l e s ( T c =• X.^ + ............ X n ) ' . F r o m - t h i s p r o c e s s p r e d i c t i o n s o f new Y c v a l u e s c an be o b t a i n e d f o r g i v e n X ^ a n d X2 v a l u e s . M u l t i p l e r e g r e s s i o n a n a l y s i s a l s o g i v e s a q u a n t i t a t i v e c o n f i d e n c e measure f o r t h e c l o s e n e s s o f f i t o f t h e r e l a t i o n s h i p and;.the v a l i d i t y o f t h e r e l a t i o n s h i p a s a p r e d i c t i v e d e v i c e . I t a l s o e s t a b l i s h e s t h e w e i g h t s t o be a t t a c h e d t o e a c h o f t h e s e l e c t e d v a r i a b l e s shown i n T a b l e 7. The t r a d i t i o n a l g r a v i t y mode l T ^ j •= P j E j i s s u b j e c t e d . t o t h e i t e r a t i v e d i - j p r o c e s s . T h a t i s , t h e above c o n s t r u c t i s t e s t e d i n v a r i o u s f o r m s - t o s ee i f i t c a n b e u s e d t o d e s c r i b e t h e n a t u r e o f i n t e r c i t y a i r t r a v e l . T a b l e s 2 , 3 and 4. show t h e r e s u l t s o f t h e s e a d a p t a t i o n s t o t h e d i s t a n c e o r i e n t e d g r a v i t y m o d e l . The m o d i f i c a t i o n s i n c l u d e t h e u s e o f l i n e h a u l p r i c e and l i n e h a u l t i m e . I n o r d e r t o p r o j e c t t h e s e v a r i a b l e s - i n t o t h e f u t u r e , c e r t a i n m a j o r a s s u m p t i o n s m u s t be r e c o g n i z e d , (b ) A s s u m p t i o n s S e v e r a l r e c e n t d e v e l o p m e n t s w i l l a f f e c t t h e n a t u r e o f i n t e r c i t y t r a v e l i n t h e f u t u r e . T h e i r i m p a c t u p o n a i r t r a v e l w i l l be s i g n i f i c a n t . F o r e x a m p l e , t h e p r o v i s i o n o f a s u p e r s o n i c t r a n s p o r t v e h i c l e i s e x p e c t e d t o m a r k e d l y i n c r e a s e t h e demand f o r l o n g h a u l a i r t r a v e l j u s t a s t h e s h i f t f r o m p i s t o n t o j e t a i r c r a f t a r o u n d I960 c au sed a n u p s w i n g i n a i r t r a v e l . P r o v i s i o n o f s u p e r s o n i c s e r v i c e w o u l d p e r m i t a b u s i n e s s m a n f r o m V a n c o u v e r , f o r e x a m p l e , t o spend a f u l l d a y i n M o n t r e a l o r T o r o n t o as w e l l a s t r a v e l 5 e a s i l y between the two c i t i e s the same day. However, the f u l l benefits of t h i s supersonic speed may be frustrated by the long ground t r i p s due to congestion on a i r p o r t access routes. U n t i l metropolitan rapid t r a n s i t systems l i n k c i t y centres and a i r p o r t s , or the a i r p o r t i s relocated at more accessible points, actual i n t e r c i t y a i r t r a v e l w i l l not approach poten-t i a l a i r t r a f f i c l e v e l s . However, the subject of a i r p o r t a c c e s s i b i l i t y i s beyond the scope of t h i s t h e s i s . The development of a better short haul a i r c r a f t w i l l increase the use of a i r transportation. At the present time, there i s no c r a f t operating i n Canada which i s able to provide profitable'service f o r t r i p s within a radius of 225 miles-from a base city*'. Perhaps e x i s t i n g j e t a i r c r a f t such as the Caravelle, the D.C. 9, or the Boeing 737 w i l l be able to provide sucE services economically at s l i g h t l y higher fares than those presently charged. Experimental no-reservation a i r coach- service as provided by Eastern A i r l i n e s i n the "Boston-Washington Corridor" has apparently been successful. S i m i l a r i l y , the P a c i f i c Western A i r l i n e s i s providing an a i r -bus service between Calgary and Edmonton. I t i s evident though that f e a s i b i l i t y studies are required to determine the present and future r o l e of the short haul a i r c r a f t within the general a i r transportation industry. I t i s possible that the major break through concerning short haul c r a f t i s i n the area of vertical-takeoff-and-landing a i r c r a f t and short-haul-takeoff-and-Ianding a i r c r a f t (V.T.O.Ii. and S.T.Q.L.). The question involves the l i k e l i h o o d of -the development of economical equipment. Per-formance data available at the present time indicates- that the cost of operating the S.T.O.Ir. equipment i s as high as $0.20 per seat mile . This means that the S.T.O.L. fares would have to be over twice as great as the 7 present economy fares, and more than four times as.great as r a i l fares . 6 In order to realize the f u l l benefit of the S.T.O.L. aircraft, airports must-fee located-at most accessible points so as to minimize the travel time between the aerodrome and the nucleus or nuclei of the metropolitan region. A third equipment improvement of significance to intercity a i r travel" i s the high.speed passenger train. In Canada, i n July, 1967, the Canadian National Railways w i l l inaugurate i t s 125 m.p.h, "Turbo-Trains" i n the "Montreal-Toronto Transport Corridor". The impact of these new r a i l ser-vices upon a i r transport between these c i t i e s w i l l be substantial. This has not as yet been documented . An analogy can be drawn between the Canadian situation and the situation i n Japan where the Japanese National Railway introduced fast train service i n 1965 on the Tbkyo-Osakavroute. Similarly i n the United States, an experimental high speed r a i l service has been inaugurated between Boston and New London, Connecticut. I t i s anticipated that the United States Government w i l l introduce a high speed r a i l service from Washington to Boston -to serve the 35 million residents of Megalopolis... In both cases, passengers embark at the downtown terminals, travel at speeds as high as 125 m.p.h., and disembark at a downtown loca-tion i n destination centres. The obvious result i s that total travel time by train w i l l not d i f f e r significantly from total time by a i r on short haul t r i p s . Furthermore, the airlines w i l l experience d i f f i c u l t y trying to offer competitive fares. The degree of success*of .these new experimental passenger train services places d i f i n i t e limitations upon the val i d i t y of predicting short haul a i r t r a f f i c over a long time period. The future performance of a i r transport as a high volume carrier w i l l also be governed by the capacity of airports and_the adequacy of a i r . t r a f f i c control f a c i l i t i e s . Airports i n New York City currently average better than one take-off or landing every minute during peak hours? There i s very limited space available for expansion at present sites,. As a result, the plans of the New York Port Authority to* construc.t_a new jetport have hot been completed, as there i s considerable discussion about the functional division of long haul and short haul a i r terminal f a c i l i t i e s . t A closely related problem involves congestion of the airway approach facilities*." I t remains to be seen i f a i r " t r a f f i c control problems and a i r lane congestion w i l l l i m i t the increased u t i l i z a t i o n of a i r travel. In spite of these difficulties,, the New York Port Authority assumes that a i r travel w i l l be the -predominant form of transportation for trips of more than 500. miles i n length. The Authority predicts that trips of 100 miles to 500 miles w i l l be made by r a i l transportation. Buses and commuter trains w i l l be competitors for t r a f f i c i n the 50 to 200 mile range. Competition- between the modes w i l l centre on prices, total travel time, scheduling, services and amenities. As i n the past i n Canada and the United States, the Government w i l l play an important role i n determining the form of intercity travel for the future. For example, the United States Government has paid 90 percent of the cost of fabricating the f i r s t supersonic a i r c r a f t . The Governments of Canada and the United States are active i n cost sharing arrangements for the ultimate provision of high speed rail—passenger service i n densely populated sectors of both countries. In the a i r transportation industry, the Government i s responsible for the following: (l} a i r fare structure; (2) allotment.of routes to the individual a i r carriers; and, (3). distribu-tion of subsidies to the individual carriers. (c) Thesis Definitions^ Before discussing the factors which affect intercity a i r passen-8 ger t r i p generation, i t i s necessary to" clearly define the terminology to be used. 1. Trip -— For the purpose of this thesis, a t r i p i s defined as a one-way movement by a i r transportation betweeri~-an origin and destination terminal. Normally, a t r i p involves more than! one trans-port mode as a person travels between an origin and a destination. 2. Metropolitan Vancouver — a region as defined by the Census of Canada. Metropolitan Vancouver, then, i s a regional governmental institution used to describe the central City of Vancouver and i t s contiguous peripheral^comrmanities. I t i s not known i f this governmental unit corresponds to the a i r catchment area (hinterland) of the Vancouver International Airport. 3. Base City — the geographic location from where a l l the a i r "trips'" . originate. In this thesis the base cit y i s Metropo-l i t a n Vancouver:as described above. 4. Reference City — the geographic location at which a l l the a i r "trips" terminate. 5. Prime' Tr a f f i c Centre — This term i s sydonymous with a reference c i t y . The study'arbitrarily selected 25 t r a f f i c centres to which the bulk of the Vancouver a i r "trips" are destined. The rank of these t r a f f i c centres i s established according to the actual t r a f f i c movements to them from Vancouver as i s recorded by the A i r Transport B o a r d . 6. Price — the term i s equivalent to the inter c i t y a i r l i n e price. I t i s s t r i c t l y the cost of travelling from an origin a i r terminal to a destination a i r terminal. 7. ^T-ime— the term i s equivalent to the intercity a i r travel time. I t i s s t r i c t l y the time required for travel from an origin a i r terminal to a destination a i r terminal. 8. Ground Transportation — refers to the means of transport that the a i r traveller, uses i n order to reach or depart from the a i r terminal. I t may be a car, a subway train, a'computer train, or a helicopter. 9. Local Transportation — the term i s equivalent i n meaning to "ground transportation". B. A^r Transportation and the Community (a) General Discussion At this point i t i s important to establish the role that a i r trans 9 p o r t a t i o n plays i n community development* As t h i s study i s concerned with t h e determination of trends i n a i r passenger t r a f f i c , i t i s important to e s t a b l i s h -the p o s i t i o n o f the a i r p o r t i n the community str u c t u r e . I t i s upon community structure that the trends i n a i r transportation w i l l have the greatest impact. The following quotations c l e a r l y e s t a b l i s h the a i r -port f a c i l i t y i n the metropolitan matrixs -• "What then i s the r e s p o n s i b i l i t y o f the community i n the development and administration of the a i r p o r t ? The f i r s t r e s p o n s i b i l i t y i s to recognize the a i r p o r t f o r what i t r e a l l y i s — a working t o o l used f o r a i d i n g the development, advancement, and maintenance o f a community's economic and s o c i a l well-being dedicated to the p u b l i c convenience" In the words of the l a t e President John F. Kennedy: "But however d i f f i c u l t i t may be to foresee the f u l l dimensions of the a i r age, there can be l i t t l e doubt that the metropolis o f the future must have a well-equipped, well-designed and well-managed a i r p o r t . The f a t e o f a . _ c i t y and i t s population may w e l l depend upon the extent to which i t i s w i l l i n g to devote i t s human and f i n a n c i a l resources to a i r p o r t development" 1 2. (b) Economic Impact Even i n t h i s temporary subsonic age, the a i r p o r t contributes s u b s t a n t i a l l y to the general w e l l being of a metropolitan region. This i s w e l l i l l u s t r a t e d by the experience of the C i t y of A t l a n t a , Georgia, which has a population of over 1,000,000 and possesses one of the ten b u s i e s t a i r p o r t s i n the United States. "During the years since i t s establishment, the A t l a n t a A i r p o r t has grown to become one of the nation's major centres of a i r transportation. This growth has created A i r p o r t employment f o r thousands of persons, and has contributed m a t e r i a l l y to the growth of"home building> commercial, and i n d u s t r i a l a c t i -v i t y throughout southern A t l a n t a and the. I r i - G i t i e s region. For the future, the advances i n a i r transportation generally w i l l continue to be powerful forces i n the f u r t h e r develop-ment of the ,area w l3. In the NeW lork-Uew Jersey region, passengers moving through the region's 10 airports spend several hundred million dollars every year on hotel accom-modations, food, drink, l o c a l transportation,- and entertainment. In addi-tion, 70,000 people throughout the area (including taxi drivers, hotel and restaurant workers, sales clerks and others) are employed because of a i r passenger and cargo a c t i v i t i e s . In fact, a i r transportation provided ,'JIA. employment for some 121,000 people i n 1965 i (c) A i r Transportation and Planning An airport i s an integral part of a metropolitan community, and i s a strong force helping to shape a region. I t i s imperative that the planner understand the airport function and incorporate airports into regional development plans. In a study by Peterson the,planning agencies of eleven geographically scattered metropolitan regions,were surveyed i n order to estimate the. r 15 probable impact that jet aircraft would have on each metropolitan region. . The study was concerned with the planning philosophy of the agencies toward their airports and a i r transportation i n general. The results of the sur-vey indicated that i n most instances responsibility for integrating a i r transportation and i t s f a c i l i t i e s into the metropolitan infrastructure had hot been-accepted by the planning agencies. A lack-of understanding of the relationship of a i r transportation to the metropolis and the impact of this force i n the metropolitan community was apparent. I t - i s important to recognize that not a l l c i t i e s are potentially dependent upon a i r transportation. The degree of dependency i s a variable which is- related to geographic factors, the economic, social, and p o l i t i c a l attributes of the community. I t i s the primary objective of this thesis to evaluate the most significant transport factors of a i r passenger t r a f f i c generation. The case study application i s limited to a discussion of 11 domestic air passenger traffic generated at Vancouver's International Airport. Subsequent chapters are concerned with the evaluation of the selected transport variables that affect air passenger traffic generation. A des-cription and review of air traffic forecasting methods is carried out in Chapter II. Chapter III is devoted entirely, to-a discussion of the signi-ficance of the'gravity model ito:..air traffic prediction. InChapter IV linear regression analysis is used to obtain the relative significance of each variable as an air traffic determinant. Chapter V outlines the basic method of research. The thesis concludes with Chapter VI, entitled, "Appraisals and Conclusions--— Recommendations for Further Study". 12 FOOTNOTES 1 These s t a t i s t i c s appear i n Table 1 of t h i s study-on page 3. 2 A i r Transport Board, A i r l i n e Passenger Origin and Destination  S t a t i s t i c s - Domestic Report - 1965f (Ottawa: The Board, 1965). 3 The Fina n c i a l Post (Toronto). February 8, 1967j p. 1. 4 A i r Transport Board, A i r l i n e Passenger Origin and Destination  S t a t i s t i c s - Domestic Report - 1965. (Ottawa: The Board, 1965). 5 - P. F. Oehm, "The A i r Passenger Hinterland of Cin c i n n a t i , Ohio", Cincinnati (Unpublished Master of Arts Thesis, Geography Department, University of Ci n c i n n a t i , 1966), p. 15. 6 International A i r Transport Association, "Symposium on Supersonic  A i r Transport". (Montreal: 14th Technical Conference, A p r i l 17 - 21, 1961), p. 47. 7 The r a i l fares referred to i n t h i s study are the Red fares charged by the Canadian National Railways throughout Canada. 8 A i r Canada and the Canadian National Railways are currently con-ducting a j o i n t market survey i n the "Montreal-Toronto Transport Corridor". 9 New York Port Authority, Airport Requirements and Sit e s i n the  Metropolitan New Jersey and New York C i t y Region. (New York City: The Authority, 1961). ' 10 A i r Transport Board, l o c c i t . p. 84. 11 W. H. Levings, "Community Opportunities and Re s p o n s i b i l i t i e s i n the Development and Administration of Airp o r t s " . Report on F i r s t Northwest  Airport Management Conference. (Eugene: University of Oregon Bureau of Municipal Research and Service, 1953), p. 34« 12 College of Business Administration of Boston College, The Role of Aviation and Airports i n the Future Development of Greater Boston. (Boston: Proceedings of a Conference at the College of Business Administration of Boston College, 1958), p. 30. 13 Atlanta Metropolitan Planning Commission. Airport Area Survey  Memorandum of Recommendations - A Study of T r a f f i c Improvement Needs  i n the Communities Near the Atlanta Municipal A i r p o r t . (Atlanta: The Commission, I960), p. 1. 14 New York Port Authority, A Report on Airport Requirements and Sites  i n the Metropolitan New York and New Jersey Region". (New York Ci t y : The Authority, 1961), p. 5. 13 15 J . E. Peterson, Ai r p o r t s ^ f o r J e t s . (Chicago: American Society of Planning O f f i c i a l s , 1959), p. 9. CHAPTER I I A REVIEW OF AIR TRAFFIC FORECASTING METHODS 15 This chapter reviews some of the techniques used by researchers to formulate a conceptual framework which can reliably forecast a i r passenger t r a f f i c . Development of a i r t r a f f i c forecasting methods i s also reviewed. This thesis emphasizes the evolution and adaptation of the gravity and potential model for forecasting a i r passenger t r a f f i c . The predictive model developed here i s an adaptation of the general potential model con-cept. The following predictive methods are reviewedj The Market Analysis Technique; The National Income Method; The City Analysis"Approach; and, The Econometric Model. The Market Analysis Technique A i r travel i s considered here as one of several commodities i n compe-t i t i o n for the buyer's dollars. This approach accepts the proposition that each t r i p results from a more or less carefully weighed decision by the traveller, made under more or less compelling circumstances, and tempered by the traveller's background and experience, his resources, his tastes and preferences, and other primarily personal considerations 1^. The problem i s considered on the same basis as a broad national mar-keting research project. The main purpose i s to determine what economic and demographic conditions explain the decisions that result i n a i r travel. Then, by applying the findings of the market analysis to the persons ex-pected to f a l l under similar demographic and economic groups i n the future and by assuming similar behaviour of members of these groups with respect to a i r travel, i t Is possible to estimate the volume of a i r travel developed by the population. 16 Using this approach, a National Travel Market Survey was conducted 17 during 1955 . The findings were applied to the corresponding United States census classifications of the entire population of the years 1950 and 1955. The results of this procedure indicated a reasonable degree of r e l i a b i l i t y . This method was used by the Eno Foundation to estimate the 18 a i r travel market for 1970 and 1975 . -The National Income Method This method centres upon the relationship between total intercity common carrier t r a f f i c and national income. The relationship between these two factors yields an estimate of total Intercity common carrier passenger miles. By estimating the a i r industry's share of total intercity common carrier passenger miles, total a i r passenger miles are computed. By applying the estimated average length of air,,, trips to total a i r passenger miles, estimated passenger miles may be translated into total a i r passenger t r i p s . This aggregate number may be further subdivided into the volume of t r a f f i c carried by each national a i r carrier. The carriers can assign the share of t r a f f i c to each of their passenger routes. The Gity Analysis Approach This..approach i s designed to show the relationship between a city's population and the a i r passenger t r a f f i c i t generates. In 1955 i t was determined that 90$ of the total domestic a i r passenger t r a f f i c was generated 19 by 87 metropolitan areas . The a i r trips generated by each metropolitan area are then related to i t s population to yield a passenger-population^ ratio. By projecting population for these areas, and by applying the projected passenger-population ratio, total a i r passenger volumes are computed for each metropolitan area. 17 The Econometric Model A i r Canada has developed an econometric model which has been used 20 successfully to predict t r a v e l habits on A i r Canada's Canadian routes , The model i s stated as follows: an ao Bi Bo X - AY X 1 Y 2 ... z x X z 2 / where: X represents t r a f f i c per head; the Y terms represent the moving averaged socio-economic variables on a per capita basis; the Z terms represent the p o l i c y variables and are related to t r a f f i c per head f o r the same period as the Y terms; the a's and B's are e l a s t i c i t i e s of t r a f f i c to the variable that they are powering. They represent average e l a s t i c i t i e s f o r the period of the h i s t o r i c a l data; A represents a constant. The model attempts to r e l a t e socio-economic and p o l i c y variables to a i r t r a f f i c with a view to estimating e l a s t i c i t i e s and forecasting t r a f f i c three to ten years ahead, on an Origin and Destination or an Area to Area basis. This i s achieved by a series of computer programmes which carry out a regression analysis and feed forecasts of socio-economic variables into the regression equation so that t r a f f i c per head can f i n a l l y be predicted from t h i s equation. The coe f f i c i e n t s of t h i s equation are found by a regression analysis of h i s t o r i c data. The Gravity Model as an A i r T r a f f i c Forecasting Method 21 H. G. Carey was the f i r s t person to observe that a g r a v i t a t i o n a l force of in t e r a c t i o n exists i n s o c i a l phenomena. More than 100 years ago, 18 he described man as ....... ''the molecule of society1* whose ....... "great-est need Is that of association with his -fellow man". The "great law of molecular attraction", Carey said, " i s the indispensable condition of the existence of the being known as man". In Carey's words, the law i s as follows: "Man tends of necessity to gravitate towards his fellow man. Of a l l animals he i s the most gregarious, and the greater the number collected i n a given space the greater i s the attractive force there exerted gravitation i s ....... i n the direct ratio of the mass, and i n the inverse one of distance."1 22 Except for some work by E. G. fiavenstein i n 1885, the conceptual framework was not considered for approximately 65 years. Ravenstein showed that the net direction of movement of migration was towards large.cities. The volume of migration Increased i n proportion to some function of the population of the large cities and decreased as the distance between the origin and destination cities Increased. "A population," he said, "attracts 23 migrants from other centres i n relation to i t s P/d." In 1924., E. C. Young of Cornell University completed studies of the movements of farm population i n the United States. Young's construction of migration phenomena centred around the use of the force of gravitational attraction formula — the use of distance squared i n the denominator of the attraction formula rather than distance to the f i r s t power. The distinction for discovering applications for gravity and potential models belongs to Rei l l y , Zipf, Rice, and Stewart, as well as the United States C i v i l Aeronautics Administration. ReiHy2""- observed i n 1929 that for two towns competing for r e t a i l trade, the distance to the point between the two towns at which both shared, equally i n trade i s expressed i n the following equation: 19 PI - P2 r l - r2 where: PI and P2 = the populations of towns 1 and 2; r l and r2 = the distances from towns 1 and 2 to the point of equilibriumj r l +• r2 = d = the.distance separating the towns. 25 26 2*7 Zipf , Stewart , and Rice generalized the concept i n the 1940's 28 at approximately the same time that the C i v i l Aeronautics Administration advocated the use.of the theory which stated that a i r t r a v e l between two points varies d i r e c t l y as the product of the two populations and inversely with.the .distance between them. Zipf returned to Carey's construct of the force of interaction between two masses: d i - j . where: A ^ j = the amount of a i r t r a v e l between points i and j ; K - = a constant; P j = the population of point i ; Pj = the population of point j ; d i _ j = the l i n e a r distance between points i and j . Zipf measured f o r c i t y pairs the movement of railway express, the move-ment of passengers t r a v e l l i n g by highway c a r r i e r s , the aggregate fares paid by highway passengers, the number of passengers t r a v e l l i n g by railways, and airway t r a f f i c , i n r e l a t i o n to': where.: .I j _ j . - the amount of interaction between points i and j ; K - a constant; P^ = the population of point i ; -20 Pj = the population of point j ; cLj_j = the linear distance between points i and j . Zipf therefore adapted the conceptual framework to apply to other modes of passenger transportation as well as to the movement of goods between two population centres. He also pointed out that the gravity formulae yield the most reliable travel information when they are applied to aggregate movement between any two points rather than movement by any particular mode. 29 In 194-8, John Q. Stewart of Princeton University studied a variety of interactions and communications between urban centres. He observed that the number of undergraduates and alumni by states for Princeton, Yale, and Harvard varied directly as the population of the state and inversely as the distance from the campus of the student's homes. Stewart observed similar results for the movements of bank cheques and money orders, pedestrian t r a f f i c , and long distance telephone c a l l s . Rice applied the P^Pj/dj - dj concept at about the same time that i t was being studied by Zipf. In 1947, Rice prepared a document for the New Haven Railroad i n which he compared potential and actual t r a f f i c along the New Haven's routes. He applied weights to the populations i n the formula. The term "normal wealth people" was originated by Rice to describe popula-tions which had been adjusted by a wealth factor (per capita income). The result was that potential t r a f f i c more closely coincided with actual t r a f f i c when the wealth adjustment was made. Rice found high correlations between potentials adjusted for wealth and distance, and actual t r a f f i c . Using these techniques, the less lucrative routes of the New Haven were singled out for further action regarding their level of services. This concept was subsequently used successfully by the Greyhound Bus Company. Rice's modified formula follows: 21 T , . - K ( P W ) . ( P W ) . x J *• ' -' where: L . = the total number of passengers travelling between points J i and P^ = the population of point i j P . = the population of point j j J W = a wealth factor (l.O being the national average). 30 Stewart and Dodd generalized the use of population modifiers for determining an Index of Interactance. Stewart found that some areas and citi e s have influence greater than i n proportion to their populations. He decided to carry the physical analogy one step further and to assign molec-ular weights to the populations of different regions, just as specific weights are attached to molecules of the; physical mass. Stewart's equa-tion i s as follows: A i - j = K ( u p ) j <u p),j d i - j i . where: Aj_j = the total attraction between points i and j ; P^ = the population of point i j P J = the population of point j j d^ j = the linear distance between points i and j ; u =the molecular weight attached to the. population point. Dodd. suggested many, subfactors of the "molecular, weight" which should be considered i n the formula,such as differential income, age, education, sex, occupation, marital status, and p o l i t i c a l and .religious a f f i l i a t i o n s . He took the highest value of any subfactor as unity and expressed the other values as a proportion of unity. Dodd sought a higher degree of coincidence between actual and predicted values of the quantity of interactance. Therefore, " i f multiplying pbpu-22 lation by mean age results i n a higher predictance, then age i s a specific condition needing to be taken into account he said. John Stewart,and William Warntz of the American Geographical Society have succeeded i n computing and presenting graphically the surfaces of population potentials for the United States''""' (see Map l ) . As an out-growth of Stewart's earlier work, these maps reflect the progress made i n applying the general concepts of gravity and potential models. Stewart's potential of population, i s expressed as follows* «t-j . . . where: = the potential at region i j P. = the population of region j ; d. . =the linear distance separating regions i and j j K = a constant. Stewart and Dodd processed data from more than 3,000 counties i n the United States.. They calculated the total potential for each county. The three dimensional map they constructed i s designed so that the height of a f i c t i t i o u s mountain i n each county represents the total potential i n that county. The resulting surface can easily be depicted on a contour map (see Map l ) " ^ 2 . Recent tests of A applied to a i r t r a f f i c forecasting w i l l be discussed b r i e f l y i n the next, chapter. contour interval - 5Q,000/miIe__ 6 B T~ % r 24-FOOTNOTES 16 The Port of New York Authority (Aviation Department, Forecast and Analysis D i v i s i o n ) , Air-Travel Forecasting. 1965 - 1975. (Saugatuck, Connecticut: The Eno Foundation f o r Highway T r a f f i c Control, 1957), p. 19. 17 I b i d , p. 20. 18 I b i d , p. 19. 19 I b i d , p. 61. 20 I . Elce, "The Econometric Model f o r Marketing", Paper delivered at  the A i r l i n e Group International Federation of Operational Research  Societies Symposium i n 1965 at Chicago. Montreal, A i r Canada, (June, 1965), p. 6. 21 H. C. Carey, P r i n c i p l e s of S o c i a l Science (Philadelphia: J . B. Lippincott and Company, 1859), p. 41• 22 E. C. Ravenstein, "The Laws of Migration", i n Journal of the Royal  S t a t i s t i c s Society. 48 (June, 1885), p. 167 - 235 and Vol. 52 (June, 1889), p. 241 - 305. 23 E. C. Young, The Movement of Farm Populations f (Ithaca: Cornell A g r i c u l t u r a l Experimental Station, B u l l e t i n 426, 1924). 24, W. J . R e i l l y , The Law of R e t a i l Gravitation. (New York C i t y : ¥. J . R e i l l y and Company, 1931). 25 G. K. Z i p f , »?The P1P2/D Hypothesis: The Case of• Railway Express", i n Journal of Psychology. 22 (July, 1946), p. 3 - 8 . 26 J . Q. Stewart, "Demographic Gravitation: Evidence-and Applications", i n Sociometry. XI (February and May, 194-8), p. 31 - 58. 27 R.. A. Rice, "Taking the Guesswork Out of the Passenger Business", i n Railway Age. (November 20, 1948). 28 U. S. Department of Commerce, C i v i l Aeronautics Administration, The  Gravity Model as a Predictive Device f o r A i r Passenger T r a f f i c . (Washington: C i v i l Aeronautics Administration, J u l y , 1943). Stewart, l o c c i t . S. C. Dodd, "The Interactance Hypothesis: A Gravity Model F i t t i n g Physical- Masses and Human Groups", in-American Sociological- Review, ( A p r i l , 1950), p. 245 - 256. J . Q. Stewart and W. Warntz, "Macrogeography and Social Science", i n Geographical Review. ( A p r i l , 1958), p. 167 - 184. 29 30 31 25, Map 1, Source: Ibid, p. 171. Map 1 shows the contours of the "potentials of population" f o r the United States, 194.0. The poten-t i a l i s a measure of the propinquity of people. Each i n d i v i d u a l contributes to the t o t a l potential at any place an amount equal to the r e c i p r i c a l of his distance away. Contours therefore are i n units of persons per mile. CHAPTER III INFLUENCE OF URBAN POPULATION AND DISTANCE ON AIR TRAFFIC 27 This chapter i s concerned with a discussion of the development and the results of empirical tests of a number of theories of gravitational interactance, as. they relate to a i r passenger t r a f f i c . Regression analy-sis i s the primary method of investigation i n these studies. Regression analysis has been used by two investigators, Hammer and 33 Ikle . They devised a logarithmic formula for "force of attraction" as follows: A i - j * H£i &A • log Aj_j a log K +• log P i log Pj - log d i _ j where: A.±-j " the total attraction between points i and j ; P^ = the population of point i j P j -the population of point j ; di^_j -the linear distance between points i and j . Inclusion of city weights i n the analysis requires the addition of two terms, log Wi and log W^ , to the right hand side of the above equation. Wi and Wj are city weights for ci t i e s i and j respectively. Rather than assume an exponent of d equal to unity (inverse linear relationship between frequency of interaction and distance), Hammer and Ikle estimated the exponent by applying the condition that the difference between actual and potential t r a f f i c should be a minimum. They adjusted the logarithmic form of the above equation to: K P ± W± P - W. - d i _ . - A i _ r Hammer and Ikle made the result equal to zero and solved for the estimate of the exponent. In the same manner they solved for estimates of the ci t y weights Wi and Wj. Hammer and Ikle determined c i t y weights for 27 United 28 34 States cities and an exponent equal to approximately 1.74. • Hammer and Ikle found that a significant positive correlation exists between city weights and each of the following variables; number of pro-prietors, managers, and officials as a percentage of total city population. Also, that there was a positive correlation between city weights and per capita retail sales and the number of rooms available for transients divided by the population of the. city under study. Furthermore, there was a negative correlation between city weights and the percentage of families with incomes greater than $5,000.00 per annum.. 35 Professor Samuel B. Richmond used multiple regression analysis td predict air passenger traffic for Denver, Colorado. His multiple regres-sion equation, using 1952 data, is as follows: log ^ - 1.97986 + 6.71529 log X 2 - 0.84913 log X^ where: X-^  = the number of origin and destination passengers for 1952;, X£ -the number of hotel registrants in Denver hotels; and, X3 =the number of intermediate stops. Using this equation, Richmond obtained a correlation coefficient of 0.91. •Richmond also studied many factors such as population, distance, telephone messages from Denver, number of persons renting cars at the airport, number of students attending Denver colleges, and circulation figures for Denver newspapers. Population figures of the base city and the reference city divided by the linear distance between the two urban centres were also included. He rejected a l l of the above criteria and chose as the best measure of "community of interest", the number of hotel registrants from various outside cities registered In Denver hotels. The next consideration was the quality of airline service. He deter-mined that the quality of the best flight Is related to the number of 29 enroute stops which the f l i g h t makes between the base c i t y and the reference c i t y . Richmond1 also considered distance f o r possible i n c l u s i o n as a t h i r d f a c t o r , but a f t e r a n a l y s i s he concluded., that h o t e l r e g i s t r a n t data was a more s i g n i f i c a n t f a c t o r and i t accounted f o r the influence o f distance f o r t r i p s i n excess of 200 miles from Denver. Richmond's equation i s presented as a t o o l f o r p r e d i c t i n g a i r passen-ger t r a f f i c between two urban p o i n t s . The r e l i a b i l i t y and a v a i l a b i l i t y of h o t e l r e g i s t r a n t f i g u r e s appear to pose a problem f o r most urban study areas. A l s o , would i t be possible to p r e d i c t the number of hot e l r e g i s t r a n t s f o r a study c i t y given an h o t e l r e g i s t r a n t s ' index f o r another c i t y that has been studied i n t h i s manner — f o r example, Denver? Due to tbese apparent l i m i t a t i o n s , Richmond proposed that h i s equation be used under the following s p e c i a l conditions: when new a i r l i n e service i s i n i t i a t e d between two points and when the q u a l i t y of e x i s t i n g service i s changed. In a r e l a t e d study at Denver, Richmond found that a i r passenger t r a f -f i c tended to be a d i r e c t function of distance f o r short distances and, beyond a c r i t i c a l distance of 120 to 200 miles, there appeared to be no r e l a t i o n between t r a f f i c volumes and l i n e a r distances-^. I n a study of the a i r passenger t r a f f i c a t C i n c i n n a t i , Ohio i t was determined that there i s a c o r r e l a t i o n between a i r t r a f f i c and the l i n e a r 37 distance between urban centres . There appeared to be an i r r e g u l a r s o r t of v a r i a t i o n i n C i n c i n n a t i ' s passenger generation with distance, i n which distance as such i s p a r t i c u l a r l y important i n s e t t i n g the minimum zone o f interaction,, but i s of varying importance to t r a f f i c centres beyond the f r i n g e of t h i s zone. The r e l a t i o n s h i p , then* i n the short distances appears 30 to be some sort of d i r e c t function, whereas beyond the c r i t i c a l distance, there i s very l i t t l e observable relationship at a l l . I t i s apparent from the Cincinnati study that Cincinnati's main a i r t r a f f i c i n teraction i s with the larger of the metropolitan areas i n the United States, and, i n e f f e c t , shows the greater correlation between c i t y s i ze and the t r a f f i c which i s generated. To further i l l u s t r a t e t h i s apparent positive correlation at C i n c i n n a t i , a scatter diagram and a regression l i n e were established to r e l a t e population s i z e and the volume of t r a f f i c generated. By u t i l i z i n g t h i s l i n e a r equation, c o e f f i c i e n t of c o r r e l a t i o n , rho - 0.851 38 was determined . Therefore, based on the evidence presented i n the Cincinnati case study,, the volume of i n t e r c i t y a i r passenger t r a f f i c appears to be more dependent upon the population of a t r a f f i c centre than upon the l i n e a r d i s -tance between t h i s t r a f f i c centre and the base c i t y ^ . This chapter has outlined instances where gravity models have been used i n t h e i r t r a d i t i o n a l form to t r y to predict a i r passenger t r a f f i c between-two population centres. This t r a d i t i o n a l theory of g r a v i t a t i o n a l interactance has been modified by a number of investigators such as Hammer, I k l e and Richmond i n an attempt to explain the nature of i n t e r c i t y a i r t r a f f i c , a t each study c i t y . Regression analysis i s the primary method of investigation i n each case. I t i s the purpose of Chapter IV to develop the predictive model to be used i n t h i s thesis and to explain the significance of the variables. 31 FOOTNOTES 33 G. Hammer and F., I k l e , " I n t e r c i t y Telephone and A i r l i n e T r a f f i c Related to Distance and the Propensity to Interact", i n Sociometry. (December, 1957), p. 306 - 316. 34- I b i d , p. 311 o 35 S. Richmond, "Forecasting A i r Passenger T r a f f i c by Mult i p l e Regression Analysis", i n Journal of A i r Law and Commerce; (Autumn, 1955), p. 435 -444. 36 S. Richmond, " I n t e r s p a t i a l Relationships Affecting A i r Travel", i n Land Economics. XXXIII (February, 1957), p. 65 - 73. 37 P. Oehm, The A i r Passenger Hinterland of Cinc i n n a t i . Ohio. Cinc i n n a t i , (Unpublished Masters"thesis"in the Geography Department at the University of C i n c i n n a t i , 1966), p. 14. 38 I b i d , p. 15. 39 I b i d , p. 16. CHAPTER IV VARIABLES INFLUENCING INTERCITY AIR PASSENGER TRAFFIC 33 The informational requirements f o r the planning and evaluation of transportation f a c i l i t i e s and p o l i c i e s are not f u l l y s a t i s f i e d unless i t i s possible to estimate with reasonable confidence passenger demands be-tween s p e c i f i c l ocations. These demands should be d i f f e r e n t i a t e d by mode ( i e . automobile, bus, r a i l and a i r ) , and by sector of the t r a v e l market ( i e . business and personal travel).. The awareness of these t r a v e l demands has prompted much research i n i n t e r c i t y t r a v e l patterns. One sector i n which attention i s being focus-sed i s on those factors which a f f e c t a i r t r i p generation within the i n t e r -c i t y matrix. Transportation researchers are not only asking the questions where are people t r a v e l l i n g ? , but as w e l l , what causes and enables them to t r a v e l ? , and why does one section of a nation generate more t r i p s than another? There are many factors that a f f e c t the number of t r i p s made between urban centres. However, i t i s extremely d i f f i c u l t to f i n d objective mea-sures of any phenomena that involves the psychology of a large segment of the population. I t i s , however, possible to make some assumptions. An observer can assume that the price of a i r transportation between two points i s c l o s e l y related to the number of t r i p s made by the residents of these two t r a f f i c centres. l e t , what f o r example i s the effect of population, i n t e r c i t y l i n e a r distance, i n t e r c i t y l i n e t r a v e l time on the number of t r i p s generated from a given region? The purpose of t h i s chapter i s to analyze the major factors which influence the t o t a l number of i n t e r c i t y a i r t r i p s made by residents of an urban areas i n t h i s study — metropolitan Vancouver. The variables se-lected f o r Investigation include: (1) i n t e r c i t y l i n e t r a v e l p r i c e ; 34 (2) intercity l i n e travel time; (3) intercity linear distance; and, (4) population. A mathematical expression i s presented to i l l u s t r a t e the impact that each of these factors has upon intercity a i r travel. The variables i n the model are stated i n terms of demand elasticity, that i s , the percentage change i n demand i s due to a unit percentage change i n one of the-explanatory variables. For example, price e l a s t i c i t y measures the responsiveness of volume of a i r travel to changes i n the leve l of interci t y a i r fares. Numerically, this can be defined as the percentage change i n volume of travel which results from a one percent change i n fares. Percentages are calculated i n both cases as, the change from the smaller number: i e . a reduction i n fare from $100 to $80 i s regarded as a change of 25 percent. E l a s t i c i t y i s represented by the formula"*0: dp q dp P where: e_ z price elasticity;. p i s the price and q i s the quantity which i s bought at each price l e v e l . I f the-demand i s elastic (ep) - l ) , a reduction i n fares w i l l lead to a more than proportionate increase i n volume of travel and, therefore, increase total revenue earned. I f demand i s inelastic (e^ l ) , a reduction i n fares w i l l lead to a less than proportionate increase i n volume of travel and, therefore, reduce total revenue earned. I f e l a s t i c i t y of demand i s unity ( e p = - l ) r a"reduction i n fares w i l l lead to an exactly proportionate increase i n volume of travel, and there-fore, total revenue earned w i l l remain constant. AIR PASSENGER TRAFFIC- INTERVAL 2 , 0 0 0 PERSONS (in thousands) • >' 36 A.. A i r Transportation, Variables: Considered (1) Intercity Travel Price Price i s an important variable i n determining the level of inter-c i t y a i r travel. The changes i n quantity of travel purchased as t r i p ; p r i c e varies must be measured i n order to estimate demand. Also, the influence of price on travel behaviour may be affected by t r i p purpose, for example, the demand for business trips i s less sensitive to price changes than the demand for personal t r i p s . Figure 1 illustrates the relationship between interci t y a i r travel demand and t r i p price between Vancouver and i t s 25 prime a i r t r a f f i c cen-tres. In order to explain the general significance of thls^linear asso-ciation, a regression l i n e , Yc ~ 11.5 - 0.2X'was established. By u t i l i z i n g this equation, a coefficient of correlation of rho ^ 0.76 was determined. Appendix A sets out the s t a t i s t i c a l derivation of this coefficient of correlation. (2) Intercity Line Travel Time Another important factor associated, .with the determination of Intercity a i r travel demand i s travel time. For common carrier trips, travel time includes both time spent aboard the carrier (line haul time) and the time spent to get to and from the terminal (local time). I t i s important to measure lo c a l time associated with common carrier trips i n studying inter c i t y a i r travel where lo c a l times constitute a large pro-portion of the total travel time of a short haul t r i p . Reductions i n total travel time can be accomplished in several ways: vehicle speeds can be increased, terminals, can be added or relocated closer to origins and destinations of the users ( i e . downtown vertical take-off and landing ports), and l o c a l transportation networks can be greatly improved. AIR PASSENGER TRAFFIC- INTERVAL 2,000 PERSON: (in thousands) 33 7V > m < r-m > r H o H 2 — O ) 2 X m -38 N e a r l y a l l t r i p s by common c a r r i e r r e q u i r e a ndnimum o f two modal t r a n s f e r s : one i n the o r i g i n c i t y and one i n the d e s t i n a t i o n c e n t r e , and a i r t r a n s p o r -t a t i o n o f f e r s no excep t ion t o t h i s r u l e . I n the - o r i g i n c i t y the passenger u t i l i z e s some means o f t r a n s p o r t a t i o n to get to the a i r t e r m i n a l and a l s o a l l o w s s u f f i c i e n t t ime to ensure t h a t he meets the a i r l i n e scheduled depar -t u r e t i m e . S i m i l a r de lays are i n c u r r e d r a t the d e s t i n a t i o n p o i n t i n w a i t i n g f o r baggage and ground t r a n s p o r t a t i o n . An impor tant t ime c o n s i d e r a t i o n e n t e r i n g i n t o the demand f o r a i r t r a n s -p o r t a t i o n i s the s chedu le . S i n c e the a i r t r a v e l l e r w i t h a d e f i n i t e ' a p p o i n t -ment a t h i s d e s t i n a t i o n must make h i s t r i p a c c o r d i n g t o the c a r r i e r schedu le , he has t o take a -scheduled t r i p t h a t a r r i v e s i n s u f f i c i e n t t ime a t the des -t i n a t i o n c i t y t o a l l o w f o r t e r m i n a l de lays and .ground t r a n s p o r t a t i o n . T h i s t h e s i s cons ide r s o n l y the impact o f i n t e r c i t y l i n e t r a v e l t ime on the q u a n t i t y o f i n t e r c i t y a i r p a s s e n g e r j t r a v e l . F i g u r e 2 i l l u s t r a t e s the r e l a t i o n s h i p between intercity a i r t r a v e l demand and l i n e t r a v e l t ime between Vancouver and i t s 25 pr ime a i r t r a f f i c c e n t r e s . A r e g r e s s i o n l i n e o f Y c - 1 3 . 2 - 0 .7X was e s t a b l i s h e d and by u s i n g t h i s equa t ion , a c o e f f i -c i e n t o f c o r r e l a t i o n o f rhO ~ 0 .77 was de termined . Appendix B se t s out the s t a t i s t i c a l d e r i v a t i o n o f t h i s c o e f f i c i e n t o f c o r r e l a t i o n . (3) I n t e r c i t y L i n e a r D i s t a n c e I t i s assumed t h a t the c l o s e r two t r a f f i c cent res are l o c a t e d t o each o t h e r , the l e s s a i r t r a f f i c w i l l be generated between them. T h i s /I yo s i t u a t i o n i s shown to e x i s t a t Chicago"^"-and-at C i n c i n n a t i . The l a t t e r s tudy r e v e a l e d t h a t there are no major t r a f f i c cen t res w i t h i n a r a d i u s o f 225 m i l e s o f the C i t y o f C i n c i n n a t i . The c l o s e s t t r a f f i c cen t re to Vancouver i s the C i t y o f V i c t o r i a which i s o n l y 4-7 a i r m i l e s d i s t a n t . The s i g n i f i c a n c e o f the V i c t o r i a t r a f f i c , w i t h i n such c lose , p r o x i m i t y t o 0 FIG.3 REGRESSION LINE ( Yc = 8.5+O.I X ) TO EXPLAIN RELATIONSHIP BETWEEN TRAFFIC AND DISTANCE -i 1 i 1 1 i 1 i 1 1 1— 1 1 1 1 i 1 i 100 ZOO 300 400 500 600 700 600 900 1000 IIOO IZOO 1300 1400 1600 I60O 1700 1800 /900 2000 2100 2200 (in miles) LINEAR AIR DISTANCE ( INTERVAL = 100 MILES ) Vancouver Is obviously due to the physical water b a r r i e r between the two centres. This thesis does not consider i n depth the significance of l i n e a r distance to a i r t r a f f i c . However, Figure 3 shows the relationship between i n t e r c i t y a i r t r a v e l demand and i n t e r c i t y l i n e a r distance between Cincinnati and i t s 25 prime a i r t r a f f i c , centres... A regression l i n e of Yc = 8.5 •"- G.1X was established and from i t a c o e f f i c i e n t of correlation of rho = 0.65 was determined. Appendix C sets out the s t a t i s t i c a l computation of t h i s coef-f i c i e n t of correlation. (4) Population Population of t r a f f i c centres i s an important determinant of t r i p generation. In a study conducted at Cincinnati , a c o e f f i c i e n t of correla-t i o n of rho - 0.85 was established. Figure 4- i l l u s t r a t e s t h i s relationship between c i t y population s i z e and i t s a b i l i t y to generate a i r passenger t r a f f i c . Appendix D presents the s t a t i s t i c a l computation f o r the regression l i n e Ye = 1.7 + 3.3X. Appendix E shows that there i s , as expected, a strong correlation between i n t e r c i t y a i r t r a f f i c registered at Vancouver and the population of the selected 25 prime Vancouver a i r t r a f f i c centres. B. Other Variables Not Considered, There i s evidence demonstrating that the characteristics o f employment such as occupation and i n d u s t r i a l composition have an important influence upon a i r t r a v e l , p a r t i c u l a r l y t r a v e l f o r business proposes"*-*. Some indus-t r i e s such as wholesale, r e t a i l , and professional services tend to generate large numbers of t r i p s per employee, while others such as manufacturing, agriculture, and personal services tend to generate vary low numbers of t r i p s per employee (see Appendix F ) . A2 Another important variable to be considered i n explaining intercity-t r a v e l demand by a i r i s personal income. Income which i s a measure of the a b i l i t y to afford t r a v e l , plays an important r o l e i n the determination of personal t r a v e l demand. The average income of a i r t r a v e l l e r s i s higher, f o r example, than that f o r other modes . Consequently, Income changes w i l l a f f e c t the t o t a l number of t r i p s as well as the d i s t r i b u t i o n of these t r i p s by mode. I t i s probable that a i r t r a f f i c originating at Vancouver i s influenced by transcontinental r a i l services, p a r t i c u l a r l y those operated by the Canadian National Railways (see Appendix G). However, a consideration of the competitive impact of the railways upon Vancouver's i n t e r c i t y a i r t r a v e l i s beyond t h i s study's scope. In addition to the above factors, there may be differences i n people's attitudes toward t r a v e l l i n g i n general and toward a i r t r a v e l i n p a r t i c u l a r . For example, some people are unwi l l i n g to use a i r transportation even though a l l the socio-economic circumstances indicate an a i r t r i p . Sometimes these predispositions are due to certain q u a l i t i e s of t r a v e l by a p a r t i c u l a r mode, such as general l e v e l of comfort or differences i n apparent safety. These attributes are p a r t i c u l a r l y d i f f i c u l t to account f o r and measure. C. The Relationship Between the Selected Variables In order to measure the relationships- between the explanatory variables and the demand f o r i n t e r c i t y t r a v e l , i t i s necessary to choose an e x p l i c i t form f o r the relationships, that i s , a s p e c i f i c mathematical expression. An economic measure of the relationship between an explanatory variable and a demand quantity i s e l a s t i c i t y . The e l a s t i c i t y of demand with respect to a p a r t i c u l a r explanatory variable i s the percent change i n demand per percent A3 change i n the value of the explanatory variable. The use of e l a s t i c i t y measures to re l a t e demand to the explanatory variable provides the a b i l i t y to forecast percentage changes i n demand f o r given percentage changes i n 717 the explanatory variable :. Several assumptions are possible i n r e l a t i n g the e l a s t i c i t y of demand to l e v e l s of the explanatory variables. The f i r s t assumption i s that e l a s t i c i t y i s constant, that i s , the same regardless of the l e v e l of the explanatory variables. For very large changes i n the l e v e l s of the explana-tory variables, the assumption of constant e l a s t i c i t y i s weak. However> f o r small changes i n the l e v e l of the explanatory variable, the assumption of constant e l a s t i c i t y i s s a t i s f a c t o r y . The only model that results i n con-s t a n t - e l a s t i c i t y i s one that explains the logarithm of demand as a l i n e a r LB function of the logarithms of the explanatory variables . This form of the relationship offers several advantages i n estimation and interpretation. In expressions with many variables, i t i s possible to i s o l a t e the effect . of single variables on demand: and errors i n the scale of the explanatory variables. Analysis of the relationship between the explanatory variables and demand indicate that separate models should be used to describe business and personal t r a v e l . For example, a change i n price or i n t r a v e l time w i l l a f f e c t business t r a v e l d i f f e r e n t l y than personal t r a v e l . S i m i l a r l y , the community of interest between c i t i e s may be di f f e r e n t f o r business than f o r personal t r a v e l . The model used to estimate the demand f o r i n t e r c i t y a i r t r a v e l consists of the following equation: l o g - D ^ =s n 0 log N ± + n d log + p log t t log T±_. where: D< . - the number of t r i p s o r i g i n a t i n g at c i t y i going to c i t y j ; Nj_ = a measure of the population or employment of the o r i g i n c i t y 44 i used i n the demand relationship; N. = a measure of the population or employment of the destination * c i t y j used i n the demand relationship; n Q - the e l a s t i c i t y of t r i p demand with respect to the measure of population or employment i n the o r i g i n c i t y i ; = the e l a s t i c i t y of t r i p demand with respect to the measure of population or employment i n the destination c i t y j ; P. . =• a measure of price of t r a v e l from c i t y i to c i t y j ; 1— j p = the e l a s t i c i t y of t r i p demand with respect to the price measure of t r a v e l between c i t i e s i and j ; , T. . = a measure of t r a v e l time f o r t r i p s going from c i t y i to c i t y j ; t - the e l a s t i c i t y of t r i p demand with respect to the t r a v e l time measure between c i t i e s i and D. Variables Used i n the Model i ' ' ' Before proceeding to a discussion of the thesis methodology, i t i s necessary to discuss the basis f o r selection of-the e x p l i c i t measures to be Msed i n the model. The choice of variables involved consideration of t h e i r relevance i n estimating the demand equations and the ease with which they could be predicted f o r future time periods. (1) I n t e r c i t y Line Travel P r i c e Pares f o r i n t e r c i t y a i r t r i p s consist of both l i n e haul fare and ground transportation cost at the base and the destination c i t i e s . I d e a l l y the cost variable used i n a demand model should be a composite of the above two factors, but due to the general lack of l o c a l cost data, only the l i n e haul cost variable i s considered. Published data i s available f o r l i n e haul t r a v e l fares on established routes. However, most carriers feature special fares such as round t r i p discounts, family plans, children's fares, and many other permutations and 45 combinations within the general regulated fare structure. As data i s not available by type or cost of tickets, i t i s necessary to estimate the actual average fares. I t i s assumed, therefore, that the standard one way economy fares are an approximation of the actual,.average fares. (2) Intercity Line Travel Time The total time taken for a trip from point of origin to point of destination consists of the following: line haul time, local travel, time, waiting times at terminals, and schedule delays. Line haul time i s con-sidered to be the most important by many travellers. However, as trips become shorter i n time/distance, the proportion of line time involved i n total travel time becomes less significant. Ideally, therefore, the time variable used i n a demand model should be a composite of a l l the above time factors. However, due to the paucity of local travel time data, the time variable used here w i l l consider only the line haul portion of the total travel time period. In the case of a single daily schedule between a given pair of points, the determination of average l i n e haul time i s simple. When multiple schedules are available i n a higher density market, this becomes more complex. These schedules include trips at a l l times of the day, trips with varying numbers of stops and trips at varying speeds.... In order to simplify the determination of average line haul times, i t was assumed that a l l pas-sengers choose the shortest l i n e haul time available for a given arrival time i n the destination city. The number of stops en route i s not considered except as i t i s reflected i n the elapsed lin e haul time. (3) Intercity Linear Distance The variable intercity travel time, i s considered to be a more sensitive determinant of a i r t r a f f i c than linear distance. Therefore, 46 linear distance i s not incorporated as a component i n the model. (4) Population The measure of population used i n the model i s the total popu-lation of the defined urban region. (5) Quantity of Travel The measure selected as the dependent variable i s the number of one way a i r trips for either business or personal purposes. The a v a i l a b i l i t y of data and the volume of a i r t r a f f i c between ci t i e s influenced the selec-tion of the sample sets of c i t y pairs. Ideally i t i s desirable to have data available for a suitable cross section of c i t y pairs for at least two time periods, so that parameters which explain t r a f f i c may be estimated and so that any shifts over time i n the values of these parameters may be determined. The model developed considers mainly the transportation factors which influence a i r travel demand. The parameters used here are lin e haul cost (price) and lin e haul time. The model describes the number of trips originating at a base city ( i e . Metropolitan Vancouver) and terminating at a reference c i t y . The model developed here may be used to describe interci t y a i r trips on selected Canadian routes such as Vancouver to Toronto, Vancouver to Calgary, and Vancouver to Victoria. Chapter V describes how ifche model may be used to predict a i r t r a f f i c . 47 FOOTNOTES 40 Stephen P. Wheatcroft, E l a s t i c i t y of Demand for North Atlantic  Travels A Study for the International A i r Transport Association,,' (Montreal: Quebec, 1964), p. 60. 41 Edward J . Taaffe, The A i r Passenger Hinterland of Chicago. (Chicago: University of Chicago Press, 1952), p. 47. 42 Peter F. Oehm, The A i r Passenger Hinterland of Cincinnati. Ohio. Cincinnati, (Unpublished Masters thesis i n the Geography Department, University of Cincinnati, 1966), p. 13. 43 Ibid, p. 14. 44 Ibid, p. 15. 45 John B. Lansing, The Travel Market: "1964 - 1965. (Ann Arbor: Michigan, University of Michigan, 1966), p. 59. 46 John B. Lansing", Mode Choice i n Intercity Travel: A Multivariate  S t a t i s t i c a l Analysis. (Ann Arbor: Michigan, University of Michigan, 1964), p. 47 - 49. 47 Wheatcroft, loc c i t . p. 60. 48 Wheatcroft, loc c i t . p. 61. CHAPTER V METHOD OF RESEARCH 49 This thesis examines a segment of the air traffic flow pattern of a single metropolitan region, Vancouver. It considers quantitatively the main determinants of air passenger traffic originating at the Vancouver International Airport. As outlined in Chapter IV, i t is assumed that the main determinants of air passenger traffic are price, line time, and the population of both the origin (Vancouver) and the destination,centres. The study considers the nature of the air spatial Interaction between Metropolitan Vancouver and its 25 prime traffic generators. The selection of one base metropolitan region permits a quantitative analysis of the traffic determinants of this region. The spatial interaction of a region is studied in an effort to .-derive a conceptual framework to explain its determinants-. It is the purpose of this thesis to test its applicability as a device to both describe and forecast the nature of air traffic between an origin and a destination city. This chapter outlines the methods utilized to test the applicability of the theoretical framework developed in Chapter IV. This thesis is limited in space to the consideration of Vancouver's passenger traffic between centres in Canada. In time, i t is limited to the consideration of the middle 1960's period, with main emphasis being placed upon the year 1965. In terms of data, the S t u d y emphasizes annual airline passenger totals between Vancouver and 25 prime traffic centres which are served by Air Canada, Canadian Pacific Airlines, and Pacific Western Airlines. The demand model postulated in Chapter IV permits direct estimation of the elasticity of demand for air transportation with respect to changes in each of the explanatory variables. As an initial step in estimating Major T ra f f i c Centres in CANADA. Winnipeg Montreal "Ottawa Toronto London Map 2 Major Traffic Centres in BRITISH COLUMBIA 52 the e l a s t i c i t y , normal linear regression techniques were used to test the importance of the selected variables upon a i r t r a f f i c . A. Non-Computerized Research (a) The Gravity Model Assuming that the gravity model approach i s valid and that the independent variables selected for use i n the thesis are significant determinants of intercity a i r passenger t r a f f i c , several iterative tests on the Vancouver a i r t r a f f i c were carried out. The f i r s t test used the gravity model and i s stated as follows: where: - the 1966 population of Metropolitan Vancouver; Pj = the 1966 population of the reference city; d j . -the linear distance between cities i and j . Table 2,.shows the results of the test for Vancouver's 25 prime t r a f f i c centres* With few exceptions, the traditional gravity model does not adequately describe the nature of a i r t r a f f i c emanating from Vancouver International Airport. Next, the distance variable used i n the previous test was replaced by the variable intercity line time. The gravity model, then, assumed the following, form: where: P^ - the 1966 population of Metropolitan Vancouver; Pj - the 1966 population of the reference city; t ^ _ . = the intercity travel time between cities i and j . TABLE 2 INTERCITY TRAFFIC USING LINEAR DISTANCE VARIABLE IN THE GRAVITY MODEL (a) 1966 ACTUAL CALCULATED METRO LINEAR 1965 1965 REFERENCE CITY POPULATION DISTANCE TRAFFIC i n TRAFFIC i n DIFFERENCE in Thousand*1. i n Miles Thousands Thousands i n (b) £ (c) (d) (e) Thousands 1 Toronto, Ont. 2 Calgary, Alta. 2,145 2,116 37.9 40.1 2.2 328 474 31.4 61.2 29.8 3 Edmonton, Alta. 399 524 28.9 66.4 37.5 4 Victoria, B.C. 172 47 24.1 32.4 8.3 5 Winnipeg, Man. 505 1,179 18.7 38.2 19.5 6 Montreal, Que. 2,419 2,348 17.1 38.1 21.0 7 Prince George, B.C. 24 326 15.2 36.5 21.3 8 Prince Rupert, B.C. 14 470 13.8 26.1 12.3 9 Port Hardy, B.C. 1 223 12.7 44.1 31.4 10 Powell'River, B.C. 12 95 10.1 11.2 1.1 11 Terrace-Kitimat, B.C. 18 432 8.3 36.8 24.5 12 Castlegar, B.C. 3 250 7.5 10.7 3.2 13 Kelowna, B.C. 17 , 179 7.3 6.8 0.5 14 Sahdspit, B.C. i 468 7.0 16.2- 9.2 15 Ottawa, Ont. 489 2,348 5.9 19.8 13.8 16 Regina, Sask. 131 853 5.9 13.5 7.6 17 Penticton, B.C. 15 i62 5.8 8.2 2.4 18 Saskatoon, Sask. 115 797 4.0 12.4 8.4 19 Campbell River, B.C. 8 118 4.0 5.9 1.9 20 Fort St. John, B.C 7 507 3.9 12.1 8.2 21 Granbrook, B.C. 8 338 3.7 21.2 17.5 22 Kamloops, B.C. 11 162 3.6 5.4 1.8 23 Whitehorse, Yukon, 4 1,15© 3.4 3.1 0.3 24 Comox, B.C. 3 96 2.6 2.8 0.2 25 London, Ont. 207 2,205 1.9 15.9 14.0 The Base City i n the study i s Metropolitan Vancouver whose 1966 population was 884,000. Ir * Jr * - i — 1 i s the form of the gravity model used i n this table, where P repre-^ i - j sents population and d represents distance. SOURCE: Dominion Bureau of Statistics, Canada Census. 1966. SOURCE: Air Canada, Canadian Pacific Airlines and Pacific Western. SOURCE: Canada, Air Transport Board, Airline Passenger Origin and Destination S t a t i s t i c s . Ottawa: 1965. Calculated t r a f f i c volume using gravity model. (a) (b) (c) (d) (e) 54 TABLE 3 INTERCITY TRAFFIC USING INTERCITY TRAVEL TIME VARIABLE IN THE GRAVITY MODEL (a) 1966 INTERCITY ACTUAL CALCULATED METRO TRAVEL 1965 1965 REFERENCE CITY POPULATION, ..TIME; ' : TRAFFIC i n TRAFFIC i n DIFFERENCE i n Thousands in- Hours Thousands Thousands i n (b) (c) (d) (e). Thousands 1 Toronto, Ont. 2 Calgary, Alta. 2,145 4.1 37.9 46.3 8.4 328 1.1 31.4 26.4 5.0 3 Edmonton, Alta. 399 1.3 28.9 27.1 1.8 4 Victoria, B.C. 172 0.4 24.1 38.1 14.0 5 Winnipeg, Man. 505 2.5 18.7 17.8 0.9 6 Montreal, Que. 2,419 5.3 17.1 40.4 22.3 7 Prince George, B.C. 24 1.9 15.2 11.2 4.0 8 Prince Rupert, B.C. U 2.5 13.8 5.1 8.7 9 Port Hardy, B.C. 1 1.3 12.7 6.9 5.8 10 Powell River, B.C. 12 0.8 10.1 13.1 3.0 11 Terrace-Kitimat, B.G. 18 2.3 8.3 6.7 1.6 12 Castlegar, B.C. 3 2.0 7.5 13.5 6.0 13 Kelowna, B.C. 17 1.0 7.3 15.1 7.8 14 Sandspit, B.C. 1 2.3 7.0 3.5 3.5 15 Ottawa, Ont. 489 6.3 5;9 6.9 1.0 16 Regina, Sask. 131 3 i'l 5.9 3.7 2.2 17 Periticton, B,C. 15 1.0 5.8 13.3 7.5 18 Saskatoon,- Sask. 115 3.5 4.0 4.1 O.I 19 Campbell River, B.C. 8 0.8 4.0 8.8 4.8 20 Fort St. John,-B.C. 7 3.2 3.9 1.9 2.0 21 Cranbrook, B.C. 8 3.0 3.7 2.1 1.6 22 Kamloops, B.C. 11 1.0 3.6 9.7 6.1 23 Whitehorse, Yukon 4 6.5 3.4 5.4 2.0 24 Comox, B.C. 3 0.8 2*6 3.3 0.7 25 London, Ont. 207 6.1 1.9 3.7 1.8 The Base City i n the study i s Metropolitan Vancouver whose 1966 population was 884,000. (a) (b) (c) (d) i s SOURCE: SOURCE: SOURCE: the form of the gravity model used i n this table, where P. repre-sents population and t represents intercity travel time. Dominion Bureau of Statistics, Canada Census. 1966. Air Canada, Canadian Pacific Airlines, Pacific Western Airlines. Canada, A i r Transport Board. Airline Passenger Origin and  Destination Statistics. Ottawa: 1965. (e) Calculated t r a f f i c volume using gravity model. 55 TABLE 4 INTERCITY TRAFFIC USING INTERCITY TRAVEL PRICE VARIABLE IN THE GRAVITY MODEL (a) * REFERENCE CITY 1966 METRO POPULATION i n Thousands *?(b) INTERCITY TRAVEL PRICE i n $100>a (c) ACTUAL 1965 TRAFFIC, i n Thousands (d) CALCULATED 1965 TRAFFIC i n Thousands (e) DIFFERENCE i n Thousands 1 Toronto, Ont. 2,H5 1.1 37.9 27.5 10.4 2 Calgary, A l t a . 328 0.3 31.4 40.4 9.0 3 Edmonton, A l t a . 399 0.3 28.9 42.7 13.8 4 V i c t o r i a , B.C. 5 Winnipeg, Man. 172 0.1 24.1 15.2 8.9 505 0.6 18.7 23.2 4.5 6 Montreal, Que. 2,419 1.2 17.1 27.5 10.5 7 Prince George, B.C. 24 0.4 15.2 22.7 6.5 8 Prince Rupert, B.C. 14 0.4 13.8 18.1 4.3 9 Port Hardy, B.C. 1 0.3 12.7 17.2 4.5 10 Powell River, B.C. 12 0.1 10.1 18.9 8.8 11 Terrace-Kitimat, B.C. 18 Oil 8.3 19.1 10.8 12 Castlegar, B.C. 3 0.2 7.5 14.4 6.9 13 Kelowna, B.C. 17 0.2 7.3 7.5 0.2 14 Sandspit, B.C. 1 0.4 7.0 19.5 12.5 15 Ottawa, Ont. 489 1.2 5.9 36.1 10.2 16 Regina, Sask. 131 0.6 5.9 19.4 13.5 17 Penticton, B.C. 15 0.2 5.8 6.6 0.8 18 Saskatoon, Sask. 115 0.6 4.0 16.8 12.8 19 Campbell River, B.C. 8 0.1 4.0 7.1 3.1 20 Fort St. John, B.C. 7 0.5 3.9 12.5 8.6 21 Cranbrook, B.C. 8 0.3 3.7 2.3 1.4 22 Kamloops, B.C. 11 0.2 3.6 4.9 1.3 23 Whitehorse, Yukon 4 0.8 3.4 4.4 1.0 24 Comox, B.C. 3 0.1 2.6 2.7 0.1 25 London, Ont. 207 1.1 1.9 16.2 14.3 The Base C i t y i n the study i s Metropolitan Vancouver whose 1966 population was 884,000. (a) P. P (b) (c) (d) Pl-A SOURCE: SOURCE: SOURCE: i i s the form of the gravity model used i n t h i s table, where P repre-sents population and p represents i n t e r c i t y t r a v e l p r i c e * Dominion Bureau of S t a t i s t i c s , Canada Census. 1966. A i r Canada, Canadian P a c i f i c A i r l i n e s , P a c i f i c Western A i r l i n e s . Canada, A i r Transport Board, A i r l i n e . Passenger Origin and  Destination S t a t i s t i c s , Ottawa: 1965. (e) Calculated t r a f f i c volume using gravity"model. 56 TABLE 5 INTERCITY TRAFFIC USING NON-COMPUTERIZED LINEAR REGRESSION RELATIONSHIP BETWEEN POPULATION, TIME AND PRICE VARIABLES (a) 1966 ACTUAL CALCULATED METRO 1965 1965 REFERENCE CITY POPULATION TRAFFIC i n TRAFFIC i n DIFFERENCE i n Thousands Thousands Thousands i n (b) (c) (d) Thousands 1 Toronto, Ont. 2,145 37.9 19.7 18.2 2 Calgary, A l t a . 328 31.4 11.8 19.6 3 Edmonton, A l t a . 399 28.4 12.2 16.7 4 V i c t o r i a , B.C. 172 24.1 11.5 12.6 5 Winnipeg, Man. 505 18.7 12.5 6.2 6 Montreal, Que. 2,419 17.1 20.7 3.6 7 Prince George, B.C. 24 15.2 9.8 5.4 8 Prince Rupert, B.C. 14 13.1 9.7 3.4 9 Port Hardy, B.C. 1 12.7 9.9 2.8 10 Powell River, B.C. 12 10.1 10.0 0.1 11 Terrace-Kitimat, B.C. 18 8.3 9.7 1.4 12 Castlegar, B.C. 3 7.5 9.8 2.3 13 Kelowna, B.C. 17 7.3 10.0 2.7 14. Sandspit, B.C. 1 7.0 9.7 2.7 15 Ottawa, Ont. 489 5.9 11.7 5.8 16 Regiha, Sask; 131 5.9 10.5 4.6 17 Penticton, B.C. 15 5.8 10.0 4.2 18 Saskatoon, Sask. 115 4.0 10.4 6.4 19 Campbell River, B.C. 8 4.0 10.0 6.0 20 Fort St. John, B.C. 7 3.9 9.6 5.7 21 Cranbrook, B.C. 8 3.7 9.6 5.9 22 Kamloops, B.C. 11 3.6 10.0 6.4 23 Whitehorse, Yukon 4 3.4 8.9 5.5 24 Comox, B.C. 3 2*6 10.0 7.4 25 London, Ont. 207 1.9 10.4 8.5 The Base C i t y i n the study i s Metropolitan Vancouver whose 1966 population was 884,000. (a) Yc = 6.4 + 4.7X - 0.071 - 0.2Z i s the form of the l i n e a r regression l i n e used to compute the "Expected 1965 T r a f f i c " ; where: X = the combined population of the two t r a f f i c centres; Y = the i n t e r c i t y l i n e p r i c e between the two t r a f f i c centres; Z = the i n t e r c i t y l i n e t r a v e l time between the two-traffic centres. (b) SOURCE: Dominion Bureau of S t a t i s t i c s , Canada Census, 1966. (c) SOURCE:- Canada, A i r Transport Board, A i r l i n e Passenger Origin and Destination' S t a t i s t i c s . Ottawa: 1965. (d) Calculated t r a f f i c volume using gravity model. 57 Table 3 shows the actual and computed traffic volumes. The difference between the actual and computed traffic volumes Is less than when inter-city linear distance is used in the gravity model (see Table 2). Tables 2 and 3 show that linear distance and intercity travel time, considered as separate variables, do not adequately explain Vancouver's intercity air passenger traffic. The next test considered the intercity line price (fare) in the gravity model as follows: P i P 1 where: P^ = the 1966 population of Metropolitan Vancouver; P j = the 1966 population of the reference city; p^_j -=. the intercity travel price between cities i and j . Table L. shows the actual and computed volumes. It shows that the disparity between the actual traffic and that explained when the price variable Is used in the gravity model, continues to increase, (b) Linear Regression Analysis The tests carried out above show that the gravity model, using each variable as a separate air traffic determinant, is not an adequate descriptive tool. The next step in the analysis involved the combination of linear regression lines into one equation to explain Vancouver's inter-city air travel. This equation was constructed independent of computer multiple linear regression analysis. The derivation of this linear equa-tion is as. follows: (1) Ic « -5.5 + U . l X where: Yc = the intercity air passenger traffic; X =. the1 combined population of Metropolitan Vancouver and each reference city. TABLE 6 MULTIPLE REGRESSION ANALYSIS APPLIED TO SELECTED VARIABLES VARIABLE .NUMBER. MEAN STANDARD DEVIATION CORRELATION X vs Y -REGRESSION COEFFICIENT STD. ERROR OF'REG. COEFFICIENT COMPUTED T VALUE I 2 3 4 5 Dependent 2.56399 0.4-6799 572.44397 724.87976 273.85192 11.38798 1.83890 0.35322 701.55615 324i80230 625.86340 9.89441 -0.15705 0.11469 0.37418, 0.43055 0.57475 - 4.73484 24.85763 - 0.00687 0.00831 0.01079 3.08354 20.47755 0.00621 0.00655 0.00484 -1.53552 1.21389 -1.10539 1.26764 2.22578 Intercept ............................ 6.846I6 Multiple Correlation ............... 0.75333 Standard Error of Estimate 7.31317 ANALYSIS OF VARIANCE FOR THE REGRESSION DEGREES SUM SOURCE OF VARIATION OF FREEDOM OF SQUARES MEAN SQUARES F VALUE Attributable to Regression 5 1333.42090 266.68414 4.98638 Deviation from Regression 19 1016.16736 53.48249 . . . 24 2349.58838 TABLE OF RESIDUALS CASE NO. Y VALUE Y ESTIMATE RESIDUAL 1 0.00000 6.846I6 -6.84616 SOURCE: Multiple Regression Analysis carried out by I.B.M. Computer 7044 59 (2) Yo - 11.5 - 0.2 Y where: Y = the intercity line price between Metropolitan Vancouver and each reference, c i t y . (3) Yc = 13.2 - 0.7 Z where: Z= the intercity l i n e time between Metropolitan Vancouver and each reference c i t y . Equations ( l ) , (2) and (3) are each related to intercity a i r t r a f f i c (Yc). Equation (4) i s formulated by adding these equations together ("that i s , (l) + (2) + (3) - (4)) (see Appendix H): (4) l e 6 . 4 + 4-7 X - 0.07 Y - 0.2 Z. Table 5 shows the results of these computations. Equation (4) more ade-quately explains the nature of long distance t r a f f i c than any of the previous constructs. I t also appears to apply,topmost of the a i r t r a f f i c destined to such- medium distance centres as Port Hardy, Terrace-Kitimat, Castlegar, Kelowna and Sandspit. B; Computerized Research Multiple Linear Regression- Analysis As a further step i n estimating the e l a s t i c i t y , multiple linear regression regression techniques were used to test the importance of the selected variables i n explaining Vancouver's intercity a i r t r a f f i c . This analysis was performed on an I.B.M. 7044 computer. The results of this analysis are shown i n Table 6. The data i n -Table 7 shows the relative.,,significance of the selected variables as established by computer analysis. The coefficients of cor-relation range.: from. Q. 12 for intercity line price to 0.58 for destination population. These coefficients of correlation are excessively low to give them credence as being strong a i r t r a f f i c indicators. When the determinants 60 were considered together by means of multiple regression analysis, a multiple correlation c o e f f i c i e n t of 0.76 was established. Even a multiple correlation c o e f f i c i e n t of 0.76 i s small f o r multiple regression analysis. TABLE 7 THE RELATIVE SIGNIFICANCE OF THE SELECTED VARIABLES AS- DETERMINED BY  MULTIPLE REGRESSION ANALYSIS ON I.B.M.'S 1QLL COMPUTER VARIABLE COEFFICIENT OF CORRELATION 1 Time - 0.16 2 Price 0.12 3 Linear A i r Distance 0.37 4. Origin Population 0.43 5 ' Destination Population 0.58 Mult i p l e Correlation 0.76 SOURCE: From Table 6 on Page 58. According to economic theory, the e l a s t i c i t y of t r a v e l demand f o r a i r t r a f f i c with respect to i t s price and i t s t r a v e l time should be negative. That i s , an increase i n price or an increase i n t r a v e l time should produce a,reduction i n t r a v e l demand. The multiple regression analysis showed that t h i s postulation was applicable to Vancouver. As the e l a s t i c i t y of these variables i s not considered i n the l i g h t of changes i n costs and t r a v e l time f o r other t r a v e l modes, I t s r e l i a b i l i t y is.-,not high. The multiple regression analysis showed that the variables selected f o r study, provide a reasonable explanation of the a i r t r a f f i c pattern at Vancouver with due regard to the l i m i t a t i o n s imposed upon the input data. These l i m i t a t i o n s of the model are discussed i n Chapter VI. 61 C. lieseareh on Future Application of the Model On the basis of the model postulated, i n Chapter IV, a forecast of 1970, 1975 and 1980 i n t e r c i t y a i r t r a f f i c could be made. The forecasts f o r these years assume changes i n the selected variables f o r each time period. Other assumptions w i l l have to be made regarding s i g n i f i c a n t p o t e n t i a l changes i n transportation technology such as the introduction of jumbo j e t service ( i n 1970), supersonic a i r c r a f t (by 1975), and down-town slaprt. haul a i r p o r t f a c i l i t i e s f o r v e r t i c a l take o f f and landing (V.T.O.L.) services (by 1980) 4 9. I t i s .anticipated that by 1970 the jumbo je t s or "Boeing big-capacity 747 j e t s " , w i l l be used on a few long distance routes. These a i r c r a f t are expected to carry approximately 490 passengers so that with increased load capacities, the i n t e r c i t y a i r prices should be reduced accordingly. The inception of the Boeing 747 w i l l have, the greatest impact, then, on the price variable of the model. I t s cruising speed w i l l be approximately 630 m.p.h. so that i t s impact on the i n t e r c i t y t r a v e l time variable w i l l be minimal. By 1975 supersonic jets w i l l be f l y i n g between long distance c i t i e s , at l e a s t between those that have large water bodies separating them. The supersonic a i r c r a f t , t r a v e l l i n g at 1,800 m.p.h., w i l l obviously have the greatest influence on the i n t e r c i t y t r a v e l time variable-(see Table 8). This a i r c r a f t i s a long distance venture. The supersonics do not reach 50 t h e i r maximum cruising speed i n distances under 700 miles^ <, This, then, rules out a supersonic f l i g h t , f o r example, between Vancouver and Calgary. The supersonic a i r c r a f t w i l l also have an impact on the i n t e r c i t y price variable. By the date of t h e i r inception, there w i l l be a fare d i f f e r e n t i a l between supersonic and subsonic j e t transports. Boeing's Marketing Research 62 Manager, Robin K. L i t t l e , estimates that the direct operating cost of the supersonic jet will.be 0.2# per seat higher than the jumbo jet (Boeing 747) TABLE 8 INTERCITY TRAVEL TIMES, lQ66r 1970 AND 1975 BETWEEN VANCOUVER AND SELECTED POINTS 1966 1970 1975 REFERENCE CITY FLYING TIME FLYING TIME FLYING TIME INTERCITY (flours) (Hours) (Hours) AIR DISTANCE (a) (b) (Miles) Toronto 4.1 3.4 1.2 2,116 Winnipeg 2.5 1.9 0.6 1,179 Montreal 5.3 3.7 1.3 2,343 Ottawa 6.3 3.7 1.3 2,348 Saskatoon 3.5 1.3 0.4 797 London 6.1 3.5 1.3 2,205 (a) The,elapsed time computation assumes that the 630 m.p.h. Boeing 747 ~ aircraft f l y the route. The time computed also assumes that the route has non stop service. (b) The elapsed time computation assumes that the 1,800 m.p.h. Boeing supersonic aircraft f l y the route. The time computed also assumes that the route has non stop service. Boeing i s placing substantial confidence i n Its 747 aircraft as a forerunner to the supersonic: especially i n the area of costs not directly related to the flying of the supersonic transport. The two planes are both heavier and much larger than any passenger aircraft flying today. This means that airports w i l l have to expand extensively to handle these a i r -craft. For example, loading f a c i l i t i e s w i l l have to be rearranged and passengers rerouted and baggage handling f a c i l i t i e s redesigned completely*^2. Boeing hopes to niaximize the efficiency of terminal operations, and, there-fore, reduce terminal costs. 63 By 1980 Metropolitan-Toronto plans to have a downtown "Transportation Centre" to accomplish an integration of its regional transportation system with its local system. As part of this Transport Centre, a downtown S.T.O.L. port is planned so that certain planes can take off in midtown, and, thus, 53 eliminate the city centre to airport trip . Ganadair, designers and manufacturers of the CL-&4 V.T.O.L. are confi-dent that their V.T.O.L.'s and S.T.O.L.'s will be in operation as intercity transport carriers in about seven years'^. The CL-84. can take off and land vertically, and in sjaraight flight has a top cruising speed of 330 m.p.h. This type of technological advancement has particular significance for the short distance air routes (see Table 9)• Its greatest impact will be on the time variable, as intercity travel price probably will not be reduced sub-stantially. The provision of downtown S.T.'O.L. ports in Canada's major cities will have a monumental influence on the transportation infrastruc-ture in our metropolitan regions. However, these interesting conjectures, and potential realities of 1980, regarding downtown S.T.O.L. ports, cannot be pursued here in any more detail. The air travel forecaster also should consider new developments in the competing modes of transport. For example, high speed, Canadian National trains are, and will prove to be a successful means of moving a large number of people between two traffic centres at a reasonable price, within an air competitive time interval. This Is presently the situation in the "Montreal-55 Toronto Transportation Corridor" . Automated highways and pressurized tube train t r a v e l ^ are technological considerations which also should concern the long range air travel forecaster. However, in these situations, the assumption of constant elasticity would be of doubtful validity, and the model would produce misleading results. For example, a large change in 64 a i r time would c e r t a i n l y have the effect of reducing the e l a s t i c i t y . TABLE 9 INTERCITY TRAVEL TIME, 1966 AND 1980 BETWEEN VANCOUVER AND SELECTED POINTS REFERENCE CITY INTERCITY AIR DISTANCE (Miles) 1966 FLYING TIME (Hours) 1980 FLYING TIME (Hours) (a) Calgary 474 1.1 1.4 Edmonton 524 1.3 1.6 V i c t o r i a 47 0.4 0;2 Prince George 326 1.9 1.0 Port Hardy 223 1.3 0.7 Powell River 95 0.8 0.3 Kelowna 179 1.0 0.5 Sandspit 468 2.3 1.4 Comox 96 0.8 0.3 (a) The elapsed time computation assumes that 330 nup.h. Canadair CL-84 V.T.O.L. a i r c r a f t f l y the route. The time computed also assumes that the route has non stop service. This chapter has outlined the basic method of research. The main techniques u t i l i z e d are the gravity model and multiple -regression analysis. By using these tools of analysis i n an i t e r a t i v e manner, a relationship has been established between a i r t r a f f i c and the selected variables: popu-l a t i o n , i n t e r c i t y l i n e a r distance, i n t e r c i t y l i n e p r i c e , and i n t e r c i t y l i n e time. The v a l i d i t y of t h i s relationship i s affected by constraints i n space, i n time, and i n data. These constraints w i l l be considered i n Chapter VI. The relationship established appears to have forecast a p p l i c a b i l i t y on certain i n t e r c i t y routes. The v a l i d i t y of the model as a predictive 65 device will be dependent on technological changes in the air transportation industry, and also on the competitive capacity of other modes of travel. 66 FOOTNOTES 49 The Globe and M a l l (Toronto). April.13, 1967, p. 1. 50 The Vancouver Sun. January 10, 1967, p. 10. 51 I b i d , p. 10. 52 I b i d , p. 10. 53 C i t y of Toronto, Planning Board, A New Plan f o r Toronto f (Toronto: The Board, 1966), p. 14. 54 The Fin a n c i a l Post (Toronto). December 31, 1966, p. 1. 55 The Toronto D a i l y Star. December 28, 1966, p. 16. 56 The Fin a n c i a l Post (Toronto). November 19, 1966, p. 28. CHAPTER VI APPRAISALS AND CONCLUSIONS — RECOMMENDATIONS FOR FURTHER STUDY 68 A. Appraisal of Methodology (a) S e l e c t i o n of Study .Variables and C i t i e s The basic problem with studies i n the a i r l i n e industry centres around the f a c t that h i s t o r i c a l data i s analyzed f o r a number of years and then projections are made assuming that these past r e l a t i o n s h i p s w i l l con-tinue i n t o the fut u r e . Few of the studies attempt to assign weights to the f a c t o r s that influence a i r l i n e t r a f f i c to a given degree at a c e r t a i n p o i n t on the time continuum. Therefore, f o r the purpose of es t a b l i s h i n g a fo r e c a s t i n g base, i t should be assumed that growth and change of a i r t r a v e l patterns w i l l be determined by f a c t o r s which change over time. On a micro l e v e l , the l i s t o f f a c t o r s i s long and includes such determinants as psychology of the mass market, q u a l i t y and saf e t y of a i r t r a v e l compared to a l t e r n a t i v e s , l e v e l of the G.N.P., income, wealth and so on. However, on the macro l e v e l , i t i s assumed that the most s i g n i f i c a n t determinants of i n t e r c i t y a i r t r a v e l are the t o t a l population of i n t e r a c t i n g c i t i e s , the l i n e t r a v e l p r i c e , the l i n e time, and the a i r distance between these two c i t i e s . Table 7 shows the r e l a t i v e s i g n i f i c a n c e to be a l l o t t e d to each of these a i r t r a f f i c determinants. The measure selected as the dependent v a r i a b l e i s the number of one way a i r t r i p s f o r business or non business purposes f o r a selected c i t y p a i r . Although several considerations entered i n t o the s e l e c t i o n of the sample sets of c i t y p a i r s f o r a n a l y s i s , f i r s t and foremost was the a v a i l -a b i l i t y of data. Chosen f o r a n a l y s i s were Vancouver's 25 prime t r a f f i c 57 centres. This data i s a v a i l a b l e from the A i r Transport Board f o r 1965 . However, while the a v a i l a b l e data f o r a i r t r a v e l , a t t r i b u t e s the t r a f f i c 69 to the l a r g e r c i t i e s i n Canada, some of the t r a f f i c may o r i g i n a t e or terminate i n the surrounding r u r a l hinterlands of these c i t i e s - ^ . A l l t r a f f i c centres i n the study are served by a l t e r n a t i v e modes of transport. This w i l l be important to future i n v e s t i g a t o r s who may f i n d t h i s study u s e f u l i n examining population, p r i c e , and-time e l a s t i c i t i e s f o r a l l modes of transport. For t h i s reason, i t i s fortunate that the 25 t r a f f i c centres are served by a i r transport and at l e a s t one other com-p e t i t i v e common c a r r i e r . The sample contains the major c i t i e s i n Canada which w i l l be s i g n i -f i c a n t l y influenced by major technological changes i n the a i r transpor-t a t i o n industry. Furthermore the bulk of the Canadian population i s included within the selected sample. As w e l l , i t contains c i t i e s of va r i e d s i z e s as w e l l as c i t i e s l o cated at various distances from each other. For example, the study contains 9 short distance t r a f f i c centres (up to 300 miles a p a r t ) ; 9 medium distance centres (300 - 800 miles a p a r t ) ; and, 7 long distance centres (800 miles and over). An equally important c r i t e r i o n i n the s e l e c t i o n of a base i s that i t must be po s s i b l e to describe and pro j e c t i t s b a s i c socio-economic and transport c h a r a c t e r i s t i c s . The metropolitan region i s chosen since data i s a v a i l a b l e which corresponds c l o s e l y to the t r a f f i c generating areas (hinterlands) served by the given a i r terminal. (b) S e l e c t i o n of Gravity Model Approach The g r a v i t y model T^_j = P^ Pj was subjected to the i t e r a t i v e • d i - 3 process i n t h i s t h e s i s . That i s , the above construct was tested i n various forms to see i f i t could be used to describe the nature of i n t e r -c i t y a i r t r a v e l . Tables 2, 3 and U show the r e s u l t s of these adaptations 70 to the distance oriented gravity model. The modifications include the use of line haul price and li n e haul time. Some of the limitations placed on the usefulness of the gravity model were recognized, and, therefore, an effort was made to modify i t so as to enhance i t s beneficial qualities,. However, the limitation of time available precludes further iterative study. There i s the implied assumption that the t r a f f i c pairs are "homogenous", i e . comparable i n every respect. How-ever, i t i s soon realized that there are dissimilarities between t r a f f i c communities. An attempt should be made to account for these differences i n their t r a f f i c potential. Accordingly, a functional classification of ci t y markets i s needed i n Canada to help determine the t r a f f i c generation 59 qualities of each c i t y type * The population data used i n the formula i s taken from federally defined demographic areas which may not necessarily coincide with the t r a f f i c generation boundaries for a particular c i t y region. In fact, i t i s plaus-ible that these t r a f f i c boundaries w i l l fluctuate according to the existing competitive transportation f a c i l i t i e s , the geographical location of the cit i e s and their, airports. The formula does not account for these micro attributes of the city population. Accordingly, i t i s important to designate zones of t r a f f i c generation, either on an arbitrary basis by means of sampling transportation users to determine their "true" origins 60 and destinations . The formula or any of i t s adaptations do not compensate for varying degrees of public acceptance that might be associated with an individual airline's reputation and period of established service. I t was assumed that the services of A i r Canada, Canadian Pacific Airlines, and Pacific Western Airlines are well known and are reputable. 71 (c) Selection of Linear Multiple Regression Technique Regression analysis finds the "best" equation relating a de-pendent variable (Yc) to any number of independent variables (X^+ Xg ... X n ) . Pictorally, regression finds a plane passing closest to a clustre of points i n space (a point i s a "Y value" corresponding to a pair of "X^ and Xg values"). A formula based on past data Is computed. From this, .process predictions of new Yc values can be obtained from given X-^  and Xg values (see Table 10). Multiple regression analysis provides a quantitative confidence measure for the closeness of f i t of the relation-ship and the validity of the relationship as a predictive device. For a variety of reasons multiple regression analysis i s useful i n this thesis. The reasons for using the technique can be summarized as follows: (l) to summarize large quantities of data;1 (2) to find an ap-proximate relationship between the variables; (3) to find an underlying law; (A) to predict new or future occurrences; (5) to estimate the relative strength of the contributing factors of a relationship; and, (6) to project on the basis of the sample input data. Using I.B.M. f'S programme for use on the I.B.M. 70AA, a multiple re-gression analysis was run for the five independent variables and the one dependent variable. The correlations for each separate variable are shown i n Table 6. The multiple linear regression coefficient for a l l of the variables interacted simultaneously i s 0.76. Due to the fact that the relationship as postulated only accounts for 76$ of the intercity a i r travel, two main problems must be attacked. One concerns the achievement of a, higher coefficient of multiple correlation through the inclusion i n the regression analysis of some of the factors not included for consideration i n the thesis, pr through the use of better 72 TABLE 10 PREDICTED INTERCITY AIR TRAFFIC USING MULTIPLE REGRESSION ANALYSIS ACTUAL PREDICTED INTERCITY INTERCITY % REFERENCE CITY AIR TRAFFIC (Y Value) AIR TRAFFIC (Y Estimate) RESIDUAL DIFFERENCE 1 Toronto, Ont. 37.9 30.4 7.5 21.1 2 Calgary, Alta. 31.4 16.4 15.0 48.7 3 Edmonton, Alta. 28.9 15.9 13.0 45.1 4 Victoria, B.C. 5 Winnipeg, Man. 24.1 14.7 9.4 37.5 18.7 16.6 2.1 11.1 6 Montreal, Que. 17.1 28.0 -10.9 64.9 7 Prince George, B.C. 8 Prince Rupert, B.C. 15.2 11.5 3.7 26.7 13.8 8.3 5.5 42.8 9 Port Hardy, B.C. 12.7 12.6 0.1 0.8 10 Powell River, B.C. 10.1 11.4 - 1.3 10.1 11 Terrace-Kitimat, B.C. 8.3 9.4 - 1.1 12.5 12 Castlegar, B.C. 7.5 6.9 0.6 7.5 13 Kelowna, B.C. 7.3 12.4 - 5.1 71.4 L4 Sandspit, B.C. 7.0 9.3 - 2.3 28.5 15 Ottawa, Ont. 5.9 8.5 2.6 50.2 16 Regina, Sask. 5.9 10.2 - 4.3 66.2 17 Penticton, B.C. 5.8 12.4 -.6.6 116.6 18 Saskatoon, Sask. 4.0 7.8 - 3.8 96.2 19 Campbell River, B.C. 4.0 11.4 - 7.4 175.0 20 Fort St. John, B.C. 3.9 6.4 - 2.5 74.2 21 Cranbrook, B.C. 3.7 3.5 0.2 5.0 22 Kamloops, B.C. 3.6 12 .'3 - 8.7 225.0 23 Whitehorse, Yukon 3.4 5.2 . - 1.8 55.3 24 Comox, B.C. 2.6 11.4 - 8.8 300.0 25 London, Ont. 1.9 1.9 0.0 " 0.0 SOURCE: Multiple Regression Analysis-carried out by I.B.M. Computer 7044. measures of some of the factors that have been used. As an example of the la t t e r , better measures of the intercity time variable, to include ground travel time, undoubtedly would enhance the usefulness of the time factor. The other problem concerns lowering of the standard deviation of intercity t r a f f i c . I t - i s . apparent that-cities with the same population and economic function do not necessarily .behave i n a similar manner with 73 respect to t r a f f i c generation. Perhaps a breakdown of the cities into t r a f f i c generating cells would reduce the standard deviations to: a point where regression equations could be reliably used to predict t r a f f i c (see footnotes 3 and 4-) • In order to reduce this v a r i a b i l i t y between the actual t r a f f i c level and the computed t r a f f i c level values, the process of constrained regression could be applied.to the variables. In constrained regression, the mini-mization process i s subjected to a set of constraints which l i m i t the amount of v a r i a b i l i t y of the estimates that can be used i n minimizing the sum of squares. I f properly specified constraints are used, a more useful model for predictive purposes w i l l result. B. Validity of Method In this section two pertinent questions can be posed: (l) how good or reliable, i s the straight line f i t ? } and, (2) how much confidence should be placed upon a prediction..using, the straight line f i t ? An overall appraisal of the equation^ f i t to the data" indicates a relatively high degree of goodness of f i t (rho =• 0.76). However, the result must be viewed with extreme caution. Although the equation f i t s reasonably well for 76$ of the t r a f f i c occurrences, there i s a great deal of residual v a r i a b i l i t y present.in the-data (see Table 10). I t i s clear that the five variables do not explain a l l of the v a r i a b i l i t y i n intercity a i r travel. For example, the time and price variables incorporate several components, yet only the line haul portion of the total time and total price component i s considered. I t i s int u i t i v e l y plausible that the d i f -ferent components of the time variable, for example, have different degrees of influence on a i r demand. The equation does not attempt to measure any n differences i n weight to be attached to local travel time, to terminal delay time, or to line haul time. In using the formula to forecast the effect of major technological changes, consideration should be given to the assumption of constant el a s t i c i t y . A large change i n a i r travel price or a i r travel time w i l l undoubtedly result i n a change i n the elasticity. Reductions i n travel price or travel time can be expected to reduce the ela s t i c i t y . C Validity of the Hypothesis (a) Review of the Hypothesis In Chapter I , i t i s stated that an understanding of the nature of present and future a i r t r a f f i c enables the transportation planner to foresee the future spatial structure and Its general relationship to the inter c i t y transport network. The airport's role as a major generator of transport movements" i s often overlooked or underestimated by planners. A comparison can be drawn between airports and other terminals, such as those used for intercity r a i l operations. In ..the. same manner that these , v > . . . . terminals have influenced urban development i n the past, the airport i s and can be.expected to do so to a greater degree i n the future. Before the impact of the airport on the regional urban structure can be ascer-tained, i t i s necessary to establish the position and function of the a i r -port within the regional transportation infrastructure. In order to deter-mine the airport's position i n a region, i t i s necessary to know the pre-sent and future travel movements emanating from i t and terminating at i t . Therefore, i n order to determine the relative significance of selected factors upon Vancouver's intercity a i r travel, a hypothesis was formulated. INTERCITY AIR PASSENGER TRAFFIC IS INFLUENCED BY FOUR MAJOR 75 FACTORS: POPULATION, INTERCITY AIR DISTANCE, INTERCITY LINE TIME, AND INTERCITY LINE PRICE. THIS SET OF INDE-PENDENT VARIABLES CAN BE POSTULATED IN A MATHEMATICAL MODEL TO ADEQUATELY DESCRIBE AND FORECAST LEVELS OF INTERCITY AIR PASSENGER TRAFFIC. A description and review of a i r t r a f f i c forecasting methods i s carried out i n Chapter I I . Five methods are outlined including: the market analysis approach, the national income method, the city analysis technique, the econometric model, and the gravity model technique. The gravity model technique i s selected for emphasis. Chapter II presents a brief history of the- evolution of the gravity model as a device to predict t r a f f i c . I t has been shown hi s t o r i c a l l y that the gravity model i s a valid predictive device for use i n forecasting the gross t r a f f i c movements between two urban centres. Chapter I I I i s devoted to a discussion.of the significance of the gravity model to a i r t r a f f i c prediction. As generally conceived, the gravity model relates the influence of urban population and interurban distance to inter-c i t y a i r t r a f f i c movements. This traditional theory of gravitational interactance has been modified.,by a number of a i r transportation researchers. Multiple regression analysis i s the primary method of investigation i n each of these studies. The variables used, i n the hypothesis have been shown to have validity i n some United States c i t i e s . In Chapter IV linear regression analysis i s used t© obtain the rela-tive significance of each variable as an a i r t r a f f i c determinant. The va l i d i t y for inclusion of a .variable as a factor i n a i r t r a f f i c generation i s determined by the coefficient of correlation for that variable. The coefficients of correlation for the selected variables ranged from 0.76 to 0.85. This tends to indicate that the selected variables are valid components of the relationship. 76 Chapter V outlines the basic method of research used. The main techniques used include the gravity model and, the multiple regression analysis technique. By using these tools of analysis i n an iterative manner, several valid relationships have been established between a i r t r a f f i c and the selected variables. However, while these relationships are considered to be intuitively plausible, their validity i s affected by constraints placed upon them i n time, i n space, and i n data. From these relationships certain generalizations are possible. Conclusions from these generalizations are discussed i n the next section. (b) Conclusions Gravity models are useful i n examining the relationship between demographic factors, transport factors, and intercity a i r passenger t r a f f i c . On the basis of regression analysis most of the selected factors investi-gated are related to a i r passenger t r a f f i c . For example, intercity a i r t r a f f i c i s positively correlated with population (rho = 0.85) and with intercity line time (rho = 0.77). Distance proved to be a variably important factor. I t appears to influence a i r t r a f f i c i n a definite manner according to the population of the city. It. i s less of a resistive factor for travel involving large c i t i e s . Smaller ci t i e s exhibit more travel inhibiting f r i c t i o n (see Table 10). The time factor i s an important consideration in,.some cases. In particular, differences i n time resulting from different types of equip-ment may influence a traveller's decision. The apparent f r i c t i o n effect of distance for travel among smaller cities may only reflect the fact that slower aircraft are used to serve these small communities. I t i s possible that the, introduction of short haul j et aircraft w i l l eliminate 77 this difference. I t was thought that i f intercity line time instead of distance was used i n the P; P. equation, the deterring effect of intermediate stops might be accounted for. However, Tables 2 and 3 do not conclusively indicate that this i s the case. The use of total time i n the formula might, prove to be more meaningful than intercity line time. Because of the straight line relationship between t r a f f i c and the selected factors, i t seemed plausible that the resulting regression equa-tion could be used as a predictive formula to forecast intercity a i r t r a f f i c . This proved, however, to be feasible only i n certain cases, such as a i r travel among larger population centres. In many cases the standard deviations are low, and,, thus, predictions are reasonably accurate (see Table 10). For example, when annual predicted t r a f f i c i s within 20 percent of actual annual t r a f f i c , i t i s . accepted as a good projection. However, the relationships established here leave much of the a i r t r a f f i c v a r i a b i l i t y unexplained. Consequently, areas for further study are suggested i n the concluding portion of this thesis. P;> Recommendations for Further Study As well as the inadequacies, of the basic information necessary for a complete study of intercity a i r transport demand and i t s variations over time, definitive Information should be obtained relating to the purpose of a i r travel. A i r Canada and the Canadian National Railways are currently conducting a.joint survey to establish t r i p purposes i n the "Montreal-Toronto Transportation Corridor". Data regarding the loc a l travel time portion of intercity a i r trips 78 (particularly travel times to and from the a i r terminals) and terminal delay times also need to be extensively investigated. This necessitates a detailed study of the time and price variables i n order to determine whether the components of time and price contribute equally to a i r travel demand. I t i s possible, for example, that a reduction of 15 to 30 minutes i n transportation time to or from the terminal i s more important i n i t s Impact on a i r travel than a reduction of an hour i n line haul time. Similarly, the price of getting to and from terminals may be relatively more influential i n the travel decision than-the actual intercity price. Further study, then, should be carried out to determine the appropriate weights to be attached^to" the various components of a t r i p . The forecasts presented i n this thesis are based on a., single set of assumptions with respect to future developments i n the a i r transportation industry. I t would be beneficial to conduct further studies to determine the sensitivity of the forecasts to alternative assumptions and projections with respect to the selected variables. Within the scope of the above general limitations and problems, a series of direct recommendations for further investigation have been formulated. 1. Micro studies should be conducted i n a number of Canadian metro-politan regions to obtain a complete appreciation of metropolitan travel habits. These studies would consider local points or origination and destination, purposes of a i r travel, complete travel times and prices, and the relationship between choice of mode and price and quality of transportation services ( i e . time, transfer requirements, comfort, pres-6 l tige and location of terminal f a c i l i t i e s ) 2. Further analyses -should be undertaken to test the response of 79 e s t i m a t e d a i r t r a v e l vo lumes t o a w i d e r a n g e o f a l t e r n a t i v e a s s u m p t i o n s ( s i m u l a t i o n mode l ) w i t h r e s p e c t t o t h e s e l e c t e d v a r i a b l e s . I t s h o u l d be n o t e d t h a t t h e f o r e c a s t s o b t a i n e d - f r o m t h e r e l a t i o n s h i p s e s t a b l i s h e d h e r e a r e c o n d i t i o n a l . T h a t i s , t h e y depend upon c e r t a i n assumed v a l u e s b e i n g a s s i g n e d t o t h e v a r i a b l e s t o d e t e r m i n e t h e f o r e c a s t a i r t r a f f i c f l o w s . I t i s c l e a r t h a t t h e s e s t a t e m e n t s a b o u t t h e c a u s a l v a r i a b l e s a r e t h e m -s e l v e s c o n d i t i o n a l and s u b j e c t t o u n c e r t a i n t y . I f t h e s e u n d e r l y i n g t i m e and p r i c e r e l a t i o n s h i p s were m o d i f i e d ( s e e J T a b l e s 8 and 9 ) , i t w o u l d be u s e f u l t o d e t e r m i n e t h e i r i m p a c t on a i r t r a v e l demand. 3 . F u r t h e r d a t a s h o u l d be c o l l e c t e d r e g a r d i n g t h e s e p a r a t i o n o f s e r v i c e c l a s s e s (economy, f i r s t c l a s s , t o u r i s t , r e d , w h i t e and b l u e f a r e s , and so on) b y common c a r r i e r . T h i s s h o u l d be done f o r a l l common c a r r i e r s s o t h a t d i r e c t i n t e r m o d a l c o m p a r i s o n s c o u l d be made w i t h t r a v e l p r i c e s . 4. F u r t h e r a n a l y s i s s h o u l d be p e r f o r m e d on t h e r e s i d u a l s o f t h e r e g r e s s i o n e s t i m a t e s . D u r i n g t h e c o u r s e o f t h i s t h e s i s , i t was n o t p o s -s i b l e t o a n a l y z e t h e r e s i d u a l s o f t h e r e g r e s s i o n a n a l y s i s . F u r t h e r e x -a m i n a t i o n o f t h e s e r e s i d u a l s may r e v e a l n o n - l i n e a r i t i e s w h i c h may i m p r o v e t h e f o r e c a s t i n g a b i l i t y o f t h e r e l a t i o n s h i p . 5 . - A s t u d y s h o u l d be c o n d u c t e d t o d e t e r m i n e t h e i m p a c t t h a t f a s t i n t e r c i t y r a i l s e r v i c e s h a v e on a i r t r a v e l demand. T h i s s u r v e y I s n o t c r u c i a l p r e s e n t l y a t V a n c o u v e r . I t w o u l d be more r e l e v a n t l y a p p l i e d t o t h e h i g h d e n s i t y " M o n t r e a l - T o r o n t o T r a n s p o r t a t i o n C o r r i d o r " where t h e C a n a d i a n N a t i o n a l R a i l w a y s i s i n t r o d u c i n g f r e q u e n t non s t o p " T u r b o - T r a i n s " i n J u l y , 1 9 6 7 . 6 . Some a u t h o r i t i e s b e l i e v e t h a t t h e new T r a n s p o r t a t i o n Commi s s i on f o r Canada w i l l p r o v i d e u s w i t h a n o p e r a t i v e F e d e r a l T r a n s p o r t a t i o n P o l i c y . T h i s p o l i c y s h o u l d i n c l u d e n a t i o n a l o b j e c t i v e s t o g u i d e t h e deve l opment o f 80 the various modes within an integrated network, where each mode w i l l u t i l i z e i t s inherent advantages. The P o l i c y undoubtedly w i l l a l t e r the a l l o c a t i o n of the service areas f o r each means of transport. I t would be b e n e f i c i a l to determine the r e l a t i v e p o s i t i o n (threshold) r e g i o n a l l y o f each mode within t h i s integrated transportation network. 7. This study has b r i e f l y analyzed the transport variables of p r i c e and time which influence the l e v e l of a i r t r a f f i c a t Vancouver. Further research should be conducted to e s t a b l i s h the importance of the difference between a i r f a r e and the cost of competitive surface transportation. I n other words, when w i l l people pay more to t r a v e l by air ? Perhaps only when the time and inconvenience of a t r i p by surface transportation exacts a greater p r i c e from the t r a v e l l e r than the di f f e r e n c e i n f a r e s . This suggests a r e l a t i o n s h i p between the p r i c e o f t r a v e l by two competitive c a r r i e r s compared with the di f f e r e n c e i n t h e i r i n t e r c i t y t r a v e l times. 8. Further studies should be conducted to determine the v a r i a t i o n i n i n t e r c i t y a i r t r a v e l between c i t i e s performing d i f f e r e n t s e r v i c e func-. 6 2 t l o n s ( i e . marketing,-manufacturing, i n s t i t u t i o n a l ; 9. The ultimate objective of students of transportation planning should be to develop a computer model o f the nation's transportation system. I d e a l l y , one. would then be able to feed the computer, data, regarding economic, demographic, and s p a t i a l c h a r a c t e r i s t i c s of c i t i e s , operating costs of equipment,; i n t e r c i t y t r a v e l times by mode, i n order to obtain information concerning predicted i n t e r c i t y a i r t r a f f i c , , type of equipment needed, schedules, and other pertinent output information. The formula f o r p r e d i c t i n g i n t e r c i t y a i r t r a f f i c , then, would form one of the-many subroutines of the computer model. si FOOTNOTES 57 Canada, A i r Transport Board, A i r l i n e Passenger Origin and Destination  S t a t i s t i c s - Domestic Report f (Ottawa: The Board, 1965), p. 84. 58 For a micro study of the industry, the exact o r i g i n and destination of each passenger could be obtained from a i r l i n e t i c k e t and reservation information. 59 Canada to the best of my knowledge does not have a c l a s s i f i c a t i o n of i t s c i t i e s according to t h e i r function. Chauncy Harris c l a s s i f i e s United States c i t i e s as follows: Manufacturing, R e t a i l , D i v e r s i f i e d , Wholesale, Transportation, Mining, University, Resort and Governmental. Source: Chauncy H a r r i s , "A Functional C l a s s i f i c a t i o n of C i t i e s i n the United States". Geographical Review. XXXIII, 19-42, p. 88. A more recent service c l a s s i f i c a t i o n of c i t i e s i n the United States has been prepared by Howard Nelson* Howard J . Nelson,. "A Service C l a s s i f i c a t i o n of American C i t i e s " , Economic Geography. XXXI, J u l y , 1955,, p.. 189. A s i m i l a r urban c l a s s i f i c a t i o n should be prepared f o r Canadian c i t i e s . 60 Dr. T. Heaver of the Commerce Department, University of B r i t i s h Columbia, i s currently conducting a micro study of t h i s type at Vancouver. He has divided- the Metropolitan Vancouver region into a number of c e l l s i n order to determine the a i r t r a v e l propensity f o r each of these c e l l u l a r structures. 61 See footnote #4. 62 See footnote #3. BIBLIOGHAPfll 83 A. BOOKS Brewer, S. H„, B r i t i s h Columbia's Needs f o r a United Regional A i r Transport  Systemi Vancouver; University of B r i t i s h Columbia, Faculty of Commerce and business Administration, 1965. Carey, H. 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Whitacker, J . R., "Regional Interdependence", Journal of Geography. 31 (1932), pp. 164 - 165. Zipf, P., "The P1P2/D Hypothesis: On the Intercity Movement of Persons", American Sociological Review. 11 (194-8), pp. 677 - 686. Zipf, G. K., "The P1P2/D Hypothesis: The Case of Railway Express", Journal of Psychology. 22 (July, 1946), pp. 3 ^ 8 . C. GOVERNMENT PUBLICATIONS Atlanta Metropolitan Planning Commission, Airport Area Survey Memorandum  of Recommendations: A Study of Tr a f f i c Improvement Needs i n the  Communities Near the Atlanta Municipal Airport. Atlanta: The Commission, I960. Canada, A i r Transport Board, Ajriine,.Passenger Origin and Destination Statistics — Domestic Report. Ottawa: The Board, 1965. International A i r Transport Association (I.A.T.A.), Symposium on Super- sonic A i r Transport. 14th Technical Conference, A p r i l 17 - 21, 1961, Montreal: 1961. O f f i c i a l A i r l i n e Guide. New York City: American Aviation Publications, July, 1966. 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Department of Commerce, Civil Aeronautics Administration, The Gravity  Model as a Predictive Device for Air Passenger Traffic. WashingtonJ C i v i l Aeronautics Administration, July, 194-3. D. TRANSPORTATION BIBLIOGRAPHIES Blaisdell, R. P., Sources of Information in Transportation. Evanston: Northwestern University Transportation Center Press, 1964. Northwestern University. Current Literature in Traffic and Transportation.  April f 1958 — - — T Evanston:- Illinois],"Northwestern University Transportation Center, (semi-monthly). Siddall, W. R., Transportation Geography A Bibliography. Manhattan: Kansas State University Press, 1964. Wolfe, R. I., An Annotated Bibliography of the Geography of Transportation, unpublished, Octoberj 1961. E. UNPUBLISHED Garrison, W. L., and Tobler, W., The Location of Transportation Routes: Connections Between Two Points. (Portion of an unpublished report: "Transportation Geography Study", by the Transportation Center at Northwestern University for the U. S. Army Research Command). Garrison, W. L., and Marble, D., The Structure of Transportation Networks. (Portion of an unpublished report by the Transportation Center at Northwestern University for the U. S. Army Research Command). Oebm, P. F., The Air Passenger Hinterland of Cincinnati. Ohio. (Unpublished Masters thesis, Department of Geography, University of Cincinnati, Cincinnati, 1966). Watson, J. D., Airline Pricing in Canada. (Unpublished paper, Vancouver, August, 1965). F. CORRESPONDENCE Letter to the Author from Mr. J. M. Robbins, Chief, Planning and Development, Pacific Western Airlines, Vancouver, dated November 2, 1966. Letter to the Author from Miss Marjorie Windeler, Operations Research, Air „Canada, Montreal, dated January 5, 1967. 90 L e t t e r to the Author from Mr. R. H. Bradley, Chief, A v i a t i o n S t a t i s t i c s Centre, A i r Transport Board, Ottawa, dated January 3, 1967. L e t t e r to the Author from Mr* W. B. Statton, Sales Analyst, Canadian P a c i f i c A i r l i n e s , Vancouver, dated November 14, 1966. APPENDICES APPENDIX A Correlation between Intercity Travel Price and A i r Passenger Traffic r.= 0.76 TRAFFIC AND PRICE 93 Y*, (I) X2 XY REFERENCE CITY AIR TRAFFIC PRICE (Thousands) ($100»s) 1 Toronto 37.9 1,436.4 l o l 1.2 41.7 2.. Calgary 31.4 985.9 .3 .1 9.4 3 Edmonton 28.9 829.2.. a .1 8.5 4 Victoria 24.1 580.8 . i .01 2.4 5 Winnipeg 18.7 349.7 .6 .4. 11.2 6 Montreal 17.1 292.4 1.2 1.4 20.5 7 Prince George 15.2 230.0 .4 .2 6.1 8 Prince Rupert 13.8 190.4 .2 5.5 9 Port Hardy 12.7 163.3 .3 .1 3.8 10 Powell River 10.1 102.0 .1 .01 1.0 11 Terrace-Kitimat 8.3 68.9 .4 .2- 2.5 12 Castlegar 7.5 56.3 .2 .04 1.5 13 Kelowna 7.3 53.3 .2 .04 ,1.5 14 Sandspit 7.0 49.0 .4 .2 '2.8 15 Regina 5.9 34.8 .6 .4 3.5 16 Penticton 5.8 33.6 .2 .04 1.2 17 Ottawa 5.7 32.5 1.2 1.4 6.8 18 Fort St. John 4.0 16.0 .5 .3 2.0 19 Saskatoon 3.9 15.2 .6 .4 2.3 20 Campbell River 3.8 14.4 .1 .01 .4 21 Kamloops 3.7 13.7 .2 .04 .7 22 Cranbrook 3.6 12.7 .3 .1 1.1 23 Whitehorse 3;4 11.6 .8 .7 2.7 24- Comox 2.6 7.4 .1 .01 .3 25 London 1.9 3.6 1.1 1.2 ' 2.1 (Y2 :;: (xY = 284i3 = 5,583.1 = 11.7 - 9.0 = 141.5 I = 11.4 X = 0.5 xy -< x 2 -£xY - X-^ Y 141.5 - 0.5 x 284.3 -0.7 ix2 - xCx 9.0 - 0.5 x 11.7 9.0 - 5.6 ir2 = £ Y 2 - Y £ Y = 5,583.1 - 11.4 x 284.3 = 2.346.1 - ^xy = -0.7 - -0.2 &2 3.4 a = Y - bX = 11.4 - (-0.2 x 0.5) = 11.4 - (-0.1) = 11.4 + 0.1 1^1^ 5 Ye = a +• bX = 11.5 + (-0.2)X Yc - 11.5 - 0.2XY 94 CITY X • PRICE (| - Hundreds) Y AIR TRAFFIC (Thousands) Yc Yc 2 1 Toronto 1.1 37.9 11.3 127.7 2 Galgary .3 31.4 11.4- 129.7 3 Edmonton .3 28.9 11.4 129.7 4 Victoria .1 24:1 11.5 132.3 5 Winnipeg .6 18.7 11.4 129.7 6 Montreal 1.2 17.1 11.3 127.7 7 Prince George .4 15.2 11.4 129.7 8 Prince Rupert •4 13.8 11.4. 129.7 9 Port Hardy- .3 12.7 11.4 129.7 10 Powell River .1 10.1 11.5 132.3 11 Terrace-Kitimat .4 8.3 11.4 129.7 12 Castlegar ' .2 7.5 11.5 132.3 13 Kelowna .2 7.3 11.5 132.3 U Sandspit .4 7.0 11.4 129.7 15 Ottawa .6 5.9 11.4 129.7 16 Regina .2 5.8 11.5 132.3 17 Penticton 1.2 5.7 11.3 127.7 18 Saskatoon .5 4.0 11.4 129.7 19 Campbell River .6 3.9 11.4 129.7 20 Fort St. John .1 3.8 11.5 132.3 21 Cranbrook .2 3.7 11.5 132.3 22 Kamloops .3 3.6 11.4 129.7 23 Whitehorse .8 3.4 11.3 127.7 24 Comox .1 2.6 11.5 132.3 25 London 1.1 1.9 11.3 127.7 r c KYc 2" f?i255;3 5,583.1 - /0.583 = 0.76 Yc APPENDIX B Correlation between Intercity Airline Time and Ai r Passenger Traffic r r 0.77 96 TRAFFIC AND TIME (Y) Y 2 (X) x 2 XY REFERENCE-CITY AIR TRAFFIC TIME (Thousands) ,(Hours) 1 Toronto 37.9 1,436.4 4.1 16.8- 155.4 2 Calgary 31.4 985.9 1.1 1.2 34.5 .3 Edmonton 28.9 829.2 1.3 1.7 37.7 4 Victoria 24.:1 580.8 0.4 0*2 9.6 5 Winnipeg 18.7 349.7 2.5 6.3 46.8 6 Montreal 17.1 29214 5.3 28.1 90*6 7 Prince George 15.2 230*0 1.9 3.6 28.9 8 Prince Rupert 13.8 190.4 2;5 6.3 24.5 9 Port Hardy 12.7 163.3 '1.3 1.7 16". 5 10 Powell River --10.1 102.0 0.8 0:6 8.1 11 T erraee-Kitimat 8*3 68.9 2.3 5.3 19.1 12 Castlegar 7.5 56.3 2.0 4.0 15.0 13 Kelowna- 7.3 53.-3 1.0 1.0 7.3 14 Sandspit 7.0 49.0 2.3 5.3 16*1 15 Ottawa 5.9 32.5 6.3 39.7 37.2 16 Regina 5.8 34.8 3.1 9.6 18.0 17 Penticton 5.7 33.6 1.0 1.0 5.7 18 Saskatoon 4..0 15.2 3.5 12.3 14.0 19 Campbell River 3.9 14-4 0.8 0.6 3.1 20 Fort St. John 3.8 16.0 3:2 10.2 12.2 21 Cranbrook 3.7 12.7 3.0 9.0 11*1 22 Kamloops 3,.6 13.7 1.0 1.0 3.6 23 Whitehorse 3.4 11.6 6.5 42.3 21.1 24 Comox 2.6 7.4 0.8 0*6 2.1 25 London 1.9 3.6 6.1 37.2 11.6 <y2 U (x 2 X^Y . - 284.3 = 5,583.1 _-63.1 = 245.6 = 649.8 Y = 11.4 X = 2,5 ^xy = £xY - X^Y b - 649.8 - 2.5 x 284.3 = - 60.8 ' — a ^ x 2 - ^ X 2 - X^X = 245.6 - 2.5 x 63.1 ^ y 2 -^Y 2 - Y^Y ;-= 5,583.1 - 11.4 x 284.3 Y ~ 2,346.1 y c =• £xy = -60.8 - -0.7 * x 2 8 7 ' 8 - Y - bX • - 11.4 - (-0.7 x 2.5) ^ 11.4 - (-1.8) = 11.4 + 1.8 ^13,2 = a-+- bX • " = 13.2 + (-0.7)X = 13.2 - 0.7X 97 CITY X TIME (Hours) I AIR TRAFFIC (Thousands) Yc Y c 2 1 Toronto A.l 37.9 10.3 106.1 2 Calgary 1.1 31.4 12.5 156.3 3 Edmonton 1.3. . 28.9 12.3 151.3 4 Vi c t o r i a 0.4. """24.1 12~9 166^ 4 5 Winnipeg 2.5 18.7 11.4 129.9 6 Montreal 5.3 17.1 9.5 90.1 7 Prince George 1.9 15.2 11.9 141.6 8 Prince Rupert 2.5 13.8 11.4 129.9 9 Port Hardy 1.3 12.7 12,1 146.4 10 Powell River 0;8 10.1 12,8 I64.O 11 T errace-Kitimat 2.3 8.3 11.6 134.6 12 Castlegar 2.0 7.5 11.8 139.2 13 Kelowna 1.0 7.3 12.5 156.3 14 Sandspit 2.3 7.0 11.6 134.6 15 Ottawa 6.3 5.9 8.8 77.4 16 Regina 3.1 5.8 11.0 121.0 17 Penticton 1.0 5.7 12.5 156.3 18 Saskatoon 3.5 4.0 10.7 114.5 19 Campbell River 0;8 3.9 12.8 I64.O 20 Fort St. John *" 3.2 3.8 11.0 121.0 21 Cranbrook 3.0 3.7 11.1 123.2 22 Kamloops 1.0 3.6 12.5 156.3 23 Whitehorse 6.5 3i4 8.6 74.0 24 Comox 0.8 2.6 12.8 I64.O 25 London 6.1 1.9 8.9 79.3 = 3,297.1 r ~ 3,297.1 = 5,583.1 '0.591 = 0.77 APPENDIX G CorrelationJbetwe'em Linear Distance and A i r Passenger Tr a f f i c r - 0.65 99 (Y) Y 2 (X) X 2 XY REFERENCE CITY AIR TRAFFIC DISTANCE (Thousands) (Miles - 100's) 1 New York City 51 2,601 5.7 32.5 '290.7 2 Chicago 36 1,296 2.5 6.3 90.05 3 Miami 14 196 9.5 90.3 133.0 ,4 Cleveland 12 144 2.2 4.8 26.4 5 Detroit 11 121 2.4 5.8 26.4 ;, 6 Washington 1 10 100 4.0 16.0 40.0 7 Los Angeles 9 81 18.9 357.2 170.1 8 Boston - 8 64 7.48 54.8 59.2 9 Pittsburg 8 64 2.66 6.8 20.8 10 Philadelphia 8 64 5.0 25.0 40.0 11 St. Louis 7 49 3.18 9.6 21.7 12 Atlanta 7 49 3.7 13.7 25.9 13 Tampa : 6 36 7.8 60.8 46.8 14 San Francisco 6 36 20.49 416.6- 122.4 15 Louisville 5 25 0.9 0.8 4.5 16 Kansas City 3 9 5.4 29.2 16.2 17 Dallas 3 9 8.1 65.6 24.3 18 Charleston 3 9 1.6 2.5 4-8 19 Minneapolis 3 9 6.1 37.2 18.3 20 Nashville 3 9 2.4 5.8 : 7.2 21 New Orleans 2 4 7.1 50.4 14.2 22 Indianapolis 2 : 4 l;0 1.0 2.06 23 Milwaukee 2 4 3.2 10.2 6.4 24 Hartford 2 4 6.5 42.3 13.0 25 Columbus 2 4 1.0 1.0 2.0 ^Y = 224 d 2 ••: ^X « 120.1 ^XY Y = 9.0 = 4,992 X =4.8 - 1,357.7 =•1,141.3 £xy (xi - X^Y » 1,141.3 - 4.8 x 224 ^ 66.1 ^ x 2 (x2.- xCx ~ 1,357.7 - 4.8 x 120.1 = 781.2* ^ y 2 ^ ^ 2 - - Y C Y = 4,992.0 - 9.0 x 224 = 2n976.0 t> - im = 66.i = o.i 781.2, a = I - bX = 9.0 - 0.1 x 4.8 a - i y Yc » a + bX Yc = 8;5 + 0.1X r = 2,103 4,992 = /.421 = 0.65 APPENDIX D Correlation between City Population and A i r Passenger Traffic r = 0.85 101 (Y) Y 2 (X) X 2 XY REFERENCE CITY AIR TRAFFIC POPULATION (Thousands) (Millions) 1 New.York C i t y 51 2,601 10.5 110.3 535.5 2 Chicago 36 1,296 6.2 38".r 233.2 3 Miami 14 196 0.9 0.8 12.6 4 Cleveland 12 144- 1.8 3.2 21.6 5 Detroit 11 122 3.8 14.4 41.8 6 Washington 10 100 0:8 0.6 8.0 7 Los Angeles 9 81 6.7 44-9 6.1 8 Boston 8 64 2.6 6.8 20.8 9 Pittsburg 8 64 2.4 5.8 19.2 10 Philadelphia 8 64 3.6 12.9 28.8 11 S t . Louis 7 49 1.6 2.6 11.2 12 Ottawa 7 49 1*0 1.0 7.0 13 -Tampa 6 36 0*7 o;5 4.2 14 San Francisco 6 36 2.8 7.6 16.8 15 L o u i s v i l l e 5 25 0.'6 0.4 3.0 16 Kansas C i t y 3 9 0.7 0.5 2.1 17 Dallas 3 9 1.1 1.2 3.6 18 Charleston 3 9 0.3 0.1 0.9 19 Minneapolis 3 9 1.5 2.3 4.5 20 Nashville 3 9 0.4 0.2 1.2 21 New Orleans 2 4 0.9 0.8 1.8 22 Indianapolis 2 4 0.7 0.5 1.4 23 Milwaukee 2 4 1.2 1.4 2.4 24. Hartford 2 4 0.5 0.3 1.0 25 Columbus : '2 4 0.7 - 0.5 1*4 = 224 (Y2 (x = 54.0 (*• ^XY 1 = 9.0 = 4,992 X ~ 2.2 =-_269.2 = 989.1 (xi - X^Y 989.1 - 2.2 x 224 xy = * x 2 = < X 2 - X ^ X = 269.2 - 2.2 x 54.0 = 150.4 b 5 a -a ~ Cx 2 492.8 = 3.3 150.4 Y - bX • • 9.0 - 3.3 x 2.2 1.7 = ^ Y 2 - f ^ Y - 4,992 ^ 9.0 x 224 = 2,976.0 Yc r a f bX Yc * 1.7 +• 3.3X 102 CITY •I1 POPULATION (Millions) Y AIR TRAFFIC (Thousands) Yc Yc 2 Y Yc 1 New York City 10.5 51 36 1,296 15 2. Chicago 6.2 36 22 484 U 3 Miami 0.9 14 5 25 9 4 Cleveland 1.8 12 8 64 4 5 Detroit 3.8 11 24 576 - 13 6 Washington 0.8 10 4 16 6 7 Los Angeles 6.7 9 24 576 - 15 8 Boston 2.6 8 10 100 *- 2 9 Pittsburg 2.4 8 10 100 - 2 10.Philadelphia 3.6 8 u 196 - 6 11 St. Louis 1.6 7 7 49 12 Atlanta 1,0 7 5 25 2 13 Tampa 0.7 6 4 16 - 2> 14, San Francisco 2.8 6 11 121 - .-5:-15 Louisville 0.6 5 4 16 1 16 Kansas City 0.7 3 4 16 - 1 17 Dallas 1.1 3 5 25 - 2 18 Charleston 0.3 3 3 9 19 Minneapolis 1.5 3 7 49 - 4 20 Nashville 0.4- 3 3 9 21 New Orleans 0.9 2 5 25 - 3 22 Indianapolis 0.7 2 4 16 - 2 23 Milwaukee 1.2 2 6 36 - 4 24 Hartford 0.5 2 3 9 - 1 25 Columbus 0.7 2 4 16 - 2 *Yc 2 = 3,862 APPENDIX E Correlation between City Population and A i r Passenger Traffic 104 (Base C i t y — Vancouver — 884,000 population) REFERENCE CITY 1966 METRO POPULATION i n Thousands (a) ACTUAL 1965 AIR TRAFFIC i n Thousands (b) 1 Toronto 2,145 37.9 2 Calgary 328 31.4 3 Edmonton 399 28.9 4 Victoria 172 24.1 5 Winnipeg 505 18.7 6 Montreal 2*419 17.1 7 Prince George 24 15.2 8 Prince Rupert 14- 13.8 9 Port Hardy 1 12.7 10 Powell River 12 10.1 11 Terrace-Kitimat 18 8.3 12 Castlegar 3 7.5 13 Kelowna 17 7.3 14' Sandspit 19 7.0 15 Ottawa 489 . 5.9 16 Regina 131 5.9 17 Penticton 15 5.B 18 Saskatoon 115 4.0 19 Campbell River 3 4.0 20 Fort St. John 7 3.9 21 Granbrook 8 3.7 22 Kamloops 11 3.6 23 Whit'ehorse 4 3.4 24 Comox 3 2.6 25 London 207 1.9 (a) SOURCE: D.B.S.f 1966. (b) SOURCE: A i r Transport Board. Airline Passenger Origin and Destination Statistics. Domestic Report. 1965. APPENDIX F Distribution of Labour Force and, ... . . . . ',\ Business Trips Per Employee by Industry Category 195© and i960 106 DISTRIBUTION OF LABOUR FORCE AND BUSINESS TRIPS PER EMPLOYEE BY INDUSTRY CATEGORY 1950 AND i960 PERCENT OF TOTAL NUMBER OF INDUSTRY CATEGORY LABOUR FORCE BUSINESS TRIPS PER EMPLOYEE 1950 I960 Wholesale and Retail 18.90$ 19.01$ 1.78 Professional Services 8.68 12^21 1.71 Business Services. 0.65 1.23 1.63 Government Services 4.53 5L.17 1.11 Transportation, Communication and U t i l i t i e s 8.00 7.19 1.10 Mining 1.68 1.65 1.07 42.44$ 45.86$ Construction 6.22 6.15 0.92 Finance and Insurance 3.45 4.35 0.87 Manufacturing (except Printing and Publishing) 24.86 26.39 0.57 Repair Services 1.71 1.37 0.56 Amusement and Recreation 0.88 0.81 0.43 Printing and Publishing 1.55 I.84 0.45 Agriculture,. Forestry and Fishing 12.65 7.01 0.20 ^Personal Services 6.24 6.22 0.17 57.56$ 54.14$ I960 ..... . 1*004. SOURCE: Computed from data reported i n the i960 survey of the Survey Research Centre^ University of Michigan, Ann Arbor. APPENDIX G Rail Competition provided by-Canadian. National Railways and Canadian Pacific Railway between Vancouver and Selected Points (May 1, 1967) 108 RAIL COMPETITION PROVIDED BY CANADIAN NATIONAL RAILWAYS AND' CANADIAN PACIFIC RAILWAY BETWEEN VANCOUVER AND SELECTED POINTS (May 1, 1967) DAILY NUMBER AVERAGE DAILY C.N. C.P.R. ELAPSED OF TRAINS NUMBER FARE FARE TIME DEPARTING TO OF PASSENGERS (a) (b) (in Hours) (c) Edmonton 3 #18.00 #21.00 22 Calgary 2 21.00 25 Saskatoon 3 23.00 28 Regina 2 25.00 28.50 31 Winnipeg 5 29.00 34.00 38 Toronto 5 48.00 52.50 . 67 Montreal 5 50.00 55.00 70 I t i s not possible to- obtain the actual number of passengers entraining at Vancouver for each of the selected destination points. However, both G.N. and CP. Railways are able to provide the approximate total number of persons boarding eastbound trains at Vancouver seasonally as follows: C.N. C.P.R. TOTAL Winter 150 - 300 75 - 125 225 - 425 Summer 400 - 500 275 - 325 675 - 825 (a) The C.N. fare used i s the White Fare i n effect i n May and June, 1967. (b) The C.P.R. fare used i s that i n effect i n May, 1967. (e) The elapsed travel times are obtained from the public CN. and C.P.R. passenger time-tables effective on A p r i l 30, 1967. APPENDIX H Derivation of Equation 6.4- + 4-.7X - 0.07X - 0. 110 DERIVATION OF EQUATION Yc ^  6.4 4.7X - 0.07Y - 0,22 BY MEANS OF SIMULTANEOUS EQUATIONS (1) Yc * -5.5 + U.1X (2) Yc = 11.5 - 0.2Y (3) Yc = 13.2 - 0.7Z Total ..... 3Yc = 19.2. + M-IX - 0.2Y - 0.72 Yc = 19.2 U.1X - 0.2Y - 0.72 3 - 6.4 •+" 4,7X - 0.07Y - 0i22 Therefore, equation U) Yc = 6.4 » 4.7X - Q.07Y - 0.22 

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