UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Dynamic programming model for selection of optimum logging road surface Jolliffe, Harold A 1976

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1976_A6 J64.pdf [ 3.57MB ]
Metadata
JSON: 831-1.0100111.json
JSON-LD: 831-1.0100111-ld.json
RDF/XML (Pretty): 831-1.0100111-rdf.xml
RDF/JSON: 831-1.0100111-rdf.json
Turtle: 831-1.0100111-turtle.txt
N-Triples: 831-1.0100111-rdf-ntriples.txt
Original Record: 831-1.0100111-source.json
Full Text
831-1.0100111-fulltext.txt
Citation
831-1.0100111.ris

Full Text

A DYNAMIC PROGRAMMING MODEL FOR SELECTION OF OPTIMUM LOGGING ROAD SURFACE by HAROLD A . JOLLIFFE B . S . F . , 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 , 1968 A THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY i n THE FACULTY OF FORESTRY We a c c e p t t h i s t h e s i s as c o n f o r m i n g to t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA Sep tember , 1976 (5) Harold A l f r e d J o l l i f f e , 1976 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my Department or h i s representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Faculty of Forestry The University of B r i t i s h Columbia Vancouver, B.C Canada ABSTRACT The s e l e c t i o n of optimum road surfacing f o r logging roads i s studied. A dynamic program model that simulates d i f f e r e n t road surfaces, over the length of the road, i s developed to a r r i v e at the optimum combination of road surfaces. The model simulates the t r a v e l , of up to three d i f f e r e n t v e h i c l e types over the road. The ph y s i c a l c h a r a c t e r i s t i c s of the road, the road surface and the vehicles are used to determine t r a v e l speeds. Travel speed and ve h i c l e operating costs are used to f i n d v e h i c l e costs r e l a t i v e to the road surface. These costs are combined with surface construction and maintenance costs to f i n d the optimum combination of surfaces. Testing of the model revealed that volume of wood was of l e s s importance than road gradient i n the determination of the optimum combination of road surfaces. ) - i i -TABLE OF CONTENTS Page ABSTRACT i TABLE OF CONTENTS . • i i L I S T OF TABLES i v L I S T OF FIGURES . . . . . v ACKNOWLEDGMENTS v i CHAPTER I INTRODUCTION 1 1.1 Road s t a n d a r d and s u r f a c e s e l e c t i o n . . . . 1 1.2 A n o t h e r a p p r o a c h t o the p r o b l e m . . . . . 2 1.3 O b j e c t i v e s o f t h e s t u d y . . . . . . 3 CHAPTER I I DYNAMIC PROGRAMMING MODEL 4 2 . 1 G e n e r a l dynamic p rog ramming f o r m u l a t i o n . . . 4 2 . 2 I n t r o d u c t i o n o f r o a d s u r f a c i n g p r o b l e m . . . 5 2 . 3 F o r m u l a t i o n o f r o a d s u r f a c i n g p r o b l e m . . . 6 2 . 4 Comments on t h e s t a t e o f t h e s y s t e m . . . . 7 CHAPTER I I I COST CALCULATIONS AND VARIABLES 11 3 . 1 C o n s t r u c t i o n and M a i n t e n a n c e c o s t s . . . . 11 3 . 2 V e h i c l e o p e r a t i n g , t i r e and m a i n t e n a n c e c o s t s . . 11 3 . 3 V e h i c l e s u r f a c e , and a l i g n m e n t v a r i a b l e s . . . 12 CHAPTER I V PROGRAMMING THE MODEL ! 4 4 . 1 G e n e r a l a s s u m p t i o n . . . . . . . 14 4 . 2 Computer P r o g r a m . . . . . . . . 14 4 . 3 Speed f u n c t i o n s . . . . . . . . 15 4 . 3 . 1 Maximum s a f e c u r v e speed . . . . . 15 4 . 3 . 2 Maximum s a f e s p e e d f o r s t o p p i n g . . . 15 4 . 3 . 3 Maximum s a f e speed o f d e s c e n t . . . . 21 4 . 3 . 4 Maximum a v a i l a b l e s p e e d o f v e h i c l e . . . 21 4 . 3 . 5 S o l u t i o n o f c u b i c r e l a t i o n s h i p s . . . 21 4 . 4 P r o g r a m o u t p u t . . . . . . . . 21 CHAPTER V MODEL RESULTS 2 3 5 . 1 H y p o t h e t i c a l p r o b l e m . . . . . . . 23 - i i i -5 . 2 L e n g t h o f m i n o r s e c t i o n s 5 . 3 S i g n i f i c a n t r e s u l t s 5 . 4 I m p o r t a n c e o f number o f v e h i c l e s 5 . 5 C h a n g i n g s u r f a c e s a l o n g t h e r o a d CHAPTER V I DISCUSSION AND CONCLUSIONS 6 . 1 A r e a s o f f u r t h e r i n v e s t i g a t i o n 6 . 2 C o n c l u s i o n . BIBLIOGRAPHY . APPENDIX 1 Maximum s a f e c u r v e speed . APPENDIX 2 Maximum s a f e s p e e d f o r s t o p p i n g APPENDIX 3 Maximum s a f e speed o f d e s c e n t . APPENDIX 4 Maximum a v a i l a b l e s p e e d o f v e h i c l e APPENDIX 5 S o l u t i o n o f c u b i c e q u a t i o n APPENDIX 6 The compute r p r o g r a m APPENDIX 7 Sample o f a p r o g r a m o u t p u t APPENDIX 8 D a t a f o r h y p o t h e t i c a l p r o b l e m . - i v -LIST OF TABLES TABLE I Vehicle variables TABLE II Surface variables TABLE I I I Alignment variables LIST OF FIGURES FIGURE 211 Generation of states i n s i m p l i f i e d problem FIGURE 4.1 Flow diagram of the program . . . . FIGURE 5.1 E f f e c t of t r a f f i c density and grade on optimum surface . . . . . . . . FIGURE A l . l Cross-^section of v e h i c l e i n tipp i n g condition on superelevated curve . . . . . FIGURE Al.2 Cross-section of vehi c l e i n s l i p p i n g condition on a superelevated curve . . . . - v i -ACKNOWLEDGEMENTS I wish to express my gratitude to Assistant Professor G.G. Young, Faculty of Forestry, who as s i s t e d i n the formulation of the problem and under whose d i r e c t i o n t h i s study was undertaken. His assistance and constructive c r i t i c i s m were of great be n e f i t . The thesis was reviewed by Dr. D.D. Munro, and by Dr. D. Haley. Their comments and suggestions were greatly appreciated. F i n a n c i a l assistance was granted the author i n the form of teaching assistantships by the University of B r i t i s h Columbia. - 1 -CHAPTER I INTRODUCTION 1.1 Road standard and surface s e l e c t i o n A road standard states the l i m i t s placed on alignment and other p h y s i c a l c h a r a c t e r i s t i c s of a road, including surfacing, and usually s p e c i f i e s the design speed. The s e l e c t i o n of the optimum road standard for a logging road involves the accounting f o r , and estimation of a l l factors that have a bearing on costs. This i s generally accomplished by the estimation of unit costs f o r , hauling, construction and maintenance, and the estimation of the t o t a l volume to be hauled over the road. The costs estimated r e l a t e to average phy s i c a l c h a r a c t e r i s t i c s of the road, and do not vary with alignment within a standard s p e c i f i e d . There i s always a unique standard that produces lowest cost on a section of road where the volume of wood to be transported i s constant. A higher standard would be optimum only i f there i s an increase i n volume, which r e s u l t s i n a lower t o t a l cost per unit. This w i l l occur i f the hauling cost per unit i s decreased enough to j u s t i f y the increase i n construction and maintenance cost required f o r the higher standard. The road surface i s s p e c i f i e d by the road standard, thus, the s e l e c t i o n of road standard r e s u l t s i n the surface also being selected, and there being a unique surface i f volume i s constant. The decision to upgrade the surface on an e x i s t i n g road i s generally made on the basis of a t o t a l cost a n a l y s i s . To determine what portion of the en t i r e road should be upgraded the road i s divided into sections dependent on volume of wood to be transported. For example, a - 2 -mainline road would be divided into sections having the lengths equal to the distances between spur roads. The minimum length of section to be studied i s determined by the minimum length for which a contractor i s w i l l i n g to set up his equipment. Again the method of solving the problem gives a s o l u t i o n where there i s a unique surface on any section. Most designers admit,that i n some areas, where there i s very poor alignment, that a change to a lower q u a l i t y surface within a section may be j u s t i f i e d . The main problem with the above methods of determining optimum road surface i s the determination of hauling costs. Hauling costs may be determined by using average h i s t o r i c a l costs on s i m i l a r roads. H i s t o r i c a l costs may also be combined with t r a v e l time estimates to a r r i v e at hauling costs on new roads. Travel times are based e i t h e r on h i s t o r i c a l data f o r s i m i l a r roads or on the design speed. Travel time should be based on the i n t e r a c t i o n of v e h i c l e and road c h a r a c t e r i s t i c s . Another problem i s that surface s e l e c t i o n i s based on the logging truck alone and there i s no consideration of other t r a f f i c on the road, f o r example, crew busses and service v e h i c l e s . 1.2 Another approach to the problem Getting away from the unit cost concept popularized by Matthews (1942) i s d i f f i c u l t but can be j u s t i f i e d by the use of computers. Levesque (1975) developed a simulation model that determines t r a v e l times for logging trucks r e l a t i v e to the p h y s i c a l c h a r a c t e r i s t i c s of the road. He suggested the use of these t r a v e l times to determine the best of alternate road alignments. This allows one to get away from unit hauling costs and r e l a t e the costs more d i r e c t l y to the p h y s i c a l - 3 -c h a r a c t e r i s t i c s of the road. The approach however, s t i l l has the drawback that i t considers a uniform surface over the length of road and does not allow for changing surfaces. The development of a dynamic programming model allows the changing of road surface,~such that a lower q u a l i t y surface may be considered for a section a f t e r a section with a higher q u a l i t y surface. 1.3 Objectives of the study The aim of the study i s twofold. F i r s t , to develop a dynamic pro gramming.model that w i l l simulate d i f f e r e n t road surfaces, over the e n t i r e length of road, to a r r i v e at the optimum combination of road surface, for a given road alignment. Secondly, to study the e f f e c t of the road para-meters on optimum road surface. - 4 -CHAPTER II DYNAMIC PROGRAM MODEL 2.1 General dynamic programming formulation Dynamic programming i s a operations research technique, that makes use of a sequential decision process based on the p r i n c i p l e of optimality. The p r i n c i p l e was f i r s t stated by Bellman (1957) and restated by Wagner(1969) as: "An optimal p o l i c y must have the property that regardless of the route taken to enter a p a r t i c u l a r state, the remaining decisions must constitute an optimal p o l i c y for leaving that s t a t e " 1 A l l dynamic programming problems must be decomposable into stages with a p o l i c y decision to be made at each stage. The various p o l i c y decisions, with the states of a p a r t i c u l a r stage, w i l l r e s u l t i n various states associated with the next stage. To solve the problem one begins by find i n g the optimal p o l i c y f or each state of the l a s t stage. This one-stage problem i s usually t r i v i a l , the combination of a l l possible decisions with a single input state. Beyond the one-stage problem a recursive r e l a t i o n s h i p i s formulated with equations developed to f i t the p a r t i c u l a r s i t u a t i o n being studied. The optimal p o l i c y f o r each state with n stages remaining i s i d e n t i f i e d with the recursive r e l a t i o n s h i p given the optimal p o l i c i e s f o r each state with n-1 stages remaining. St a r t i n g with the state information for the l a s t stage the problem i s solved moving backward stage by stage, u n t i l the i n i t i a l stage i s reached and the optimal.policy of the f i r s t stage i s found. '''Wagner, H.M. 1969. P r i n c i p l e s of Operations Research,Prentice H a l l , Inc., New Jersey, p. 257. - 5 -2.2 Introduction of road surfacing problem Four items used i n the s o l u t i o n of the problem need a b r i e f introduction at th i s point to avoid l a t e r confusion. They are, v e h i c l e types, t r a f f i c density, road sections, and road surfaces. Three d i f f e r e n t v e h i c l e types are allowed f o r , rather than j u s t the logging truck. This permits the i n c l u s i o n of costs and benefits r e l a t e d to vehicles other than logging trucks that are using the roads. For example, crew busses can t r a v e l f a s t e r on good q u a l i t y road surface, and consequently there w i l l be les s t r a v e l time allowances paid to employees. The i n i t i a l idea of three types of vehicles was for the i n c l u s i o n of logging trucks, crew busses, and service v e h i c l e s . In the formulation of the problem the three v e h i c l e types are allowed f o r by making the states at any stage a vector. The three components of the vector are related to the speeds of the three vehicles. T r a f f i c density i s used i n the ca l c u l a t i o n s rather than using volume of wood d i r e c t l y . The t r a f f i c density of each veh i c l e type i s the number of t r i p s that v e h i c l e w i l l make over the road each year. In the case of logging trucks the number of t r i p s i s simply the yearly volume of wood divided by the average load s i z e . The other v e h i c l e t r a f f i c d ensities may be found from the number of operating days per year and number of t r i p s per day. The t r a f f i c densities must be found for each year of the planning period, allowing f o r v a r i a t i o n i n density over time. The road being studied i s f i r s t divided into main sections, with constant t r a f f i c d e n s i t i e s . This i s equivalent to the sections discussed e a r l i e r i n the introduction, as being pieces of road between junctions, where the amount of wood to be hauled over the road remains - 6 -constant. Secondly, the road i s divided into subsections. The subsections are pieces of road where the physi c a l c h a r a c t e r i s t i c s remain constant, i . e . , the alignment variables l i s t e d i n Table III are constant over a subsection. Road surfaces are the running surfaces of the road, that part of the road i n contact with the wheels of the ve h i c l e s . D i f f e r e n t surfaces make i t harder or easier to r o l l a wheel over the surface. The f r i c t i o n between road surface and wheels, determines the l i m i t s to the t r a c t i o n and stopping e f f o r t that can be generated by the v e h i c l e . In the hypothetical problem i n Chapter V the three surfaces used were earth, gravel, and pavement. The type of surface also has a bearing on the speed l i m i t , determined by smoothness of r i d e or v i s i b i l i t y i n dusty conditions. Road surface type also has a large e f f e c t on both v e h i c l e . and road maintenance costs. 2.3 Formulation of road surfacing problem Road surfacing i s to be applied i n stages to each subsection of the road, i . e . , the short section of road of uniform c h a r a c t e r i s t i c s w i l l be the stage. The p a r t i c u l a r surface applied i n any stage i s the decision. The state of the system w i l l be the r e s u l t i n g speed of the loaded vehicles leaving the subsection of road. I t i s noted that determination of the state of the system does not include the speed of the empty vehicles and i s explained and j u s t i f i e d i n Section 2.4. The optimal combination of surfaces i s found by simulating the t r a v e l of vehicles from the loading end of the road to the dump or delivery end of the road. The recursive formula derived i s : - 7 -where f (S ) = minimum {C_ „. + f , (S.. )} for n = 1, 2, 3, n n , „ S K n-1 n-1 ( S n _ r K ) f (S ) = the minimum t o t a l cost to complete subsection n, n n and a l l previous subsections, with the output speed of subsection n represented by . S n = the state of the system, an integer valued vector found from the speed of the loaded vehicles leaving subsection n. K = the dec i s i o n v a r i a b l e (road surface type) used on subsection n. C n v = the cost to construct, maintain and operate over subsection n with surface K and state S_ . 'S K n The stage coupling function i s : S = F (S , r, v, k) n n-1 where the actual output speeds f o r subsection n-1, represented by Sn_^, are used with the road alignment ( r ) , v e h i c l e c h a r a c t e r i s t i c s (v) and the surface properties (k) of surface K, to compute the output speeds of subsection n represented by . 2.4 Comments on the state of the system The number of possible states (loaded speeds) f or any stage (subsection of road) i s not known at the outset. There w i l l often be -8-more than one way to obtain the same state at a given stage. It i s necessary to calculate the r e s u l t i n g state obtained by the use of each surface with each f e a s i b l e input state, to f i n d the minimum cost of each new state. A s i m p l i f i e d version of the problem i s , i l l u s t r a t e d i n Figure 2.1, using a maximum of 5 states and 2 possible surfaces. C a l c u l a t i o n of the state numbers f o r each stage was reduced to a maximum of 15 per vehicle type. In the case of three veh i c l e types 3 t h i s r e s u l t s i n a maximum of 15 states. To get the greatest number of states, and for the most e f f i c i e n t use of storage, indices were calculated for each vehicle f o r each stage. The indices at each stage were calculated from the loaded speeds r e s u l t i n g from the combination of the lowest input state vector (lowest input speed) and the lowest q u a l i t y surface. The indices were set such that the r e s u l t i n g speeds from t h i s f i r s t combination gave a state vector of (2,2,2). The indices were used to convert the loaded speeds, r e s u l t i n g from the remaining combinations of input states and road surface, to integer valued state vectors. As each new state vector was determined i t was checked to see i f there was already a lower cost p o l i c y to obtain that state, i f not the actual v e h i c l e speeds and a l l other necessary information was saved. The speed of the empty vehic l e was not considered i n c a l c u l a t i n g the state number. To f i n d a true i n d i c a t o r of the empty speed, the empty speed i n the next subsection of road must be known, to be able to find the a c c e l e r a t i o n or deceleration resistance. This was found to be impossible and s t i l l maintain a dynamic programming approach to the problem. To calculate empty speed the i n i t i a l speed at the end of the subsection was assumed to be one mile per hour (m.p.h.). This assumption - 9 -FEASIBLE STATE NUMBERS X _o o - X - o -o X X o •o • X >- X o . o. X n-1 n+1 STAGE (Subsection number of road) LEGEND: Feasible states Surface 1 Surface 2 Least cost route to state O O Figure 2.1 Generation of states i n s i m p l i f i e d problem. - 10 -makes the empty speed independent of the following subsection, hence, there i s no carry-over e f f e c t associated with empty speed and no reason to incorporate i t into c a l c u l a t i o n of the state number. The i n i t i a l speed i s used i n only one of the f i v e speed functions and i s only i n the c r i t i c a l function about one tenth of the time. The associated error i s compensated for i n two ways. F i r s t , the t r a v e l time i s calculated from the maximum empty speed over the section rather than the average speed. Second, the empty v e h i c l e must stop or slowdown when approaching a loaded v e h i c l e on a logging road. A s i t u a t i o n which puts the vehicle i n the assumed state quite frequently. - 11 -CHAPTER III COST CALCULATIONS AND VARIABLES 3.1 Construction and maintenance costs The construction cost i s subdivided into four components. The basic surfacing cost of each surface, i s the cost to b u i l d a unit length of surface, on l e v e l grade, when the surfacing material i s within one mile. The second component allows an increase i n surfacing cost r e l a t i v e to each successive f i v e per cent increase i n grade. The t h i r d component i s to allow for increased cost due to increase i n distance to material source. The l a s t component allows for a saving i n surfacing cost i f there i s already a lower q u a l i t y surface i n place. The cost of maintaining the surface i s subdivided into three components. The basic maintenance cost i s the cost to maintain a unit length of the surface, for one year, with a minimum t r a f f i c load. Maintenance costs are increased by increasing grade and t r a f f i c density. A l l future maintenance costs are discounted to present d o l l a r values. 3.2 Vehicle operating, t i r e and maintenance costs Operating costs are calculated from v e h i c l e rates which give the operating cost per unit time. The costs of t i r e s and maintenance, which are mainly dependent on distance, should not be included i n the v e h i c l e rate. The v e h i c l e rate must include the pay rate of the operato and the associated overhead costs. In the case of crew transportation v e h i c l e s , the t r a v e l time allowances of the employees r i d i n g the v e h i c l e and associated overhead must be incorporated into the machine rate. The - 12 -allowances, that are r e l a t i v e to time spent on the v e h i c l e , paid to passengers must be incorporated into operating costs, so that an increase i n vehicle speed r e f l e c t s the benefit of less t r a v e l time cost. The t o t a l operating cost i s then the product of t r i p time, t r a f f i c density and v e h i c l e rate a l l discounted to present d o l l a r s . The v e h i c l e maintenance and t i r e cost i s calculated on a unit distance t r a v e l l e d basis. The costs must be arri v e d at for each v e h i c l e t r a v e l l i n g on each surface, the higher costs being associated with the lower q u a l i t y surface. T i r e and maintenance cost then are the product of distance, t r a f f i c density and cost per unit distance. The t o t a l costs then must be discounted to present d o l l a r s . 3.3 Vehicle, surface and alignment variables The input variables used to solve the problem are l i s t e d i n Tables I, II and I I I . Table I. Vehicle Variables Symbol Variable Units WE Empty weight tons WL Loaded weight tons WR Rotating weight tons HE Height to center of gravity empty feet HL Height to center of gravity loaded feet 0 Projected distance from center of gravity to outside wheels feet FAE Frontal area empty s q . f t . FAL Frontal area loaded s q . f t . BHP Brake Horse Power horse power BC Braking capacity per cent (BHP) - 13 -Table I I . Surface Variables Symbol Variable Units SPLIM Speed l i m i t m.p.h. R R o l l i n g resistance pounds per ton F C o e f f i c i e n t of f r i c t i o n pounds per pound Table I I I . Alignment Variables Symbol Variable Units G Grade (+ favourable) per cent (- adverse) per cent SL Section length feet SDE Sight distance empty feet SDL Sight distance loaded feet CR Curve radius feet BETA Superelevation degrees PK E x i s t i n g Surface — - 14 -CHAPTER IV PROGRAMMING THE MODEL 4.1 General Assumption The general assumption i s that, as the loaded vehicles w i l l be more affected by the physi c a l c h a r a c t e r i s t i c s of the road alignment and surface than the empty veh i c l e s , the optimum p o l i c y f o r the problem w i l l be determined by the loaded vehicles and not the empty v e h i c l e s . Generation of an optimum p o l i c y i n the d i r e c t i o n of t r a v e l of the loaded v e h i c l e does not necessarily mean the p o l i c y w i l l be optimum f or the empty vehic l e or for the e n t i r e system. The o v e r a l l optimum would be the optimum f or the combined system of loaded and empty vehicles where both are influenced by the input speed from the previous sections. An area of further i n v e s t i g a t i o n may be to tr y by some i t e r a t i v e process to combine optimal or suboptimal p o l i c i e s f o r loaded and empty vehicles to f i n d the true optimal p o l i c y . It must be stressed that the model as developed i s a type of a c y c l i c network. An a c y c l i c network i s one that has an optimal p o l i c y i n one d i r e c t i o n and cannot be reversed without changing the assumptions or conditions used i n the model. 4.2 Computer program The number of cal c u l a t i o n s necessary to ensure that a l l possible states are generated, and the optimal state f o r each section i s av a i l a b l e for the backward pass, led to the use of the computer to ca l c u l a t e a l l the state values and costs. The program i s written i n FORTRAN IV language - 15 -f o r an IBM 370 c o m p u t e r . The p r o g r a m i s o u t l i n e d i n t h e c o n c e p t u a l f l o w d i a g r a m o f F i g u r e 4 . 1 . The p rog ram i s l i s t e d i n A p p e n d i x 6 w i t h an e x p l a n a t i o n o f i n p u t f o r m a t t i n g . 4 . 3 Speed f u n c t i o n s The speed f u n c t i o n s a r e t h e h e a r t o f t he m o d e l . These f u n c t i o n s g e n e r a t e t h e l i m i t i n g speeds on e a c h s e c t i o n and f r o m t h e speeds t h e v e h i c l e t r i p t i m e s a r e c a l c u l a t e d . The t r i p t i m e s a r e u s e d t o o b t a i n t h e v e h i c l e o p e r a t i n g c o s t s . F u n c t i o n s subprograms a r e u s e d f o r t h e s p e e d f u n c t i o n s i n t h e compute r p r o g r a m . 4 . 3 . 1 Maximum s a f e c u r v e speed Maximum s a f e c u r v e speed i s t h e maximum s p e e d a v e h i c l e can n e g o t i a t e a c u r v e w i t h o u t s l i d i n g t o t h e o u t s i d e o r t i p p i n g o v e r . The r e l a t i o n s h i p s i n v o l v e d a r e d e v e l o p e d i n A p p e n d i x 1. The f u n c t i o n s u b p r o g r a m i s c a l l e d SLIDE and r e q u i r e d the f o l l o w i n g v a r i a b l e s f o r s o l u t i o n : CR, F , BETA, H , 0 ; where H i s HE o r H L , d e p e n d i n g on t h e c a s e b e i n g c o n s i d e r e d . 4 . 3 . 2 Maximum s a f e s p e e d f o r s t o p p i n g Maximum s a f e speed f o r s t o p p i n g i s t h e maximum speed a t w h i c h a v e h i c l e i s a b l e t o s t o p s a f e l y b e f o r e h i t t i n g a n o t h e r v e h i c l e , o r an o b s t r u c t i o n on t h e r o a d , a f t e r t h e o p e r a t o r has o b s e r v e d t h e v e h i c l e o r o b s t r u c t i o n . The r e l a t i o n s h i p s i n v o l v e d a r e d e v e l o p e d i n A p p e n d i x 2 . The f u n c t i o n s u b p r o g r a m i s c a l l e d STOP and r e q u i r e s t h e c o e f f i c i e n t o f f r i c t i o n and s i g h t d i s t a n c e f o r s o l u t i o n . INITIALIZE 1. A l l o l d state t o t a l cost to maximum cost { f 0 ( S 0 ) = MAX}1 2. Set one old state to zero cost { f 0 ( l ) = 0.0} INPUT Main section data (road section with constant t r a f f i c density) INPUT Subsection road parameters Figure 4.1 Flow diagram of the program. for s i m p l i c i t y the state vectors used i n the flow diagram are one-dimensioal "making the vectors three-dimensional only increases the number of loops. - 17 -* COMPUTE The costs that are independent of speed for each possible surface I INITIALIZE 1. Set a l l new state t o t a l costs to maximum cost { f n ( S n ) = MAX} 2. Set status = 0.0 Figure 4.1 Flow diagram of the program - continued. - 18 -COMPUTE 1. Loaded and empty speeds of a l l vehicles 2. Present discounted cost of a l l future operating costs Figure 4.1 Flow diagram of the program - continued. - 19 -1. Total a l l costs of new states 2. Add cost of input old state for t e s t i n g {TEST = C s K + f ^ C S ^ i ) } Yes 1. I t i s a lower cost route to a new state 2. Transfer a l l information of new state {including f n ( S n ) = TEST} 0 © Figure 4.1 Flow diagram of the program - continued. Figure 4.1 Flow diagram of the program - continued. - 21 -4.3.3 Maximum safe speed of descent Maximum safe speed of descent i s the constant speed at which the braking capacity of the vehicle's engine and the resistance forces are exactly balanced by the force of gravity p u l l i n g the vehicl e down the grade. The re l a t i o n s h i p s involved are developed i n Appendix 3. The function subprogram i s c a l l e d SPEED and requires the following variables f o r s o l u t i o n : R, W, G, BHP, BC, FA; where W = WE or WL and FA = FAE or FAL. 4.3.4 Maximum ava i l a b l e speed of v e h i c l e Maximum av a i l a b l e speed i s the speed l i m i t e d by the a b i l i t y of the engine to generate t r a c t i v e e f f o r t . The re l a t i o n s h i p s involved are developed i n Appendix 4. There are two function subprograms, POMPHF for the loaded veh i c l e and POMPHI for the empty v e h i c l e . The difference between the two being that the second uses an input speed of one m.p.h. The variables necessary f o r s o l u t i o n other than input speed are: R, W, G, SL, BHP, FA, CC; where CC i s the fac t o r used f o r acceleration and deceleration as explained i n Appendix 4. 4.3.5 Solution of cubic r e l a t i o n s h i p s The r e l a t i o n s h i p s developed f o r the functions i n Section 4 .3.3 and 4.3.4 resulted i n cubic equations i n the unknown va r i a b l e speed. The s o l u t i o n of the cubic equations i s explained i n Appendix 5. 4.4 Program Output A sample of the program output i s given i n Appendix 7. A l l f e a s i b l e states f o r each section are l i s t e d such that the backward pass can be made to f i n d the optimal p o l i c y . - 22 -The f i r s t l i n e f o r each state gives the following: ALT state number which connects the present section of road with the following section for backward pass DOLRMC t o t a l accumulated road maintenance cost DOLRCC t o t a l accumulated road surfacing cost DOLTOT t o t a l accumulated cost SURFACE surface used on the present section OLD ALTER-NATIVE state number from the previous section which resulted i n the present state (If the present state i s part of the optimum p o l i c y then the o l d a l t e r n a t i v e i s also optimum), The second and succeeding l i n e s f o r each state give the following information for each v e h i c l e type: VEHICLE vehic l e number EMPTY MPH Empty speed at s t a r t of section LOADED MPH Loaded speed at end of section TRIP TIME To t a l accumulated t r a v e l time i n minutes DOLOP Total accumulated operating cost DOLTIR To t a l accumulated t i r e cost DOLMAV Tot a l accumulated v e h i c l e maintenance cost. - 23 -CHAPTER V MODEL RESULTS 5.1 Hypotehtical problem The hypothetical problem was made up using three v e h i c l e types and three road surfaces. The vehicles used were highway logging trucks, 18 passenger crew busses and 3-ton service v e h i c l e s . Operating rates were based on current IWA wage rates and costs published i n B.C. Logging News (March, 1976). The three surfaces were dirt,, gravel and pavement. Current t i r e costs r e l a t i v e to the three surfaces are not a v a i l a b l e , but costs f o r the l a t e 1950's are given i n the Logging Road Handbook by Byrne (1960). Current t i r e costs f o r gravel surfaces were taken from B.C. Logging News (March, 1976). T i r e costs f o r d i r t and pavement were i n f l a t e d to current costs proportional to the increase i n t i r e costs f o r gravel surfaces. A ten year amortization period with an i n t e r e s t rate of ten per cent was used. The road alignment was made up from personal experience of the author i n road layout and construction. Road grade was varied between -6% (adverse) and +15% (favorable), being representative of system roads being constructed i n the forest industry. The number of t r i p s per year f o r logging trucks were varied from 1 to 24 thousand per year, equivalent to approximately 1 to 24 m i l l i o n cubic feet of wood per year. The t r a f f i c d e nsities f o r crew busses was 10% of logging truck d e n s i t i e s , and service vehicles were 10% of crew bus d e n s i t i e s . -23-CHAPTER V MODEL RESULTS 5.1 Hypothetical problem The hypothetical problem was made up using three vehicle types and three road surfaces. The vehicles used were highway logging trucks, 18 passenger crew busses and 3-ton service v e h i c l e s . Operating rates were based on current IWA wage rates and costs published i n B.C. Logging News (March, 19 76). The three surfaces were d i r t 1 , gravel and pavement. Current t i r e costs r e l a t i v e to the three surfaces are not ava i l a b l e , but cost for the lat e 1950's were given i n The Logging Road Handbook by Byrne (1960). Current t i r e costs f o r gravel surfaces were taken from B.C. Logging News (March, 1976). T i r e costs f o r the other surfaces were i n f l a t e d to current costs proportional to the increase i n t i r e costs f o r gravel surfaces. The c a p i t a l cost of the road surface was to be amotrized over a ten year period. To do t h i s an i n t e r e s t rate of ten per cent was used to discount future costs, of surface maintenance and vehic l e operation. The road alignment was made up from personal experience of the author i n road layout and construction. Road gradient was varied between -(adverse) and +15% (favorable), being representative of system roads being constructed i n the forest industry. The number of t r i p s per year f o r logging trucks were varied from 1 to 24 thousand per year, equivalent to approximately 1 to 24 m i l l i o n cubic feet of wood per year. The t r a f f i c d ensities f o r crew busses was 10% of logging trucks, and service vehicles were 107o o f crew bus--densities. The costs used are given i n Appendix 8 '''native clay and rock mixture. - 24 -5.2 Length of subsections The importance of the length of the subsections was not r e a l i z e d u n t i l near the end of the study and almost caused a complete f a i l u r e of the dynamic program model. I f the length of a l l the subsections are over 150 feet, the dynamic program model w i l l give the same r e s u l t as a simple model that only calculates the costs f o r the three surfaces using the minimum cost a l t e r n a t i v e from the previous section. This occurs because i n a long section the vehicles are able to reach a maximum speed not determined by the acc e l e r a t i o n or deceleration resistance. When t h i s occurs the optimum i s independent of input speed. Therefore, there i s no incentive to spend extra d o l l a r s on the present section, to increase the input speed to the next section, because i t w i l l have no e f f e c t on the f i n a l speed i n the next section. When t h i s occurs the optimal p o l i c y i s to use the minimum cost state i n a l l subsections. 5.3 S i g n i f i c a n t r e s u l t s Two s i g n i f i c a n t r e s u l t s arose from the hypothetical problem. F i r s t , the e f f e c t of t r a f f i c density (volume of wood) on optimal p o l i c y was comparatively small. Second, the e f f e c t of grade on optimal p o l i c y was comparatively large. These r e s u l t s are the opposite of what was expected a f t e r a review of the l i t e r a t u r e regarding road standard s e l e c t i o n . The l i t e r a t u r e on road standards emphasizes the use of volume of wood hauled or t r a f f i c density to determine the optimum road standard. Road standards only place an upper and lower l i m i t on grade for each standard. Although surface s e l e c t i o n i s not the same problem as standard s e l e c t i o n i t i s one of the main factors incorporated into standard s e l e c t i o n . The - 25 -r e l a t i v e e f f e c t s of t r a f f i c density and grade on optimal surface are shown i n Figure 5.1. 5.4 Importance of d i f f e r e n t types of vehicles The value of using three v e h i c l e types i n the model i s question-able. The hypothetical problem was rerun using only the logging truck. The r e s u l t s were the same although the sections where the surface was about to change did have much smaller marginal costs between a l t e r n a t i v e surfaces. There i s a danger, however, when using one ve h i c l e type that the higher q u a l i t y surface i s not chosen soon enough. Two or more v e h i c l e types should be used when secondary vehicles comprise a major portion of t o t a l transportation costs. 5.5 Changing surfaces along the road There i s no allowance made i n the program.for the extra cost involved by changing from one surface to another. I t i s obvious from the res u l t s that i n cases where there are d i f f e r e n t sustained grades with d i f f e r e n t optimal surfaces that the extra t r a n s i t i o n cost would be over-come. - 26 -24 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ N 12 1^ 2 1 -6 -4 -2 +0 +2 +4 +6 +8 +10 +12 +14 PER CENT GRADE Legend: Surface 1 ( d i r t ) Surface 2 (gravel) \ > \ ' \ ^ > s \ Surface 3 (pavement) Figure 5.1 E f f e c t of t r a f f i c density and grade on optimum surface. -27-CHAPTER VI DISCUSSION AND CONCLUSIONS 6.1 Areas of further i n v e s t i g a t i o n This study frought to l i g h t many questions that should be investigated further. There are two main categories of research that could be carried out. F i r s t , modifications to the model and second, extension of the technique beyond the problem of road surfaces. Modifications to the model Improvement of the model could possible be made by addition to or modification of the model i n the following ways: 1. Incorporation of curve resistance into the model. 2. The use of speed p r o f i l e s f o r estimation of speed of vehicles as used by Roberts (1966) and Levesque (1975). 3. Consideration of changing weather and i t s e f f e c t s on road surface c h a r a c t e r i s t i c s . 4. Allowance fof improved morale and job e f f i c i e n c y of employees as a r e s u l t of higher q u a l i t y surfaces. 5. Consideration to t r a f f i c i n t e r a c t i o n and delay times f o r surface maintenance as a function of t r a f f i c density and surface type. 6. V a r i a t i o n i n load size of vehicles with season. Extension of Technique There i s a p o s s i b i l i t y of extending the technique developed into the f i e l d of road standards, to be used for defining as well as choosing optimum road standards. The technique also has p o s s i b i l i t i e s f or extension into the woods, possibly to study yarding optimization. -28-6.2 Conclusion A dynamic programming model was developed to se l e c t the optimum road surface for an e x i s t i n g logging road. Two main conclusions arose from t e s t i n g of the model on a hypothetical road. 1. Road gradient i s the most important c r i t e r i a f o r s e l e c t i o n of optimum road surface. 2. T r a f f i c density or volume of wood to be transported i s of minor importance next to gradient i n s e l e c t i o n of optimum road surface. The project indicates that road surfacing should change over the length of a road, i f the road has a large v a r i a t i o n i n grade. The practice i n the forest industry i s to maintain a constant road surface regardless of gradient. Greater demand for wood and less accessible timber, dictate that roads be b u i l t i n more rugged terrain,^and that there w i l l be a wider v a r i a t i o n i n grades. Therefore, industry and government should take a new look at road surfacing, so that more v a r i a t i o n over the length of road i s possible. The model does give some short sections of varying surfaces. These are v a l i d i n the case when the alternate surfaces are d i r t and gravel, as gravel can e a s i l y be applied to short sections of road. In the case where the v a r i a t i o n i s between gravel and pavement, the technical problems of constructing short sections of pavement and the problems of joi n i n g the surfaces,^the short sections should be eliminated. In the l a t t e r case the same optimal p o l i c y can be arrived at using a simple model that takes the minimum cost f o r each subsection of road and the dynamic programming model i s not necessary. The model can be used to decide the surfacing p o l i c y when two or three d i f f e r e n t q u a l i t y gravel surfaces are to be applied to a given road. - 29 -BIBLIOGRAPHY Adamovich, L. 1968. Lecture on t r a c t i v e e f f o r t . Given to Forest Harvesting class at University of B r i t i s h Columbia. . 1974. Road network and roadspacing planning. Paper presented for Seminar.New Requirements i n f o r e s t road engineer-ing FP2406 University of B r i t i s h Columbia, Faculty of Forestry and Centre for Continuing Education. 11pp. American Association of State Highway O f f i c i a l s (AASHO). 1965. A p o l i c y on geometric design of r u r a l highways. Washington, D.C, 650 pp. Bellman, R.E. 1957. Dynamic programming, Princeton University Press, New Jersey. 342 pp. B.C. Logging News, March. 1976. Highway coastal log truck rates, Vancouver, B.C. l p . Boyd, C.W. and G.G. Young. 1969. A study on equipment replacement, maintenance, inventory and repair p o l i c y f o r one class of v e h i c l e s . Unpublished report, Faculty of Forestry, University of B r i t i s h Columbia, 62 pp. Byrne, J . J . , R.J. Nelson and P.H. Googins. 1960. Logging road handbook: the e f f e c t of road design on hauling costs. U.S. Department of Ag r i c u l t u r e , A g r i c u l t u r e Handbook 183, 65 pp. Harkness, W.D. 1959. Truck performance and minimum road standards. Woodl. Sect. Index, Canadian Pulp and Paper Assoc. No. 1981 (B-8-a), 10 pp. Hay, W.W. 1961. An introduction to transportation engineering. John Wiley & Sons Inc., New York. 505 pp. Hennes, R.G. and M. Ekse. 1969. Fundamentals of transportation engineer-ing. McGraw-Hill, Inc., New York. 613 pp. H i l l i e r , F.S. and G.J. Lieberman. 1967. Introduction to operations research. Holden-Day, Inc., San Francisco. 639 pp. Levesque, Y. 1975. A deterministic simulation model of logging truck performance. Unpublished thes i s , University of B r i t i s h Columbia. 107 pp. • Matthews, D.M. 1942. Cost control i n the logging industry. McGraw-Hill, Inc., New York. 374 pp. N i k o l i c , S. 1972. Theoretical basis f or determining the optimum density of a forest road network. Sumanstuo, Beognull, Yugoslavia Translation from Environment Canada. 17 pp. - 30 -P a t e r s o n , W . G . e t a l . 1 9 7 0 . A p r o p o s e d f o r e s t r o a d c l a s s i f i c a t i o n s y s t e m . P u l p and P a p e r R e s e a r c h I n s t i t u t e o f C a n a d a , P o i n t e C l a i r e , P . Q . , Woodlands P a p e r N o . 2 0 . 45 p p . P e r r i n , P . Y . 1 9 6 8 . P r a c t i c a l method o f n e t w o r k o p t i m i z a t i o n f o r wood t r a n s p o r t a t i o n by t r u c k . L a v a l U n i v e r s i t y , Q u e b e c . 10 p p . P e u r i f o y , R . L . 1 9 7 0 . C o n s t r u c t i o n p l a n n i n g , e q u i p m e n t , and m e t h o d s . M c G r a w - H i l l , I n c . , New Y o r k . 696 p p . R i g g s , J . L . 1 9 7 5 . I n t r o d u c t i o n t o o p e r a t i o n s r e s e a r c h and management s c i e n c e . M c G r a w - H i l l , I n c . , New Y o r k . 497 p p . R o b e r t s , P . O . , and J . H . S u h r b i e r . 1966 . Highway l o c a t i o n a n a l y s i s : an example p r o b l e m . M I T , R e p o r t N o . 5 . T a b o r e k , J . J . 1 9 5 7 . M e c h a n i c s o f v e h i c l e s . M a c h i n e D e s i g n , The P e n t o n P u b l i s h i n g C o . , C l e v e l a n d . 93 p p . Wagner , H . M . 1 9 6 9 . P r i n c i p l e s o f o p e r a t i o n s r e s e a r c h , P r e n t i c e - H a l l , I n c . , New J e r s e y . 937 p p . W e a s t , R . C . e t a l . 1 9 6 4 . M a t h e m a t i c a l t a b l e s f rom handbook o f c h e m i s t r y and p h y s i c s . The C h e m i c a l Rubber C o . , C l e v e l a n d , O h i o . 458 p p . - 31 -APPENDIX 1 MAXIMUM SAFE CURVE SPEED The c e n t r i f u g a l f o r c e o n a v e h i c l e i n a c u r v e l i m i t s t h e s p e e d o f t h e v e h i c l e i n one o f two w a y s . E x c e s s i v e s p e e d may r e s u l t i n t i p p i n g o r t h e v e h i c l e may s l i p t o t h e o u t s i d e o f t h e c u r v e . T i p p i n g o c c u r s when t h e r e s u l t a n t f o r c e v e c t o r a c t i n g o n t h e c e n t e r o f g r a v i t y i n t e r s e c t s t h e g r ade l i n e a t a p o i n t b e y o n d t h e p o i n t o f c o n t a c t o f t h e o u t s i d e w h e e l s and t h e g r o u n d ( F i g u r e A l . l ) . S l i p p i n g o c c u r s when t h e f r i c t i o n a l f o r c e on the w h e e l s a c t i n g t owards t h e c e n t e r o f t h e c u r v e a l o n g t h e g r o u n d , i s e x c e e d e d by t h e r e s u l t a n t o f v e h i c l e w e i g h t and t h e c e n t r i f u g a l f o r c e , a c t i n g away f rom t h e c e n t e r o f t h e c u r v e a l o n g t h e g r o u n d ( F i g u r e A 1 . 2 ) . F i g u r e A l . l C r o s s - s e c t i o n o f a v e h i c l e i n t i p p i n g c o n d i t i o n on a s u p e r e l e v a t e d c u r v e . - 32 -C o n d i t i o n s f o r n o n - t i p p i n g d r i v i n g c a n be d e r i v e d by e q u i l i b r i u m o f t h e moments a b o u t A ( F i g . A l . l ) as f o l l o w s : R H = R 0 ( A l . l ) x y where R = r e s u l t a n t i n x - d i r e c t i o n l b . x R = r e s u l t a n t i n y - d i r e c t i o n l b . y H = h e i g h t to c e n t e r o f g r a v i t y f t . 0 = p r o j e c t e d d i s t a n c e f rom c e n t e r o f g r a v i t y t o o u t s i d e w h e e l s , f t . s i n c e where C = W v2 g CR ' R x = C cosg - W sinf R y = C sing + W cosf C = c e n t r i f u g a l f o r c e , l b . W = w e i g h t o f v e h i c l e s , l b . v = s p e e d , f t / s e c . 2 g = a c c e l e r a t i o n o f g r a v i t y , f t / s e c . CR = r a d i u s o f c u r v a t u r e , f t . g = a n g l e o f s u p e r e l e v a t i o n , d e g . By r e p l a c i n g C , R and R i n e q u a t i o n ( A l . l ) x y . g CR (0 + H tang) , 2 c , V m a X = { (H - 0 tang) } f t ' / s e C " - 33 -g i v e s t h e maximum speed o n a c u r v e p r i o r t o t i p p i n g . C h a n g i n g t o m i l e s p e r h o u r t h e e q u a t i o n becomes , c to r CR (0 + H t a n g ) , • S , max = 3 .9 { ^ o' t ang )" * m . p . h . ( A 1 . 2 ) S l i p p a g e o c c u r s when EFF - (C - W ) F i g u r e A 1 . 2 C r o s s - s e c t i o n o f a v e h i c l e i n s l i p p i n g c o n d i t i o n on a s u p e r -e l e v a t e d c u r v e . - 34 -C o n d i t i o n s f o r s k i d - f r e e c u r v e d r i v i n g c a n be d e r i v e d by e q u i l i b r i u m o f t h e f r i c t i o n a l , c e n t r i f u g a l and w e i g h t f o r c e s p a r a l l e l t o t h e r o a d s u r f a c e . L e v e s q u e (1975) d e r i v e d t h e f o l l o w i n g : g CR ( t a n g + y ) h v , max = { rz — T ^ T } f t . / s e c . ( A 1 . 3 ) s ' (1 - y t ang ) s where v , max = maximum speed o n c u r v e p r i o r to s l i p p i n g u = c o e f f i c i e n t o f s l i d i n g f r i c t i o n , s E q u a t i o n A 1 . 3 c a n be m o d i f i e d by e x p r e s s i n g t h e f r i c t i o n a l c o e f f i c i e n t i n t e rms o f t h e f r i c t i o n a l a n g l e u = t an$ s a l s o c o n v e r t i n g t o m i l e s p e r h o u r i , '2 S , max = 3 .9 { CR tan(.3+ 0) } m . p . h . ( A 1 . 4 ) The maximum s a f e c u r v e s p e e d as c o n t r o l l e d by c e n t r i f u g a l f o r c e i s t h e s m a l l e r o f t i p p i n g s p e e d S t > max ( A 1 . 2 ) and s l i p p i n g speed S , max ( A 1 . 4 ) . - 35 -APPENDIX 2 MAXIMUM SAFE SPEED FOR STOPPING The s a f e speed i s l i m i t e d by t h e s i g h t d i s t a n c e w h i c h a l l o w s room to s t o p b e f o r e h i t t i n g an o b s t r u c t i o n on t h e r o a d . On l o g g i n g r o a d s , where t h e r e i s n o t enough room t o p a s s , b o t h d r i v e r s must h a v e t i m e t o r e a c t and a p p l y t h e b r a k e s t o come t o a c o m p l e t e s t o p b e f o r e c o l l i s i o n . The s t o p p i n g d i s t a n c e o f a v e h i c l e i s t h e sum o f r e a c t i o n d i s t a n c e and b r a k i n g d i s t a n c e . R e a c t i o n d i s t a n c e i s t h e d i s t a n c e t r a v e l l e d f rom t h e t i m e a d r i v e r s i g h t s an o b j e c t r e q u i r i n g a s t o p u n t i l he has a p p l i e d t h e b r a k e s . B r a k i n g d i s t a n c e i s t h e d i s t a n c e t r a v e l l e d w h i l e t h e b r a k e s a r e a p p l i e d . A r e a c t i o n t i m e o f 2 . 5 s e c o n d s b e t w e e n . s i g h t i n g an o b s t a c l e and a p p l y i n g t h e b r a k e s i s recommended by t h e AASHO ( 1 9 6 5 ) . R e a c t i o n d i s t a n c e r e q u i r e d f o r e a c h d r i v e r t o a p p l y t h e b r a k e s w o u l d t h e n be RD = 2 . 5 x 1.47 S = 3 . 6 7 S f t . ( A 2 . 1 ) where RD = r e a c t i o n d i s t a n c e , f t . S = s p e e d , m . p . h . B r a k i n g d i s t a n c e o n l e v e l g r a d e r e q u i r e d t o s t o p a v e h i c l e f r o m a g i v e n speed was d e r i v e d by L e v e s q u e (1975) t o b e , BD = f t V <A2'2> 64.32 v s - 36 -where BD = b r a k i n g d i s t a n c e , f t . v = s p e e d , f t / s e c . y = c o e f f i c i e n t o f s l i d i n g f r i c t i o n s C o n v e r t i n g e q u a t i o n ( A 2 . 2 ) t o s p e e d , s , i n m i l e s p e r h o u r , B D ' 2 9 S 9 M < A 2 - 3 ) s t h e e f f e c t o f g r a d e on b r a k i n g d i s t a n c e i s c o n s i d e r e d t o be e q u a l b u t o f o p p o s i t e d i r e c t i o n f o r t h e two d r i v e r s , t h e r e f o r e , t h e b r a k i n g d i s t a n c e f o r b o t h d r i v e r s i s two t i m e s t h e d i s t a n c e r e q u i r e d on l e v e l g r a d e . Maximum s a f e s p e e d f o r s t o p p i n g as a f u n c t i o n o f s i g h t d i s t a n c e (SD) and t h e c o e f f i c i e n t o f f r i c t i o n i s f o u n d by a d d i n g e q u a t i o n s ( A 2 . 1 ) and ( A 2 . 3 ) m u l t i p l y i n g by two and s o l v i n g t h e r e s u l t i n g q u a d r a t i c e q u a t i o n f o r S S 2 - + 7 .34 S- - SD = 0 ( A 2 . 4 ) 5 9 . 8 u s - 37 -APPENDIX 3 MAXIMUM SAFE SPEED OF DESCENT The maximum s a f e speed o f a l o g g i n g t r u c k i s a l s o c o n t r o l l e d by t h e b r a k i n g c a p a c i t y o f t h e t r u c k . L o n g s t e e p g r a d e s r e s u l t i n e x c e s s i v e h e a t i n g o f s e r v i c e b r a k e s , t h e r e f o r e , most l o g g i n g t r u c k s a r e e q u i p p e d w i t h some s o r t o f r e t a r d i n g d e v i c e s u c h as a J a c o b s e n g i n e b r a k e . The c a p a c i t y o f e n g i n e r e t a r d e r s i s u s u a l l y e x p r e s s e d as a p e r c e n t o f b r a k e h o r s e power and can be e x p r e s s e d as a f u n c t i o n o f s p e e d . BE = 3 7 5 ; C B H P ( A 3 . 1 ) where BE = b r a k i n g e f f o r t , l b . BC = b r a k i n g c a p a c i t y , % BHP= b r a k e h o r s e power S = s p e e d , m . p . h . The t o t a l b r a k i n g f o r c e i n c l u d e s a i r r e s i s t a n c e and r o l l i n g r e s i s t a n c e . A i r r e s i s t a n c e i s g i v e n by the f o l l o w i n g e q u a t i o n d e v e l o p e d by T a b o r e k ( 1 9 5 7 ) . R = C 0 . 0 1 A S 2 ( A 3 . 2 ) a a where R = a i r r e s i s t a n c e , l b . a 2 - 4 C = a i r r e s i s t a n c e c o e f f i c i e n t , l b - s e c - f t a A = f r o n t a l a r e a , s q . f t . - 38 -U s i n g a v a l u e o f 0 . 3 , s e l e c t e d f rom T a b o r e k ( 1 9 5 7 ) , f o r t he a i r r e s i s t a n c e c o e f f i c i e n t f o r l o g g i n g t r u c k s e q u a t i o n ( A 3 . 2 ) becomes , R = 0 . 0 0 3 A S 2 ( A 3 . 3 ) a R o l l i n g r e s i s t a n c e i s d i r e c t l y p r o p o r t i o n a l t o v e h i c l e w e i g h t and i s e x p r e s s e d as pounds p e r t o n o f v e h i c l e w e i g h t . The t o t a l f o r c e s t e n d i n g t o s t o p t h e v e h i c l e t h e n a r e , B = 3 7 5 ^ C B H P + 0 . 0 0 3 A S 2 + R W ( A 3 . 4 ) where B = t o t a l b r a k i n g f o r c e s , l b . R = r o l l i n g r e s i s t a n c e , l b . / t o n W = v e h i c l e w e i g h t , t o n s To m a i n t a i n a c o n s t a n t o r c o n t r o l l e d s p e e d o f d e s c e n t t h e above b r a k i n g f o r c e s must b a l a n c e t h e g r a d e f o r c e t e n d i n g t o a c c e l e r a t e t h e v e h i c l e . The g rade f o r c e i s e x p r e s s e d a s , GF = - 2 0 W G ( A 3 . 5 ) where GF = g r a d e f o r c e , l b . G = g r a d e as p e r c e n t , n e g a t i v e when v e h i c l e t r a v e l l i n g d o w n h i l l . F o r m u l a A 3 . 5 i s an a p p r o x i m a t e r e l a t i o n s h i p and h o l d s t r u e o n l y f o r g r a d e s l e s s t h a n 15%. - 39 -C o m b i n i n g e q u a t i o n s ( A 3 . 4 ) and ( A 3 . 5 ) 375 BC BHP + 0 i 0 0 3 A S 2 + R W + 2 0 W G = 0 ( A 3 . 6 ) s i m p l i f i e d i n t o c u b i c f o r m i n t e rms o f S , A 3 . 6 becomes 3 , W (R + 20 G) 375 BC BHP , . S + 0 . 0 0 3 A S + 0 . 0 0 3 A " ° { A 5 ' 7 ) t he maximum s a f e speed o f d e s c e n t i s f o u n d by s o l v i n g the c u b i c e q u a t i o n ( A 3 . 7 ) as shown i n A p p e n d i x 5 . - 40 -APPENDIX 4 MAXIMUM A V A I L A B L E SPEED OF VEHICLE The s p e e d o f a v e h i c l e i s l i m i t e d by t h e a v a i l a b l e power o f t he e n g i n e . The power o f t h e v e h i c l e must be a b l e t o overcome t h e r e s i s t a n c e to m o t i o n c a u s e d b y : r o l l i n g , a i r , g r ade and a c c e l e r a t i o n . The f o r c e a v a i l a b l e t o overcome t h e s e r e s i s t a n c e s i s measu red as r i m p u l l and c a n be f o u n d f rom the r e l a t i o n s h i p be tween b r a k e h o r s e power , speed and r i m p u l l . RP = r i m p u l l , l b . EE = e f f i c i e n c y o f v e h i c l e power t r a i n u s u a l l y c o n s i d e r e d to be 85% BHP= b r a k e h o r s e power S = s p e e d , m . p . h . R o l l i n g r e s i s t a n c e i s g i v e n i n A p p e n d i x 3 and t h e r e s i s t a n c e s o f a i r and g r ade a r e g i v e n by e q u a t i o n s ( A 3 . 3 ) and ( A 3 . 5 ) . The a c c e l e r a t i o n r e s i s t a n c e i s g i v e n by t h e f o l l o w i n g e q u a t i o n . f r o m Hay ( 1 9 6 1 ) . RP EE 375 BHP S ( A 4 . 1 ) where AR 6 6 . 8 W ( S2 - S I 2 ) SL ( A 4 . 2 ) where AR a c c e l e r a t i o n o r d e c e l e r a t i o n r e s i s t a n c e l b . S I i n i t i a l s p e e d , m . p . h . SL d i s t a n c e t o a c c e l e r a t e o r d e c e l e r a t e , f t . - 41 -E q u a t i o n ( A 4 . 2 ) does n o t a c c o u n t f o r t h e a c c e l e r a t i o n o f t h e r o t a t i n g p a r t s o f v e h i c l e s . A c c o r d i n g t o A d a m o v i c h (1968) t h i s c a n be a c c o u n t e d f o r by m o d i f y i n g t h e f a c t o r 6 6 . 8 as f o l l o w s . CC = 6 6 . 8 + 6 6 . 8 ( A 4 . 3 ) w where CC = m o d i f i e d f a c t o r f o r e q u a t i o n ( A 4 . 2 ) WR = w e i g h t o f r o t a t i n g p a r t s , t o n s . C o m b i n i n g r o l l i n g r e s i s t a n c e and e q u a t i o n s : ( A 3 . 3 ) , ( A 3 . 5 ) , ( A 4 . 2 ) and ( A 4 . 3 ) and e q u a t i n g t o e q u a t i o n ( A 4 . 1 ) y i e l d s , R W + 0 . 0 0 3 A S I 2 + 20 WG + C C W ^ " S I ^ = ° - 8 5 3 7 5 B M > ( A 4 . 4 ) S i m p l i f y i n g i n t o c u b i c f o r m i n t e rms o f S, S 3 + {W(20 G+R) - S I 2 + 0 . 0 0 3 A S I 2 -z^zz } S 3 1 8 . 7 5 BHP SL =  CC w v E q u a t i o n A 4 . 5 assumes t h a t S i s g r e a t e r t h a n S I , i . e . , t he v e h i c l e i s a c c e l e r a t i n g . The maximum a v a i l a b l e speed i s f o u n d by s o l v i n g t h e c u b i c e q u a t i o n ( A 4 . 5 ) as shown i n A p p e n d i x 5 . When t h e r e i s n o t s u f f i c i e n t power a v a i l a b l e . t o a c c e l e r a t e the v e h i c l e i t must d e c e l e r a t e , o r r e m a i n a t c o n s t a n t v e l o c i t y . F o l l o w i n g - 42 -t h e above p r o c e d u r e the f o l l o w i n g c u b i c e q u a t i o n f o r d e c e l e r a t i o n c a n be d e r i v e d : S 3 + {W(20G+R) + ^ f ^ S I 2 + 0 . 0 0 3 A S I 2 ^ T ^ > S + 3 1 8 . 7 5 BHP SL = Q  CC W E q u a t i o n A 4 . 6 assumes t h a t S w i l l be l e s s t h a n S I , i . e . , t h e v e h i c l e i s d e c e l e r a t i n g . The maximum a v a i l a b l e speed i s a g a i n f o u n d by t h e s o l u t i o n o f t h e c u b i c e q u a t i o n as shown i n A p p e n d i x 5 . - 43 -APPENDIX 5 SOLUTION OF CUBIC EQUATIONS The s o l u t i o n o f t he r o o t s o f t h e c u b i c e q u a t i o n s i n t h e f o r m x 3 + ax + b = 0 where x = unknown v a r i a b l e a = c o e f f i c i e n t o f unknown to f i r s t power b = c o n s t a n t t e rm i s g i v e n by Weast ( 1 9 6 4 ) . " F o r s o l u t i o n l e t , -t h e n t h e v a l u e s o f x w i l l be g i v e n b y , A j . T> A + B . A - B I =- A + B A - By r-x = A + B , ^ — + — 2 — V ~ ' 2 2 * ~ t h e r e w i l l be one r e a l r o o t and two c o n j u g a t e i m a g i n a r y r o o t s . t h e r e w i l l be t h r e e r e a l r o o t s o f w h i c h two a t l e a s t a r e e q u a l . t h e r e w i l l be t h r e e r e a l and u n e q u a l r o o t s . " 1 W e a s t , R . C . e t a l . 1964 , M a t h e m a t i c a l T a b l e s f r o m Handbook o f C h e m i s t r y and P h y s i c s . The C h e m i c a l Rubber C o . , C l e v e l a n d , O h i o . p . 3 2 0 . i 2 3 i 2 3 I f b _ a _ 1 1 4 27 ' I f ^ + % < 0 , - 44 -The i m p o r t a n t f a c t o r (T) i n d e t e r m i n a t i o n o f t h e t y p e o f r o o t s t o e x p e c t i s , ( A 5 . 1 ) The v a l u e o f T i s p o s i t i v e i n most c a s e s when s o l v i n g e q u a t i o n s ( A 3 . 7 ) , ( A 4 . 5 ) and ( A 4 . 6 ) , and the o n l y r e a l r o o t i s g i v e n b y , ( A 5 . 2 ) I n t h e c a s e o f e q u a t i o n ( A 3 . 7 ) T becomes n e g a t i v e when t h e g r ade a p p r o a c h e s z e r o , and t h e maximum s a f e s p e e d o f d e s c e n t i n c r e a s e s b e y o n d t h e speed l i m i t s o f t h e r o a d s u r f a c e s . T becomes n e g a t i v e i n t h e c a s e s o f e q u a t i o n s ( A 4 . 5 ) and ( A 4 . 6 ) when t h e r e i s a s m a l l a c c e l e r a t i o n o r d e c e l e r a t i o n . The t h r e e r o o t s t h a t o c c u r i n a l l t h r e e e q u a t i o n s when T i s n e g a t i v e a r e c h a r a c t e r i z e d as f o l l o w s : l a r g e , n e g a t i v e l a r g e , p o s i t i v e s m a l l , p o s i t i v e The c o r r e c t r o o t i s S^ , t he s m a l l e s t p o s i t i v e r e a l r o o t , b e c a u s e c a n n o t be t h e c o r r e c t r o o t , as any l a r g e r e s i s t a n c e o r f o r c e c a n t h e o r e t i -c a l l y be overcome by t h e t r a c t i v e power o r d r a g p r o d u c e d a t a l o w p o s i t i v e s p e e d , and S£ canno t be t h e c o r r e c t r o o t , b e c a u s e t h e r e i s o n l y a s m a l l e x c e s s o f t r a c t i v e power o r d r a g a v a i l a b l e and hence o n l y a s m a l l change i n s p e e d . - 45 -The t h r e e r e a l r o o t s c a n be f o u n d f r o m t h e t r i g o n o m e t r i c r e l a t i o n s h i p g i v e n by Weast ( 1 9 6 4 ) , as f o l l o w s : "Compute the v a l u e o f t h e a n g l e 0 i n t h e e x p r e s s i o n , -cos 0 = -t h e n x w i l l have t h e f o l l o w i n g v a l u e s . -2 V ^ | c o s f , l\jr^~% cos ( | + 1 2 0 ° ) , l\l - f cos (| + 2 4 0 ° ) . u l Weas t , R . C . e t a l . 1 9 6 4 . M a t h e m a t i c a l T a b l e s f r o m Handbook o f C h e m i s t r y and P h y s i c s . The C h e m i c a l Rubber C o . , C l e v e l a n d , O h i o . p . 3 2 0 . - 46 -APPENDIX 6 THE COMPUTER PROGRAM A 6 . 1 I n p u t C a r d s The i n p u t c a r d s e x p e c t e d by t h e p r o g r a m a r e i n t h e f o l l o w i n g o r d e r : 1. The f i r s t c a r d g i v e t h e number o f y e a r s t o a m o r t i z e t h e s u r f a c i n g c o s t s , number o f v e h i c l e s , maximum number o f s t a t e s p e r v e h i c l e (up t o 1 5 ) , number o f d i f f e r e n t s u r f a c e s , number o f m a i n s e c t i o n s and t h e d i s c o u n t r a t e as a d e c i m a l . FORMAT (5110 , F 1 0 . 5 ) . The f o r m a t u sed f o r a l l t h e r e m a i n i n g i n p u t c a r d s i s 1 0 F 8 . 2 e x c e p t f o r one c o n t r o l c a r d (18) f o r e a c h m a i n s e c t i o n . 2 . The n e x t c a r d g i v e s t h e s p e e d l i m i t i n m . p . h . f o r e a c h o f t h e s u r f a c e s s t a r t i n g w i t h t h e l o w e s t q u a l i t y s u r f a c e . 3 . The i n i t i a l speeds o f t h e l o a d e d v e h i c l e s a r e e n t e r e d on t h e n e x t c a r d . The speeds a r e t h e speeds o f v e h i c l e s a p p r o a c h i n g t h e r o a d u n d e r s t u d y f rom t h e woods end o f the r o a d . 4 . The n e x t c a r d ( s ) i s ( a r e ) f o r t h e s u r f a c i n g f a c t o r s o f r o l l i n g r e s i s t a n c e (pounds p e r t o n ) , c o e f f i c i e n t o f f r i c t i o n , b a s i c s u r f a c i n g c o s t ($ p e r s t a t i o n " ' " ) , and b a s i c s u r f a c e m a i n t e n a n c e c o s t ( $ / s t a . ) . The f o u r v a l u e s a r e g i v e n f o r e a c h s u r f a c e i n t u r n s t a r t i n g f r o m the l o w e r q u a l i t y s u r f a c e . I n t h e c a s e o f 3 s u r f a c e s , t h e f i r s t c a r d w o u l d c o n t a i n t h e i n f o r m a t i o n f o r 2 s u r f a c e s , and t h e s e c o n d c a r d t h e i n f o r m a t i o n f o r t h e t h i r d s u r f a c e . "*" S t a t i o n i s a u n i t o f l e n g t h o f one h u n d r e d f e e t a b b r e v i a t e d S T A . 5.. The s a v i n g s i n s u r f a c i n g c o s t r e s u l t i n g f r o m a l o w e r q u a l i t y s u r f a c e a l r e a d y b e i n g i n p l a c e a r e g i v e n on t h e n e x t c a r d . The f i r s t s equence b e i n g t h e s a v i n g s i f s u r f a c e 1 i s i n p l a c e and s u r f a c e 1 t o t h e l a s t s u r f a c e i s t o be b u i l t , t h e s e c o n d i s when s u r f a c e 2 i s i n p l a c e , and t h e t h i r d i f t h e r e a r e t h r e e s u r f a c e s when s u r f a c e 3 i s i n p l a c e . 6 . The n e x t s e r i e s o f c a r d s i s f o r i n c r e a s e s i n s u r f a c i n g c o s t ( $ / S T A . ) and s u r f a c e m a i n t e n a n c e c o s t ( $ / S T A . ) due t o i n c r e a s e d g r a d e . The p r o g r a m e x p e c t s t h e f i r s t c a r d to have s e v e n v a l u e s f o r i n c r e a s e d s u r f a c i n g c o s t s due t o f i v e p e r c e n t jumps i n g r a d e f o r s u r f a c e 1 and t h e s e c o n d s e v e n s i m i l a r v a l u e s f o r s u r f a c e m a i n t e n a n c e . Two more c a r d s f o r e a c h s u r f a c e a r e t o f o l l o w . 7. Twenty v a l u e s on two c a r d s f o r e a c h s u r f a c e i n s equence a r e e x p e c t e d t o g i v e s u r f a c e m a i n t e n a n c e c o s t ( $ / S T A . ) due t o d i s t a n c e to m a t e r i a l s o u r c e o f up t o t w e n t y m i l e s . 8. The same p r o c e d u r e i s f o l l o w e d f o r t he t w e n t y v a l u e s f o r e a c h s u r f a c e f o r t h e i n c r e a s e i n s u r f a c i n g c o s t ( $ / S T A . ) due t o i n c r e a s e d t r a f f i c d e n s i t y . 9. The n e x t c a r d c o n t a i n s t h e v e h i c l e w e i g h t s i n t o n s g i v i n g t h e empty , l o a d e d and r o t a t i n g w e i g h t s f o r e a c h v e h i c l e i n t u r n . 1 0 . I n sequence on one c a r d t h e f r o n t a l a r e a empty ( s q u a r e f e e t ) and l o a d e d , as w e l l as b r a k e h o r s e power f o r e a c h v e h i c l e i s i n p u t . 1 1 . The h e i g h t to c e n t e r o f g r a v i t y ( f e e t ) empty and l o a d e d and p r o j e c t e d d i s t a n c e f rom c e n t e r o f g r a v i t y to o u t s i d e o f w h e e l s i s on the n e x t c a r d f o r e a c h v e h i c l e i n s e q u e n c e . - 48 -1 2 . The n e x t c a r d c o n t a i n s t h e b r a k i n g c a p a c i t y as a d e c i m a l p e r c e n t o f b r a k e h o r s e power , and t h e o p e r a t i n g c o s t i n d o l l a r s p e r m i n u t e f o r e a c h v e h i c l e i n s e q u e n c e . 1 3 . T i r e m a i n t e n a n c e c o s t s i n d o l l a r s p e r m i l e a r e on the n e x t c a r d . F o r e a c h s u r f a c e i n t u r n t h e t i r e c o s t s f o r a l l v e h i c l e s a r e e n t e r e d on the c a r d . 1 4 . S i m i l a r l y the v e h i c l e m a i n t e n a n c e c o s t s i n d o l l a r s p e r m i l e a r e on t h e n e x t c a r d . 1 5 . The f o l l o w i n g s e t s o f c a r d s f rom 16 t o 19 a r e r e q u i r e d f o r e a c h m a i n s e c t i o n . 1 6 . The n e x t c a r d ( s ) c o n t a i n s t h e t r a f f i c d e n s i t y f o r t h e f i r s t v e h i c l e t y p e f o r e a c h y e a r o f t h e a m o r t i z a t i o n p e r i o d . T r a f f i c d e n s i t y i s t h e number o f t r i p s p e r y e a r f o r e a c h v e h i c l e t y p e . 1 7 . S i m i l a r l y a d d i t i o n a l i n p u t c a r d s a r e u s e d to e n t e r t h e t r a f f i c d e n s i t i e s o f t he o t h e r v e h i c l e s t y p e s . 1 8 . The n e x t c a r d i s t h e c o n t r o l c a r d f rom t h e m a i n s e c t i o n u s i n g a d i f f e r e n t f o r m a t . The number o f s u b s e c t i o n s i n t h e c u r r e n t m a i n s e c t i o n and t h e d i s t a n c e i n m i l e s t o t h e m a t e r i a l s o u r c e f o r e a c h s u r f a c e i s g i v e n . FORMAT ( 1 8 , 7 F 8 . 2 ) . 1 9 . T h e r e i s one c a r d f o r e a c h s u b s e c t i o n , w i t h i n t h e m a i n s e c t i o n , c o n t a i n i n g t h e f o l l o w i n g i n f o r m a t i o n : Grade ( p e r c e n t ) , S e c t i o n l e n g t h ( f e e t ) , S i g h t d i s t a n c e empty ( f e e t ) , S i g h t d i s t a n c e l o a d e d ( f e e t ) , R a d i u s o f c u r v a t u r e ( f e e t ) , P r e s e n t s u r f a c e ( r e a l f o r m a t ) , and S u p e r e l e v a t i o n ( d e g r e e s ) . - 49 -A 6 . 2 C o m p u t a t i o n t i m e r e q u i r e m e n t s The amount o f t i m e r e q u i r e d f o r a p r o g r a m r u n depends on t h r e e t h i n g s : 1. t h e t o t a l number o f s u b s e c t i o n s , 2 . t he number o f v e h i c l e t y p e s and s u r f a c e s , 3 . t h e number o f s t a t e s f o u n d f o r e a c h s e c t i o n . The f i r s t two a r e c o n t r o l l e d by t h e u s e r and t h e t h i r d i s a r e s u l t o f t h e p r o g r a m . The c o m p l e t e r u n w i t h t h r e e v e h i c l e s and t h r e e s u r f a c e s , on l o w g r a d e s , r e q u i r e s abou t 0 . 7 5 s e c o n d s p e r s e c t i o n . The same r u n on s t e e p e r more l i m i t i n g g r a d e s r e q u i r e s o n l y a b o u t 0 . 2 5 s e c o n d s p e r s e c t i o n , b e c a u s e t h e number o f s t a t e s p e r s e c t i o n i s r e d u c e d by l e s s speed v a r i a t i o n . D r o p p i n g f rom t h r e e t o one v e h i c l e r e q u i r e s abou t o n e - f i f t h t h e t i m e . On a two m i l e s e c t i o n o f r o a d w i t h 110 s u b s e c t i o n s , 3 v e h i c l e s , 3 s u r f a c e s and mode ra t e g r a d e s t h e r u n t o o k 61 s econds o f compute r t i m e . A 6 . 3 FORTRAN l i s t i n g o f compute r p r o g r a m (See f o l l o w i n g 11 p a g e s ) . - 50 -DIMENSION T IME(3 ,15 ,15 ,15 ) ,D0L0P (3 ,15 ,15 ,153 1 1, J O L D U 5 , 1 5 , 1 5 ) ,DOLRCC( 15,15,15) ,DOLRMC (15 ,15 , 15 3 2 2, DOLTOT(15 ,15 ,15 ) , SPLC3 ,15 ,15 ,15 ) , SPE13 ,15 ,15 ,15 ) 3 3, JOLDN(15,15,15), ISURNC15,15,153.DOLRMNC15,15,15) 4 4, DLORCNU 5,15,15 3 ,SPEN( 3,15,15,15.) ,SPLN(3, 15,15,15) 5 5, T IMEN(3,15,15,15) ,D0L0PNC3,15,15,153 6 DIMENSION D0LMAN(3,15,15,15) ,DOLRCNU5,15,153 7 1, DTN{.15,15,15) ,DDLMAV (3, 1 5 , 1 5 , 1 5 ) , ISUR { 15 , 15,153 8 2, DQLT IR(3 , 15 ,15 ,15 ) ,DCLT IN (3 ,15 ,15 ,153 9 DIMENSION SPLIMI3) ,R(3) , F( 3) , BASURCO) ,BASURMl 3) 10 1 , SC IG (3 ,7 ) ,WE(3 ) , SM IG(3 , 7 ) , SM I 0(3,203 , SCI DIS{ 3 ,203 11 2, FAE (3 ) , FALC33 , PDRC<33,PDRMl31,PDT(3 ,33,PDM(3,33 12 3, DOPN(33, S E ( 3 ) , S L L ( 3 ) , H £ ( 3 ) , H L ( 3 ) , 0 0 ( 3 3 , S A V 4 3 . 3 ) - 13 4 , BHP(3) , BC {3 ) ,VEHOPC(3 ) ,VEHT IR (3 ,33,VEMC(3,3) ,CE (33 14 5, TRADEN(3 , 25 ) ,DMS(3 ) ,WL(33 ,WR{3 ) ,CL (33 ,T (33 15 C INITIALIZATION 16 DO 1 J3= l , 15 17 DO 1 J2=l,.15 18 DO 1 J l = l , 1 5 19 DOLRCC l J l , J 2 , J 33=0 . 0 20 DOLRMCCJ l ,J2 ,J3 )=0 .0 21 DOLTOT(J l , J2 »J33 =9.E10 22 DO 1 1-1*3 23 TIME ( I , J l , J 2 , J 3 3 = 0 . 0 24 DOLOP ( I , J 1 , J 2 , J 3 3 = 0 . 0 25 DOLT I R ( I , J l , J 2 , J 3 3 =0.0 26 1 D0LMAV( I , J1 , J2 , J3 )=0 .0 27 READ (5,5013 NYEARS,IM,JN,KM,NOMASE,RI NT 28 501 FORMAT (5110,F10.53 29 READ (5 ,5023 (S PL IM(K),K=l ,KM 3 30 502 FORMAT (1OF 8,23 31 READ (5 ,502) ( S P L ( I , 1 , 1 , 1 ) ,1=1,IM) 32 DOLTOT(1,1,13=0.0 33 C READ SURFACES 34 READ (5,5023 (R(K3,F(K3,BASURC{K3,BASURMlK3,K=1,KM 3 35 READ (5,5023((SAV(K,KK3,K=1,KM),KK=1,KM3 36 DO 2 K=1,KM 37 READ ( 5, 5023 (SC IG(K,K13,K1 = 1,7) 38 2 READ (5,5023 (SM IG(K,K l3 ,K l=1 ,73 39 READ (5,5023 (JSMIDtK,KD3,KD=1,203,K=1,KM3 40 READ ( 5 , 5 0 2 ) ( ( S e i D I S ( K , K D ) ,KD=1,203 ,K=1,KM 3 41 C READ VEHICLES 42 READ(5,5023 CHE(13,HL(13,00( I ) ,1=1, IM3 43 READ ( 5,5021 (WE(13,WL(13 , WR(13,1 = 1,1MJ 44 READ ( 5,5023 (FAE< I ) , F A l ( I ) , B H P ( I ) ,1 = 1,IM) 45 READ (5,502) (BC( I 3,VEHOPC(13,1 = 1,IM) • 46 READ (5,502) i(VEHTIR(!,K3 ,1=1,1M3,K=1,KM 3 47 READ (5,502)( (VEMC( I ,K) , I=1, IM3,K=1,KM3 48 C CALCULATE CL( 13 AND CE( I ) 49 DO 3 I=1,IM 50 CL( 13 = 66.8 + 66.8*{WR(I 3/WLI 1 3 3 51 3 CE(13=66.8+66.8*(WR(I3/WE(I)3 52 - 51 -C START READING SECTIONAL INFORMATION (MA INj 53 DO 111 NM=1,NOMASE 54 DO 4 I = 1,IM 55 4 READ (5,5021 (TRADEN(I,1 I),11=1,NYEARS) 56 READ (5,5031 NOSEC,(DMS<K),K=1,KM) 57 503 FORMAT ( I 8 . 7 F 8 . 2 ) 58 C START READING INDIVIDUAL SECTIONAL INFORMATION 59 DO 222 NS = 1,NOSEC 60 READ (5,502) G,SL,SDH,SDL,CR.PK,BETA 61 KK = PK 62 C START OPTIMIZATION WITH MINOR SECTIONS 63 STATUS=0.0 64 KI = l + ABS(G/5. J, 65 FL1=SL/100. 66 FL2=SL/5280. 67 DO 8 K = l,KM 68 KS=DMS(K) 69 PDRC(K)=FL1*(8ASURC(K)-SAV(K,KK) + SCIG(K,K I) 70 1 +SCIDIS(K,KS) ) 71 FACT=0.0 72 DO 9 IY=1,NYEARS 73 RKD=0.0 74 DO 10 1=1,1M 75 10 R K D = R K D + T R A D E N ( I » I Y ) * ( W L ( I ) + W E ( I ) ) / 7 0 0 0 0 . 76 KD=RKD+1 77 IF (KD.GT.20) KD=20 78 9 FACT=(8ASURM(K)+SMIGCK.KI)+SMID(K,KD))/U.+RINT) 79 1**1Y +FACT 80 PDRM(K)=FL1*FACT 81 DO 11 1=1,IM 82 FACT=0.0 83 FACT1=0.0 84 DO 12 IY=l,NYEARS 85 FACT=FACT+VEHTIR(I,K)*TRADEN(I , I Y ) / ( 1 . + R I N T ) * * I Y 86 12 FACT1=FACT1+VEMC(I,K)*TRADEN<I , IY)/11.+RINT)**IY 87 PDT(I »K)=FL2*FACT 88 11 PDM(I,K)=FL2*FACT1 89 8 CONTINUE 90 DO 13 J 3 = l f J M 91 DO 13 J2=1,JM 92 DO 13 J1=1,JM 93 13 D T N ( J l , J 2 , J 3 ) = 9 . E 1 0 94 DO 333 K=1,KM 95 SUM=0.0 . 96 DO 14 I=1»IM .. 97 14 SUM=SUM+PDT(I» K)+PDMCI»K) 98 S UM=SUM + PDRC(K)+PDRM(K) 99 DO 444 J3=1,JM 100 DO 444 J2=1,JM 101 DO 444 J l = l , J M 102 DON=0.0 103 IF (DOLTOT{J1,J2,J3).GE.9.E10) GO TO 555 104 - 52 -GG=G*t-1.0J 105 RR = R C'K) 106 FB=F(K3 107 DO 15 1=1 , I M 103 W W = W L(I) 109 SS = SPL( I , J 1 , J 2 , J 3 ) 11-0 BB=BHP(I) 111 FF=FAL(I3 112 C A = C l _ m 113 3A=BC(I3 114 WA=WE(I3 115 FC=FAE(I) 116 CD=CEU) 117 SLL(I3=POMPHF (RR,WW,GG,SS,SL,BB,N,FF,CA3 118 S-S PEED(RR,WW,GG,B B,BA,F F,N 3 119 IF ( S L U I 3 . G T . S 3 S L t ( 1 3 =S 120 S=ST0P(FB,SDL3 121 IF ( S L L ( I ) . G T . S ) S L L ( n = S 122 H=HL{ I ) 123 0 = 0 0 ( 1 ) 124 S = SL I DE ( C R,FB» BETA» H» 0 ) 125 IF ( S L L ( I ) - G T . S J S L L ( I J = S 126 IF (SLL{I3.GT.SPLIMCK33 S L L ( I 3=SPLIM{K3 127 IF ( S L L ( I ) . L T . l . O ) S L L ( I ) = 1 . 0 128 S £ ( I ) = S P L I M ( K 3 129 S=SPEED(RR,WA,G,BB,8A,FC,N) 130 IF ( S E ( I ) . G T . S ) S E ( I ) = S 131 S = STOP(FB » SDE) 132 IF ( S E ( I ) . G T . S 3 S E ( I ) = S 133 H=HE(I')' 134 S=SLIDE{CR,F8,BETA,H,Q) 135 IF (SE( IJ.GT-.S) SE( I J=S 136 S = POMPHI (RR,WA,G,SS,SL,BB,i\l,FC,CD) 137 IF ( S E ( I ) . G T . S ) SE(I3=S 138 IF (SE( 13 .LT.1.03 SE ( I)=1*0 139 T ( I J = S L / < 8 8 . * S E ( I ) ) + S L / ( 8 8 . * S L L ( 1 3 ) 140 DOPN (I)=T{I)#VEHQPC(I)*TRADEN(1,1) 141 DO 30 IYE=2,NYEARS 142 30 DOPN(I)=DOPN(I)+T(!3*VEHOPC(I)*TRADEN(I,IYE)/(1.+ 143 1RI N T ) * * I Y £ 144 15 D0N=DGN + DOPN(I 3 145 IF {STATUS.NE.O.O) GO TO 98 146 STATUS=l-0 147 JAF1=SLL(13-2 148 J A F 2 = S l L ( 2 } - 2 149 J A F 3 = S L U 3 3 - 2 150 JN1=2 151 JN2=2 152 JN3=2 153 GO TO 99 154 98 CONTINUE 155 - 53 -JN1=SLL(1)/1.5-JAF1 156 JN2 = S L U 2 ) / 1 . 5 - J A F 2 157 J N 3 = S L L ( 3 ) / 1 . 5 - J A F 3 158 IF(JN1.GT.JM) JN1=JM 159 IF{JN2.GT. J M J JN2=JM 160 IF{JN3.GT.JM) JN3=JM 161 IF (JN1.LT.1) JN1 = 1 162 IF (JN2.LT.1) JN2=1 163 IF (JN3.LT.11 JN3=1 164 99 CONTINUE 165 SCJ=SUM+DON+DOLTOT(Jl,J2,J3) 166 IF (SCJ.GT.DTN(JN1,JN2,JN3)) GO TO 555 167 DTN (JN1,JN2,JN3J= SCJ 168 ISURN (JN1,JN2,JN3)= K 169 D O L R M N ( J N I , J N 2 , J N 3 ) = PDRM(K) 170 D O L R C N l J N I , J N 2 , J N 3 1 = PORC(K) 171 JOLDN ( J N I , J N 2 » JN3) = J3+J2*100+JI*10000 172 DO 20 1=1,IM 173 SPEN ( I , J N 1 , J N 2 , J N 3 ) = S E ( I ) 174 SPLN ( I , J N 1 , J N 2 , J N 3 ) = S L L ( I ) 175 TIMEN (I » JNI,JN2 » JN3 ) = T ( I ) 176 DOLOPNCI,JNI,JN2,JN3)= DOPN(I) 177 DOLTINt I ,JN1,JN2,JN33 = P D T t l . K ) 178 20 O O L M A N I I , J N I , J N 2 , J N 3 ) = P O M ( I , K ) 179 555 CONTINUE 180 444 CONTINUE 181 333 CONTINUE 182 DO 21 J 3 = 1 , J M 183 DO 21 J2=l,JM 184 DO 21 J1=1,JM 185 DOLTOT (J1»J2»J3) = D T N i J 1 , J 2 , J 3 J 186 IF ( D T N U l , J 2 , J33.GE.9.E10) GO TO 21 187 I S U R J J l , J 2 , J 3 ) = I S U R N ( J l , J 2 , J 3 ) 188 J O L D ( J l , J 2 , J 3 ) = J 0 L D N ( J l , J 2 , J 3 ) ' 189 J J I = J O L D N ( J l , J 2 , J 3 ) / 1 0 0 0 0 190 J J 2 = J 0 L D N ( J i , J 2 , J 3 ) 7 1 0 0 - J J 1 * 1 0 0 191 J J 3 = J 0 L D N ( J l , J 2 , J 3 ) - J J 2 * 1 0 0 - J J 1 * 1 0 0 0 0 192 D O L R C N ( J 1 , J 2 , J 3 ) = D 0 L R C C ( J J 1 . J J 2 , J J 3 ) + D 0 L R C N ( J l , J 2 , 193 1J3) 194 D O L R M N t J l , J 2 , J 3 ) = D 0 L R M C { J J 1 , J J 2 , J J 3 ) + D 0 L R M N ( J l , J 2, 195 1J3) 196 DO 22 1=1,IM 197 SPE ( I , J 1 , J 2 , J 3 ) = S P E N U » J 1 , J 2 , J 3 ) 198 SPL ( I , J 1 , J 2 , J 3 ) = S P L N ( I , J 1 , J 2 , J 3 ) 199 TIMEN ( I , J 1 , J 2 , J 3 J = TIME (I ,JJ1»JJ2,JJ3)+TIMEN ( I 200 1 , J 1 , J 2 , J 3 ) 201 DOLOPNU, J l , J 2 , J 3 ) = DOLOP ( I » J J i , J J 2 , J J3 )+DOLOPN( I 202 1,J1,J2,J3) 203 D O L T I N C I , J 1 , J 2 , J 3 ) = D O L T I R ( I , J J l , J J 2 , J J 3 ) + D Q L T I N ( I 204 1 , J 1 , J 2 , J 3 ) 205 22 DOLMAN ( I ,Jl,J2 »J3) = DOLMAVC I , J J 1 , J J 2 , J J 3 J+Q.OLMAN ( I 206 1 , J 1 , J 2 , J 3 3 207 - 54 -21 CONTINUE 208 C OUTPUT STAGE HEADING 209 WRITE (6,602) NM,NS 210 602 FORMAT!//' MAIN S E C T I O N NUMBER',14,5X,'SUBSECTION* 211 I t ' NUMBER ' , 1 43 212 DO 25 J3=1,JM 213 DO 25 J2=1,JM 214 DO 25 J1=1,JM 215 IF ( D T N ( J l , J 2 , J 3 3 . G E . 9 . E 1 0 ) GO TO 23 216 D O L R C C t J l , J 2 , J 3 ) = 0 0 L R C N ( J l , J 2 , J 3 3 217 D O l R M C t J l , J 2 , J 3 ) = D 0 L R M N ( J l , J 2 , J 3 ) 218 DO 24 1=1 , I M 219 TIME ( I , J l , J 2 , J3)= TIMEN ( I , J 1 , J 2 , J 3 ) 220 DOLOP ( I , J l , J 2 , J 3 ) = DOLOPNU , J l , J 2 , J 3 ) 221 D O L T I R ( I , J 1 , J 2 , J 3 3= DOLT I N ( I , J 1 , J 2 , J 3 ) 222 24 D O L M A V ( I r J l , J 2 , J 3 3 = DOLMAN(I,J1,J2,J33 223 WRITE ( 6 , 603) J l , J 2 , J3,D0LRMC( J1,,J2,J3) ,DGLRCC i J 1 , J 2 224 1, J 3 3 , D 0 L T 0 T ( J l , J 2 , J 3 3 , I S U R C J l , J 2 , J 3 3 , J O L D I J l , J 2 , J 3 ) 225 603 FORMAT (/' ALT ',31 3,4X,'DOLRMC =',F10.2,4X,•DOLRC * 226 l ' C =•,F10.2,5X,'DQLTQT =',F10.2,5X,'SURFACE =',I3 227 2,5X,'OLD ALTERNATIVE =',I7) 228 DO 44 1=1,IM 229 44 WRITE (6,604) I , S P E ( I , J 1 , J 2 , J 3 ) , S P L { I , J 1 , J 2 , J 3 3 230 1» T I M E ( I , J 1 , J 2 , J 3 ) , D O L O P ( I » J 1 , J 2 , J 3 ) 231 2, D 0 L T I R ( I , J 1 , J 2 , J 3 ) , D 0 L M A V ( I , J 1 , J 2 , J 3 ) 232 604 FORMAK IX ,* VEHICLE' , 13 ,3X, • EMPTY MPH =*,F5.2,3X, 233 1 * LOADED MPH =•,F5.2,3X,'TRIP TIME = •,F6.1,3X, 234 2'DOLOP =•,F9.2,3X,'D0LTIR =•,F3.2,3X,•DOLMAV =' 235 3, F8.2) 236 23 CONTINUE 237 25 CONTINUE 238 222 CONTINUE 239 111 CONTINUE 240 STOP 241 END 242 - 55 -FUNCTION POMPHF (R,W,G,SI,SL,BHP,N»FA,CCJ 243 C 244 C R=COEFFICIENT OF ROLLING RESISTANCE POUNDS PER TON OF 245 C VEHICLE WEIGHT 246 C • W=VEHICLE WEIGHT IN TONS 247 C POMPHF=MAXIMUM SPEED(FINAL} AS LIMITED BY THE POWER OF 248 C THE VEHICLE 249 C G=GRADE AS A PERCENT 250 C S1=SPEED WHEN ENTERING THE SECTION 251 C SL=LENGTH OF THE SECTION IN FEET 252 C BHP=BRAKE HORSE POWER OF VEHICLE 253 C FA=FRONTAL AREA OF VEHICLE IN SQUARE FEET 254 C CC=CORRECTIQN FACTOR FOR THE TWO TYPES OF MASS IN A 255 C MOVING VEHICLE 256 C NOTE ALL SPEEDS EXPRESSED AS MILES PER HOUR 257 IF CSI.EQ.O.O) SI=0.1 258 RP=318.75*BHP/SI 259 TR=0.003*FA*SI*SI+R*W+20.*W*G 260 IF (TR.GT.RP) CC=CC*(-1.0i 261 XB=BHP*(-318.750)/ICC*W/SL) 262 XA={W*{20.#G+R)-CC*W/SL*SI*SI + 0 . 0 0 3 * F A * S I * S I J / ( C C * 263 1W/SL) 264 T=XB*XB/4.0+XA**3/27.0 265 IF (T.GE.O.O) GO TO 10 266 PHI=ARC0SCXB/(-2.)/(SQRT(XA**3/{-2 7 . ) ) ) J / 3 . 267 Z=2.*SQRT<XA/{-3.)) 268 P1=Z*C0S(PHI+4.1888) 269 P3=Z*C0S(PHI+2.0944) 270 P2=Z*C0S(PHI) 271 IF ( P l . L E . O . O ) Pl=80. 272 IF (P2.LE.0.0) P2=80. 273 IF CP3.LS.0.Q) P3=80. 274 IF ( P 2 . L T . P I ) P1=P2 275 IF i P 3 . L T . P 1 3 P1=P3 276 POMPHF=PI 277 GO TO 5 278 10 YA=SQRT i T) 279 YB=XB*(-1.0)/2.0 280 SP=Y8+YA 281 SN=YB-YA 282 IF { SP.GE.O.O.) GO TO 1 283 A = i ( A B S ( S P J - } * * l l . / 3 - ) ) * ( - l - 0 ) 284 GO TO 2 285 1 A=SP**(1./3.3 286 2 IF (SN.GE.O.O) GO TO 3 287 8= { (ABS(SN) ) * * i l . / 3 . .) ) * ( - 1 . 0 ) 288 GO TO 4 289 3 B = S N * * l l . / 3 . ) 290 4 POMPHF=A+B 291 IF {POMPHF.LE.1.0) P0MPHF=1.11 292 5 IF ITR.GT.RPi CC=CC*(-1.0) 293 RETURN 294 END 295 - 56 -F U N C T I O N POMPHI (R , W, G , S I , S I , BHP , N , FA , C C ) 2 9 6 C 2 9 7 C R = C Q E F F I C I E N T OF R O L L I N G R E S I S T A N C E POUNDS P E R T O N O F 2 9 8 C V E H I C L E W E I G H T 2 9 9 C W = V E H I C L E W E I G H T IN T O N S 3 0 0 C POMPHI=MIN IMUM S P E E D ( I N IT I A L ) AS L I M I T E D BY T H E POWER 3 0 1 C T H E V E H I C L E 3 0 2 C G = G R A D £ AS A P E R C E N T 3 0 3 C S L = L E N G T H OF T H E S E C T I O N IN F E E T 3 0 4 C BHP= B R A K E H O R S E POWER OF V E H I C L E 3 0 5 C FA = F R O N T A L A R E A O F V E H I C L E IN S Q U A R E F E E T 3 0 6 C C C = C O R R E C T I O N F A C T O R FOR T H E TWO T Y P E S O F MASS IN A 3 0 7 C M O V I N G V E H I C L E 3 0 8 C N O T E A L L S P E E D S E X P R E S S E D AS M I L E S P E R HOUR 3 0 9 S I = 1 . 0 3 1 0 R P = 3 1 8 . 7 5 * B H P / S I 3 1 1 T R = 0 . 0 0 3 * F A * S I * S I + R * W + 2 0 . * W * G 3 1 2 I F ( T R . G T . R P i C C = C C * ( - 1 . 0 ) 3 1 3 X A = ( W * ( 2 0 . * G + R ) - C C * W / S L + 0 . 0 0 3 # F A ) / ( C C * W / S L ) 3 1 4 X B = B H P * ( ~ 3 1 8 . 7 5 0 ) / ( C C * W / S L ) 3 1 5 T = X B * X B / 4 . 0 + X A * * 3 / 2 7 . 0 3 1 6 I F ( T . G E . O . O ) GO TO 1 0 3 1 7 P H I = A R C 0 S ( X 3 / { - 2 . ) / " t S O R T C X A * * 3 / C - 2 7 . i ) ) ) / 3 . 3 1 8 Z = 2 . * S Q R T ( X A / ( - 3 . ) ) 3 1 9 P 1 = Z * C 0 S ( P H I + 4 . 1 8 8 8 J 3 2 0 P 3 = Z * C 0 S ( P H I + 2 . 0 9 4 4 ) 3 2 1 P 2 = Z * C 0 S { P H I ) 3 2 2 I F { P l . L E . O . O ) P l = 8 0 . 3 2 3 I F ( P 2 . L E . 0 . 0 ) P 2 = 8 0 . 3 2 4 I F ( P 3 . L E . 0 . 0 ) P 3 = 8 0 . 3 2 5 I F ( P 2 . L T - P 1 3 P 1 = P 2 3 2 6 I F ( P 3 . L T . P 1 3 P 1 = P 3 3 2 7 P O M P H I = P 1 3 2 8 GO TO 5 3 2 9 10 YA = S Q R T <T) 3 3 0 Y B = X B * ( - 1 . 0 ) / 2 . 0 3 3 1 S P = Y B + Y A 3 3 2 S N = Y B - Y A 3 3 3 I F ( S P . G E . O . O ) GO TO 1 3 3 4 A= { ( A B S ( S P ) ) * * ( l . / 3 . ) > * ( - 1 . 0 ) 3 3 5 GO T O 2 3 3 6 1 A = S P * * ( 1 . / 3 . J 3 3 7 2 IF ( S N . G E . O . O ) GO TO 3 3 3 8 . B= { { A B S ( S N J J * * C 1 . / 3 . ) J * ( - 1 . 0 ) 3 3 9 GO TO 4 3 4 0 3 B = S N * # ( 1 . / 3 . ) 3 4 1 4 POMPHI=A+B 3 4 2 I F ( P O M P H I . L E . 1 . 0 ) P 0 M P H I = 1 . 2 2 3 4 3 5 I F ( T R . G T . R P 3 C C = C C * ( - 1 . 0 ) 3 4 4 R E T U R N 3 4 5 END 3 4 6 - 57 -FUNCTION S P E E D ( R , W , G , B H P , B C , F A , N3 3 4 7 c 3 4 8 C R = C O E F F I C I E N T OF R O L L I N G R E S I S T A N C E POUNDS PER TON OF 3 4 9 C V E H I C L E WEIGHT 3 5 0 c w= WEIGHT OF V E N I C L E IN TONS 351 C G= GRADE AS A PERCENT 352 C BHP = BRAKE HORSE POWER 3 5 3 C FA = FRONTAL AREA I N SQUARE F E E T 3 5 4 C SPE ED= THE CONSTANT S P E E D OF DESCENT IN M I L E S PER HOUR 3 5 5 C 3 5 6 I F ( G . G E.O.O) GO TO 10 3 5 7 XB=BC*BHP*37500./FA/0-3 358 X A = W * ( 2 0 . * G + R ) / 0 . 0 0 3 / F A 3 5 9 Z= X 8 * X B / 4 . 0 + X A * * 3 / 2 7 . Q 3 6 0 I F ( Z . L E . O . O J GO TO 5 3 6 1 YA= S Q R T(Z) 3 6 2 Y B = X B * ( - 1 . 0 3 / 2 . 0 3 6 3 SP=YB+YA 3 6 4 SN=YB -YA 3 6 5 I F ( S P . G E . 0 . 0 3 GO TO 1 3 6 6 A= ( ( A B S ( S P ) ) * * < ! . / 3 . J ) * ( - 1 . 0 ) 3 6 7 GO TO 2 3 6 8 1 A = S P * * ( l . / 3 . ) 3 6 9 2 I F ( S N . G E . O . O J GO TO 3 3 70 B= ( ( - A B S ( S N ) ) * * C 1 . / 3 . ) J *<-1.0) 3 7 1 GO TO 4 3 7 2 3 B = S N * * ( 1 . / 3 . ) 3 7 3 4 SPEED=A+B ' 3 7 4 I F ( S P E E D . L T . 0 . 0 3 S P E £ D = 6 9 . 0 0 3 7 5 I F ( S P E E D . L E . 5 . 0 3 S P E E D = 5 . 0 3 7 6 GO TO 20 377 5 CONTINUE 3 7 8 P H I = A R C 0 S ( X B / ( - 2 . 3 / ( S Q R T ( X A * * 3 / ( - 2 7 . 3 ) ) 3 / 3 . 3 7 9 Z = 2 . * S Q R T ( X A / ( - 3 . 3 ) 3 8 0 Pl-Z*COStPH 1 + 4 . 1 8 88 3 381 P 3=Z * C 0 S ( P H 1+2 . 0 9 4 4 3 3 8 2 P 2=Z * C 0 S ( P H I 3 3 8 3 I F ( P l . L E . O . O ) P l = 8 0 . 3 8 4 I F ( P 2 . L E . 0 . 0 ) P 2 = 8 0 . 3 8 5 I F ( P 3 . L E . 0 . 0 3 P 3 = 8 0 . 3 8 6 I F ( P 2 . L T . P 1 ) P1=P2 3 8 7 I F ( P 3 . L T . P 1 3 P1=P3 3 8 8 SPEED=P1 3 8 9 GO TO 20 3 9 0 10 S P E E D = 7 0 . 0 0 3 9 1 20 CONTINUE 392 RETURN 3 9 3 END 3 9 4 - 58 -FUNCTION STOP(F,SIGHTD3 395 C 396 C F= COEFFICIENT OF FRICTION 397 C SIGHTD= SIGHT DISTANCE IN FEET 398 C STOP= THE SPEED AS LIMITED 8Y THE STOPPING DISTANCE 399 C NOTE SPEED IS IN MILES PER HOUR 400 C 401 A=1.0/59.8/F 402 B=7.34 403 C = S IGHTD*(-1.1 404 CALL -SOLVEQIA,B,C,Y,Z) 405 IF (Y.EQ.-1000.) GO TO 1 406 STOP=Y 407 IF (Y.LE.O.) STOP=Z 408 RETURN 409 1 STOP=0.0 410 RETURN 411 END 412 - 59 -SUBROUTINE SOL V £ Q ( A , B , C ,Y ,Z) 413 c 414 c A= COEFFICIENT OF THE SQUARED TERM 415 c B= COEFFICIENT OF THE TERM TO THE FIRST POWER 416 c C= CONSTANT TERM 417 c Z = FIRST ROOT 418 c Y= SECOND ROOT 419 c NOTE IF ROOTS ARE COMPLEX Y IS SET AT -1000 420 c AND Z AT 1000 421 c 422 DISC = B*B-4.*A*C 423 I F ( 0 I S C 3 5,6,7 424 5 Y = -1000. 425 Z = +1000. 426 RETURN ; 427 6 Y = -B/(2.0*A3 428 Z = -B/(Z.O^A) 429 RETURN 430 7 S = SQRTIDISC) - 431 Y = l-B+S)/(2 . 0*A) 432 Z = (-B-S)/(2.0*A3 433 RETURN 434 END 435 - 60 -FUNCTION SLIDE (CR» F,BETA »H»0) 436 C 437 C H= HEIGHT OF CENTER OF GRAVITY 438 C 0= PROJECTED DISTANCE FROM CENTER OF GRAVITY 439 C TO OUTSIDE WHEELS 440 C S= TIPPING SPEED MPH 441 C CR= RADIUS OF CURVATURE FEET 442 C F= COEFFICIENT OF FRICTION (ROAD SURFACE) 443 C SLIDE= MAXIMUM SPEED IN MILES PER HOUR AT WHICH IT IS 444 C POSSIBLE TO TRAVEL AROUND A CURVE 445 C B£TA= SUPERELEVATION IN DEG. 446 C ' • 447 IF (CR.GE.1000.) GO TO 1 448 FTAN=F*0.616 449 B=BETA*3.1415927/180. 450 C=ATAN(FTAN ) - 4 5 i A=CR*TAN(B+C) 452 SLIDE=3.90*SQRTCA) 453 S=3.9*SQRT(CR*(0+H*TAN(B))/(H-0*TAN{B))) 454 IF ( S . L T . S L I D E ) SLIDE'S 455 RETURN 456 1 SLIDE=70. 457 RETURN 458 END 459 - 61 -APPENDIX 7 SAMPLE OF PROGRAM OUTPUT The f o l l o w i n g sample o f p r o g r a m o u t p u t i s r e d u c e d f r o m t h e s t a n d a r d 15 i n c h by 11 i n c h compute r o u t p u t . The s e c t i o n 3-1 i s an e x c e r p t f rom a p r o g r a m r u n w i t h 5 m a i n s e c t i o n s u s i n g t h r e e v e h i c l e s and t h r e e s u r f a c e s . I t i s an example o f an a l t e r n a t i v e t h a t i s c h o s e n by t h e dynamic p r o g r a m mode l t h a t i s n o t t h e minimum c o s t s t a t e f o r t h e s e c t i o n . The dynamic p r o g r a m b a c k w a r d p a s s r e v e a l s a l t e r n a t i v e 9 - 8 - 9 w i t h s u r f a c e 3 t o be t h e opt imum p o l i c y w h i l e t h e minimum c o s t s t a t e f o r t h e s e c t i o n i s a l t e r n a t i v e 6 - 5 - 7 w i t h s u r f a c e 2 . VEHICLE I EMPTY M P H = 19.12 VEHICLE 2 EMPTY MPH » 2 3 . 0 7 V E H I C L E 3 EMPTY «PH =21.66 I pATED MpH = 1 7 . 2 9 LPADEO MPH " 4 0 . 9 7 LOADED MPH =39.49 TRIP TIME>= TRIP T IMt" TRIP TI ME = 8 . 6 4 . 5 4. 8 DOLOP » 297211. 37 OOLOP « 2082 .76 DDLOP = 110.72 DOLTIP = 11 75.38 DOLMAV = 770 .40 00LT1P * 26 .77 DOLMAV a 2 6 . 7 7 DOLTIR = 3 . 9 9 DOLMAV » 3 .85 ALT 10 10 14 OCLtVC = 11686.'=3 OCLRCC « 23010 .00 DOLTOT V E H I C L E 1 EMPTY M P H =19.12 LOADED M P H =17.46 TRIP T I ME = B. 7 69104 .63 SURFACE = 3 OLD ALTERNATIVE • 80913 DOLOP = 30260.94 OOLTi P. = 1082 .28 DOLMAV = 712.21 VEHICLE 2 VEHICLE 3 EMPTY M P H =23.07 EMPTY «"H =21.66 L C A P E D M P H L P A O E J M P H = 3 8 . 4 7 =40.55 TRIP TIME= TRIP T1ME= 4 . 6 4 . 8 DOLOP DOLOP 2182 .32 112 .89 DOLT1R DOLT1R 2 4 . 7 9 3 .88 OOLMAV = DOLMAV = ALT 10 13 14 DCLRwc"= 12123 .19 DQLRCC = 1 9 4 6 0 . 0 0 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LCAOEO MPH =17.61 TRIP TIME= 8 .5 V t H I C L E 2 E^PTY MPH =23. 07 LPAPEO MPH =42.16 TRIP TIME= 4 . 5 64983 .33 SURFACE = 3 OLD ALTERNATIVE OOLOP = 29246.10 DOLT IR = 1152 .11 DOLMAV = DOLOP = 2074 . 78 POL Tl R = 26. 30 POLMAV = VEHICLE EMPTY MPH =21.66 LCADED MPH =40 .55 TRIP TIME= 4 . 8 DOLOP = 110 .34 OOLTIR = ALT 10 14 15 OCLRMC = 11742 .23 PCLPCC = 21380 .00 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LOADED MPH =17.32 TRIP TIME= 8 .5 VEHICLE 2 EMPTY " P H =23 .07 LOADED MPH =44 .77 TRIP TIME= 4 . 4 VEHICLE 3 EMPTY MPH =21.66 LPAPED MPH =43.13 TRIP T IM E = 4 . 7 ALT ID 15 15 OCLBMC = 11551 .75 OCLRCC = 2 2 3 4 0 . 0 0 DOLTOT VEHICLE 1 EMPTY WPH =19.12 L PADED MPH =17.46 TRIP T IM E = 8 . 4 VEHICLE 2 'FMPTY "PH =23.07 LOADED MPH =46.17 TRIP TIME= 4 . 4 VEHICLE 3 EMPTY M P H =21.66 LPAPED MPH =44.64 . TRIP TI ME = 4 . 7 24 . 79 3 .56 = 81213 7 5 6 . 4 3 2 6 . 3 0 3 .96 OOLMAV = ' 6 6 3 2 8 . 3 8 • SURFACE = 3 OLD ALTERNATIVE "DOLOP = 29151 . 78 OOLTIR = 1105 .56 OOLMAV = DOLOP = 2052 .79 DOL Ti R = 2 5 . 3 7 DOLMAV = DOLOP = 109.23 DOLTIR = 3 . 8 9 DOLMAV = 3 .78 = 81415 7 2 8 . 5 0 2 5 . 3 7 3. 64 6 6 6 8 6 . 3 1 SURFACE = 3 OLD ALTERNATIVE DOLOP = 28792 .89 DPLTIR = 1082 .28 DOLMAV = OOLOP = 2039 .08 DOLTIR = 2 4 . 9 0 OOLMAV = OOLOP = 108.52 DOLTIR = 3 . 8 5 OOLMAV = = 81515 714 .54 24 .90 3 .57 MAIN SECT ION KUVrtER SUeSECT ION NUMBER A L T 1 V E H I C L E _y j r i_ IC_LE_ V E H I C L E A L T 5 V E H I C L E V E H I C L E V E H I C L E ALT 5 VEHICLE VEHICLE VEHICLE 1 na.PMC = 13536 .44 D C L R C C = 1 4 4 6 0 . 0 0 D O L T O T E M P T Y M P H =11.31 L O A D E D M P H = 3 .36 T R I P T I M E = 9 .2 __£ i^FTY v P H = l f e . ! 7 L C A P E D M P H = 9 . 3 4 T R I P T IM E= 4 . 7 E M P T Y MPH =14.43 L C A D E O M P H = 7.71 T R I P T I ME= 5 .0 69919 .38 SURFACE = 1 OLD ALTERNATIVE DOLOP = 36873 .69 DOLTIR = 1443 .04 DOLMAV = OOLOP = 246 8 .46 DOLTIR = 32 .12 DOLMAV = OOLOP = 133 .18 OOLTIR 1 DCLFMC = 13499 .57 DOLRCC = 14460 .00 DOLTOT EMPTY MPH =16.92 LCA TFD MPH = 9 . 3 2 TRIP TIME = 9 . 2 EMPTY MPH =21.23 LCAPED MPH =22 .39 TRIP TIME= 4 . 7 E M P TY vPH =19.70 LPAPED M°H =20.55 TRIP T I ME = 5.1 2 D C l ^ C = 13763.7P DCL °CC = 14070 .00 DOLTOT E M P T Y M P H = l o . 9 2 IPAnEO M P H = 9 .38 TRIP TI ME = 9 . 4 EMPTY " P H =21 .23 LOADED MPH =25.16 TRIP TI ME = 4 . 8 EMPTY «PH =19.70 LOADED MPH =23.02 TRIP TIME= 5.1 4 . 6 5 DOLMAV 6 7 3 5 9 . 3 8 SURFACE = 2 . OLD ALTERNATIVE DOLOP = 34529 .89 OOLTIR = 1396 .49 DOLMAV = OOLOP = 2 3 6 7 . 0 9 DOLTIR * 31 .42 DOLMAV = DOLOP = 126 .66 OOLTIR = 4 ,54 POJLMAV_=_. 6 8 2 6 0 . 2 5 SURFACE = 2 DOLOP = 35498 .90 DOLTIR . DOLOP = 2387 .56 OOLTIR « DOLOP = 128 .09 DOLTIR = OLD ALTERNATIVE 1419 .77 DOLMAV = 3 1 . 7 7 OOLMAV = 4 . 6 0 . DOLMAV = "ALT'""" 7 1 2 O C l ^ C = 13296. BO J ' lLPCC = 1 5 4 2 0 . 0 0 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LOADED MPH =12.67 TRIP TI ME= 9 .2 VEHICLE Z EMPTY MPH =23. 07 LCAPEO MPH =24.24 TRIP TI ME = 4 . 7 VEHICLE 3 EMPTY MPH =21.66 LOAOED MPH = 2 2 . 5 2 " TRIP TIME= 5.0 6 7 4 2 4 . 2 5 SURFACE = 3 0 LD' ALTER NAT IVF DOLOP = 33968 .55 DOLTIR = 1326 .67 OOLMAV = DOLOP = 2351 .84 DOLTIR = 3 0 . 0 2 DOLMAV = DOLOP = 125 .72 DPLTIR = 4 . 4 3 DOLMAV = = 1 0 1 0 1 . 9 0 7 . 7 2 3 1 . 4 2 4 . 5 4 * 2 C 2 0 2 91 9 . 3 6 3 1 . 7 7 4 . 6 0 = 10101 8 6 5 . 8 3 3 C . C2 4 . 3 3 ALT 2_ VEHICLE 1 V E H I C L E 2 VEHICLE . 3 ALT 7 3 VEHICLE 1_ ~VE"ii iCLE 2 VEHICLE 3 ALT 6 3 VEHICLE 1 VEHICLE 2 OPLPMC 13800 .65 DCLRCC = 14070 .00 DOLTOT = 70221 . 1 9 SURFACE = 1 E M P T Y "PH =11.31 L P A O f J MPh = 3 . 9 b TRIP TIME = 9 . 4 OOLOP = 37309 .63 OOLTIR = 1466.32 OOLMAV = F M P T Y W P H =16 .17 ICAPEO MPH =17.20 TRIP TIME= 4 . 8 DOLOP = 2427 .08 DOLTIR = 3 2 . 4 7 D0LM1V = e ^ P T Y MPH =14 .43 LOADED MpH =15.15 TRIP TIME = 5.1 DOLOP.= 130 .48 DOLTIP .=• . 4 .71 DOLMAV = OLD ALTERNATIVE = 1010_1 9 4 2 . 6 3 3 2 . 4 7 4 .71 3 nriRMC = 13561 .P I PCLPCC = 1 5 0 3 0 . 0 0 DOLTOT = 6 8 3 3 1 . 2 5 SURFACE = 3 OLD ALTERNATIVE _E M P TY M ? H =19. 1 2 LPAPED M°H =12. 7 5. J RIP TI M E«_ 9 . 4 DOLOP » 3494 2.. .1.4 DOLTIP » 1349 .94 O.0,kMA.V..,?_ EMPTY MPH = 23.~07 LCADEO MPH =27.02 TRIP TI ME= 4 . 8 DOLOP = 2373 .83 DOLTIR = 3 0 . 3 7 OOLMAV = EMPTY MPH =21.66 IPAPEO MPH =24 .97 TRIP T IME« 5.1 DOLOP * 127. 24 DOLTIR = 4 . 4 9 DOLMAV » . OCL c MC = 1 3 4 9 9 . 5 7 - DOLRCC = 14460 .00 DOLTOT EMPTY ' ' PH =1(J.92 LOAPEO MPH =11.01 TRIP TIME= 9 .2 EMPTY MPH =21.23 LCAPED MPH =27.92 TRIP T1 ME= 4 . 7 6 7 1 4 0 . 9 4 SURFACE = 2 OLD ALTERNATIVE DOLOP » 34319 .68 OOLTIR - 1396 .49 DOLMAV = DOLOP = 2359 .22 OOLTIR •= 3 1 . 4 2 DOLMAV = " 20202 J 7 _ 7 . 4 6 _ 3 0 . 3 7 4 .3 9 » 50101 9 0 7 . 7 2 31 .42 V E H I C L E 3 E M F T Y '--PH = I S . 70 ' L C A P E D MPH = 2 5 . 8 1 T R I P T I M E = 5 . 1 DOLOP = 1 2 6 . 3 1 D O L T I R = 4 . 5 4 DOLMAV = 4 . 54 ALT 6 4 V E H I C L E 1 V E H I C L E 2 V E H I C L E 3 ALT 7 V E H I C L E 1 V E H I C L E 2 . V E H I C L E 3 5 O P L R M C = 1 3 7 6 3 . 7 8 O C L P C C * 1 4 0 7 0 . 0 0 O O L T C ' T . F J . P T Y " P H = 1 6 . 9 2 L O A D E D M P H = 1 1 . 0 3 T R I P T I M E = 9 . 4 E M P T Y M P H = 2 1 . 2 3 L C A P E D M P H = 2 9 . 4 9 T R I P T I M E = 4 . 8 5 V P T Y M P H = 1 9 . 7 0 L O A D E D M P H = 2 7 . 1 8 T R I P T I M E = 5 . 1 6 8 0 8 5 . 7 5 S U R F A C E « 2 . DOLOP = 3 5 3 2 7 . 8 8 D O L T I R = OOLOP = 2 3 8 4 . 19 D O L T I P = DO LOP = 1 2 7 . 9 9 D O L T I £ = OLD A L T E R N A T I V E = 5 0 1 0 2 1 4 1 9 . 7 7 OOLMAV = 9 1 9 . 3 6 3 1 . 7 7 OOLMAV = 3 1 . 7 7 4 . 6 0 DOLMAV = 4 . 6 0 5 VriBfC. = 1 3 3 C 9 . 0 9 D O L R C C = 1 5 4 2 0 . 0 0 DOLTOT t N P T Y " P H = 1 6 . 9 2 LOADED MPH = 1 2 . 8 . ? T R I P T I ME= 9 . 2 r i - ' P l y I'PH = 2 1 . 2 3 L P A P F O MPH = 2 9 . 0 5 T R I P TI ME= 4 . 7 E M P T Y MPH = 1 9 . 7 0 L C A P E D MPH = 2 7 . 0 1 T R I P TI ME = 5 . 1 6 7 4 7 1 . 8 8 S U R F A C E = 2 DOLOP = 3 3 9 2 7 . 9 1 D O L T I R = DOLOP « 2 3 5 1 . 1 6 D O L T I R = OOLOP = 1 2 5 . 8 1 DOLT IP . = OLD A L T E R N A T I V E = 7 C 1 0 1 1 3 7 3 . 2 2 OOLMAV = 3 9 3 . 7 6 3 0 . 9 6 OOLMAV = 3 0 . 9 6 4 . 5 0 OOLMAV = 4 . 4 7 ALT 8 4 5 C P H K C = 1 3 2 9 6 . 8 0 D C L R C C = 1 5 4 2 0 . 0 0 DOLTOT V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L E A D E D MPH = 1 4 . 5 0 T R I P T IME= 9 . 2 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L T A P E D MPH = 2 9 . 7 0 T R I P T IME= 4 . 7 V E H I C L E 3 E M P T Y " P H " = 2 1 . 6 6 L C A D E O MPH = 2 7 . 7 1 T R I P TI ME= 5 . 1 6 7 3 1 3 . 4 4 " S U R F A C E = 3 OLD A L T E R N A T I V E = 5 C 1 0 1 DOLOP = 3 3 8 6 3 . 1 4 D O L T I F = 1 3 2 6 . 6 7 OOLMAV = 8 6 5 . 8 3 DOLOP = 2 3 4 6 . 6 5 D O L T I R = 3 0 . 0 2 OOLMAV = 3 0 . 0 2 DOLOP = 1 2 5 . 5 4 D O L T I R = 4 . 4 3 DOLMAV = 4 . 3 3 ALT. O r L P M C = 1 3 5 7 3 . 3 0 DCL PCC 1 5 0 3 0 . 0 0 DOLTOT = 6 8 4 1 9 . 4 4 S U R F A C E = 2 OLD A L T E R N A T I V E = 7 0 2 0 3 V E H I C L E V E H I C L E V E H I C L E 1 E M P T Y "P .H = 1 6 . 9 2 2 E M P T Y M P H = 2 1 . 2 3 3 E M P T Y " O H = 1 9 . 7 0 L I M P E D MPH = 1 2 . 8 4 L P A O E O MPH = 3 0 . 0 0 L O A D E D MPH = 2 8 . 4 7 T R I P T IME= . 9 . 4 T R I P T IME= 4 . 8 T R I P T I M £ = 5 . 1 DOLOP = 3 4 9 3 6 . 6 4 OOLOP = 2 3 7 8 . 3 4 DOLOP = 1 2 7 . 5 3 D O L T I R = 1 3 9 6 . 4 9 DOLMAV = 9 0 5 . 3 9 D O L T I R = 3 1 . 3 0 OOLMAV = 3 1 . 3 0 D O L T I R = 4 . 5 6 DOLMAV = 4 . 5 3 5 6 C P L P M C = 1 3 4 9 9 . 5 7 O O L R C C = 1 4 4 6 0 . 0 0 O O L T O T 1 FMI-TY " P H = 1 6 . 9 2 LOADF D I 'PH = 1 1 . 6 0 T R I P T I ME= 9 . 2 E M P T Y V P H E M P T Y M P H • 2 1 . 2 3 •  1 9 . 70 L P A P E D M P H = 3 0 . 0 0 L C A D E O M P H = 2 8 . 9 2 T R I P T IME= T R I P T IME= 4 . 7 5 . 1 6 7 0 5 5 . 6 3 S U R F A C E = 2 O L D A L T E R N A T I V E = 6 0 3 0 3 D O L O P * 3 4 2 3 3_. 4 6 D O L TI P = 1 3 9 6 . 4 9 00 l> iAV_= 9 0 7 . 7 2 ,., " D U L O P = 2 3 6 0 . 1 5 D O L T I R = 3 1 . 4 2 D O L M A V = 3 1 . 4 2 O O L O P = 1 2 6 . 3 2 D O L T I R = 4 . 5 4 D O L M A V = 4 . 5 4 ALT 7 V E H I C L E V E H I C LE 5 o On " M C " = i 3 3 0 9 . 0 9 O O L R C C = 1 5 4 2 0 . 0 0 DOLTOT 1 EMPTY MPH = 1 6 . 9 2 LOADED MPH = 1 2 . 3 7 T R I P T I M E * 9 . 1 2 E M F T Y MPH = 2 1 . 2 3 L P A P E D MPH = 3 0 . 0 0 T R I P T IME= 4 . 7 V E H I C L E A L T S VE H i ; LE V E H I C L E V E H I C L E E M P T Y M P H = 1 9 . 7 0 L O A D E D M P H = 2 9 . 7 - , T R I P T I M E = 5 . 1 5 6 na°MC = 1 3 5 6 1 . 0 1 D O L R C C = 1 5 0 3 0 . 0 0 D O L T O T 1 CMPTY M P H = 1 9 . 1 2 L P A P E D M P H = 1 4 . 5 2 T R I P T I M E = 9 . 4 2 E M P T Y M P H = 2 3 . 0 7 L O A D E D MpH = 3 1 . 2 4 T R I P T I M E = 4 . 8 3 F M P T Y i-'PH = 2 1 . 6 6 L P A P E D M P H = 2 9 . 0 4 T R I P T 1 M E = 5 . 1 6 7 4 1 4 . 5 6 S U R F A C E = 2 DOLOP = 3 3 8 6 7 . 7 0 D O L T I P = _D0 L OP = 2 3 5 4 . 0 8 DOLT 1R -• DOLOP = OLD A L T E R N A T I V E = 6 0 4 0 4 1 3 7 3 . 2 2 DOLMAV = 8 9 3 . 7 6 3 0 . 9 6 OOLMAV = 3 0 . 9 6 1 2 5 . 8 4 D O L T I R = 4 . 5 0 OOLMAV = 4 . 4 7 6 8 2 5 9 . 6 9 S U R F A C E = 3 ' DOLOP = 3 4 8 7 2 . 18 DOLT I R = DOLOP = 2 3 7 2 . 1 5 D O L T I R = DOLOP = 1 2 7 . 25 D O L T I R -• OLD A L T E R N A T I V E .= 5 0 1 0 2 1 3 4 9 . 9 4 OOLMAV = 8 7 7 . 4 6 3 0 . 3 7 DOLMAV = 3 0 . 3 7 4 . 4 9 DOLMAV = 4 . 3 9 ALT 9 5 6 OCLRMC = 1 3 1 0 6 . 3 2 O O L R C C = 1 6 3 8 0 . 0 0 D O L T O T V E H I C L E 1 E M P T Y ".'PH = 1 9 . 1 2 1 0 A D E 0 MPH = 1 6 . 2 9 T R I P TI M E = ^ " 5 . 1 V E H I C L E 2 E M F T Y " P H " = 2 3 . 0 7 L CAE ED M P H = 3 0 . 81 T R I P T I ME = 4 . 7 V E H I C L E 3 E M F T Y " P H = 2 1 . 6 6 LOAPF.O MPH = 2 0 . 3 9 T R I P TI ME= 5 . 1 6 7 7 2 8 . 0 3 S U R F A C E = 3 DOLOP = 3 3 5 5 4 . 5 9 D O L T I R = " D O L O P = 2 3 3 8 . 9 8 ' D O L T I R = DOLOP = 1 2 5 . 0 7 D O L T I R = OLD A L T E R N A T I V E = 7 0 1 0 1 1 3 0 3 . 3 9 DOLMAV = . 8 5 1 . 3 6 2 9 . 5 6 OOLMAV = " 2 9 . 5 6 4 . 4 0 DOLMAV = 4 . 2 6 A L T 2 5 V E H I C L E I V E H I C L E 2 V E H I C L E ' 3 A L T 3 5 V E H ' I C ' L E " l V E H I C L E 2 V E H I C L E 3 A L T 5 5 V E H I C L E 1 V E H I C L E 2 V E H I C L E 3 A L T " " b' 5 V E H I C L E I V E H I C L E ? 7 0 C L a M C = 1 2 8 5 4 . 39 D O L R C C = 1 6 7 / 0 . 00 DOLTCT EMPTY M P H = 1 6 . 9 2 LOADED MPH = 5 . 7 4 T R I P T IME= 9 . 0 E M P T Y MPH = 2 1 . 2 3 L C A P E D MPH = 3 0 . O C T R I P T I M £ = 4 . 6 E M P T Y MPH = 1 9 . 7 0 L O A O E O MPH = 3 0 . 0 0 " T R I P TI ME = 4 . 9 7_ J>C1 " " £ _ « _ 1 3 0 4 4 . 8 7 O C L P C C = 1 5 6 1 0 . 0 0 _ D O L T P T _ " E M P I Y MPII = l o . 9 * 2 LOADED MPH = 6 . 9 0 T R T P f t M " E ' . " ~9T6 EMPTY MPH - 2 1 . 2 3 LPAPF.D «PH » 3 0 . 0 0 T R I P T I M E " 4 . 6 E M F T Y " p H = 1 9 . 7 0 . . L O A D E D MPH. =3 0 . 0 0 .T'R 1 P . T l'ME= 4 . 9 7 D C L P M f . = 1 2 8 5 4 . 3 9 O C L P C C = 1 6 7 7 0 . 0 0 ' OOLTOT E M P T Y " P H = 1 6 . 9 2 LOADED M P H = 1 0 . 3 3 T R I P T I ME= 8 . 9 6 8 3 2 5 . 2 5 S U R F A C E = 2 OLD A L T E R N A T I V E = 9 1 0 1 1 DOLOP = 3 4 0 4 9 . 17 D O L T I R = 1 3 2 6 . 6 7 OOLMAV = 8 6 8 . 15 D P L O P = 2 2 6 7 . 5 0 D O L T I P = 3 0 . 1 4 DOLMAV » .. 3 0 . 1 4 DOLOP = 1 2 0 . 3 1 " D O L T I R = 4 . 4 1 DOLMAV = 4 . 3 4 6 7 3 6 5 . 8 1 S U R F A C E = 2 _ O L P A L T E R N A T I V E « 8 0 8 0 9 "DOLOP'""=""" 3Ta"i 3". 7 2 OOL T I?~='"'1"34T''94 OOLMAV = 6 8 2.1 k~ DOLOP « 2 2 7 4 . 4 1 D O L T I R • 3 0 . 6 1 DOLMAV = 3 0 . 6 1 DOLOP « 1 2 0 . 6 6 D O L T I R = 4 . 4 5 D P L M A V =. .. . 4 . 4 1 6 7 2 3 2 . 3 0 S U R F A C E = 2 DOLOP = 3 2 9 5 4 . 8 5 D O L T I P . = OLD A L T E R N A T I V E 1 3 2 6 . 6 7 DCLMAV • 4 0 5 0 7 8 6 8 . 15 E M P T Y M P H = 2 1 . 2 3 L O A O E O M P H = 3 0 . 0 0 E V P T Y M P H = 1 9 . 7 0 L O A D E D M P H = 3 0 . 0 0 T R I P TIME= T R I P T I M e = 4 . 6 4 . 9 OOLOP = 2 2 6 8 . 8 6 D O L T I R DOLOP = 1 2 0 . 3 9 D O L T I R 7 OCL»MC = 1 3 2 3 5 . 3 5 O O L R C C = 1 4 8 5 0 . 0 0 DOLTOT E M P T Y >'PH = 1 6 . 9 2 LOADED M P H = 1 1 . 8 0 T R I P T I M E - 8 . 9 E M P T Y M P H = 2 1 . 2 3 L P A P E O MPH = 3 0 . 0 0 T R I P T1ME= 4 . 6 " " 6 5 8 3 5 . 7 5 S U R F A C E • 2 O L D A L T E R N A T I V E « 6 0 5 0 7 D O L O P » 3 3 0 0 8 . 7 3 D O L T I R » 1 3 7 3 . 2 2 O O L M A V « 8 9 6 . 0 8 D O L O P = 2 2 8 0 . 2 9 D O L T I R = 3 1 . 0 7 O O L M A V * 3 1 . 0 7 V E H I C L E 3 EMPTY " P H =19.70 LOADED MPH =30.00 TRIP TIME= 4.9 OOLOP = 120.96 DOLTIR = 4.48 DOLMAV = 4.48 ALT Z__ 5_ 7. 0CLRMC_ = 13044__87 DOLRCC _= .15810.00 D OLTOT __r.__66197.25__ SURFACE = 2 OLD ALTERNATI VE_____ 70507 VEHICLE l '" EMPTY "PH " = T 6 . 9 2 ~ L O A D E D MPH =12.81 TRl"p~T"lME= ' D Q l Q p - 32644.5 5 DOLTIR = 1349.94 DOLMAV = 882. 12 VEHICLE 2 EMPTY MPH =21.23 LOADED MPH =30.00 TRIP TIME= 4.6 DOLOP = 2275.00 DOLTIR = 30.61 DOLMAV = 30.61 VEHICLE 3 EMPTY MPH =19.70 LOADED MPH =30.00 TRIP TIM.E= 4.9 DOLOP = 120.69 DOLTIR = 4.45 OOLMAV = 4.41 ALT 9 6 7 OCLRMC = 13296.80 DOLRCC = 15420.00 DOLTOT = 67256.25 SURFACE = 3 OLD ALTERNATIVE = 60303 VEHICLE_ 1 EMPTY MPH_=19. 12 J.OADE0 MPH =15.09 TRIP_TIME= 9.2 DOLOP =_33806.64 DOLTIR = 1326.67 DOLMAV = 865.83 VEHICLE 2 "EMPTY « P H =23. 07 " LOADED MPH =32.93 TRIP 1I ME = 4.7 DGLOP = 2345.85 DOLTIR = 30.02 DOLMAV = 30.02 VEHICLE 3 EMPTY M P H =21.66 LOADED MPH =30.74 TRIP TIME= 5.1 OOLOP = 125.61 DOLTIR = 4.43 DOLMAV = 4.33 A L T 9 8 7 D O L P M C = 1 2 5 8 4 . 0 3 D O L R C C = 1 8 8 9 0 . 0 0 O O L T O T = 6 7 7 7 5 . 9 4 S U R F A C E = 3 O L D A L T E R N A T I V E = 6 0 5 0 3 V E H I C L E 1 E M P T Y M ° H = 1 9 . 1 2 L O A D E D M P H = 1 5 . 3 2 T R I P T I M E = 8 . 8 D O L O P = 3 1 8 2 2 . 1 3 D O L T I R = 1 2 3 3 . 5 7 D O L M A V = 8 1 2 . 2 9 V E H I C L E 2 E M P T Y M P H ^ 2 3 . 0 7 L O A D E D M P H _ = 3 4 . 7 2 _ T R I P T I M E = 4 . 6 D O L O P = _ 2 2 4 4 . 7 6 _ _ D O L T I R = 2 8 . 2 8 D O L M A V = 2 8 . 2 8 " V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 " L C A O E D M P H = 3 0 . 7 3 " T R I P T I M E = 5 . 0 D O L O P = 1 2 4 . 2 1 " D O L T I R = 4 . 2 7 D O L M A V = 4 . 0 6 A L T 9 7 8 O P L R M C = 1 3 1 0 6 . 3 2 D O L R C C = 1 6 3 8 0 . 0 0 O O L T O T = 6 7 6 4 9 . 8 8 S U R F A C E = 3 O L D A L T E R N A T I V E = 6 0 4 0 4 V E H I C L E I E M P T Y M O H = 1 9 . 1 2 L C A P E D M P H = 1 5 . 8 8 T R I P T I M E = 9 . 1 D O L O P = 3 3 4 7 6 . 9 7 D O L T I P = 1 3 0 3 . 3 9 D O L M A V = 8 5 1 . 8 6 V E H I C L E 2 E M P T Y M O H = 2 3 . 0 7 L C A P E D M P H = 3 3 . 6 7 T R I P T I M E = 4 . 7 O O L O P = 2 3 3 8 . 3 6 O O L T I R = 2 9 . 5 6 O O L M A V = 2 9 . 5 6 V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 L O A D E D M P H _ = 3 1 . 5 3 _ T R I P__T I M E = _ _ 5 . 1 _ _ D O L O P „ = 1 2 5 . 1 5 D O L T I R = 4 . 4 0 D O L M A V = _._ 4 . 2 6 ALT 10 7 8 OCLPMC = 13106.32 DCLRCC = 16380.00 DOLTOT = 67693.19 SURFACE = 3 OLD ALTERNATIVE = 80405 VEHICLE 1 EMPTY M P H =19.12 LOADED M P H =17.13 TRIP TI ME= 9.1 OOLOP = 33519.34 DOLTIP = 1303 .39 DOLMAV = 851.36 VEHICLE 2 EMPTY M P H =23.07 LOADED MPH =34.16 TRIP TI ME= 4.7 DOLOP = 2339.25 DOLTIR = 29.56 DOLMAV = 29.56 VEHICLE 3 EMPTY MPH =21.66 LOADED MPH =32.07 TRIP TIME= 5.1 OOLOP = 125.21 OOLTIR = 4.40 DOLMAV = 4.26 ALT" 9 " 6 8 DOLPMC = 129C3.55 DCLRCC = 16870.00 DOLTOT = 66816.50 SURFACE = 3 OLD ALTERNATIVE = 60505 VEHICLE 1 EMPTY M P H =19.12 LOADED MPH =15.28 TRIP TIME= 8.9 OOLOP = 32473.20 DOLTIR = 1280.12 OOLMAV = 840.22 VEHICLE 2 EMPTY M P H =23.07 LCAPED M P H =34.72 TRIP TI ME= 4.6 DOLOP = 2258.25 DOLTIR = 29.21 OOLMAV = 29.21 VEHICLE 3 EMPTY M P H =21.66 LOADED MPH =32.73 TRIP TIME= 5.0 DOLOP = 124.17 DOLTIR = 4.34 DOLMAV = 4.20 ALT 10 8 8 DCLPMC_ = 13370_.53 DCL RCC_ = _15_990.00 D0LI0T_ = _ 68690. 13 SURFACE = 3_ . OLD ALTERNATIVE.?. 80505 VEHICLE 1 EMPTY MPH=l"9.12 LOADED MPH~=17.14 TRIP TI ME= 9.4 DOLOP = 34576.86 DOLTIR = 1326.67 DOLMAV = 863.50 VEHICLE 2 EMPTY MPH =23.07 LOADED MPH =35.13 TRIP TIME= 4.8 OOLOP = 2366.94 DOLTIP = 29.91 DOLMAV = 29.91 VEHICLE 3 EMPTY V P H =21.66 LPAPED MPH =32 .39 TRIP TIME= 5.1 DOLOP = 127.05 DOLTIR = 4.46 DOLMAV = 4.32 ALT 11 8 8 OCLPMC = 12915. 84 OCLRCC = 17340.00 OOLTOT = 68112.94 SURFACE = 3 OLD ALTERNATIVE « 90505 VEHICLE 1 EMPTY M P H =19.12 LOADED MPH_=18.13 TRIP_TIME=_ 9.1 DOLOP = 33215.57 DOLTIR = 1280.12 DOLMAV = 837.90 VEHICLE 2 EMPTY W P H =23. 07" LOADED MPH =34.92 TRIP TI ME = 4. 7 DOLOP = 2331.98 DOLTIR = 29.09 OOLMAV = 29.09 VEHICLE 3 EMPTY MPH =21.66 LOADED MPH =32.88 TRIP TIME= 5.0 DOLOP = 124.76 DOLTIR = 4.36 DOLMAV = 4.19 A L T 1 0 1 0 8 O C L P M C = 1 2 3 9 3 . 5 5 D C L R C C = 1 9 8 5 0 . 0 0 D O L T O T = 6 8 2 1 5 . 5 6 S U R F A C E = 3 O L D A L T E R N A T I V E = 8 0 8 0 5 V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L O A D E D M P H = 1 7 . 4 3 T R I P T I M E = 8 . 7 D O L O P = 3 1 5 4 2 . 4 7 D P L T I R = 1 2 1 0 . 2 9 D O L M A V = 7 9 8 . 3 3 V E H I C L S _ 2 E M P T Y M P H = 2 3 . 0 7 L C A D E O M P H _ = 3 8 . 2 6 T R I P T I M E = _ 4 . 6 _ D O L O P = _ 2 2 3 3 . 2 2 . . . D O L T I R . .=_ 2 7 . 8 1 D O L M A V = . 2 7 . 8 1 V E H I C L E 3 " E M P T Y M P H = 2 1 . 6 6 L O A C E D M P H = 3 2 . 0 6 T R I P " T I M _ = 5,6 D O L O P = 1 2 3 . 8 1 OOLTIR » 4 . 2 4 O O L M A V = 3 . 9 9 A L T 1 1 1 2 8 D P I PMC- = 1 2 2 0 3 . 0 7 O C L R C C = 2 0 8 1 0 . 0 0 D O L T O T = 6 8 6 4 7 . 3 1 S U R F A C E = 3 O L D A L T E R N A T I V E = 9 1 0 0 5 V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L C A P E D M P H = 1 8 . 6 5 T R I P T I M E = 8 . 7 O O L O P = 3 1 2 5 3 . 6 7 D O L T I R = 1 1 8 7 . 0 2 D O L M A V = 7 8 4 . 3 6 V E H I C L E 2 E M P T Y M.PH = 2 3 . 0 7 L C A P E D M P H = 4 0 . 6 5 T R I P T I M E = 4 . 6 D O L O P = 2 2 2 3 . 0 2 D O L T I P . = 2 7 . 3 5 O O L M A V = 2 7 . 3 5 _V.EH_I.C_LE 3 EMPTY "PH = 2 1 . 6 6 . LCADEO MPH =32.87 TRIP TIME' 5 . 0 _P_OIO.P__= 1 . 2 3 . 3 6 . D O L T I R . . = 4 . 2 0 . . D O L M A V . .= 3 . 9 2 A L T 8 8 9 0 C L ° M C = 1 2 7 1 3 . 0 7 D O L R C C = 1 7 8 3 0 . 0 0 D O L T O T = 6 7 3 1 1 . 5 6 S U R F A C E = 3 O L D A L T E R N A T I V E = 5 0 5 0 7 V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L O A D E D M P H = 1 4 . 9 8 T R I P T 1 M E = 8 . 8 D O L O P " 3 2 2 4 7 . 2 9 D O L T I R = 1 2 5 6 . 6 4 D O L M A V = 3 2 6 . 2 6 V E H I C L E 2 E M P T Y M ° H = 2 3 . 0 7 L O A D E D M P H = 3 4 . 7 2 T R I P T I M E = 4 . 6 O O L C P = 2 2 5 2 . 6 2 D O L T I R = 2 8 . 7 4 D O L M A V = 2 8 . 7 4 V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 L O A D E D M P H = 3 4 . 1 1 T R I P T I M £ = 4 . 9 D O L O P = 1 1 9 . 5 6 D O L T I P . = 4 . 3 1 D O L M A V = 4 . 1 3 A"LT 9 8 9 D C L R M C = 13032. 58 D O L R C C = 1 5 8 1 0 . 0 0 O O L T O T = 6 6 0 4 2 . 5 0 S U R F A C E = 3 O L D A L T E R N A T I V E = 60507 V E H I C L E 1 E M P T Y M P H =19.12 L P A P E D M P H =15 .30 T R I P T I M E = 8.9 D O L O P = 3 2 5 9 1 . 6 3 D O L T I R = 1 3 0 3 . 3 9 O O L M A V = 8 5 4 . 1 9 V E H I C L E 2 E M P T Y M P H = 2 3 . 0 7 L C A P E D M P H =34.72 T R I P T I M E = 4.6 D O L O P = 2262.66 D O L T I R = 2 9 . 6 e O O L M A V = 2 9 . 6 8 V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 L C A P E D MPH = 3 4 . 1 1 T R I P T I M E = 4 . 9 DOLOP = 1 2 0 . 0 5 D O L T I R = 4 . 3 8 D O L M A V = 4 . 2 7 . A L T 11 6 9 0 C L » M C = 1 3 1 8 0 . 0 5 .. O O L R C C .= . 1 6 9 5 0 . 0 0 D G L T O T = 6 9 1 1 0 . 5 0 S U R F A C E = 3 O L D A L T E R N A T I V E = 9 0 6 0 6 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L O A D E D MPH = 1 8 . 1 4 T R I P T I ME= 9 . 3 D O L O P = 3 4 2 7 3 . 3 4 D O L T I R = 1 3 0 3 . 3 9 D O L M A V = 8 4 9 . 53 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L O A D E D MPH = 3 5 . 9 8 T R I P TI ME= 4 . 8 D O L O P = 2 3 6 0 . 0 1 D O L T I R = 2 9 . 4 4 D O L M A V = 2 9 . 4 4 V E H I C L E 3 E M P T Y MPH = 2 1 . 6 6 L O A D E D MPH = 3 3 . 8 0 T R I P T I M E = 5 . 1 OOLOP = 1 2 6 . 6 2 D O L T I R = 4 . 4 2 O O L M A V = 4 . 2 5 A L T 10 9 9 DOLRMC = 1 3 1 C 6 . 3 ? O O L R C C = 1 6 3 8 0 . 0 0 D O L T O T = 6 7 6 9 5 . 5 0 S U R F A C E = 3 O L D A L T E R N A T I V E = 8 0 6 0 6 j V E H I C L E 1 E M P T Y MPH = 1 9 . 1 2 L O A D E D MPH = 1 7 . ? : i T R I P T I M E = 9 . 1 O O L O P = 3 3 5 1 9 . 7 7 D O L T I R = 1 3 0 3 . 3 9 D O L M A V = 8 5 1 . 8 6 j V E n l C L E 2 E M P T Y " P H = 2 3 . 0 7 L O A D E D MPH = 3 6 . 2 6 T R I P T IME= 4 . 7 DOLOP = 2 3 4 0 . 9 3 D P L T I R = 2 9 . 5 6 DOLMAV ='" 2 9 . 5 6 V E H I C L E 3 E M P T Y MPH = 2 1 . 6 6 L O A D E D MPH = 3 4 . 0 2 T R I P T I M E = 5.1 D O L O P = 1 2 5 . 4 3 D O L T I R = 4 . 4 0 D O L M A V = 4 . 2 6 A L T 1 0 1 0 9 O C L R M C = 1 2 7 1 3 . C 7 D C L R C C = 1 7 8 3 0 . 0 0 D O L T O T = 6 7 2 5 4 . 8 8 S U R F A C E = 3 OLD A L T E R N A T I V E = 8 0 8 0 6 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L O A D E D M P H = 1 7 . 3 8 T R I P T I M E = 8 . 9 DOLOP = 3 2 1 9 2 . 2 4 D O L T I R '= 1 2 5 6 . 8 4 D O L M A V = 8 2 6 . 26 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L C A P E D M P H = 3 8 . 2 6 T R I P T I M E = . 4 . 6 _ . 0 0 L 0 P = 2 2 4 6 . 7 0 D O L T I P = 2 R . 7 4 D O L M A V = . 2 8 . 7 4 V E H I C L E 3 E M P T Y " P H = 2 1 . 6 6 L C A P E D M P H = 3 4 . 0 9 T R I P T IME= 5 . 0 DOLOP = 1 2 3 . 8 0 D O L T I R » 4 . 3 1 D O L M A V = 4 . 1 3 A L T 1 3 c IQ Q C L E M C = 1 291 5. 84 P O L " C C = 1 7 3 4 0 . 0 0 O O L T O T = 6 8 0 8 4 . 9 4 S U R F A C E = 3 0 L P A L T F RN A T I V E = g 0 6 0 7 V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L P A P E D " P H = 1 7 . 6 6 T R I P T I ME= 9 . 1 DOLOP = 3 3 1 8 5 . 9 7 D O L T I P . = 1 2 8 0 . 12 D O L M A V = 8 3 7 ^ 9 0 V E H I C L E 2 E M P T Y M P H = 2 3 . 0 7 L C A P E D M P H = 3 6 . 7 9 T R I P T I M E = 4 . 7 DOLOP = 2 3 3 3 . 4 1 D O L T I R = 2 9 . 0 9 O O L M A V = 2 9 . 0 9 V E H I C L E 3 E M P T Y " P H = 2 1 . 6 6 L O A D E D M P H = 3 4 . 5 8 _ TR IP T I M E = .5 .1 D O L O P = 1 2 4 . 9 7 D O L T I P , = . 4 . 3 6 D O L M A V = 4 . 1 9 A L T 11 9 1 0 O C L " M C = 1 2 9 1 5 . 8 4 D C L R C C = 1 7 3 4 0 , 0 0 D O L T O T = 6 8 1 2 7 . 1 9 S U R F A C E = 3 OLD A L T E R N A T I V E = 9 0 7 0 7 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L P A P E D " P H = 1 8 . 5 2 T R I P T I M E = 9 . 1 DO L OP = 3 3_2 2 7 . 1 2 D O L T I R = 1 2 8 0 . 1 2 D O L M A V = 83 7^9 0 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L C A P E D M P H = 3 7 . 1 8 T R I P T I ME = 4 . 7 DOLOP = ' 2 3 3 4 . 4 3 D O L T I R = 2 9 . 09 O O L M A V = 2 9 . 0 _ 9 V E H I C L E .3 E M P T Y M P H = 2 1 . 6 6 L C A P E D M P H = 3 5 . 0 1 T R I P T IME= 5 .1 O O L O P = 1 2 5 . 0 3 O O L T I R = 4 . 3 6 O O L M A V = 4 . 1 9 A L T " 1 0 1 0 10 D C L ' ^ C = 1 3 1 0 6 . 3 2 " " D O L R C C = 1 6 3 8 0 . 0 0 " D O L T O T = 6 7 7 0 1 . 7 5 " S U R F A C E = 3 ~ O L D A L T E R N A T I V E = 8 0 7 0 8 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L O A D E D M P H = 1 7 . 3 9 T R I P T I M E = 9 . 1 OOLOP = 3 3 5 2 7 . 2 3 D n L T I R = 1 3 0 3 . 3 9 O O L M A V = 8 5 1 . 8 6 V E H K L E 2 E M P T Y " P H = 2 3 . 0 7 L Q A r E O M P H = 3 7 . 6 4 T R I P T I ME= 4 . 7 OOLOP = 2 3 3 9 . 6 7 DOL TI P. = 2 9 . 5 6 D P L M A V _ = 2 9 . 1 6 V E H I C L E 3 E M P T Y MPH .^^.~Zt> L C A P E D M>H = 3 5 . 2 7 T R I P T"lME = 5.1 DOLOP"» 125'.50" D O L f 1R = . '4 .~40 " O O L M A V = "V.Zb A L T 11 1 0 1 0 OCL^MC = 1 2 7 2 5 . 3 6 D G L R C C = 1 8 3 0 0 . 0 0 D O L T O T = 6 8 5 3 2 . 8 1 S U R F A C E = 3 O L D A L T E R N A T I V E = 1 0 0 7 C 8 V E H I C L E 1 E " P T Y " ° H = 1 9 . 1 2 L O A D E D MPH = 1 9 . 0 1 T R I P f ' l M E = 9 . 0 D O L O P = 3 2 9 0 9 . 3 0 D O L T I R = 1 2 5 6 . 84 D O L M A V = 8 2 3 , 9 3 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L O A D E D MPH = 3 7 . 7 4 T R I P T I ME = 4 . 7 O O L O P = 2 3 2 7 . 0 8 O O L T I R = 2 8 . 6 3 O O L M A V = 2 8 . 6 3 V E H I C L E 3 F M P T Y M P H = 2 1 . 6 6 L P A P E D M P H = 3 5 . 6 0 T R I P T IM E= 5 . 0 D O L O P = 1 2 4 . 5 0 D O L T I P = 4 . 3 3 D O L M A V = 4 . 1 2 A L T 11 11 1 0 D P L R " C = 1 2 0 8 6 . 32 O O L R C C = 2 2 3 4 0 . 0 0 O O L T O T = 7 1 6 5 3 . 3 8 S U R F A C E = 3 OLD A L T E R N A T I V E = 9 0 9 0 7 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L P A P E D M P H = 1 8 . 5 8 T R I P T I M E = 9 . 0 DOLOP = 3 2 7 6 9 . 0 5 D O L T I R = 1 1 6 3 . 7 4 DOLMAV = 7 6 8 . 0? V E H I C L E 2 E M P T Y " P H ' = 2 3 . 0 7 L O A D E D " P H =3 9 . 9 1 TR IP T IM E = 4 . 7 D O L O P = 2 3 3 8 . 7 3 D O L T I P . = 2 6 . 77 D O L M A V = ' 2 6 . 7 7 V E H I C L E 3 E M P T Y " P H = 2 1 . 6 6 L P A D E O M P H = 3 5 . 0 9 T R I P T I M £ = 5 .1 DOLOP = 1 2 5 . 9 5 D O L T I R = 4 . 1 9 O O L M A V = 3 . 8 4 A L T 11 l-> 10 D P L ° M C = 1 2 5 2 2 . 5 9 O O L R C C = 1 8 7 9 0 . 0 0 DOLTO 'T = 6 7 6 8 4 . 3 1 S U R F A C E = 3 O L D A L T E R N A T I V E = 9 1 0 0 7 V E H I C L E 1 E ." F T Y " P H = 1 9 , 1 2 L O A D E D MPri = 1 9 , 5 6 T R I P TI ME = 8 . 8 O O L O P = 3 1 9 0 1 . 0 2 . D O L T I R = 1 2 3 3 . 5 7 D O L M A V = 8 1 2 . 2 9 V E H I C L E 2 E M P T Y MPH = 2 3 . 0 7 L C A P E D MPH = 4 0 . 6 5 T R I P T I ME= 4 . 6 DOLOP = 2 2 3 6 . 5 1 O O L T I R . = . 2 0 . 2 8 D O L M A V = 2 8 . 2 8 V E H I C L E " 3 E M P T Y M P H = 2 1 . 6 6 L O A D E D M P H = 3 5 . 0 9 T R I P T I " . £ = 5 . 0 " " DOLOP = 1 2 3 . 4 0 D O L T I P = 4 . 2 7 O O L M A V = 4 . 0 6 A L T 11 13 1 0 D P L C M C = 1 2 3 3 2 . 1 1 D C L R C C = 1 9 7 5 0 . 0 _ 0 D O L T P T = 6 8 0 9 0 . 5 6 S U P F A C E = 3 C L P A L T E R N A T I V E = 1 0 1 1 0 8 V E n l C L E 1 E M P T Y MPH = 1 9 . 1 2 L O A D E D MPH = 1 9 . 1 3 T R I P T I M E = 8 . 7 D O L O P = 3 1 5 8 5 . 5 9 D O L T I R = 1 2 1 0 . 2 9 O O L M A V = 7 9 8 . 3 3 V E H I C L E 2 E M P T Y MPH = 2 3 . 0 7 L T A D E O MPH = 4 2 . 2 7 T R I P T I M E = 4 . 6 D O L O P = 2 2 2 7 . 4 3 D O L T I R = 2 7 . 8 1 D O L M A V = 2 7 . 8 1 V E H I C L E 3 _E.MPT Y_MPK__=21, 6 6 J . P . A r E D _ M P H _ = 3 5... 7 0 T RI P__fl_M.E= 5.0 DOLOP. = __l 5 O O L T I R_.= 4 . 2 4 DOLMA.V ..= 3 . 9 9 ... A L T 10 10 11 D C l = M C = 1 2 8 4 2 . 1 0 O O L R C C = 1 6 7 7 0 . 0 0 O O L T C T = 6 6 4 8 1 . 3 8 S U R F A C E ' = 3 O L D A L T F R N A T I V E = 8 0 8 0 9 V E H I C L E 1 E M P T Y " P H = 1 9 . 1 2 L O A D E D MPH = 1 7 . 4 0 T R I P T I M E = 8 . 9 O O L O P = 3 2 3 1 1 . 3 3 O O L T I R = 1 2 8 0 . 1 2 O O L M A V = 8 4 0 . 2 2 V E H I C L E 2 E M F T Y MPH = 2 3 . 0 7 L O A D E D MPH = 3 8 . 2 6 T R I P T1ME= 4 . 6 D O L O P = 2 2 5 1 . 1 1 D O L T J R = 2 9 . 2 1 O O L M A V = 2 9 . 2 1 V E H I C L E 3 E M P T Y MPH = 2 1 . 6 6 L O A D E D MPH = 3 7 . 3 2 T R I P T IME= 4 . 9 DOLOP = 1 1 9 . 4 8 D O L T I R = 4 . 3 4 D O L M A V = 4 . 2 0 A L T 11 10 11 DOLRMC = 1 2 9 1 5 . 8 4 D O L R C C = 1 7 3 4 0 . 0 0 O O L T O T = 6 8 1 3 6 . 0 6 SURFA~CF = 3 O L D A L T E R N A T I V E • 9 0 8 0 8 V E H I C L E 1 E M P T Y MPH = 1 9 . 1 2 L O A D E D MPH = 1 8 . 5 9 T R I P T I M E * 9 . 1 D O L O P = 3 3 2 3 6 . 7 2 O O L T I R = 1 2 8 0 . 1 2 D O L M A V = 8 3 7 . 9 0 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L C A P E D V P H = 3 8 . 6 2 T R I P T I M E = 4 . 7 O O L O P = 2 3 3 3 . 6 0 O O L T I R = 2 9 . 0 9 O O L M A V = 2 9 . 0 9 VEHICLE E*FTY MPH =21.66 LCADEO MPH =36.33 TP.IP TIM_ = 5.1 OOLOP = 125.13 DOLTIR 4.36 CCLMAv 4. 19 ALT 11 11 11 DCLP^C = 1 291 5. 84 DOLRCC = 17340.00 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LOADED MPH =lfl.61 TRIP T1ME= 9.1 VEHICLE 2 EMPTY =22.07 LCADED MPH =39.70 TRIP TIME= 4.7 VEHICLE E M P T Y M P H =21.66 LOADED M P H =37.32 T R I P T I M E " 5. 1 68136.00 SURFACE = 3 DOLOP = 33241.38 OOLTIP = DOLOP = 2329.02 DOLTIR = J}0L0P___ _124.9?_ DOLJJJL ALT U 12 11 DCl ?MC = 12534. 68 DCLRCC = 19260. 00 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LOADED MPH =18.59 TRIP TI ME = 9.0 VEHICLE 2 EMPTY »PH =23.07 LOADED MPH =40.65 TRIP T IME= 4.7 VEHICLE 3 EMPTY M P H =21.66 LCADED MPH =36.34 TRIP TIME= 5.2 OLD ALTERNATIVE 1280.12 DOLMAV = 29.09 OOLMAV = _4_. J6 0.0 L MA V _____ 69240.25 SURFACE = 3 OLD ALTERNATIVE DOLOP = 32918.19 DOLTIR = 1233.57 DOLMAV = DOLOP = 2291.07 DOLTIR = 28.16 DOLMAV = DOLOP = 127.92 OOLTIR = 4.29 DOLMAV = = 90909 637.90-29. 09 4. 19 • 91008 809. 97 28. 16 4.05 ALT 11 13 11 OOLPMC = 12344.39 DCLRCC = 20220.00 DOLTOT VEHICLE 1 EMPTY M P H =19.12 LOADED M P H =19.19 TRIP TIME' 9.0 VEHICLE 2 EMPTY MPH =23.07 LOADED M P H =42. 27 TRIP TI ME = 4.7 VEHICLE 3 EMPTY M P h =21.66 L DA DEO MPH =37.10 TRIP TIME= 5.1 69648.69 SURFACE = 3 OLD ALTERNATIVE = 101109 DOLOP = 32604.89 DOLTIR = 1210.29 DOLMAV = 796.00 OOLOP = 2202.00 DOLTIP = 27.70 00 L MAV = 27.70 DOLOP = 127.52 OOLTIR = 4.26 DOLMAV = 3.98 ALT 11 11 12 DCLPMC 12725.36 DOLRCC 18300. 00 OOLTOT 68548.44 SURFACE = OLD ALTERNATIVE VEHICLE 1 VEHICLE 2 VEHICLE 3 E M P T Y M P H =19.12 E M P T Y M P H =23.07 E M P T Y M P H =21.66 LCADEO M P H =19.22 LOADED M P H =40.47 LOADED M P H =38.15 TRIP TIME= 9.0 TRIP TIME = 4.7 TRIP TIME= 5.1 100910 DOLOP = 32929.14 DOLTIR = 1256 .84 DOLMAV = 823. 93 DOLOP = 2322.8 1 DOLTIR = 28.63 DOLMAV = 28.63 DOLOP = 124.61 . DOLTIP = . 4.33 DOLMAV = 4.12 A L T 11 12 12 D C - L B MC = V E H I C LE 1 C M P T Y M P H = 19 , VEHICLE VEHIC LE E M F T Y M P H =23.07 E M P T Y M P H =21.66 12915.84 DOLRCC = 17340.00 DOLTOT 12 LOA-OfO MPH =1B.6Q TRIP T IM E___ .9 ._0_ 4". 7 5.1 LOADED M P H =40.61 LOADED M P H =38.13 TRIP Tl ME = TRIP TIME = 67920.50 SURFACE = 3 OLD ALTERNATIVE = 91010 _0_OLOP__= _330_33.78 DOLTIR = 1280.12 DOLM AV___ 837. 90 _ DOLOP = 2321 .38 DOLTIP = 29. 09 DOLMAV = 29.09 DOLOP= 124.70 DOLTIR = 4.36 OOLMAV = 4.19 ALT 11 13 12 DDL PMC = 12215.36 DOLRCC « 21260.00 DOLTOI VEHICLE 1 EMPTY M P H =19.12 LOADED M O H =19.42 TRIP TIME = 8.9 VEHICLE_2 __FVPTY_'-PH_=2___.C7 LEAPED M P H =43_.33 TR \ P__T I ME_= 4.6.. " V E ' H T C L Y " EMPTY M;:h =21.66 LCADED MPH =37.54 TRIP T 1 ME = 5.1 ALT u 11 13 OCLPMC = 12215.36 DOLPCC = 21280.00 DOLTOT VEHICLE 1 FMPTY M P H =19.12 LOADED M P H =18.61 TRIP TIME= 9 .0 VEHICLE 2 EMPTY M P H =23.07 LCADED MPH =39.63 TRIP TIME = 4 .8 _V E ______ L E 3 EMPTY M P H =21.66 LOADED MPH =39 .49 TRIP TI ME= 5.0 70201.94 SURFACE = 3 CLD ALTERNATIVE = 101209 DOLOP = 32273.79 OOLTIR = 1187.02 DOLMAV = 782.04 DOLOP =__2274 . 10 _ 0OLTIR_« 27 .23 P0LMAV__= _2 7 . 2 3 "DOLOP"" 12 7.06 ~D0i.fi'p "= " 4.2 2"" " 0 OLMAv" " 3.91 " 70882. 13 SURFACE = 3 OLE ALTERNATIVE = 9091 1 DOLOP = 32886. 96 DOLTIR = 1187. 02 DOLMAV = 702.04 OOLOP = 2346.65 OOLTIP. = 27.23 OOLMAV = 27.23 OOLOP = 121.52 DOLTIR = 4.2.2 DOLMAV = 3.91 ALT 11 12 13 DGLRMf. = 12651. 62 DCLRCC = 17730. 00 DOLTOT VEHICLE 1 E M P T Y M P H =19.12 LOADED MPH =18.61 TRIP TIME= 8,8 VEHICLE 2 E M P T Y M P H =23.07 L CADED MPH = 4 0 . 6 5 T R I P TIME= 4.6 VEHICLE 3 EMPTY MPH =21.66 LOADED MPH =39.49 TRIP TIME= 4.9 66911.88 SURFACE = 3 OLD ALTERNATIVE = 91011 DOLOP = 32021.34 DOLTIR = 1256.84 DOLMAV = 826.26 DOLOP = 2240.92 DOLTIR = 28.74. DOLMAV = . 28.74 DOLOP = 118.97 DOLTIR = 4.31 OOLMAV = 4.13 ALT 11 13 13 D r L c u r . = 12725. 36 DOLRCC = 18300.00 DOLTOT VEHICLE 1 EMPTY MPH =19.12 LOADED MPH =19.22 TRIP TJME= 9.0 VEHICLE 2 EMPTY M P H =23.07 LCADED MPH =42.27 TRIP TIME= 4.7 VEHICLE 3 EMPTY MPH =21.66" LOADED MPH =39.84 TRIP TIME= 5.0 60454.50 SURFACE = 3 OLD ALTERNATIVE = 101111 DOLOP = 32853.21 OOLTIP = 1256.64 OOLMAV = 823.93' OOLOP = 2305.56 DOLTIP = 28.63 OOLMAV = . 28.63 OOLOP = 123.87 DOLTIR = 4.33 DOLMAV = 4.12 ALT 12 14 13 OfL^MC = 12160.C6 DOLRCC = 22910.00 OOLTOT = 71521.94 SURFACF OLD ALTERNATIVE = 101311 VEHICLE 1 VEHICLE 2 VEHICLE 3 EMPTY MPH =19. 12 EMPTY MPH =23.07 .vFTY " pH =21.66 LOADED MPH =19,61 LOADED MPH =44.34 LPAPED "PH =39.04 TRIP TIME= 8.8 TRIP TIME= 4.6 TRIP TI-ME= 5.1 ALT 11 11 14 .OCL'MC = 12024.88 OCLRCC = 22240.00 OOLTOT V r H I C L E 1 EM P T Y M P H _=_19 _J 2 LCAOFO M P H =19. ?_ T_R [ P_T J M,f, » 8, 9_ TEHFC'LE 2 EMPTY ? P H -2T .07 I f A t E O "MPH =40.39 TRIP T IME* 4.7 VEHICLE 3 EMPTY MPH =21.66 LOADED MPH =40.93 TRIP T1ME= 4.9 DOLOP = 32092.81 DOLTIR = 1163.74 DOLMAV = 765.74 OOLOP = 2242.26 OOLTIR = 26.65 DOLMAV = 26.65 DOLOP = 125.97 DOLTIR * 4.21 UOLMAV » 3.83 - 71294.38 SURFACE = 3 CLP ALTERNATIVE = 100912 _0nLOP_= 32574. 6.__ D01.T1 R _=_J.J 63, 74 POL MAV_. 7.<.i),.0.7__ DOLOP = 2340.42 DOLT 1R = 26. 77 OOLMAV = 26.77 DOLOP * 121.09 DOLTIR = 4.19 DOLMAV « 3.84 A L T 1 1 1 2 1 4 D C L P M C = 1 1 8 9 5 . 8 4 P O L R C C = 2 3 3 0 0 . 0 0 D O L T O T V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L P A D E O M P H = 1 9 . 4 9 T R I P T I M E = 8 . 9 Y E H 1 C L F 2 E M P T Y M P H = 2 3 . 0 7 L P A P E D M P H = 4 0 . 9 4 T R I P T 1 M E = 4 . 7 71S51.69 SURFACE = 3 OLD ALTERNATIVE = 101013 DOLOP- » 32246.43 DOLTIR * 1140.47 COLMAV = 754. 11 DOLOP » 2333.64 DOLTIR = 26___.Q Q_3.LM.Ay__; 2i..iCL_ r V E H I C L E 3 EMPTY MPH = 2 1 . 6 6 LOADED MPH = 4 1 . 8 1 T R I P T IME = 4 . 9 OOLOP = 1 2 0 . 7 2 D O L T I P = 4 . 1 5 DOLMAV = 3 . 7 7 A L T _ 11 _ 1 3 1 4 D C L P M C _ = 1 2 4 6 1 . 1 4 _ D O L R C C „ = 1 8 6 9 0 . 0 0 _ D O L T O T = 6 7 3 2 1 . 3 1 _ _ S U R F A C E _ = 3 O L D A L T E R N A T I V E = 1 C 1 1 1 2 V E H I C L E 1 E M P T Y M P H = 1 9 . 1 2 L O A D E D M P H = 1 9 . 2 2 T R I P T I M E = 8 . 8 D O L O P = 3 1 7 0 9 . 0 3 D O L T I P . = 1 2 3 3 . 5 7 D O L M A V = 8 1 2 . 2 9 V E H I C L E 2 E M P T Y M P H = 2 3 . 0 7 L O A D E D M P H = 4 2 . 2 7 T R I P T I ME = 4 . 6 D O L O P = 2 2 3 1 . 8 4 D O L T I R = 28 . 2 8 D O L M A V = 2 8 . 2 8 V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 L O A D E D M P H = 4 0 . 9 3 T R I P T I M E = 4 . 9 O O L O P = 1 1 8 . 5 4 D O L T I R = 4 . 2 7 D O L M A V = 4 . 0 6 A L T 1 2 1 2 1 5 D C L C M C = 1 1 7 6 6 . 8 1 O C L P C C = 2 4 3 6 0 . 0 0 D O L T O T = 7 2 3 9 7 . 6 3 S U R F A C E = 3 O L D A L T E R N A T I V E = 1 0 1 0 1 4 V E H I C L E I E M P T Y " P H = 1 9 . 1 2 • L O A D E D M P H = 19 . 6 1 _ _ T R I P T I ME= _ 8 . _8 D O L O P = 3 1 9 0 7 . 7 6 O O L T I R = 1 1 1 7 . 1 9 D O L M A V = 7 4 0 . 1 4 V E H I C L E 2 E M P T Y " P H = 2 3 . 0 7 L O A D E D M P H = 4 1 . 2 6 T R I P T I M E * 4 . 7 D O L O P = " 2 3 2 5 . 9 7 D O L T I R" = 2 5 . 8 4 D O L M A V = ' 2 5 . 6 4 V E H I C L E 3 E M P T Y M P H = 2 1 . 6 6 L O A D E D M P H = 4 2 . 7 2 T R I P T I M E = 4 . 9 D O L O P = 1 2 0 . 2 9 D O L T I R = 4 . 1 2 D O L M A V = 3 . 7 0 ALT 12 14 15 OCLRMC = 1 2 2 0 3 . 0 7 DOLRCC = 2 0 8 1 0 . 0 0 DOLTOT = 6 8 2 6 8 . 1 3 SURFACE = 3 OLD A L T E R N A T I V E = 1 0 1 3 1 4 V E H I C L E 1 EMPTY MPH = 1 9 . 1 2 LOADED MPH = 1 9 . 7 3 T R I P T IME= 8 . 6 DOLOP = 3 0 8 8 8 . 28 O O L T I R = 1 1 8 7 . 0 2 DOLMAV "= 7 3 4 . 3 6 . V E H I C L E _ 2 . EMPTY M P H = 23.0_7_ LOADED MPH = 4 4 . 3 4 . _ T R I P T IME = 4 . 5 _ D O L O P ^ 2 2 1 4 . 8 5 _ DOLT IR = 2 7 . 3 5 DOLMAV = 2 7 . 3 5 V E H I C L E . 3 EMPTY « P H = 2 1 . 6 6 LOADED MPH = 4 2 . 7 2 T R I P T I M E " 4 . 8 DOLOP = ~ 1 1 7 . 7 4 O O L T I R = ~ 4 . 2 0 DOL MA V = " " 3 . 9 2 ALT 12 15 15 0 C I R " C - 1 1 6 2 2 . 1 1 DOLRCC = 2 2 . 7 3 0 . 0 0 DOLTQT = 6 9 6 1 9 . 6 9 SURFACE = 3 OLD A L T E R N A T I V E = 1 0 1 4 1 5 V E H I C L E 1 EMPTY " P H = 1 9 . 1 2 LOADED MPH = 1 9 . 5 1 T R I P TIME= 8. '6 DOLOP = 3 0 8 0 2 . 8 7 DOLT IR = 1 1 4 0 . 4 7 DOLMAV = 7 5 6 . 4 3 V E H I C L E 2 EMPTY " P H = 2 3 . 0 7 L C A P E D MPH = 4 6 . 5 7 T R I P T IME= 4 . 5 DOLOP = 2 1 9 0 . 5 6 D O L T I R = 2 6 . 4 2 DOLMAV = 2 6 . 4 2 V E H I C L E _ 3 EMFTY_ M P H _ = 2 1 . 6 6 _ L P A P E D MPH_= 4 4 . 9 8 _ _ T R I P T I M E * __4. 8 DOLOP = 1 1 6 . 5 0 DOLT IR = _ 4 . 1 3 _ OOLMAV = 3 . 7 8 MA IN S E C T I O N M J M 8 E F . 3 S U B S E C T I O N NUMBER 2 ALT 1 1 I DCLPMC = 1 3 6 1 9 . 0 9 O C L P C C = 1 4 3 5 0 . 0 0 -DOLTOT = 7 3 0 5 8 . 4 4 SURFACE = 1 OLD A L T E R N A T I V E = 6 0 5 0 7 V E H I C L t _ 1 . E M ? T Y _ ' . ' P H ^ = i 0 . 6 7 _ LPA PED M PH_=_3 . 5_6 I R 1_P J LL M E= 9 . 4 DOLOP = 3 8 9 8 5 . 0 8 DOL TI R _ =_1547 . 7 8 _ DOLMAV = 1 0 0 0 . 82 V E H I C L E 2 EMPTY " P H = 1 5 . 5 2 LPAOEO MPH = 9 . 7 6 T R I P T I M E * 4 . 8 DOLOP = 2 6 3 4 . 7 0 DOLT I R~ = "" 3 4 . 5 6 " " " COLMAv" = 3 4 . 5 6 V E H I C L E 3 EMPTY MPH = 1 3 . 7 7 L P A P E D MPH = 8 . 0 5 T R I P T IME= 5.1 DOLOP = 1 4 1 . 8 8 DOLT I P = 5 . 0 0 DOLMAV = 5 . 0 0 ALT 5 1 1 O C I . P M C = 1 3 8 1 9 . 0 9 OOLRCC = 1 4 8 5 0 . 0 0 DOLTOT = 7 3 4 7 3 . 1 3 SURFACE = 2 OLD A L T E R N A T I V E = 1 0 1 0 1 V E H I C L E 1 E r ' P T Y M P H = 1 6 . 0 3 LOADED MPH = 1 0 . 6 3 T R I P T I ME= 9 . 4 DOLOP = 3 9 3 6 8 . 4 7 " D O L T I R = 1 5 4 7 . 7 8 OOLMAV = 1 0 0 0 . 82 V E H I C L E _ 2 EMPTY " P H = 2 0 . 4 7 LCA DED_ MPH_ = 2 3 . 16 T R I P TI ME= _ 4 . 8 OGLOP _=__ _2664 . 0 9 OOLTIR. = 3 4 . 5 6 OOLMAV = _ 3 4 . 56. V E H I C L E 3 EMPTY M P H = 1 8 . 9 0 ' L C A T E O MPH = 2 1 . 3 7 t R I P f IM fc= 5 . 2 DOLOP = " ~ 1 4 3 . 7 8 " 0 0 L T I > . ~ « ' ' 5.00 ~ 0 O L " A \ ' " « " 5.00" ALT 7 1 2 D C L g M C = 1 3 6 1 6 . 3 2 DOLRCC = 1 5 8 1 0 . 0 0 DOLTOT = 7 3 6 1 1 . 13 SURFACE = 3 OLO A L T E R N A T I V E = 1 0 1 0 1 V E H I C L E 1 EMPTY M P H = 1 8 . 2 0 L P A P E D M P H = 1 4 . 1 0 T R I P T IME= 9 . 4 DOLOP = 3 8 8 8 0 . 3 0 OOLT IR = 1 4 7 7 . 9 6 DOLMAV = 9 5 8 . 9 3 V E H I C L E 2 EMPTY MPH, = 2 2 . 3 0 L C A P E D MPH = 2 5 . 0 1 T R I P T IME= 4 . 8 DOLOP = 2 6 4 8 . 7 6 DOLT IR = 3 3 . 1 7 DOLMAV = 3 3 . 1 7 V _ E H I C L E _ 3 EMPTY MPH =20,.84 L P A P E D MPH = 2 3 . 3 3 T R I P _TJ.ME= 5.1 DOLO_P_ = 1 4 2 . 8.4 0 O L T i R _ = 4 . 9 0 OOLMAV = 4 . 7 9 ALT 2 2 2 O H . C " C = 1 4 1 2 0 . 1 7 OOLRCC = 1 4 4 6 0 . 0 0 OOLTOT = • 7 6 2 1 0 . 4 4 SURFACE = 1 OLD A L T E R N A T I V E = 1 0 1 0 1 V E H I C L E 1 EMPTY MPH = 1 0 . 6 7 L C A P E D MPH = 4 . 3 6 T R I P TIM,E= 9 . 6 OOLOP = 4 2 0 2 3 . 5 8 O O L T I R = 1 6 1 7 . 6 0 00 LMAV = 1 0 3 5 . 7 3 V E H I C L E 2 EMPTY " P H = 1 5 . 5 2 L C A P E D MPH = 1 7 . 9 0 TP. IP T IM E= 4."9 OOLOP = 2 7 2 4 . 17 DOLT IP = 3 5 . 6 1 OOLMAV = 3 5 . 6 1 V E H I C L E 3 EMPTY « P H = 1 3 . 7 7 LOADED M P H = 1 5 . 8 6 - T R I P T I M £ = 5 . 2 DOLOP = 1 4 7 . 6 0 D O L T I R = 5 . 1 8 OOLMAV = 5 . 1 3 ALT v " ' 2 2 P.-1-.MC = 1 4 C 8 3 . 3 C P?l . FCC = 1 4 4 6 0 . 0 0 DOLTOT = 7 3 7 4 9 . 7 5 S U R F A C E = 2 OLD ALTERNAT [VE""= 2 0 2 0 2 V E H I C L E 1 E M P T Y M C H = 1 6 . 0 3 LOADED MPH = 1 0 . 7 3 T R I P T IME= 9 . 6 DOLOP = 3 9 7 8 9 . 7 2 DOLT IR = 1 5 7 1 . 0 5 DOLMAV = 1 0 1 2 . 4 6 V E H I C L E 2 EMPTY M P H =20 . 4 7 LPAOEO MPH = 2 5 . 9 9 TR IP T I ME= 4 . 9 OOLOP = 2 6 1 2 . 7 1 OOLT IR = 3 4 . 9 1 OOIMAV = 3 4 . 9 1 V E H I C L E 3 E M P T Y " ° H = 1 8 . 9 0 L P A P E D MPH = 2 3 . 8 6 T R I P TIME= 5 .2 DOLOP = 1 4 0 . 5 6 DOLT IR = 5 . 0 6 DOLMAV = 5 . 0 6 ALT 7 _ 3 4__ OPL°MC_=__ 1 3 3 8 0 . 5 3 _ DCL RCC _= _ 1 _ 5 4 2 0 . 0 0 _ _ 0 O L T O T _ = _ 7 3 8 9 5 . 2 5 . _ S U R f A C E._=... .3 OLD A L T E R N A T I V E * 2 0 2 0 2 V E H I C L E " " 1 E » P T Y - M P H = 1 6 . 2 0 " " L O A D E O " P H " = 1 4 7 2 1 " "f R l > T I K E * 9 . 6 DOLOP = 3 9 3 0 7 . 5 2 O O L H R = 1 5 0 1 . 2 3 DOLMAV = 9 7 0 . 5 6 V E H I C L E 2 EMPTY M P H =22 . 30 LCA n E D M PH = 2 7 . 8 1 T R I P T IME= 4 . 9 DOLOP = 2 5 9 8 . 83 D O L T I R = 3 3 . 5 2 DOLMAV = 3 3 . 5 2 V E H I C L E 3 EMPTY MPH = 2 0 . 6 4 LOADED MPH = 2 5 . 8 0 T R I P TIME= 5 . 2 DOLOP = 1 3 9 . 7 0 DOLT IR = 4 . 9 6 POLMAV = 4 . 8 5 ALT 6 4 4 OCLRMC = 1 3 7 8 2 . 2 1 DOLRCC = 1 4 8 5 0 . 0 0 DOLTOT = 7 0 6 7 3 . 0 6 SURFACE = 2 OLD A L T E R N A T I V E = 5 0 1 0 1 V E H I C L E ^ I EMPTY M P H _=16 .03_ LOADED MPH_ = 1 2 . 4 7 „ T R J P T1 ME=_ __?_._4 DOLOP_= 3 6 8 0 3 . 3 1 O O L T I R _ = 1 5 0 1 . 2 3 _ DOLMAV = 9 7 7 . 5 5 V E H I C L E 2 EMPTY MPH = 2 0 . 4 7 LOADED MPH = 2 8 . 73 T R I P T I M E * " 4 . 8 OOLOP = " " 2 5 4 4 . 9 4 DOLTI R = 3 3 . 8 6 DOLMAV = " 3 3 . 8 6 ' V E H I C L E 3 F K P T Y M P H = 1 8 . 9 0 LOADEO MPH = 2 6 . 6 5 T R I P T I M E * 5 . 2 OOLOP = 1 3 6 . 2 8 OOLT IR = 4 . 8 9 OOLMAV = 4 . 3 9 - 6 8 -APPENDIX 8 COST DATA FOR HYPOTHETICAL PROBLEM Road s u r f a c i n g c o s t s v a r i e d w i t h s u r f a c e t y p e and r o a d g r ade as f o l l o w s : S u r f a c e t y p e B a s i c c o s t A d d i t i o n a l c o s t f o r i n c r e a s e d g r ade $/s . ta 0-5% 6-10% 11-157, d i r t 250 0 0 0 g r a v e l 500 0 0 10 pavement 1000 0 100 100 The c o s t o f m a i n t a i n i n g the r o a d s u r f a c e v a r i e d w i t h s u r f a c e t y p e , r o a d g r ade and t r a f f i c d e n s i t y as f o l l o w s : S u r f a c e B a s i c c o s t A d d i t i o n a l c o s t f o r A d d i t i o n a l c o s t f o r t y p e $ / s t a i n c r e a s e d g r ade i n c r e a s e d t r a f f i c 0-5% 6-10% 11-15% d e n s i t y m u l t i p l e s 1 2 6 12 24 d i r t 80 0 0 0 0 10 50 110 190 g r a v e l 40 0 0 5 0 5 25 50 95 pavement 10 0 10 10 0 2 10 22 38 The d i r e c t v e h i c l e o p e r a t i n g c o s t s were $ 0 . 7 5 / m i n . , $ 1 . 0 0 / m i n . and $ 0 . 5 0 / m i n . f o r l o g g i n g t r u c k s , c r e w b u s s e s and s e r v i c e v e h i c l e s r e s p e c t i v e l y . The t i r e c o s t s v a r i e d w i t h v e h i c l e t y p e and s u r f a c e as f o l l o w s : S u r f a c e t y p e V e h i c l e . type l o g g i n g t r u c k c r e w bus s e r v i c e v e h i c l e $ / m i l e $ / m i l e $ / m i l e  d i r t 0 . 5 0 0 . 1 0 0 . 1 5 g r a v e l 0 ; 3 0 0 . 0 7 0 . 1 0 pavement 0 . 1 0 0 . 0 3 0 . 0 7 I n t h e above c o s t s t h e g r a d e s were t a k e n t o be e i t h e r f a v o r a b l e o r a d v e r s e . - 6 9 -V e h i c l e m a i n t e n a n c e c o s t s as a f f e c t e d by s u r f a c e t y p e a r e as f o l l o w s : S u r f a c e t y p e V e h i c l e t y p e l o g g i n g t r u c k c r e w bus s e r v i c e v e h i c l e $ / m i l e $ / m i l e $ / m i l e  d i r t 0 . 3 0 0 . 1 0 0 . 1 5 g r a v e l 0 . 2 0 0 . 0 7 0 . 1 0 pavement 0 . 0 8 0 . 0 3 0 . 0 4 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0100111/manifest

Comment

Related Items