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A deterministic simulation of logging truck performance Levesque, Yves 1975

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A DETERMINISTIC SMJLATION OF LOGGING TRUCK PERFORMANCE by YVES LEVESQUE B. A. Sc., Laval U n i v e r s i t y , Quebec, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF ., •  MASTER OF FORESTRY i n the Faculty of FORESTRY  We accept t h i s thesis as conforniing to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1975  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 f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree 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 f o r reference  and  study.  I f u r t h e r agree that permission f o r extensive copying of t h i s thesis f o r s c h o l a r l y purposes may by h i s representatives.  be granted by the Head of my Department or  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 f o r f i n a n c i a l gain s h a l l not be allowed without my written permission.  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada  iii  ABSTRACT  A deterministic simulation model i s developed and programmed f o r a d i g i t a l computer to represent  the movement of logging trucks f o r s p e c i f i e d  alignment (actual or proposed) and  truck-parameters.  The force accelerating the v e h i c l e i s taken as the difference between transmission output wheel force and the resistance force at conditions at the instantaneous v e h i c l e speed.  steady-state  The accelerating force i s  taken as constant over a small incremented distance and r e s u l t s i n a v e h i c l e speed with new  loading conditions.  gear, and time-distance The  The process i s repeated through each  and time-speed data are obtained.  '  technique described can be used to b u i l d up a distance t r a v e l l e d -  time consumption h i s t o r y f o r a v e h i c l e on a defined route.  Such p r e d i c t i o n  enables a meaningful evaluation to be made of the time of a s p e c i f i e d trip. Such an approach produces r e s u l t s acceptably  close to observed data.  ACKNOWLEDGEMENTS  I wish to express my gratitude to Assistant Professor G. G. Young, Faculty of Forestry, who suggested the problem and under whose direction this study was undertaken.  His assistance and constructive criticism were'  of great benefit. The thesis was reviewed by Dr. A. Kozak, Assistant Professor V. G. Wellburn and by Associate Professor L. Adamovich.  Their comments were  greatly appreciated. A large part of the data was made available by Messrs. H. Waelti and L. J. Porpaczy, Forest Engineering Division of the British Columbia Forest Service.  I am most thankful to them.  Financial assistance was granted to the author i n the form of fellowships by the Quebec Department of Lands and Forests and i n the form of teaching assistantships by the University of British Columbia. Finally, I am most grateful to my wife, Claire, whose interest and stimulating understanding contributed greatly for making this entire undertaking an enjoyable and rewarding experience.  V  TABLE OF CONTENTS Page ABSTRACT  —  ACKNOWLEDGMENTS  —  i i i —  iv  LIST OF FIGURES  viii  LIST OF TABLES  ix  Chapter 1  2  INTRODUCTION  1  1.1 The road engineering process 1.2 An approach to the problem 1.3 Objective o f the study 1.4 Outline of the study  1 1 3 4  •  GENERAL ASPECT OF THE STUDY 2.1 Note on the modeling concept 2.2 Overview o f the model 2.21 General assumption • 2.3 The computer program r  3  :  5 • —  RELATIONSHIPS BETWEEN ROAD CONDITIONS AND THE SPEED OF VEHICLES 3.1 Introduction 3.2 Maximum permissible speed on curves 3.21 Assumptions 3.22 Centrifugal force as a speed control 3.221 Assumptions —• 3.23 Sight distance as a speed control 3.24 Comparaison of speed l i m i t s on curves with empiri c a l values from a previous study 3.3 Maximum permissible speed as controlled by surface conditions 3.31 Previous study • — 3.32 Winter conditions 3.4 Speed l i m i t on favorable grade -— 3.41 Sight distance as a speed control 3.42 Braking capacity as a speed control —  5 5 9 9  15 15 15 17 18 20 21 27 27 29 31 31 31 31  vi  Chapter  Page 3.5 3.6 3.7  4  4.5 4.6  6  :  32 32 34  RELATIONSHIPS BETWEEN VEHICLE CHARACTERISTICS AND SPEED 4.1 4.2 4.3 4.4  5  Speed l i m i t on adverse grade The independent v a r i a b l e s Conclusion  Introduction • Manual transmission modeling • : Torque-converter transmission modeling Method of s o l u t i o n 4.41 Manual transmission procedure 4.42 Torque-converter transmission procedure Braking ; The independent v a r i a b l e s •  —  36  —  36 36 40 42 . 42 44 44 45  MODEL TESTING  47  5.1 5.2 5.3  47 47 49  Introduction The t e s t s i t u a t i o n Predicted versus measured times  •  DISCUSSION AND CONCLUSIONS 6.1 6.2 6.3  53  Using the model to make decisions Areas o f f u r t h e r i n v e s t i g a t i o n Conclusion  BIBLIOGRAPHY  •  53 53 54 55  APPENDIX 1.  ECONOMIC EQUATIONS OF ALTERNATIVE ROAD ALIGNMENTS  57  APPENDIX 2.  EFFECTIVE ENGINE POWER  APPENDIX 3.  GRADE RESISTANCE  65  APPENDIX 4.  ROLLING RESISTANCE  66  APPENDIX 5.  AERODYNAMIC RESISTANCE  68  APPENDIX 6.  CURVE RESISTANCE  70  APPENDIX 7.  INERTIA RESISTANCE  71  APPENDIX 8.  NOMOGRAPHS ON ENGINE BRAKE DEVICE  72  APPENDIX 9.  ANALYSIS OF VARIANCE A9.1 Travel empty A9.2 Travel loaded  76 76 78  . 6 2  •  vii  Page APPENDIX 10.  APPENDIX 11.  TESTING FOR SIMILARITY OF SLOPES  A10.1 A10.2  Travel loaded Travel empty  -  •  THE COMPUTER PROGRAM A l l . 1 Input cards All.2 Computation time requirements All.3 FORTRAN l i s t i n g of computer program ;  80  •  80 82 •— —  83 83 86 87  viii  LIST OF FIGURES Figure 2.1 2.2 3.1 3.2 3.3 3.4 3.5 3.6 3.7  Page Diagram of the model Flow diagram of the program Portion of a road divided i n t o sections of uniform characteristics —•— Cross section of a v e h i c l e on a superelevated curve Grade force acting on a v e h i c l e Geometry f o r determining sight distance when sight distance i s l e s s than length of curve Transversal p o s i t i o n of parameters Geometry f o r determining sight distance when sight distance i s greater than length of curve — Comparaison o f t h e o r i t i c a l speed l i m i t s on curve with empiri c a l values • ; Maximum descent speeds assumed by the model when no engine brake i s used T y p i c a l engine data • — • Typical torque converter data — — A comparaison of actual and predicted cumulative times f o r t r a v e l loaded A comparaison of actual and predicted cumulative times f o r t r a v e l empty -• Grade resistance o f a truck Projected f r o n t a l area o f loaded and empty trucks Maxiimjm descent speed f o r 100% Jacobs engine brake controlD e t r o i t d i e s e l engine Maximum descent speed f o r 100% Jacobs engine brake control(LXimmins engine Maximum descent speed f o r 100% Jacobs engine brake controlMack engine ;  3.8 4.1 4.2 5.1 5.2 A3.1 A5.1 A8.1 A8.2 A8.3  6 12 16 18 22 24 25 27 28 33 38 41 50 51 65 69 73 74 75  ix  LIST OF TABLES Table 3.1 3.1 3.2 3.2 4.1 A2.1 A9.1 A9.2 A9.3 A9.4 A10.1 A10.2  Page MaxinMm speeds as controlled by surface 30 Coefficient of sliding f r i c t i o n (M ) • 34 Loaded tire radius i n inches (off-nighway tread) 46 Average barometric pressures for various altitudes above sea level • 63 Observed times for travel empty 76 Analysis of variance for travel empty 77 Observed times for travel loaded 78 Analysis of variance for travel loaded 79 (IXimulative actual and predicted times for each section for travel loaded 80 Cumulative actual and predicted times for each section for travel empty •— •• • -— 82  Chapter 1 INTRODUCTION  1.1  The road engineering process When i t comes to determining the standard of road to be constructed  the designer has to Lake i n t o account many things which have an important bearing on costs.  In f a c t , he i s interested i n analyzing a large number  of a l t e r n a t i v e alignments i n order to most nearly optimize h i s f i n a l l o cation from an economic standpoint.  B a s i c a l l y he has to estimate the  probable costs of a c e r t a i n type o f road f o r a c e r t a i n service l e v e l and accordingly determine whether i t i s economically j u s t i f i e d  (the reader  i s r e f e r r e d to Appendix 1 f o r more d e t a i l s ) . To do so, the decision-maker needs information that w i l l help him assess the r e l a t i v e strengths and weaknesses of each a l t e r n a t i v e .  Some  of the d i f f i c u l t i e s i n h i s analysis are the many assumptions that must be made.  These assumptions enter into the development of the hauling  time, v e h i c l e operating costs, hauling costs and road construction and maintenance costs.  Differences i n the b a s i c assumptions may throw the  f i n a l r e s u l t e i t h e r way and therefore the computations as the i n i t i a l assumptions. 1.2  are only as good  .  An approach to the problem Suppose that a designer has a model or has gained experience i n the  2  f o r e c a s t i n g o f road construction and maintenance costs.  Gain of experience  i n the f o r e c a s t i n g o f these costs could be j u s t i f i e d by the f a c t that one knows pretty well how much i t w i l l cost f o r a d d i t i o n a l miles a f t e r constructing many miles under the same conditions.  Since road construction and  maintenance costs are predicted, the remaining cost to p r e d i c t i n order to evaluate a l t e r n a t i v e road designs i s the operating cost of v e h i c l e s (hauling c o s t ) . I t i s very d i f f i c u l t f o r the road designer to p r e d i c t operating  cost  since there are not two roads with the same alignment and p r o f i l e and f u e l consumption, t i r e wear  o i l consumption and maintenance o f vehicles are  c l o s e l y r e l a t e d to them. consumption and t i r e wear.  For example, grades a f f e c t p a r t i c u l a r l y f u e l Steeper more frequent grades require extra energy  (extra f u e l ) and extra t r a c t i o n ( t i r e wear) to ascend them.  On curves extra  t i r e wear and f u e l consumption are due to the surface f r i c t i o n resistance produced by turning the steering against the d i r e c t i o n o f v e h i c l e motion. Road surface conditions a f f e c t a l l running costs ( f u e l consumption, t i r e wear, o i l consumption, r e p a i r and maintenance).  Compared to hard surfaces  extra energy i s needed on gravel surfaces and t i r e s are subject to the d e t e r i o r a t i n g e f f e c t s of v i o l e n t shocks (washboard).  O i l consumption i s  affected by dust; the more dusty the surface the greater frequency of engine o i l changes.  F i n a l l y , truck maintenance cost i s a f f e c t e d by the  roughness of the road surface on the suspension and by dust on the wear of c y l i n d e r walls.  The change from an i n i t i a l speed to a lower speed  followed by an a c c e l e r a t i o n to regain t h i s i n i t i a l speed requires again extra f u e l .  These frequent speed changes are often due to curves o r  3  i n s u f f i c i e n t road width f o r a c e r t a i n t r a f f i c density causing interferences among v e h i c l e s .  They involve also extra t i r e wear due to f r i c t i o n a l wear  during braking and t r a c t i o n wear during acceleration.  Furthermore,  maintenance cost i s increased by brake wear during deceleration and transmission wear during acceleration.  On a mile b a s i s , f o r an average truck  these running costs may be as important as §0.61 f o r repairs and maintenance, §0.16 f o r f u e l and l u b r i c a n t s and §0.32 f o r t i r e s and tubes (Boyd and Young, 1969). The determination o f operating costs as a function o f road geometry c h a r a c t e r i s t i c s , as described above, i s not known accurately yet. a l l costs involve a time element and most accounting d i r e c t operating cost as hourly costs.  However,  systems record the  In other words, with those account-  ing systems v e h i c l e s are wearing out t i r e s , consuming f u e l and accumulating other charges a t a constant time rate (machine r a t e ) .  Use of the machine  rate and p r e d i c t i o n o f the t r a v e l time would therefore enable the close estimation o f t r a v e l cost. 1.3  Objective o f the study The aim o f the study was to produce a simulation model that p r e d i c t s  travel times o f logging trucks f o r s p e c i f i e d alignment (actual o r proposed) and truck parameters.  I t i s a deterministic simulation which w i l l  output  information on the speed and time f o r a logging truck to traverse sections of the road unaffected by t r a f f i c .  Among the numerous f a c t o r s included as  independent v a r i a b l e s i n the model are the alignment, grades, surface type, and v e h i c l e c h a r a c t e r i s t i c s such as horsepower (HP) versus revolutions per minute (RPM) o f the engine, gear r a t i o s and rear axle r a t i o .  4  I t must be c l e a r that no attempt i s made i n t h i s study to p r e d i c t t r a v e l cost, only t r a v e l time.  The purpose  o f the previous explanation  (discussed i n Sec. 1.2) was to show the p o s s i b i l i t y o f using machine rate times t r a v e l time to p r e d i c t the t r a v e l cost u n t i l more accurate approach i s available. 1.4  Outline of the study Chapter 2 presents an overview o f the model.  In Chapter 3 r u l e s and  f u n c t i o n a l r e l a t i o n hips are developed to simulate v e h i c l e behavior as a function o f road geometry.  The speed o f the v e h i c l e r e l a t e d to i t s d r i v e -  l i n e c h a r a c t e r i s t i c s constitutes the core of the simulation model and i s developed i n Chapter 4.  Measured versus computed r e s u l t s along with the  findings are the subject o f Chapter 5.  This i s followed by the f i n a l  conclusions, Appendices and a l i s t i n g and output o f the computer program.  5  Chapter 2 GENERAL ASPECT OF THE STUDY  2.1  Note on the modeling  concept  Planning can be performed without developing models but the s i z e and complexity o f f o r e s t systems i s such that a n a l y t i c a l models are needed. A model i s a representation of a set of e s s e n t i a l r e l a t i o n s h i p s present i n a system.  The word e s s e n t i a l i s important because i n s i t u a t i o n s as  complex as those encountered i n road engineering and t r a f f i c systems,  one  i s forced f o r p r a c t i c a l considerations to t r y to reduce the number of v v a r i a b l e s included i n the model.  The r e l a t i o n s h i p s , i f properly expressed,  enable a model to react to a new environment  i n a manner s i m i l a r to that  of the system by which the model i s v a l i d a t e d . 2.2  Overview o f the model Vehicle t r a v e l time i s a d i r e c t function of engine RPM,  gear r a t i o s , and v e h i c l e t r a c t i v e e f f o r t ( r i m p u l l ) .  engine torque,  The l a s t i n turn i s  d i r e c t l y r e l a t e d to c e r t a i n road design c h a r a c t e r i s t i c s such as v e r t i c a l alignment or p r o f i l e , the unbalanced force caused by curves, surface type and operational r e s t r i c t i o n s .  The model takes these design c h a r a c t e r i s t i c s  and a d e s c r i p t i o n of the trucks to mimic v e l o c i t i e s , accelerations and decelerations by mathematical deterministic simulation. could be reprensented by the diagram of Figure 2.1.  Schematically t h i s  6  desired  throttle.  velocity  DRIVER  POWERPLANT  •H  tiO  o  •iH •P (ti  U.  O  rH CD >  _  •a  CD  <u (0  Si  <u  rH Q) O O at  ROAD GEOMETRY  motion  VEHICLE DYNAMICS  resistances  Figure 2.1 Diagram o f the model  The problem of expressing the performance  i n terms of kinematics  and engineering mechanics s t a r t s with the elementary concept of motion and natural laws which produce motion.  The primary concern i s with a  p a r t i c u l a r type o f motion c a l l e d t r a n s l a t i o n which denotes a displacement along a s t r a i g h t l i n e path.  The conventional concepts o f distance, time,  v e l o c i t y and a c c e l e r a t i o n are associated with t r a n s l a t i o n .  The d i f f e r e n t i a l  equations defining the translatory motion of a v e h i c l e can be expressed  7  as v = ds dt and a = dv = ds dt dt  dv = v dv ds ds  Therefore dv = a ds v  ...(2.1)  dt = dv a  ...(2.2)  and  where t = time, sec s = distance, f t v = velocity, ft/sec 2 a = acceleration, ft/sec . In a d d i t i o n to the preceeding expressions f o r time and speed, the causes of motion and the associated concepts of force, mass and a c c e l e r a t i o n must be considered.  The explanation i s found i n Newton's law of  motion from which the f a m i l i a r r e l a t i o n s h i p Force = Mass times A c c e l e r a t i o n (F=ma) i s derived.  T h i s expression provides the l i n k r e l a t i n g the v e h i c l e  translatory motion to i t s cause-the net d r i v i n g force at the wheels. This value f o r a c c e l e r a t i o n i s substitued i n the previous equations (2.1) and (2.2) to give  dv = F(v) ds mv  (2.3)  dt = m dv F(v)  (2.4)  and  8  where F ( v ) , the net d r i v i n g force a t the wheels, i s a function of v e l o c i t y (developed i n Chapter 4). In the model the road i s divided into inany sections of uniform characteristics.  The safe speed that can be maintained over each section, unaf-  fected by t r a f f i c , i s computed from the road and v e h i c l e data (developed i n Chapter 3 ) .  Then by d i v i d i n g the sections into subsections o f constant  length (ds) the time to traverse from one  subsection to the next and the  new v e l o c i t y a t the end of each subsection, keeping the forces constant over t h i s small increment, can be evaluated by v = 2 v ds f F ( v ) 1 m  ...(2.5)  t=  ...(2.6)  »  L  J  and 2  dv r  ml.  LF(V)J This process i s repeated u n t i l the maximum safe speed i s reached or dec e l e r a t i o n i s necessary.  I f the maximum safe speed i s reached then the  simulated truck t r a v e l s a t constant speed u n t i l a new speed l i m i t i s imposed r e q u i r i n g a c c e l e r a t i o n or deceleration.  Each time a new v e l o c i t y  i s computed the v e h i c l e i s checked to determine i f i t i s i n the corresponding correct gear.  I f not, s h i f t i n g i s made to the proper one.  made to determine i f braking should Start.  A check i s also  Braking w i l l begin a t the proper  time and the simulated truck w i l l be decelerate to the correct speed a t the end o f the course o r a t the end o f any interim section i f a lower speed r e s t r i c t i o n has been placed on the next section.  The time to traverse each  subsection i s accumulated leading to hauling time ( t r a v e l empty and t r a v e l loaded) p r e d i c t i o n unaffected by t r a f f i c .  9  2.21  General assumption  The general assumption i s that whenever possible the v e h i c l e i s assumed to t r a v e l a t wide open t h r o t t l e .  This assumption i s j u s t i f i e d  by the f a c t that a s k i l l f u l l d r i v e r w i l l generally achieve the maximum attainable speeds except when l i m i t e d by t r a f f i c o r operational speed r e s t r i c t i o n s on safe speed l i m i t s as c o n t r o l l e d by road geometry.  This  assumption i s supported by studies made by Campbell and Van der Jagt (1969) and by Oglesby et a.V. (1971). 2.3  The computer program The complexity  o f the mathematical r e l a t i o n s h i p s among the parameters  and the amount of c a l c u l a t i o n s required to scan a road l e d to the use o f the computer f o r the estimation o f t r a v e l time.  The program i s written  i n FORTRAN TV language f o r an IBM 360/67 computer.  The program i s composed  of two phases. The f i r s t phase deals with data i n i t i a l l i z a t i o n and preparation. B a s i c a l l y the program works with three sets of input data.  One o f these  describes the h o r i z o n t a l and v e r t i c a l alignments o f the road under study, from which the speed l i m i t s are computed, the stops that the truck i s to make and the average time i t i s to wait a t each stop.  The computation of  speed l i m i t s as c o n t r o l l e d by the road c h a r a c t e r i s t i c s simulates the knowledge and judgment of the d r i v e r when t r a v e l l i n g over the road. second s e t o f input defines the truck.  A  Input truck data includes v e h i c l e  weight (loaded and empty), f u l l t h r o t t l e HP points versus RPM,  drive-wheel  r o l l i n g radius, torque converter performance, gearbox and rear axle r a t i o s . This information i s a l l r e a d i l y a v a i l a b l e from manufacturers.  From the  truck data the t r a c t i v e e f f o r t (rimpull) a v a i l a b l e a t the wheels i s  10  computed f o r small v e l o c i t y increments.  Second degree polynomials were f i t t e d  to the rimpull versus speed points f o r each gear.  The t h i r d set of input  i s of control nature and includes the length of subsections (ds), the stations at which speed and time are to be output, and the i n i t i a l v e l o c i t i e s (empty and loaded). The second phase of the system consists of the simulation of v e h i c l e motion.  The i n i t i a l i z e d and prepared data of phase one are used to  simulate the operation of the truck over the given alignment.  The resultant  speed and time i s output and subsequently read into the second phase. Figure 2.2 i s a l o g i c a l flow diagram showing, i n a s i m p l i f i e d form, the general sequence o f computational steps through which the computer goes a t each subsection. speeds and times.  The r e s u l t o f the model i s a l i s t i n g of the v e h i c l e operating There are two l e v e l s o f output a v a i l a b l e to the user.  The lowest l e v e l gives: 1. T o t a l length of the course. 2.  Round t r i p time.  3. Travel empty and t r a v e l loaded time. 4. Time stopped. 5. Average v e l o c i t y over the course, loaded and empty. The highest l e v e l gives more d e t a i l s f o r s p e c i f i e d sections: 1. A resume of the geometry of the section. 2.  The entry and e x i t speed f o r each subsection.  3. The time to traverse each subsection and the e n t i r e section. 4. The accumulated distance within the section and since the beginning of the course.  5 . The grade, r o l l i n g , and curve resistances. 6. Plus the information of l e v e l one. The input formats are described i n Appendix  11.  12  Vehicle data  Road data  information supplied by user procedure c a r r i e d out by program  initiallization and preparation  Compute r i mpull and f i t 2nd degree polynomia] s f o r each ar  Compute speed l i m i t s  Compute resistances f o r instantaneous speed and section characteristics  Find proper gear f o r the instantaneous speed  Figure 2.2  Flow diagram of the program  Control data  Net force = rimpull - resistances  Figure 2.2  Flow diagram of the program - continued  Yes P r i n t section summary  P r i n t course summary  Figure 2.2  Flow diagram o f the program - continued  15  Chapter 3 RELATIONSHIPS BETWEEN ROAD CONDITIONS AND THE SPEED OF VEHICLES  3.1  Introduction Only i n rare iilstances i s the d r i v e r j u s t i f i e d i n using a l l the  speed provided i n h i s v e h i c l e because o f conditions of the road.  In the  model, the simulated truck w i l l enter any section o f the road (a section i s o f uniform c h a r a c t e r i s t i c s ) below or a t a s p e c i f i e d speed l i m i t .  This  chapter explains how the speed l i m i t o f each section i s deteimined. The design elements a f f e c t i n g speed are the h o r i z o n t a l alignment (road width, shoulder width, h o r i z o n t a l sight distance, degree of curvature, superelevation), v e r t i c a l alignment ( v e r t i c a l sight distance, percent o f grade) and the type o f surface.  A thorough review o f l i t e r a t u r e  a v a i l a b l e l e d to proposals offered below to approximate the e f f e c t s on t r a v e l speed o f v e h i c l e s . A plan and p r o f i l e o f a portion o f a road i s shown i n Figure 3.1. I t shows how the sections of uniform c h a r a c t e r i s t i c s are determined  from  the plan and p r o f i l e of the road. 3.2  Maximum permissible speed on curves I f a v e h i c l e enters a curve too f a s t the c e n t r i f u g a l force could  surpass the f r i c t i o n a l g r i p o f the t i r e s on the road causing i t to s l i d e o f f the road or overturn.  Once s l i p p i n g has started overturning can occur  Figure 3.1  Portion of a road divided into sections of uniform characteristics  17  should the wheels encounter even a s l i g h t obstruction (Harkness, 1959 and Paterson, 1970).  The d r i v e r controls the speed of h i s v e h i c l e also  to avoid h i t t i n g objects or other v e h i c l e s .  The c o n t r o l l i n g f a c t o r i n  t h i s case i s the safe stopping distance which i s a function of the sight distance.  For these reasons, i n the model, a truck approaching a sharp  curve w i l l decelerate ( i f necessary) before reaching the curve i n order to reduce i t s speed to the allowable speed o f the curve. 3.21 Assumptions In the present model i t i s assumed that d r i v e r behavior conforms to the following assumptions when confronted with curved courses: 1. Speeds on curves never exceed those a t which the unbalanced cent r i f u g a l force makes the d r i v e r uncomfortable. 2. Speeds on curves do not exceed the l i m i t to allow safe stopping within the a v a i l a b l e horizontal sight distance. 3. When the curve i s f l a t enough that neither c e n t r i f u g a l force nor safe h o r i z o n t a l sight distance cause the d r i v e r to reduce speed to traverse the curve, then the v e h i c l e proceeds around the curve a t the approach speed o r obeyes some other r u l e .  The approach speed i s influenced  by numerous f a c t o r s including grades, the proximity and sharpness of preceding curves, the a b i l i t y of a given v e h i c l e to accelerate and thetype of road surface. In short, a d r i v e r approaching a curve w i l l reduce the speed Of h i s v e h i c l e , i f necessary, to match to the appropriate safe stopping distance and c e n t r i f u g a l force assuring h i s comfort.  18  3.22 C e n t r i f u g a l force as a speed control The maximum speed a t which an h o r i z o n t a l curve may be negotiated, when c e n t r i f u g a l force i s the c o n t r o l l i n g f a c t o r , i s one i n which the tangential force applied through the centroid o f the v e h i c l e and i t s load i s exactly counterbalanced by the forces r e s i s t i n g tangential s l i p at the wheels or r e s i s t i n g overturning  o f the v e h i c l e .  Figure 3.2 shows  the forces acting through the center o f gravity of the v e h i c l e .  19  Conditions f o r skid-free curve d r i v i n g can be derived as follows  Smax = Ms (Fy + Wy )  2 where 2S  = sum o f the side-force reactions on a l l wheels, l b  H  = coefficient of sliding f r i c t i o n  s  F = c e n t r i f u g a l force, l b W = v e h i c l e weight, l b . The r e s u l t a n t force must not become l a r g e r than the maximum f r i c t i o n a l side-force  reaction  (F x - Wx) < Ms (Fy + Wy) — (F  cos 6  - W sin 8 ) <  (F  u  s  sin 6 + .  W cos  0)  ... (3.1)  since  F = Wv  2  gR where v = speed, f t / s e c R = radius of curvature, f t 2  g = a c c e l e r a t i o n o f gravity, f t / s e c 8 - superelevation angle, deg. By replacing F i n equation (3.1) 'gR (tan 6 + M )" g  v  s,  max  =  I  U  _(1 ~ M„ tan 8 ) _ s  f  t  /  s  e  c  gives the maximum speed on a curve as c o n t r o l l e d by c e n t r i f u g a l force. As mentioned above, once s l i p p i n g has occured, should the wheel encountered even a very s l i g h t obstruction overturning  could e a s i l y r e s u l t .  3.221  Assumptions  In the preceding equations, the v e h i c l e i s assumed to be moving with constant speed, no accelerating or braking forces are present and the c e n t r i f u g a l force i s assumed to be d i s t r i b u t e d on axles as the s t a t i c l e v e l axle weights.  The assumption of constant speed permits the use  of  the c o e f f i c i e n t of s l i d i n g f r i c t i o n (M )—^ instead of the c o e f f i c i e n t of s f r i c t i o n adjusted f o r l a t e r a l s l i d i n g (also c a l l e d l a t e r a l r a t i o , unbalanced c e n t r i f u g a l r a t i o , cornering r a t i o , unbalanced factor).  side  f r i c t i o n or side f r i c t i o n  The value of the side f r i c t i o n f a c t o r varies with each v e h i c l e and  depends p r i n c i p a l l y upon the speed of the v e h i c l e , the condition of the t i r e s and the c h a r a c t e r i s t i c s of the surface. a v a i l a b l e from which i t can be computed.  The  There i s no simple r e l a t i o n speed on a curved section  w i l l be constant except, sometimes, at the beginning and at the end of a section.  I f the preceding section of uniform c h a r a c t e r i s t i c s has a lower  speed l i m i t than the present curved section then the v e h i c l e w i l l  accelerate  up to the speed l i m i t of the curve i f enough power i s a v a i l a b l e .  On  the  other hand, a c c e l e r a t i o n or deceleration at the end of the section w i l l necessary  be  i f the next section has a speed l i m i t higher or lower tJhan the  present section.  The acceleration or deceleration w i l l be usually performed  over short distance compared with the t o t a l length of the section which j u s t i f i e s the assumption.  1/ The c o e f f i c i e n t of s l i d i n g f r i c t i o n i s defined by: r a t i o of the force necessary to move one surface over an other with uniform v e l o c i t y to the normal force pressing the two surfaces together.  21  3.23  Sight distance as a speed control  On logging roads where often the roadway i s not wide enough to allow vehicles to pass each other, the safe speed i s also l i m i t e d by the sight distance that permits two trucks approaching each other to stop without c o l l i d i n g , or one road.  truck to stop without h i t t i n g an obstruction on  the  Sight distance i s assumed to be l i m i t e d by back slope on the cut  side of the road and by timber and brush at an equivalent distance from the c e n t e r l i n e on the f i l l  side of the road.  Safe stopping distance i s the sum of two distances; one,  the distance  traversed by a v e h i c l e from the instant the d r i v e r sights an object f o r which a stop i s necessary, to the instant the brakes are applied;  and  the other, the distance required to stop the v e h i c l e a f t e r the brake a p p l i c a t i o n begins (AASHO, 1965).  Distance required to stop a v e h i c l e  from a given speed on l e v e l grade i s derived as follows F = m a = W a 8  since  awhere a i s the deceleration.  M g g  From the following equation v  2  = v  2 o  + 2 a SD  a v e h i c l e decelerating to a complete stop w i l l take the following distance on l e v e l grade 2 SD = v_ o  =  v  2 o  where SD = braking distance, f t V u  r  q  s  = i n i t i a l speed, f t / s e c = c o e f f i c i e n t of f r i c t i o n  g = gravity a c c e l e r a t i o n . A reaction time of 2.5 seconds between sighting an obstacle and applying the brake i s recommended by the AASHO (1965).  Sight  distance  required f o r each d r i v e r i n order to stop would then be 2 SD = 2.5 v + o ° 64.32 n V  s on l e v e l grade.  I f the v e h i c l e must be stopped on a grade,  stopping  distance w i l l be influenced p o s i t i v e l y or negatively by the grade force. From Figure 3.3, the grade force can be seen to be the component of the v e h i c l e weight given by F  Figure 3.3  g  = W sin 6  Grade force acting on a v e h i c l e  23  The maximum force that can be transmitted through the t i r e s i s F = M W cos s  6  The summation o f a l l forces gives H  W cos 6 + W s i n $ = W a  S  •  —  g  and a =  M  g (cos $ + s i n 0 )  Sight distance required i n order to stop would then be r 2 SD = 2.5 v + o 64.32 M (cos 8 + s i n B )  where (+) i s f o r adverse grade and (-) i s f o r favorable grade.  ..(3.2)  The speed  l i m i t as a function o f sight distance (SD) w i l l be found by solving equation (3.2) No consideration i s made f o r dynarnic axle weights caused by the grade, a i r resistance, i n e r t i a resistance and the drawbar.  It i s  f e l t that consideration o f these e f f e c t s would not add accuracy to the model and would require more data.  The errors, a t t h i s stage, are not  cumulative and the equations adopted constitute good approximations. The combined sight distance required f o r two d r i v e r s approaching each other i s expressed by K v tr _l_ SD = 5 + o  J ir 2 v o 64.32  ...(3.3)  M  The grade o f the road does not a f f e c t t h i s combined distance because a favorable grade to one d r i v e r w i l l be generally adverse to the other. The combined sight distance could be used as c o n t r o l l i n g f a c t o r on a s i n g l e lane road when no radio connnunication e x i s t s between operating vehicles  24  or when the road i s opened to the general public. As developed by Oglesby et a l . (1971), the sight distance w i l l now be expressed as a function o f the road parameters. For curves having large central angles, minimum h o r i z o n t a l sight distances occur when both the d r i v e r ' s eye and the obstruction are positioned within the c i r c u l a r curve.  Figure 3.4 shows t h i s  aspect.  sight distance  Figure 3.4  Geometry f o r determining sight distance when sight distance i s l e s s than length o f curve  The AASHO standards prescribe that the l i n e of sight f o r safe  stopping  distance combines the top of a six-^inch-high object and a driver's eye 3.75 f e e t above the roadway surface.  In t h i s study i t i s assumed that the l i n e  of sight i n t e r s e c t s the backslope a t a height of two f e e t . explains t h i s  aspect.  Figure 3.5  25  point at which l i n e of sight i n t e r s e c t s backslope  l a t e r a l p o s i t i o n of driver's eye (located at the center of the road)  Figure 3.5  Transversal  p o s i t i o n of parameters  For a l a t e r a l p o s i t i o n of driver's eye located at 10 f e e t from the foot of the backslope, M takes the following values: backslope of .5/1,  M - 11 f t  backslope of l / l , M = 12 f t backslope of 2/1,  M = 14 f t  backslope of 4/1,  M = 18 f t .  I t can be seen that the sight distance, measured around the curve, i s given by the equation SD = RA  ...(3.4)  where A i s the central angle expressed i n radians which provides exactly that sight distance.  Also the r e l a t i o n s h i p between the central angle,  26  R and M i s given by cos A = R - M 2 R therefore (3.5) Combining the previous equations (3.4) and (3.5) we get -1 SD = 2 R cos  (^)  The speed l i m i t as c o n t r o l l e d by sight distance i s obtained by replacing i n equations (3.2) and (3.3) and by solving these equations. For curves of smaller central angle, sight distance exceeds curve length.  I t i s smallest when the object and d r i v e r ' s eyes are both positioned  on the tangents a t equal distances from the curve ends. referred to Figure 3.6.  The reader i s  For t h i s s i t u a t i o n the sight distance i s the sum  of the length of the curve plus the two lengths on the tangents SD = S + 2 L where L can be expressed by the f o l l o w i n g equation L =  M - m  where m i s given by  m = R /1 - cos (0 whilst S i s given by S = R Combining these expressions  p  27  and the f i n a l r e s u l t s are obtained by replacing SD i n equations (3.2) and (3.3) and solving them.  sight distance  Figure 3.6  Geometry f o r determining  sight distance when sight distance  i s greater than length o f curve  V* 3.24 Comparaison of speed l i m i t s on curves with empirical values from a previous  study  A time-motion study o f timber hauling conducted by Campbell and Van der Jagt (1969) gives empirical values f o r the maximum curve speed versus degree of curve.  These values are compared with the maximum safe curve speeds con-  t r o l l e d by side f r i c t i o n and sight distance as computed i n the model. Figure 3.7 shows that the t h e o r e t i c a l values are reasonable. 3.3  Maximum permissible speed as c o n t r o l l e d by surface conditions Road geometry i s not the only f a c t o r a f f e c t i n g speed; the physical  state o f the surface i s another.  Such things as the type o f surface,  maintenance, t r a f f i c patterns and density, loads, weather conditions a l l  notes: 1. n  s  = 0.436 f o r a l l t h e o r i t i c a l curves  2. no grade e f f e c t was included on speed l i m i t s as c o n t r o l l e d by sight distance 3. no superelevation i s included on speed l i m i t s as c o n t r o l l e d by side f r i c t i o n  no side slope i . e . as c o n t r o l l e d by side f r i c t i o n , no superelevation  5  i 75  10 1000  2000  500  I 1500  T  800  Figure 3.7  300  250  200  175  150 _1  125  100  I  400 Comparaison of t h e o r i t i c a l speed l i m i t s on curve with empirical values  1 r 80 85 90 degree of curve 75 64 r I  curve radius ( f t )  29  roust be considered as an i n t e g r a l part o f the t r a c t i o n problem.  Since i t i s  impossible to c o n t r o l o r i s o l a t e many o t these v a r i a b l e s i t i s necessary that they be studied i n combination. 3.31  Previous  study  Campbell and Van der Jagt observed that: "On stretches over which the truck i s t r a v e l l i n g below i t s maximum speed due to other l i m i t i n g conditions (gradients or curves) the e f f e c t o f surface i s very s l i g h t . Probably, the way i n which the road surface sets an o v e r a l l maximum speed with l i t t l e or no e f f e c t on speeds already r e s t r i c t e d by gradients and curves may be explained as follows: on a surface i n good condition, trucks r o l l smoothly, maintaining good contact between the wheels and the road.  As the  surface becomes worse the d r i v e r must reduce speed to maintain control i . e . surface contact with d r i v i n g wheels.  Drivers seem to drive by the seat of  t h e i r pants, i n that, i f they remain more or l e s s i n t h e i r seats they are s a t i s f i e d that they have control and the truck is.not s u f f e r i n g unduly." Table 3.1, extracted from t h i s study, shows the speed l i m i t as cont r o l l e d by surface conditions.  These values are not used as they appear  since sight distance and surface conditions are i d e n t i f i e d separetely i n the present study.  Tangeman (1971) assumes maximum permissible speed due to  surface conditions to be 65 miles per hour on asphalt, and 60 miles per hour on gravel and earth.  Based on the values o f Table 3.1, 50 miles per  hour was adopted as a f i r s t t r i a l f o r maximum speed on gravel road.  On  paved roads the speed l i m i t becomes, very often, more a regulation than a surface c o n t r o l .  The maximum permissible speed due to surface conditions  i s an input to the model and i s l e f t to the d i s c r e t i o n o f the user.  30  Table 3.1  Maximum speeds as controlled by surface  8 f t bunk trucks Surface  Road  (gravel) width  uphill-level  12 f t bunk trucks  downhill  uphill-level  sight dti stance sight d]Lstance  sight d istance  >250ft < 500ft > 500ft < 500ft >250ft Good hard smooth Fair fairly loose rough Poor very loose rough  downhill sight c istance  <250ft  >500ft  < 500ft  single lane  40  35  35  30  40  30  40  30  double lane  50  40  50  40  40  35  50  40  single lane  40  35  35  30  30  25  30  30  double lane  45  40  45  40  30  30  30  30  single lane  35  25  25  20  20  15  20  20  double lane  35  35  35  30  25  20  25  20  notes: 1. the f i g u r e s are rounded o f f to the nearest 5 mph, which i s a reasonable level of precision. 2. a paved surface (which approaches a p e r f e c t surface) exercises no s i g n i f i c a n t r e s t r a i n t on maximum speeds. source: Campbell and Van der Jagt, Table 2, p 106  31  3.32 Winter conditions I t was found, by Campbell and Van der Jagt (1969), on sections of alignment and sight distance, that i n winter trucks were able to a t t a i n higher speed than would probably have been possible on the same portion of the road i n summer (increases of 5-10 mph being common) due to the firmness o f the frozen surface which i s f a r l e s s l i k e l y to deteriorate with t r a f f i c .  However, f o r most of the sections speed w i l l be c o n t r o l l e d  by safe stopping sight distance since M takes a lower value i n winter s conditions. 3.4  Speed l i m i t on favorable grade The mental a t t i t u d e o f the d r i v e r , the safe stopping distance and  the roughness o f the road surface are some of the major c o n t r o l l i n g f a c t o r s of logging truck speed on favorable grade. 3.41 Sight distance as a speed control The speed l i m i t as c o n t r o l l e d by sight distance, on favorable grade, w i l l be determined by solving equation  (3.2) as f o r curved sections.  value of SD i s the length of the grade to the beginning a curved section i s next.  The  of the curve where  In many instances t h i s speed l i m i t w i l l not be  attained since deceleration w i l l be necessary to match with the entry speed of the curve.  Otherwise SD w i l l be the length of s t r a i g h t road ahead.  3.42 Braking capacity as a speed control Logging trucks are too heavy to be c o n t r o l l e d on steep and long grades by t h e i r service brakes without excessive heating.  Therefore, they are  u s u a l l y equipped with a retarding device such as the Jacobs engine brake. Appendix 8 shows nomographs published by the Jacobs Company from which  32  nraximura descent speeds f o r 100% engine brake without the use o f service brakes may be found as a function o f the grade and v e h i c l e weight.  These  l i m i t i n g speeds are input by the user and are used as maximum descent speeds by the model as c o n t r o l l e d by braking capacity.  I f no l i m i t i n g  speed i s s p e c i f i e d the model assumes the empirical values o f Campbell and Van der Jagt (1969) shown i n Figure 3.8. 3.5  Speed l i m i t on adverse grade Most o f the t i n e , on adverse grade speed w i l l not be l i m i t e d by road  geometry o r surface but by engine power.  The e f f e c t of u p h i l l gradients  i s f e l t very early by both empty and loaded trucks.  On f l a t t e r grade the  high p o s i t i o n of d r i v e r ' s eye favors a safe sight distance and w i l l not a f f e c t the speed of the v e h i c l e . 3.6  The independent v a r i a b l e s Since the model i s intended as a designer's guide, the assumptions  must be consistent with the independent v a r i a b l e s a v a i l a b l e .  The independent  v a r i a b l e s a f f e c t i n g speed l i m i t s as input i n the program are: 1. Section length, f t . 2. Radius o f curvature (R), f t . 3. Superelevation, f t / f t . 4. 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 (M ) ( f o r recommended c o e f f i c i e n t s of f r i c t i o n , r e f e r to Table 3.2) . 5. Grade (G), f t / f t . 6. Distance between d r i v e r ' s eye (assumed center of the roadway) and the point at which l i n e of sight i n t e r s e c t s backslope (M), f t . 7. Maximum descent speeds as c o n t r o l l e d by engine brake, mph.  1_  ,  !  2  4  . — ,  6  ,  8  1—  10  1  source: Campbell and Van der Jagt F i g . 3 p 104 Figure 3.8  \  12 14 favorable grade (%)  Maximum descent speeds assumed by the model when no engine brake i s used  34  The expected value f o r speed l i m i t s on each section can be computed according to the d i f f e r e n t rules from the appropriate independent v a r i a b l e s . The smallest value i s kept f o r the maximum permissible speed o f the section. 3.7  Conclusion Determination o f the speed l i m i t of each section requires a-look-ahead  feature i n the model. Table 3.2  After each small increment of  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 (<u_)  Road surface type  Conditions of surface dry  wet  asphalt  0.75  0.60  gravel  0.436  0.436  earthen road  0.65  0.50  snow (hard packed)  -  0.326  ice  -  0.102  source: Harkness (1959), Taborek (1957) length, ds, a check i s made to determine i f braking should s t a r t .  A t the  proper time braking w i l l s t a r t and the v e h i c l e w i l l be slowed down to the correct speed a t the end of any i n t e r i m section i f a speed r e s t r i c t i o n has been placed on the next section. I t i s recognized that no dynamic weight transfer, a i r resistance, i n e r t i a and transmission resistances were considered i n deterinining speed l i m i t s as controlled by safe stopping distance.  I t i s f e l t that since we deal with  35  each section of the road separately the error i s not cumulative. of t h i s approach should be accurate enough and at the same time  Results  reduce  computer time. The determination o f these speed l i m i t s i s i n f a c t simulation of the knowledge and judgment  of the d r i v e r when t r a v e l l i n g over the road. A f t e r  speed l i m i t s f o r each section have been determined i t i s p o s s i b l e to simulate the motion o f the v e h i c l e over the defined road.  36  Chapter 4 RELATIONSHIPS BETWEEN VEHICLE CHARACTERISTICS AND SPEED  4.1  Introduction Equations  (2.5) and (2.6) of Chapter 2 w i l l now be expanded to i n c o r -  porate s i g n i f i c a n t v e h i c l e c h a r a c t e r i s t i c s .  The components which influence  performance p r e d i c t i o n to the greater extent are, o f course, the engine, the torque converter ( i f dealing with a torque-converter and the mechanical transmission.  transmission),  These components provide and transmit  power to the v e h i c l e ' s drive a x l e ( s ) .  In t h i s chapter each component  i s considered seperately and the r e l a t i o n s h i p of one of the other i s determined.  F i n a l l y the o v e r a l l p i c t u r e of what the v e h i c l e w i l l do on the road  i s obtained. Consideration i s given to two types of transmission: manual (defined as a stepped r a t i o gearbox incapable of power-on s h i f t s , with a d r i v e r c o n t r o l l e d clutch) and torque-converter  (defined as a hydrodynamic torque  converter i n s e r i e s with a gearbox capable of power-on s h i f t s ) .  The l a t t e r  type of d r i v e i s becoming most popular f o r heavy off-highway v e h i c l e s . 4.2  Manual transmission modeling The engine speed-vehicle speed r e l a t i o n s h i p must be accurately deter-  mined to express the net d r i v i n g force function of v e h i c l e v e l o c i t y c o r r e c t l y . In order to do so, many forces must be accounted f o r such as the a v a i l a b l e rimpull (propulsive f o r c e ) , the resistances to motion ( r o l l i n g resistance,  37  a i r resistance, grade resistance, curve resistance), and the masses to be accelerated ( i n e r t i a s ) . These requirements are easy to meet f o r a manual transmission since there i s a f i x e d r e l a t i o n s h i p between the engine and v e h i c l e speeds and a c c e l e r a t i o n i n each gear.  The r e l a t i o n s h i p between rimpull and v e h i c l e  speed i s developed from the i n s t a l l e d engine horsepower-engine  speed  (RPM)  curve obtained from manufacturers with allowance made f o r a l t i t u d e e f f e c t and accessory losses  (the reader i s referred to Appendix 2 f o r d e t a i l s ) .  Figure 4.1 shows t y p i c a l engine data as supplied by manufacturers. A f t e r allowance f o r losses, to each RPM torque value (Te). of engine RPM,  corresponds a net engine  The net engine torque, as a single valued function  gives a table of RPM values and torque values.  The engine  data are now represented i n numerical fashion as a series of points. The rimpull (F) i s r e l a t e d to engine torque by the equation F = Te Gr Ar yt r  ...(4.1)  and the engine RPM i s related to vehicle speed by the equation RPM = MPH  As mentioned above to each RPM  (5280) (12) (60) 2 w r  Ar Gr  corresponds one Te.  ...(4.2)  In the previous equations  Te represents the net engine torque which i s m u l t i p l i e d by the transmission reduction (Gr), axle reduction (Ar), and the e f f i c i e n c y (-nt), and divided by the r o l l i n g radius (r) to give the rimpull a v a i l a b l e f o r the present engine RPM  (or present vehicle speed).  normally depends on the gear i n use.  Transmission e f f i c i e n c y (-qt) In t h i s study, i t i s assumed that  transmission e f f i c i e n c y i s constant i n any given gear. i s generally accepted as a good approximation.  A f i g u r e of 0.85  38  Engine model: Type: Turbocharged & Aftercooled NTC-350 (335)  CUMMINS ENGINE COMPANY  Bore: 5-§- i n . No. o f cylinders: 6 Stroke: 6 i n . Displacement: 855 cu.in  Columbus, Indiana  Curve number: CO-3189-A1 Date:  By:  IOOO H 900 -A L350 800 -J .325  •300  L275  •P +->  o L250  t-1 CU  o -225  200  .400  .350  —I  1300  1  1  -i  1  1500 1700 Engine speed-RPM Figure 4.1 T y p i c a l engine data  r  1900  2100  39  The forces to be overcome include the component of v e h i c l e weight resolved along the gradient (Rg) (the reader i s r e f e r r e d to Appendix 3 f o r d e t a i l s ) , the r o l l i n g resistance (Rr) (Appendix 4), the aerodynamic resistance (Ra) (Appendix 5), the curve resistance (Rc) (Appendix 6), and the i n e r t i a resistance (Ri) (Appendix 7). The equation of motion under acceleration may  be written as  F = Rg + Rr + Ra + Rc + M 7 a or Te Gr Ga vt r  = Rg + Ra + Rr + Rc + My a  ...(4.3)  where M7 i s r e f e r r e d to as the t o t a l e f f e c t i v e mass of the v e h i c l e (Appendix 7).  Putting a = 0 i n t h i s equation allows the rimpull at any  constant  speed to be calculated. Under c e r t a i n circumstances the rimpull that can be developed may l i m i t e d by the adhesion between the driven t i r e s and the road.  be  It i s  assumed i n the model that whatever rimpull i s required f o r a c e r t a i n performance can be produced at the t i r e s .  I t i s understood that there  are l i m i t s to the rimpull and that the transmission of more power than i s necessary to develop can r e s u l t i n wheel spin.  However, t h i s does not  happen very often with logging trucks since they are very heavy, even when empty. Speed to distance and time to distance are r e a d i l y calculated from equation (2.5) and (2.6)  expanded as explained above.  equations (2.5) and (2.6) are discussed l a t e r i n t h i s  Methods of solving chapter.  I f s h i f t i n g time i s neglected, v e h i c l e performance w i l l be over estimated.  However s h i f t i n g time and deceleration during s h i f t i n g are  40  not included i n t h i s model. 4.3  Torque-converter transmission modeling In the case of a torque converter i n series with a gearbox, the  precise d e f i n i t i o n of t h i s r e l a t i o n s h i p i s complicated by the presence of converter s l i p .  Compatibility between the rimpull and the speed of the  vehicle may be characterized mathematically by a driveshaft speed matching technique.  The technique whereby the match between a p a r t i c u l a r engine  and a p a r t i c u l a r torque converter i s done  i s described below.  A r e l a t i o n s h i p may be established only i f the performance of the torque converter i s information.  known.  Figure 4.2  Manufacturers  supply torque converter  shows t y p i c a l data as supplied by them.  I t has been demonstrated by Ott by Ishihara and Emori that i t i s permissible to assume quasi steady conditions f o r the operation of a torque converter.  Hence, the input torque to the torque converter may  be  described by 2 T i = / Impeller r o t a t i o n a l speed I Torque converter K-factor The K-factor i s defined as the RPM divided by the square root of the torque K-factor = RPM  /yj Torque .  This K-factor establishes what the engine does with the torque converter or conversely, what demands the torque converter makes of the engine (Ordorica, 1965).  The K-factor of the engine equals the K-factor of the  torque converter Engine K-factor = Engine output shaft speed , •^Net engine output torque  41  .2  .4  .6  .8 Speed r a t i o  Figure 4.2  T y p i c a l torque converter data  and the Torque converter K-factor = Input shaft speed . yj Input torque The K-factor o f the torque converter i s a function of the torque converter speed r a t i o (Figure 4.2).  The converter speed r a t i o i s defined  as Converter speed r a t i o = Output shaft speed . Input shaft speed Matching each engine K-factor to i t s corresponding torque converter K-factor defines a function of output shaft torque against output  RPM.  The exact procedure followed by the program i s explained i n d e t a i l i n section (4.42). A f t e r the torque to the driveshaft i s available the equation of motion can be derived the same way as f o r the manual transmission. I f the speed r a t i o , torque r a t i o , and K-factor points of the torque converter are not a v a i l a b l e , only output RPM and torque points to the torque converter may be input.  In that case the program proceeds exactly  as f o r manual transmission. 4.4  Method of s o l u t i o n Linear i n t e r p o l a t i o n and curve f i t t i n g by method of l e a s t squares  are c a r r i e d out to adapt the engine and power t r a i n components to d i g i t a l programming.  The computer i s very well adapted to curve f i t t i n g s of t h i s  sort. 4.41 Manual transmission procedure 1. Read engine HP versus engine RPM points, correct HP f o r a l t i t u d e , and compute the engine torque f o r each RPM  point.  2. Beginning with the lowest gear, f i n d the engine RPM f o r a c e r t a i n  43  speed from equation (4.2) (an increment of 0.5 mph was adopted f o r the program). 3. For the RPM found i n (2) compute the corresponding engine torque by l i n e a r i n t e r p o l a t i o n between points computed i n (1). 4. For the engine torque found i n (3) compute the rimpull a v a i l a b l e to the wheel from equation (4.1). 5. Repeat (2), (3), and (4) u n t i l s h i f t i n g point i s found. 6. I f s h i f t i n g  occurs repeat (2), (3), (4), and (5) with the next  gear. 7. When the top speed i n the l a s t gear i s attained f i t a second degree polynomial to the rimpull versus MPH f o r each gear. Two conditions d i c t a t e a gear change: 1. When the governed RPM i s attained f o r a c e r t a i n speed and a p a r t i c u l a r gear. 2. When the rimpull versus MPH f o r two adjacent gears i n t e r s e c t p r i o r to governed RPM. The f i t t i n g of a second degree polynomial to the rimpull i s p a r t i c u l a r l y done to approximate the rimpull when s l i p p i n g of the clutch occurs i n f i r s t gear.  I t also gives a smooth curve f o r the rimpull of each gear  which i s used i n the simulation of v e h i c l e motion.  Without this f i t ,  rimpull a t low speed f o r the f i r s t gear would be unknown.  Higher order  polynomial f i t s were not considered since a second order gives a good approximation.  The maximum error between computed and predicted i s about  2 per cent. During the motion simulation, f o r a c e r t a i n speed and a p a r t i c u l a r section, the r o l l i n g , a i r , i n e r t i a , curve, and grade resistances are  computed.  Then f o r the actual speed the proper polynomial (proper gear)  i s found and the a v a i l a b l e rimpull computed.  The net force to accelerate  climb a grade or traverse a curve i s then computed by substracting the resistances from the a v a i l a b l e rimpull. equation (2.5) and (2.6) may 4.42  The numerical integration of  then be performed knowing a l l the v a r i a b l e s .  Torque-converter transmission procedure  1. Read engine HP versus engine RPM points, correct HP f o r a l t i t u d e , and compute the engine torque f o r each RPM p o i n t . 2. Compute the engine K-factor f o r each torque versus RPM point from (1). 3. Read torque converter speed r a t i o , torque r a t i o , and t h e i r corresponding K-factor. 4. By l i n e a r i n t e r p o l a t i o n f i n d the engine RPM f o r which the engine and torque converter K-factors are matched. 5. F i n d the output RPM r a t i o = Output  to the torque converter (Engine RPM X Speed  RPM).  6. F i n d the output torque to the torque converter (Engine torque X Torque r a t i o = Output torque). 7. Proceed as f o r manual transmission beginning a t (2). 4.5  Braking The equations used to p r e d i c t power-on performance  remain v a l i d f o r  braking, provided that the sign of Te and a i n equation 4.3 are reversed and that the transmission o v e r a l l e f f i c i e n c y i s replaced by i t s inverse . to allow f o r the transmission losses that are helping to slow the v e h i c l e The v a r i a b l e rate of deceleration experienced by a v e h i c l e , can also  45  be represented by an average rate o f deceleration.  I t i s advanced that 2  operator discomfort i s reaching an undesirable l e v e l at 8-12 f t / s e c deceleration ( C a t e r p i l l a r Tractor Co., research department).  For the  2 computer program a constant deceleration rate of 6 f t / s e c assumed.  i s conservatively  The following formula i s used to determine where braking should  start (-12) where v = f i n a l velocity, ft/sec v_ = i n i t i a l v e l o c i t y , f t / s e c s = distance to reduce the speed o r stop the v e h i c l e f o r the instantaneous speed, f t 2 (-12) = deceleration (2 X -6 f t / s e c ). 4.6 The independent v a r i a b l e s The engine and power t r a i n parameters are obtainable from the manufacturers. They are l i s t e d below with d e t a i l s when necessary. 1. Horsepower versus RPM. 2. Main transmission gear r a t i o s , a u x i l i a r y transmission r a t i o s , and rear axle r a t i o . 3. Torque converter K-factor, speed r a t i o , and torque ratio, or i f the second option i s used, output shaft speed and output torque. 4. T i r e r o l l i n g radius (see Table 4.1). Torque converter data such as torque r a t i o s , speed r a t i o s , and torque converter K-factors might be d i f f i c u l t to obtain from manufacturers. Therefore, the torque converter model has been developed to u t i l i z e the  46  r i m p u l l - v e l o c i t y curve found on most equipment s p e c i f i c a t i o n sheets i f the previous data are not a v a i l a b l e .  Tire size  Radius  9.00-20  19.2  11.00-20  20.4  12.00-20  21.2  10.00-20  19.9  11.00-22  21.4  12.00-24  23.0  10.00-22  20.8  11.00-24  22.3  14.00-24  25.3  Tire size  Radius  T i r e size  source: Kenworth Motor Truck Company  Table 4.1  Loaded t i r e radius i n inches (off-highway tread)  Radius  Chapter 5 MODEL TESTING  5.1  Introduction Since the model i s intended as a designer's guide the many  assumptions had to be consistent with the independent v a r i a b l e s a v a i l able.  The purpose of the study i s mainly to help decision-makers i n  regards to design of logging roads.  This means that the model must  predict times accurately enough to enable ranking of a l t e r n a t i v e s .  The  two following sections show how close the model i s to r e a l i t y by comparing observed and predicted times. 5.2  The test s i t u a t i o n The data used to v a l i d a t e the model were c o l l e c t e d by the B.C.  Forest Service.  Porpaczy (1973) describes the data c o l l e c t i o n as follows:  "The Prince George D i s t r i c t Time Studies Crew, i n c o l l a b o r a t i o n with the Management and Engineering Divisions of the B.C. Forest Service, carried out time studies on a road system during summer 1972.  The haul  road was marked o f f into sections with the physical measurements of 1/ the c h a r a c t e r i s t i c s of each section taken by the Road Recorder.  The  timing procedure was to record the t o t a l time lapse between section markers.  A l l haul time studies, almost s i n g u l a r l y , were conducted i n  i s o l a t i o n of extraneous f a c t o r s , such as the r e l a t i o n s h i p 1/ The B.C.F.S. Road Recorder i s an automatic vehicle-mounted system to record road geometry as the v e h i c l e traverses i t .  48  of a p a r t i c u l a r t r i p to others; the r e l a t i o n s h i p of round t r i p time to the working day, which may be more o r l e s s than 8 hours, and the subsequent d r i v e r freedom to a l l o c a t e h i s time accordingly,  That i s , there  may well be time l e f t over that could not be u t i l i z e d f o r making another t r i p as the time i s not s u f f i c i e n t f o r a round t r i p , which then i s manifested i n a slackening o f pace." The performance tests were conducted over 33 miles o f road. The road width varied from 22 to 30 f e e t , a maximum gradient of 6.3% and a maximum curvature o f 20° were also encountered. surface f o r i t s e n t i r e length.  The road had a gravelled  The route afforded a conglomerate of  curvature, gradient, and r e s t r i c t e d sight distances. Five v e h i c l e s o f gross weights of 30,000 pounds were tested.  An  average loaded weight (vehicle weight plus the payload) o f 110,000 pounds was recorded. 370 HP.  The power developed by the engines ranged from 325 HP to  A l l v e h i c l e s had a manual transmission.  The d r i v e r s employed were a l l s k i l l e d professional d r i v e r s . The time study data were analyzed to investigate: 1. The consistency o f d r i v e r performance within sections, 2. The comparison  o f performance between d i f f e r e n t trucks f o r the  t o t a l course. Consistency o f d r i v e r performance within section The c o e f f i c i e n t o f v a r i a t i o n i n time f o r each section traversed seldom exceeds 10% with an average of 8%. of the d r i v e r s i s consistent.  This indicates that the performance  49  Comparison of  performance between d i f f e r e n t  trucks f o r the t o t a l course An analysis of variance was performed and the comparison  of performance  of the i n d i v i d u a l trucks f o r travel loaded indicated no difference between the f i v e u n i t s studied even though they had d i f f e r e n t rated engine horsepower, transmission r a t i o s and were of d i f f e r e n t ages.  S t a t i s t i c a l l y there i s  a difference between the t r a v e l empty mean of each u n i t .  I t i s suspected  to be caused by a slackening of pace due to dispatching and interactions of v e h i c l e s . Appendix 9.  For more d e t a i l s on the analysis of variance  r e f e r to  Even with the difference f o r t r a v e l empty, i t was decided to  use the c h a r a c t e r i s t i c s of one of the observed trucks as a representative average to p r e d i c t times with the model. 5.3  Predicted versus measured times The simulation model computes average times of a given truck f o r a  given road.  A comparison  of the r e s u l t s of the predicted and the average  times from the time studies through each section of the road was done. Figures 5.1 and 5.2 i l l u s t r a t e the r e s u l t s .  A perfect coincidence would  have been represented by a 45° l i n e from the o r i g i n .  To v e r i f y i f the  computer p r e d i c t i o n and observed mean could be represented by a single regression a test of s i m i l a r i t y of slopes was performed*  The hypothesis of  common slope was rejected f o r both t r a v e l empty and loaded.  Refer to  Appendix 10 f o r more d e t a i l s on the tes"t_.of s i m i l a r i t y of slopes. However, the r e s u l t s obtained f o r travel loaded might be considered acceptably close.  An error of 5% f o r the t o t a l course and an average  error of 10% within each section existed data.  i n comparison  to the observed  Predicted times f o r travel empty (Figure 5.2) were too low (the  50  70 _,  l5 Figure 5.1  20  A comparison  30 ~ 40 50 60~~ Cumulative predicted (computer) mean times, minutes of actual and predicted cumulative times for travel loaded  51  70  Cumulative predicted (computer) mean times, minutes Figure 5 . 2 A comparison  of actual and predicted cumulative times f o r travel empty  52  simulated v e h i c l e t r a v e l l i n g f a s t e r than the observed v e h i c l e s ) .  An  error  of 19% on the t o t a l course and an average error of 20% within each section were detected.  Something appears to a f f e c t t r a v e l empty whilst apparently  not a f f e c t i n g t r a v e l loaded.  I t i s suspected that the n_aximura permissible  empty speed i s c o n t r o l l e d by surface conditions. 3.31,  a f i r s t t r i a l was  by surface conditions. of 40 mph  made with a speed l i m i t of 50 mph A second t r i a l was  which i s the average of Table 3.1  Van der Jagt (1969).  As mentioned i n section as c o n t r o l l e d  performed with a speed l i m i t extracted from Campbell and  A closer estimation was  obtained f o r t r a v e l empty  whilst f o r t r a v e l loaded nothing has changed since the v e h i c l e does not a t t a i n t h i s speed due  to the load constraint.  I t appears that 40 mph  be more r e l i a b l e f o r speed l i m i t as c o n t r o l l e d by surface However, even with a speed l i m i t of 40 mph  would  conditions.  the times are underestimated.  For t r a v e l loaded the load i s r e s t r a i n i n g the speed of the vehicle i n a way  that the d r i v e r s do not have any choice but to use  of the engine.  the f u l l p o t e n t i a l  Empty, since the f u l l p o t e n t i a l of the engine cannot be  attained, the d r i v e r ' s choice may  result i n variation.  On a day-to-day  basis the d r i v e r s do not operate t h e i r vehicles at t h e i r f u l l p o t e n t i a l . In other words, the operator can do no better than the program but can take considerably  longer i f he  desires.  This might explain the remaining  discrepency between the observed and predicted  times.  53  Chapter 6 DISCUSSION AND CONCLUSIONS  6.1  Using the model to make decisions Since the v e h i c l e movement i s represented i n the model i n a r e a l i s t i c  manner i t may be usr.d to investigate the reponse of the model to changes i n c e r t a i n input parameters.  Because of the large number of parameters  a f f e c t i n g the system performance t h i s s e n s i t i v i t y may be l i m i t e d to the major c o n t r o l l a b l e parameters such as curves, grades, and surface type. Results obtained from the s e n s i t i v i t y tests between the v e h i c l e and system parameters can be used to compare a l t e r n a t i v e designs of logging roads and the more economical a l t e r n a t i v e may be choosen. However, the adoption of t h i s model i s not seen as the f i n a l answer. Indeed, i t should be developed and updated i n l i n e with further research. 6.2  Areas of f u r t h e r i n v e s t i g a t i o n There i s l i t t l e doubt that the development of such program i s not a  one-step process, but instead involves a succession of development  phases.  A combination of deterministic simulation developed i n t h i s study and a stochastic simulation to generate t r a f f i c and to evaluate i t s e f f e c t s on the t r a v e l time would be an improvement.  The times predicted i n the  present study were the times that a truck should take when unaffected by t r a f f i c .  Now  i f t r a f f i c i s included i n the model loss of time w i l l  occur due to the i n t e r a c t i o n s among v e h i c l e s .  Such a model would permit  the evaluation of a l t e r n a t i v e road designs to p r e d i c t t h e i r performance  54  f o r the a n t i c i p a t e d use of the road (used f o r recreation, and  protection,  harvesting). The model was  i n road l o c a t i o n . of problem.  designed p r i n c i p a l l y to handle the problem of a l t e r n a t i v e s I t has been recognized however, that t h i s i s only one  type  Among other p o s s i b i l i t i e s are:  1. To e s t a b l i s h f o r c e r t a i n future operations the production rate of trucks.  The r e s u l t s of such p r e d i c t i o n could be used to  determine the most economical number of trucks to use i n the predicted s i t u a t i o n . 2. To s e l e c t equipment that best matches a given a p p l i c a t i o n . 3. To determine hauling costs f o r stumpage p r i c e appraisal. 6.3  Conclusion A simple model p r e d i c t i n g truck performance on a defined route  developed.  was  I t produces r e s u l t s acceptably close to experimental data  arid use of t h i s model allows parametric study of a l t e r n a t i v e s . simulation has  Such  the advantage of replacing the r e a l hardware by the computer.  The measurements on trucks under t e s t on actual t e r r a i n were recorded and analysed s t a t i s t i c a l l y . was  The performance of the complete v e h i c l e system  then assessed and d i r e c t comparaison between the simulation and  the  actual t e s t became possible. The  simulation does not eliminate thorough road t e s t i n g but  insures  that f u r t h e r research and expensive hardware construction and road testing be not undertaken u n t i l there i s a high p r o b a b i l i t y that the r e s u l t could be satisfactory.  55  BIBLIOGRAPHY  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. Anderson, J.W. , J.C., F i r e y , P.W., Ford, and W.C., K i e l i n g , 1964. Truck drag components by road test measurement. SAE Summer Meeting, Paper 881A. 12 pp. Boyd, C.W., and G.G., Young, 1969. A study on equipment replacement, maintenance, inventory and r e p a i r p o l i c y f o r one class of vehicles. 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., Googiris, 1960. Looging road handbook: the e f f e c t of road design on hauling costs. U.S. Department of Agriculture, A g r i c u l t u r e Handbook 183, 65 pp. Campbell, P.W.E., and P.S. Van der Jagt, 1969. Speed values and production of log haul roads. I n s t i t u t i o n of C i v i l Engineers Proceedings, Paper 7130S, supplementary volume, 185 pp. F i t c h , J.W. , 1969. Motor truck engineering handbook. publisher, San Francisco, 264 pp.  James W.  Fitch,  Harkness, W. D., 1959. Truck performance and minimum road standards. Sect. Index, Canad. Pulp Pap. Ass. No. 1981(B-8-a), 10 pp.  Woodl.  Ishihara, T., and R.I., Emori, 1966. Non-steady c h a r a c t e r i s t i c s of hydrodynamic d r i v e . Eleventh FISITA Congr., Preprint No. A10. Lewis, M.W. , 1969. Vehicle performance and transmission matching. Instn. Mech. Engrs. 1969-70, Vol. 184, Paper 35, 18 pp.  Proc.  Lucas, G.G., 1969. A technique f o r c a l c u l a t i n g the time-to-speed of an automatic transmission v e h i c l e . Proc. Instn. Mech. Engrs. 1969-70, Vol. 184, Paper 37, 19 pp. McKenzie, R.D., W.M., Howell, andD.E., Skaar, 1968. Computerized evaluation of d r i v e r - v e h i c l e - t e r r a i n system. SAE Transactions, V o l . 76:2, 12 pp. Oglesby, C H . , F. , A r i a s , and R.W. Clark, 1971. The e f f e c t s of h o r i z o n t a l alignment on v e h i c l e running costs and t r a v e l times. Program i n EngineeringEconomic Planning, Stanford University, report EEP37, 82 pp.  56  Ordorica, M.A., 1966. V o l . 74:4, 10 pp.  Vehicle performance p r e d i c t i o n . SAE Transactions,  Ott, A., 1966. C a l c u l a t i o n of d r i v i n g performance with reference to torque converter and power changing. Eleventh FISITA Congr., Preprint No. A10. Paterson, W. G., 1971. Transport on f o r e s t roads-1980. Canad. Pulp Pap. Ass. No. 2597(B-8-b), 8 pp.  Woodl. Sect. Index,  Paterson, W. G. , H. W., McFarlane, and W. J . , Dohaney, 1970. A proposed f o r e s t roads c l a s s i f i c a t i o n system. Pulp and Paper Research I n s t i t u t e of Canada,Woodlands Papers, W. P. No. 20, 47 pp. Peurifoy, R. L., 1970. Construction planning, equipment, and methods. McGraw-Hill Book Co., Inc.,New York. 696 pp. Petropoulos, D. P., 1971. Simulation of t r a f f i c flow on one-lane roads with turnouts. Unpublished thesis, U n i v e r s i t y of Stanford. Pike, J . N., Finning Tractor and Equipment Co. Ltd. (representing C a t e r p i l l a r Tractor Co.), 555 Great Northern Bay, Vancouver 10, B.C.. June 14, 1972. Personal correspondence. Porpaczy, L. J . , 1973. Log haul studies-1972. Columbia Forest Service, Enginnering D i v i s i o n . Roberts, P. 0., and J . H., Suhrbier, 1966. an example problem. MIT, Report No. 5.  Unpublished  report, B r i t i s h  Highway l o c a t i o n a n a l y s i s :  Taborek, J . J . , 1957. Mechanics of v e h i c l e s . Machine Design, The Penton Publishing Co., Cleveland, 93 pp. Tangeman, R.J., 1971. A proposed model f o r estimating v e h i c l e operating costs and c h a r a c t e r i s t i c s on f o r e s t roads. Transportation System Planning Project, U.S. Forest Service, 151 pp. Waelti, H., B.C. correspondence.  Forest Service, V i c t o r i a , B.C..  June 13, 1972.  Winfrey, R., 1970. Economic analysis of highways. Co., Scranton, Pensyslvania.  Personal  International Textbook  57  Appendix 1 ECONOMIC EQUATIONS OF ALTERNATIVE ROAD ALIGNMENTS  This Appendix was included to show a l l the considerations that must be made when evaluating a l t e r n a t i v e road alignments.  I t was also included  to show that by p r e d i c t i n g the t r a v e l time a b i g otep toward the a p p l i c a t i o n of t h i s concept would be made.  This concept was extracted from "Highway  Location Analysis: an example problem" by P.O. Roberts and J.H.  Suhrbier  (1966). The computation o f annual cost f o r a l t e r n a t i v e alignments i s based on the following equation r e l a t i n g i n i t i a l costs, user time and operating costs, and maintenance  costs: TAC = ACC + AUC + AMC  where TAC = t o t a l annual cost, $ ACC = annual c a p i t a l cost, $ AUC = annual user time and operating costs, § AMC = annual maintenance  cost, $  Each of these three components of annual cost can be broken down further. Annual c a p i t a l cost becomes ACC = tec (CRF) where tec = t o t a l construction cost, $  58  and CRF = c a p i t a l recovery  factor  tec = ec + sc + pc + r c + l c where ec = earthwork cost, $ sc = structures cost, $ pc = pavement cost, § dc = drainage cost, § rc = r e l o c a t i o n cost, § l c = land and right-of-way cost, § CRF = i ( l + i )  n  U+i) -l n  where i = i n t e r e s t rate and n = service l i f e , years This r e l a t i o n f o r annual construction cost holds only f o r the simple case where the service l i v e s of the various components are the same and where there i s no salvage value. Where t h i s a d d i t i o n a l refinement i s j u s t i f i e d , and i t frequently i s , the annual construction cost i s the sum of the i n d i v i d u a l components: j  ACC = X  CRF  k  [  cc  k  +  <> s v k  where j = t o t a l number of construction  categories  59  k = category presently being CRF^  considered  = c a p i t a l recovery f a c t o r f o r the appropriate  life  CC^ = construction cost category under consideration SV^ = salvage value of t h i s construction category and PWF^  = present worth f a c t o r f o r the appropriate  life  where PWF  =  i (l+i) -l n  Annual user cost becomes AUC  = EAT  (doc + utc)  where EAT = equivalent annual t r a f f i c , vehicles/year and utc = user time cost,  $/vehicle  doc = d i r e c t operating cost, $/vehicle These can be f u r t h e r broken down as EAT  = v o l + av + av - n (av) (CRF - i )  1  1  where v o l = present annual t r a f f i c volume, vehicles/year and av = annual numerical increase i n t r a f f i c volume, vehicles/year D i r e c t operating cost i s  j  60  where j = t o t a l number of v e h i c l e  classes  = percentage of vehicles of class i f c ^ = f u e l cost of class i v e h i c l e , $/vehicle t r c ^ = t i r e cost of class i v e h i c l e ,  ^/vehicle  oc^ = o i l cost of class i v e h i c l e , $/vehicle mtc^ = maintenance  cost of a c l a s s i vehicle, S/vehicle  and dpci = depreciation  cost of a class i vehicle, $/vehicle  For time cost,  j i=l where t^ = time f o r a class i v e h i c l e to t r a v e l the alignment, hours t c ^ = time cost f o r a class i v e h i c l e , $/hour and t u r ^ = cost of time u n r e l i a b i l i t y f o r a class i v e h i c l e , $ I t i s assumed that the same number of t r i p s are taken on each of a l t e r n a t i v e alignments under consideration.  In cases where the assumption  of a l i n e a r growth of t r a f f i c cannot be made, user operating and time costs may be computed f o r each i n d i v i d u a l year, then discounted to the present time and converted into annual cost as follows:  where  61  atv\ = annual t r a f f i c volume during year i doc^ = d i r e c t operating cost during year i u t c ^ = user time cost during year i and PWE\  = present worth f a c t o r f o r year i  Maintenance  costs, the t h i r d of the major component of annual cost, becomes AMC  = mi  (mc)  where mi = length of alignment, miles  and mc = equivalent annual maintenance cost of an a l t e r n a t i v e , $/mile By combining the previous equations i n t o a single equation f o r t o t a l annual cost: _  J  TAC = CRF (cc + ac + pc + dc + rc + l c ) + EAT T £  \  + oc. + mtc. + dpc. + ( t . ) (tc.) + (tur.) + (mi)  +  t r c  i  (mc)  I t i s recognized that tools discussed above are only a part of the a n a l y t i c a l evaluation and other procedure are needed f o r the planning process such as scenic view and measurement of p u b l i c i n t e r e s t .  Until  such procedures are developed the decision-maker must r e l y on l e s s sophisticated techniques.  62  Appendix 2 EFFECTIVE ENGINE POWER  The manufacturers of motor vehicles run extensive tests to determine the performance of t h e i r engine.  Usually those tests are performed under  the following stand£--d atmospheric conditions extablished by the SAE (Society of Automotive Engineers): temperature, T pressure, B  Q  = 520 degree Rankine and barometric  Q  = 29.92 inches of Hg (dry a i r ) .  From the r e s u l t s of the tests  i t i s customary to prepare charts (Figure 4.1) i n which the gross horsepower of the bare engine i s p l o t t e d against engine RPM.  The term bare engine  refers to an engine stripped of a l l accessory equipment not e s s e n t i a l to engine functionning.  To obtain the power available at the output shaft of  the engine (Pe), the power consumed by accessories (Pa) must be subtracted from the e f f e c t i v e power (P) developed under the present set of atmospheric conditions. The e f f e c t i v e power developed f o r d i e s e l engines can be calculated from P  88 P  o  (  B  " V  B  T  o  0  T  where P  D  'B  = engine power under SAE standards = p r e v a i l i n g barometric pressure under the hood  63  B  v  = p a r t i a l pressure of water vapor i n the a i r i n inches o f Hg ( i t  i s u s u a l l y neglected f o r p r a c t i c a l case) T = ambient temperature i n deg Rankine (air-intake  temperature).  Only d i e s e l engine i s considered i n the program. Since barometric pressure decreases about 1 inch of Hg per 1000 f t increase i n a l t i t u d e i t can be seen from the above expression that power losses due to atmospheric be neglected.  conditions can become substantial and should not  Table A2.1 gives the average barometric pressures f o r various  a l t i t u d e s above sea l e v e l .  A l t i t u d e above sea l e v e l , f t  Barometric pressure, i n . Hg  A l t i t u d e above sea l e v e l , f t  Barometric pressure, i n . Hg  0  29.92  6000  23.95  1000  28.86  7000  23.07  2000  27.82  8000  22.21  3000  26.80  9000  21.36  4000  25.82  10000  20.55  5000  24.87  source: Peurifoy (1970)  Table A2.1  Average barometric pressures f o r various a l t i t u d e s above sea l e v e l  I n s t a l l a t i o n and accessory losses (Pa) vary according to size and make of accessory used.  For general purposes, an engine i s derated of 10%  f o r normal accessories to determine net HP at the flywheel (Pe). The a v a i l a b l e engine torque (Me) i s r e l a t e d to Pe by the following expression Me = 5252 Pe Ne where Me i s i n l b - f t , Pe i n Hp and Ne the engine speed i s i n RPM.  65  Appendix 3 GRADE RESISTANCE  The resistance offered to movement o f a vehicle up a grade i s known as grade resistance (Rg).  The grade resistance i s force necessary to l i f t  the v e h i c l e through a height equal to that attained because of plus grade. The value of t h i s resistance i s given by Rg = W s i n 0  center of gravity  Figure A3.1  Grade resistance of a truck  66  Appendix 4 ROLLING RESISTANCE  There are many v a r i a b l e s a f f e c t i n g r o l l i n g resistance such as the kind and size of t i r e s , i n f l a t i o n pressure,  t i r e temperature, type of  roadway surface, road speed o f the v e h i c l e and, the most important o f a l l , the gross v e h i c l e weight on the t i r e s .  The r o l l i n g resistance (Rr) i s made  up of the following elements: 1. Work to compress and d e f l e c t the roadway surface. 2. Work required to f l e x the t i r e . 3. Work required to overcome f r i c t i o n . 4. A i r f r i c t i o n caused by movement of the a i r i n s i d e of the t i r e , and outside a i r resistance. For general use, i t i s necessary to determine by t h e o r i t i c a l  or experimental  work the percentage o f the t o t a l Rr contributed by each of these elements. However what i s needed, i n this model, i s a good average Rr f o r t y p i c a l vehicles and road surfaces.  The information published to date indicates  approximations o f the r o l l i n g resistance that seem  acceptable.  Paterson et a l . (1970) used the following equation f o r the r o l l i n g resistance o f trucks on gravel road Rr = (15.1 +0.088 V) where Rr = r o l l i n g resistance, l b  W 1000  67  V = v e h i c l e speed,  mph  W = gross v e h i c l e weight, l b . This approximation should be accurate enough and i s adopted i n t h i s model. The SAE recommends the following formula f o r paved surface Rr = (7.6 + 0.09 V)  W . 1000  Appendix 5 AERODYNAMIC RESISTANCE  The following three factors combine to account f o r the t o t a l a i r resistance: 1. Drag resistance as related to the outside shape and size o f the vehicle. 2. The resistance to the a i r offered by surface of the body. 3. Flow o f a i r through the v e h i c l e f o r purposes o f v e n t i l a t i n g and cooling. The greatest  single f a c t o r i n a i r resistance i s the projected f r o n t a l  area o f the v e h i c l e .  The formula f o r a i r resistance involves also a f a c t o r  f o r the weight of the a i r , the drag and skin f r i c t i o n o f the vehicle  (Ca).  From i n v e s t i g a t i o n conducted by Flynn and Kyropoulos (1962) and tests conducted a t GMC (General Motors Corp.) the a i r drag c o e f f i c i e n t (Ca) of a t r a c t o r - t r a i l e r combination i s i n the area of 0.7. The  equation given by Taborek (1957) i s Ra = 0.0026 Ca A V r  where Ra  a i r resistance, l b  Ca  •• a i r drag c o e f f i c i e n t , dimensionless  A  projected  V  r  2 f r o n t a l area, f t  speed of the vehicle r e l a t i v e to the a i r , mph.  69  This formula i s adopted i n the model without consideration f o r wind v e l o c i t y . Figure A5.1 trucks.  shows the approximate f r o n t a l areas f o r loaded and empty  These data are based on f i e l d measurements by Byrne et a l . (1970).  |_  ,  !  20  40  60  _  1  80  , 100  ,  .  120  Projected f r o n t a l area, f t Figure A5.1  Projected f r o n t a l area of loaded and empty trucks  | 140  70  Appendix 6 CURVE RESISTANCE  In most v e h i c l e performance studies curve resistance i s not included. Tests a t GMC have shown that curve resistance i s very high f o r c e r t a i n t r a c t o r - t r a i l e r combinations. mates the curve  An empirical formula i s given which approxi-  resistance (Rc) of a 76000 l b tandem tractor-tandem t r a i l e r  combination  where Rc = curve resistance, l b V = v e h i c l e speed, mph R = radius of curve, f t E = Superelevation  of curve, f t / f t  W = gross v e h i c l e weight, l b . This resistance i s subtracted from the a v a i l a b l e rimpull i n the model.  71  Appendix 7 INERTIA RESISTANCE  Probably the most important consideration i n v e h i c l e performance p r e d i c t i o n i s acceleration.  This i s d i f f i c u l t to c a l c u l a t e since the net  force d r i v i n g the v e h i c l e not only accelerates the v e h i c l e but also accelerates the r o t a t i n g components encountered throughout the drive t r a i n . Rotating i n e r t i a s include the engine flywheel, hydraulic torque converter, i n e r t i a s associated with the driveshaft and axles, and with the wheels and t i r e s of the v e h i c l e . mass f a c t o r .  The apparent increase i n mass may  be expressed as a  The mass f a c t o r i s defined as being equal to 1 plus the r a t i o  of equivalent i n e r t i a to the gross v e h i c l e weight. to the mass f a c t o r i s (Ordorica,  1965)  2 7 = 1.04  + (0.05 X Reduction) .  This approximation i s adopted i n the model.  A good approximation  Appendix 8 NOMOGRAPHS ON ENGINE BRAKE DEVICE  CD  > 00  I  •  •  GROSS  i (X co o  VEHICLE  SINGLE AXLE  1 I  i  •  \  8  8  OF POUN03  M  —  =!  1  ENGINE ^  8  • • I I i . I I I I I i I i I I 11 i J1111111 l l 111 111 111  WEIGHT.THOUSANDS  DUAL AXLE  <  1  CO  <  <  1 (Tt  <  OP  9 .  8  o o  • • I • . , • I . • . i I i . , , i i | n i . l  <n  CO TJ CD CD a  o  V*  t--  o o  ^  '\5 •  -  \  TURNING LINE  P  o  8-  CO TO H-  3 3  (D  cr  CD O O  3  r+ H T  CONCRETE OR ASPHALT PER CENT GRADE  ,  ![—,  __!  f . J  GRAVEL OR HARD PACKEO DIRT  <3  r+ & CD  co  CD  s TO H3 CD  ( | . ,. 1, 1, 1,1,1,1  r  • *»  I  C*  OO  O  O  DESCENT SPEEO" MPM-95 SQ FT VAN if* I O  O  w»  *  '  " —*| — 4 fsr L s Vw s w H t HJ. s f t H . i t. 111° t OE SCENT SPEED - M P M- TANKERS . LOG RIGS T  T  > 00 V E H I C L E .  i _Li.j..i_i.l 11 n IniilimJ  L.  ^IILLIIIUUIUOI G R O S S  W E I G H T ,  T H O U S A N D S  \  O F  P O U N D S  I  ^ III a CD CO  M i l  i l . M  SINGLE A X L E  u, VI  S SS S S SS SS  E NGINE  I'  \ \  S  I1  I  DUAL AXLE  o fD  3 rt  co (D <D  a O O C-i  P>  TURNING  o  LINE  8CO  3 TO H-  3 (D  CT* H  sO  o 3 rt  C O N C R E T E OR A S P H A L T  8  O  PER CENT GRADE-  -t  1  i ' I  CRAVELOR  ffi  -# t  H - r W r V r V  HARD P A C K E D  DESCENT  3  DIRT  S P E E D " M P H " 95  SO f T VAN  ca CD  3 TO £? CD  •if -r - rWr r |tttljtt H | H - H f H - H - f - t - ) - f - f -  r  S 6  1  DESCENT  S P E E D - M P H - " J A N K E R S , L O G RIGS  •s fl>  o  o  o  o  o  l-i. *...i,.i.J.__,i,.i.i l l--iiiiU---U-l-iilJ^ CO  GROSS -VEHICLE  WEIGHT, T H O U S A N D S O F P O U N D S i  ^  \  TURNING LINE  I CONCRETE OR ASPHALT  I tM  A  »  -  t»0l"J<B  ». ! < »  ~  O  5  * CTl CO O  ; i ; j  N  GRAVt" L OK HARD PACKED DIRT  I  DESCENT oo  o  o  S»EED " M PH - 95 SO F T VAN 5  jo  o>  |Jf^Uw|4H|Hi|jtfftf4+f+-|-+--r-t-H—| O O o O O 1  *  _»  \  \-  v  DF SCENT SPEED - M HH- TANKERS , LOG RI<_S  Appendix 9 ANALYSIS OF VARIANCE  A9.1  Travel empty  units times^\. (minutes ) \ .  84  179  181  101  58.86  63.61  58.29  58.47  55.12  58.53  58.49  61.93  53.43  58.72  59.15  61.94  58.26  55.87  60.18  60.45  53.62  64.73  54.44 53.77 60.04  Total Mean  447.54 55.94  236.73 59.78  236.11 59.03  note: Unit 130 was excluded because only one t r i p was observed.  Table A9.1  Observed times f o r travel empty  307.52 61.50  77  H  o  :  V  181 ~ 101 " 8 4 ~ 179 y  y  y  : a t l e a s t two o f the means are not equal a=0.05 c r i t i c a l region F > 3.20  Source o f v a r i a t i o n s  Columns means  SS  DF  MS  100.90  3  33.63  Error  103.98  17  6.12  Total  204.88  20  Table A9.2  Analysis of variance f o r t r a v e l empty  Conclusion: r e j e c t H  Computed F  5.5  78  A9.2 Travel loaded  >v  units  181  timesN. (minutes^v  101  84  179  130  69.60  76.17  73.28  70.17  73.34  65.37  73.25  70.70  69.10  73.51  66.32  72.69  69.80  71.00  70.27  86.4_  68.25  72.85  69.13  290.36 72.59  286.73 71.68  279.40 69.85  64.69 66.85 66.07 63.90  549.23 68.65  Total Mean  Table A9.3 Observed times f o r t r a v e l loaded  H  o  :  W  181  =  *101  =  w  84  =  v  179  =  v  130  : a t l e a s t two o f the means are not equal cc = 0.05  c r i t i c a l region F > 2.93  217.12 72.37  79  Source of v a r i a t i o n s  Columns means  SS  DF  MS  62.47  4  15.62  Error  431.28  18  23.99  Total  493.75  22  Table A9.4  Analysis of variance, f o r t r a v e l loaded  Conclusion: Accept H  Computed F  .65  80  Appendix 10 TESTING FOR SIMILARITY OF SLOPES  A10.1 Travel loaded  Actual  Predicted  25.63  49.920  48.22  30.145  31.59  53.186  50.54  11.78  32.107  33.44  59.842  57.26  17.174  17.85  32.970  34.17  61.305  58.43  19.180  20.50  35.179  35.93  67.023  63.74  21.166  22.63  38.949  39.92  70.569  66.82  23.105  23.49  43.099  43.40  Actual  Predicted  Actual  6.677  6.00  24.357  9.395  8.94  11.850  Table A10.1  Predicted  Cumulative actual and predicted times for each section for travel loaded  A conditioned regression was fitted by imposing the restriction that the intercept i s zero. 1.0219. .  The following test was then performed:  V H  b  l  :  ^TRAf 1 B d  The coefficient of regression (b^) obtained was  b  i  "  l* "  1  1  b  l- l = s.e.O^) g  1-0219 - 1 0.0091  =  2.408  which is significant at the level 0.05.  This implies that the  hypothesis of common slope should be rejected.  82  A10.2 Travel empty  Actual  Predicted  Actual  3.016  2.35  29.490  7.776  5.88  9.504  Predicted  Actual  Predicted  21.35  42.985  33.27  31.446  23.03  44.653  34.75  6.76  32.138  23.66  49.236  38.77  14.729  10.74  33.857  25.66  51.210  40.62  17.196  12.58  38.311  29.60  53.666  42.72  22.777  16.04  40.205  31.14  58.673  47.28  26.235  18.59  41.152  31.89  Table A10.2  Cumulative actual and predicted times f o r each section f o r t r a v e l empty  As f o r t r a v e l loaded a conditioned regression was f i t t e d by imposing the r e s t r i c t i o n that the intercept i s zero. (b-^) obtained was 1.2896. V  T  b  18df  i  =  The c o e f f i c i e n t of regression  The following test was then performed:  1  b  l  " 1 3  s . e . C b . ^  =  1.2896 - 1 0.0103  =  28.143  which i s s i g n i f i c a n t at the l e v e l of 0,05. of common slope should be rejected.  This implies that the hypothesis  Appendix 11 THE COMPUTER PROGRAM  A l l . l Input cards The input cards as expected by the program are i n the following order 1. The f i r s t four (4) cards are used to input information which i s output as t i t l e a t the beginning o f the output. 2. The next card i s f o r the t o t a l number of gears i . e . main and a u x i l i a r y transmissions combined.  F o r example a manual transmission with the  following gear r a t i o s gives 15 gear p o s i t i o n s . 1st  2nd  3rd  4th  MAIN TRANSMISSION  5.47  3.23  1.76  1.00  AUX. TRANSMISSION  1.60  1.19  1.00  0.84  GEAR POSITION  RATIO  1st LUD  8.75  2nd UD  6.50  1st D  5.47  2nd LUD  5.16  1st  OD  4.59  2nd UD  3.84  2nd D  3.23  2nd OD  2.71  3rd  2.09  UD  84  3rd D  1.76  3rd OD  1.47  4th UD  1.19  4th D  1.00  4th OD  0.84  5th UD  1.02  not used  5th D  0.86  not used  5th OD  0.72  note: 3rd LUD, 4th LUD, and 5th LUD are not gear p o s i t i o n s . 3. The next card(s) i s (are) f o r the gear r a t i o s i n decreasing order i . e . as shown i n 2. FORMAT(10F4.2). 4. The rear axle r a t i o i s entered on the next card. F0RMAT(F4.2). 5. The next input card should contain the r o l l i n g radius i n inches, the empty and loaded v e h i c l e weight i n pounds, and the length of l o g (38 or 48 f t ) . FORMAT(F3.1,2F6.0,F2.0). 6. The next card read determines or a torque-converter transmission.  i f the program deals with a manual FORMAT(ll).  0 i s entered f o r manual transmission 1 f o r torque converter when torque r a t i o s , speed r a t i o s , and K-factors of the torque converter are known 2 when only the output torque and output RPM to the torque converter are known. 7. I f 0 o r 1 i s read on the previous card the program expects to read on the next card the number (M) of HP versus RPM points input, the i d l e RPM, and the barometric pressure due to a l t i t u d e . 11. FORMAT(I2,F4.0,F4.2)  I f two (2) i s encountered see  85  8. The following M cards should contain one RPM versus HP each. FORMAT (F4.0,F5.1). 9 . I f I was encountered the next card i s f o r the number of r a t i o s (NRATIO) input.  I f 0 was encountered GO TO 13. F0RMAT(l2).  10. The following NRATIO cards should contain the speed r a t i o s , torque r a t i o s , and K-factors o f the torque converter.  GO TO 13. F0RMAT(2F4.2,  F5.2). 11. I f a 2 was encountered the program expects to read the number (M) of RPM versus torque to the e x i t o f the torque converter input, and the i d l e RPM which w i l l be i n that case 0. F0RMAT(I 2,F4.0). 12. Again i f a 2 was encountered the program reads M torque converter RPM versus torque. FORMAT(F4.0,F5.1). 13. Read the number (NEBRAK) o f maximum descent speed points are input (when dealing with engine brake).  I f a 0 i s input GO TO 15. FORMAT(12).  14. The following NEBRAK cards contain grade and maximum descent speed loaded and empty points as taken from engine brake chart. F0RMAT(F3.2,F4.1). 15. This card determines the number of sections to scan the road, the maximum speed as c o n t r o l l e d by surface conditions or regulation, and i f the truck are radio c o n t r o l l e d o r not (1 = radio controlled, 0 = no radio). F0RMAT(I4,F2.0,I1). 16. The following NSEC cards describe the road, one section per card. The parameters are: - number o f the section - section length i n f e e t - surface type (1 = paved, 2 = gravel)  86  - c o e f f i c i e n t of f r i c t i o n - curve radius i n feet - superelevation i n feet/foot - distance between d r i v e r ' s eye and backslope i n f e e t - the grade f o r the loaded d i r e c t i o n (+ = adverse, - = favorable). For  the empty d i r e c t i o n the grade signs are inversed by the program.  FORMAT (I4,F5.0,I1,F3.3,F4.0,F2.2,F2.0,F4.3). 17. On the next card the program reads the number (NSTOP) to make.  The  same number of stops i s assumed f o r t r a v e l empty and loaded. FORMAT(13) 18. The following NSTOP cards determine, f o r t r a v e l loaded, i n which section a stop i s to be made, how much time i s to be waited, and the reason of  the stop. F0RMAT(I4,F5.0,F5.2,22A3) 19. Same as 18 but f o r t r a v e l empty. 20. The next card contains the following control data: i n i t i a l v e l o c i t y  loaded, i n i t i a l v e l o c i t y empty, length of the subsection i n f e e t (ds), and the output l e v e l desired (1, or 2). or  The value ds should be smaller than  equal to the smallest section length. FORMAT(3F3.0,11). 21. I f the output l e v e l desired i s 2, the number of sections (NSTOUT),  where output i s desired, i s punched on the next card. F0RMAT(I4). 22. The next card(s) contain(s) the section number where output i s desired. F0RMAT(I4). 23. I f the output l e v e l i s 2, the following card(s) contain(s) the number of the section where output i s desired. F0RMAT(20l4). A l l . 2 Computation  time requirements  The amount of computer time required f o r a simulation run depends mainly on the length of the course and the length of ds used.  On the  IBM 360/67 computer and using the FORTRANH version 6 seconds of CPU time was used f o r a ds o f 100 feet, a l e v e l road (one way).  of output of 1, and 33 miles of  For l e v e l o f output 2, the time i s increase by 3 times  (output f o r 39 sections from 142 sections was requested). time w i l l also increase with the length o f the course. A l l . 3 FORTRAN l i s t i n g of computer program  The computer  (~-  $COMPILE  :  ~~  ~  i  C  TRUC<  I  C  * * * < : * * * * * * * * * * * * * * * * *  1  !\ ' '  —  12_  c***  3  9.  10  n  V  29 ^0  RC.STYPF.OUTLEV.STAOUT.G  * * * * * * *  P.OAO  * * * . * * > £ *  ,RIMP(200  MAXVLEt 500,2),MAXSPEf 500),MAXSPL(500) ,VO(2) INFO). ( 2 0 ) , I N F 0 2 ( 2 0 ) , I N F 0 3 ( ' 2 0 ) , I N F 0 6 I 2 0 ) ISTOP(30,2) ,AT(30,2 I.WAIT(30,2) .STAOUTI500 ), INF04(I2,30) 30) (VA XS P L ( 1 ) , M A X V L E ( 1 , 1 )  )» (MAXS E ( 1 ) , M A X V L E ( 1 , 2 )) P  E 01) W A L E N C E (BEHP,NETOR) DOUBLE P R E C I S I O N AN C O M M O N / V A R / X ( 2 0 0) , Y ( 2 00) , N P , N D COMMPM/COEF/ANI30,3),II COMMCN/ROAO/N(500 1M(500),GRAO(500)  c c c c c c c c c c c c c c c c c c c  19  ?"?  ACCEL,TRACE  INTEGER  EQUIVALENCE  12 13 14 15  26 27 28  A DEFINED  * * * * *  LOGICAL  DIMENSION DIMENSION DIMENSION 1, I N F 3 5 I 2 2 ,  8  ??  t  R£AL_LAS.I.i NR I V P , M AX VL E , M A X V , L T I M , L S T T I M , L AV  fS  23 '24  PROGRAM  >{:******i>  DIMENSION GRPOS(30) ,ERPM(40 I,BEHP(40).NETOR(40) ,VMPH(200) 11 ,RSHIFT(30),SH[FTV(30),GRA(25),MDESL(25),MDESE(25) DIMENSION E K F A C < 4 0 ) , C K F A C < 4 0 > , S P R ( 4 0 ) , T OF OP. ( 4 0 )  7  20 21  SIMULAT ION OVER  REAL N E T O R . L M . M C S P , M P S P . L , M D E S L , M D E S E , M A X S P L , M A X S P E , M A X D E , L O G , L V W , lNHPfJ, MAXHP .  4 5  16 17 18  MAIN  PERFORMANCE  2002 ...2004  TRUCK INPUT  DATA DATA  ) , S E C L ( 5 0 0 ) , S T Y P E ( 5 0 0 ) , U S ( 5 0 0 ) , C P . A D ( 5 0 0 1 , F ( 5 0 0 ) ,1  " R E P A R A T I O N TO BE U S E D - I N MOTION FORTRUCK DATA PREPARATION  B = B AR O M E T R I C P R E S S U R E ( I N O F H G ) F O R BEHP = BRUT E N G I N E HORSEPOWER ERPt= ENGINE RFM EVW=E MPT Y V E H I C L E WEIGHT GRA=F A V O R A B L E GRADE IN X (THE ENGINE 3RA VS.MDESG AND MDESL) GRPOS =GEAR POSITION RATIOS L V W = L 0 AD E D V E H I C L E WEIGHT M=NUMB ER O F H P V S R P M I N P U T MDESE=MAXIMUM  DESCENT  SPEED  N E B R A K = NUMB ER O F E N G I N E  NGEAR=NUMBER RAD=R D L L I N G  POINTS  INPUT  CF GEARS RADIUS  RAXLE=RcAR AXLE RPMID=IOLE RFM  RATIO  READ! 5 . 2 0 0 2 ) ( I N F O H READ!5,20021(INF02I REA ) ( 5 , 2 0 0 2 ) ( INFQ3(  I ) , 1=1 , 2 0 ) I ), 1=1,20) I ) ,1 =1 , 2 0 )  READ! 5 , 2 0 0 2 ) ( INF06( FORMAT(2 0A4) R E A 0 ( 5 , 2 0 0 4 ) N G E AR  I) .1=1 ,20)  FORMAT(12) REA)( 5,2005)(GRPOS(  I ) , 1= 1 , N G E A R I  FCR'IA T(F 4 •2I R E A D ! 5 , 2 0 0 7 ) R AD , E V W ,1. V W , L O G F 0 R M A T ( F 3 . 1 , 2 F 6 . 0 , F 2 . 0) DEThRMINE IF DEALING REACH 5, 1 0 0 0 ) K T FORMAT(11)  WITH  AITITUDE  DEVICE  IS REPPE^FNTFD  EMPTY  BRAKE  2006  1000  BRAKE  DATA PREPARATION) N E T O R = .NET E N G I N E TORQUE  F 0 R M A T Q 0 F 4 . 2 ) READ!5.20061RAXLE  C  PRESENT  M D E S L = MA X I M U M D E S C E N T S P E E D L 0 A 0 F D I N F U N C T I O N PARTICULAR ENGINE BRAKE DEVICE  2005  2007  SIMULATION  TORQUE  CONVERTER  OF G R A F O P T H I S  ( T O BE USED  IN  ROAn  RY  .  ; C  IF  KT=0  C  IF  KT = 1  C IF  C  K T= 2  31 2008 200 9,  17...  C  38 39 41  21 C  43 44  CONVERTER  WITH  A N D K - F A C TORS  DEALING  WITH  TORQUE  RPM TO  A P. E  AND TORQUE  CONVERTER  THE TOFOUE INPUT  IS  RATIOS,  AND ONLY CONVFRTER  ASSUMED  TO  OUTPUT  TORQUE  ARE A V A I L A B L E  HAVE  BEEN  FINOING O F N ETOR DO ?1 1 = 1 , M  FOR PRESENT  CORRECTED  —  F O R M A T ! I 2 , F 4 . C , F 4 . 2 1 5,2 009)t ERFMII ) , B E H P ( I ) , 1 = 1 , M l FORM4T(F4.0.F5.1)  MAX H P - ^ E H P ( M )  SPEED  AVAILABLE  REACH  ALTITUDE  AND  ATMOSPHERIC  :  CONDITIONS  NETOR(I>=5252.*NHPD/ERPM(I ) IFIKT.EQ.OIGOTO 998 COMPIJTF E N G I M F K-FACTOR DO  997  45  C C c c c  46 47 48 49  99 7  1 = 1 , *  EKFACIII=ERPM(I)/SQRT(NETOR(I CONTINUE NRATI0=NUMBER OF SPR=SPEED R4TI0 T O R OR = T O P . 0 1 )  c  RATIO  CKFAC-CCNVERTER  K-FACTOR  P R E F E R A B L E TO G E T A S REA")( 5 . 1 . 0 0 1 I N R A T I O FCR'1AT(I2I  100?  READ! 5,1 002) I S P R ( I ) FaR^4T(?F4.2.F5.?)  51 52 53 994  56 57  ,TOROR(  I N T E R P C L AT I O N TO CONVERTER EXIT  DO DO  1 =1 , N R A T I O . J=1,MM  •.,IF(C<FAC(.I),GE.EKFAC(  54 55  MANY  LINEAR TORQUE MM=M-1 93 6 995  ))  POINTS  1001  c c  50  NRATIO  THAN  PPM VS  C  59 60 61  FIND  THE OUTPUT  995  6 3 ....  C C  64 65  996  66 67  a ....  A 69  •  990 3000 998  TORQUF  J ) . A N D . C K F A C I I ) . I T . F K F A C (.14-1 I i r . O T P  DEKFAC=EKFAC(J+1)-EKFAC(J) DER»M = F R P M ( . l + 1 1 - E R P M i . l ) XRP-1=ERPM(J) + ( S L 0 P E * ( C K F A C ( I ) - E K F A C ( J I )1 _E.INT T H E T O F O I I F C O R R F S ° P M D I NG T O T H A T R P M DTO*=NETCR<J*1>-NETOR(J) • X T l ' R = N F T G P . ( J ) + ( S L O P E * ( X R ° M - E P . PM ( J ) 1 ) CONTINUE O U T ° J T R P M TO T H E TORQUE ERP^tI)=SPR(I)*XRPM  CONVERTER  OUTPUT TORQUE TC THE TORQUE NET1R(I)=NETOR( 11*TORQR(I ) CC1NTINUF IF(KT.NE.2)G0T0  POINTS  RPM AND OUTPUT  SL0°E=DT0P7DERPM  62  HP  I ) , C K F A C < I ) , I =' , N P A T * 0 )  SLO°E=QERPM/DFKFAC  58  71  TORQUE  DEALING RATIOS,  89  HPO=PD(BP,PO) N H P . l = H P r > *.,<»  42  ^  TRANSMISSION  PO-^EHP<I)  40  70  MANUAL  IN THAT CASE THE FOR ALTITUDE IF(KT.EQ.2)GOTO 990 REATI5.20C3IM.PPMID.BP  C. C  36  WITH  AND OUTPUT  C  33 34  DEALING  EXIT  CONVERTER  993  REAM5,3000)M,RPMID  -£CMAiJ[ji,F4. 0 )  R E A K 5.2CC9I(ERPMfI ),NETOR(LI REATI5,2004)NEBRAK IF(NF3RAK-F0.Clr,nT0 20  ,I=1,M|  EXIT  TO T H E  QOL  —.—  :  72 73  REACH 5 , 2 0 0 1  2001  R I M P J L L  74 75  I I , M D E S L (  AND  S H I F T I N G  I I » M D E S E t I  P O I N T  T O P S P = T Q P  20  T O P S ° = t E R P M ( M ) * 3 o l 4 1 5 S P = . 5 K = l  S P E E D  IN  C  S H I = T V (  C  R S H I F T t I ) = R I M P U L L  78 79  C O M P U T A T I O N  H I G H E S T  I l = S H I F T I N G  V E L O C I T Y AT  S H I F T  IN IN  GEAR G E A R  2  GR2=G  C 3  1 l = ( N F T O R t  I I * G R P O S (  RPO S tI+1  E N G I N E  RPM  I N C R E M E N T .  1=  1 . 2 . . . N G E A R  I = 1 , 2 . o . N G E A R  0 FAR  I  AND  1-  L I Mr  A R  4  * 2 „ * 3 . 3 . 4 1 5 9 * R AD I  0 o * 2 o * 3 < > 1 4 1 5 9 * R A D )  14  1 I N T E R P O L A T I O N  DO I Ft  M 2 . G T . E R F M ( J I  88 89  GOTO  6  5  / R A O  1+1  R P M . l = ( S P * 5 2 8 0 . * ! 2 . * P . A X L E * G R l ) / ( 6 0 . I F t R O M I . L T . R P M I O l G O T O  C  I  I  IN  86 87  .1=1  B E T W E E N  INPUT  P O I N T S  .MM  D T O < = N F T n R ( .1+3 DRP'1=EF.PM(  J + l  „ A N D „ R P M2«, L E . E R P M ( J + 1 ) ) G O T O  )-NFTOR  5  (.])  l-ERPM <J I  91  S L O P E = O T Q R / D R P M  92 93  XTOR = N F T O R  ( .1) + ( S L O P E * ( R P M 2 - E R  P  J ) ) )  M (  R I M P 2 = < X T O R * G R 2 * R A X L E * „ 8 5 * 1 2 „ l / R A D  6  95  I F t R P M l o G T . E R P M (J I . A N D o R P M J . o L E o E R P M t J + l GOTO  7  DTOR=NETOR U  + 3. I - N E T O R  S L O P E =  l-ER  R I M P 1  101 102  4  103  14  ( J I  DTOR/DP.PM l-ER.PM ( J  = ( X T 0 R * G R 1 * R A X L E * . 8 5 * 1 2 „  II)  l / R A D  C O N T I N U E GOTO  104 105  7  P M ( J 1  X T O ^ = N E T O R ( J 1 + ( S L O P E * ( RPM  100  1 ) GOTO  4  DP PM= E R P M ( J + l  98 99  15  S P = S ° + o 5 R I M P 1 = 0 . R I M P 2 = 0o  106  GOTO  15  108  3  I F U P M 1 . G E . E R P M ( M ) ) G 0 T 0 I F ( R I M P 1 . L T . R I M F 2 ) G 0 T 0  C C  VMPHt KI = V E L O C I T Y R I M P t K ) = R I M P U L L  109  V M P H ( K ) = S P  110  R I M P t  111  A = R I M P 1  112  B = R I M P 2 K=K+1  114  S P = S P + . 5  115  GOTO  M P H ;  VMPH =  A V A I L A B L E  AT  0 . , o 5 , 1 . . . . T O P S P  V E L O C I T Y  V M P H ( K )  3  C  IF  R I M P U L L  C  TO  G 1 V E R N F D  8  V M P H ( K ) = S P  117  IN  9 8  K I = R I M P1  113  V S  MPH  R P M  C U R V E S  E N T E R  FOR  TWO  A D J A C E N T  G E A R S  I N T E R S E C T  P R I O R  H E R E  R I M P I K ) = R I M P 2  118  S L 1 = ( R I M P 1 - A ) / ( V M P H t K l - V M P H I K - l  119  S L 2 = ( R I M P 2 - 3 )  C  120  I: I;  I I * R A X I . E * „ 3 5 * 3.2.  MM=  116  S P E E D  G R 1 = G R P 0 S ( I )  85  1 0 7  S M A L L  9 * R A 0 * 6 0 . * 2 . ) / ( 5 2 9 0 . * 1 2 . * R A X L E * G R P O S ( N G E A R I )  R P M 2 = ( S P ^ 5 2 B 0 . * 1 2 o * R A X L E * G R 2 ) / ( 6  96 97  FOR  GEAR  83 84  94  I  S H I F T V ( 1 ) = 0 . R S H I F T t  81  90  1 , I = 1 , N E B R A K  1= 1  76  82  GRAt  C  7 7  SO  M  F 0 R 1 A T ( F 3 . 2 , 2 F 4 , 1 I  R I M " J L L  AT  R S H I F T t I + 1  / ( V M P H ( K ) - V M P H ( K - l I  THE  S H I F T I N G  I = ( ( A * V M P H (  P O I N T  K I - R I M P l  I 1 I  J U S T  B E F O R E  * V M P H ( K - 1  S H I F T I N G  I )/ ( R I M P 1 - A  > - ( B * V M P H ( K ) ) / (P.  I  ( i  1  Ir  __  121 122 123  124  C 9  125  C  126 127 128  10  C  129 130 131  13?  ..  135  nsp=.u SP=DSP/2. RPM1=<SP*5280.*12.*GRP0S< DO 1? . 1=1 .MM  138 139 140 141 142 143 144 145 146 147 148 149  IF(RPM1.GT.5RPM(J).AND. PPrvl.LE.ERPM(J + l ) ) G O T O GOTO 1 2 t IN"4R INTFRPCI AT ION D T 0 R = N E T 0 R ( J + 1 ) -NETOR {J.) DRPM=ERPM(J+1)-ERPM(J) SLOPE=DT0R/ORPM XTO:< = NETOR ( J ) + ( S L O P E * (RPM1-ERPM( J ) ) ) RIMPI =(XT0R*GRPOS (N GE AR ) * R AXL E * . 8 5 * 1 2. ) /P. AD VMPHt K) = SP RIMPIK)=RIMP1 K=K+1 GOTO 11 CONTINUE CONTINUE KMAX=K-1  133 134  136 137  C  13  12 11  C C  150 151 152  153 154 155 156  C C .  157 158 159 160 161 162 163  c c  17  164 . 165 166  167  18  91  1MP2-B )+ <R IMP2*VMPH(K-1) (/(RIMP2-B ) ) / ( ( S L 2 - S L 1 ) / ( S L 1 * S L 2 ) 1 S H I F T V ( I + 1 ) = ( (VMPH<K-1 ) M R I M P 1 - R I M P 2 ) - V M P H ( K ) * ( A - B ) )/(VMPHIK l-VMPH 1IK-1))1/(SL1-SL2) K=KU SP=SP+.5 GOTO i o • GOVERNED R P M CICT AT E JUMP TO NEXT GEAR ENTER HERE S H I ^ T V I 1 + 1 ) = < ERPMIM ) * 3 o l 4 1 5 9 * R A D * 6 0 . * 2 . ) / ( 5 ? 8 0 . * 1 2 . * P A X L E * G P P O S (I ) 1 ) R I M P U L L AT THE S H I F T I N G POINT J U S T BEFORE S H I F T I N G RSHIF T( I + 1 ) = ( NETOP.I M ) * G R P O S ( I ) * R A X L E * . 8 5 * 1 2 . ) / R A D I=IM IF1 I+-1.LE.NCE AR 1G0T0 2 I F IM L A S T GEAP F I N D RIMPULL FROM S H I F T I N G POINT TO TOP S P F E D NDSo=SP*?„ NSP=T0PSP7.5 DO 11 J J = N D S P , N S P  NGE AR ) *P. A XL E) / ( 6 0 . * ' . * 3 . 1 4 1 5 9 * P A D ) 13  F I T T I N G OF A SECOND DEGREE POLYNOMIAL FOR RIMPULL BETWEEN DATA P R E P A R A T I O N BEFORE C A L L I N G SUBROUTINE F I T K= l DO 19 I I = 1 , N G E A R J= l X(1)=SHIFTING VELOCITY Y ( 1 ) = R I M P U L L J U S T AFTER S H I F T I N G I F(II.EO.l)Y(J)=RSHI FT(I I) IF(It.EO.l)X(J)=SHIFTV(II) IF< II .EC).1 (GOTO 23 X ( J I = S H I F T V I I I) RPM AT THE S H I F T I N G V E L O C I T Y R P M = X ( J ) * 5 2 3 0 „ * 1 2 . * R A X L E * G R P O S ( I I ) / ( 6 0 . * 2 . * R A D * 3 . 14159) L I N E A R I N T E R P O L A T I O N TO F I N D RIMPULL J U S T AFTER S H I F T I N G DO 13 1=1.MM I F ( R P M . G T . E P F M ( I ).AND.RPM.LE.ERPM( 1 + 1 ) ) G O T O 17 GOTO 1 8 DT0}=NFT0R(I+1)-NETOR(I) ORPn=ERPM(1+1 l - E R P M I I I SLO°E=DTOR/ORPM XTO^= NFT.QS.(_I..l+i_SLQP E* ( RPM-ERPMI I ) ) ) Y ( J ) = X T O R * G R P O S ( I I ) * R A X L E * . 35 *12 . / R AD CONTINUE I F ( I I + 1 . G T . N C F A R I S H I F T V I I 1 + 1 )=VMPH(KMAX1  EACH  GFAR  —  \  —  —  168 169 170 171 172 113 174 175 176 177 178 -129,  180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199  200 201 202 203 204 205 206 207  23  22  :  g?  I F ( 1 1 + 1 . G T . N G E A R I R S H I F T ( I 1 + 1 I = R I M P ( K MAX I I F ( V M P H ( K ) . G E . S HI FT V< I I + l ) . G O T O 2 2 J=J+1 Y(J)=RIMP(K) X(JI=VMPH(K) K=K+1 GOTO 2 3 J = J+1 NP= I Y ( J ) =RSHIFT( I I+l l X(J)=SHIFTV(II+l) LU2£J  IF(?\|P.EQ.2)ND =1 CALL F I T 19 CONTINUE WRITE(6,2012) 2 0 1 2 FORMAT( * 1 • , ' T R U C K PERFORMANCE SIMULATION') W R I T E I 6 . ;-:01 3 ) 201 3 FORMAT (1 X ****^ft***>i i , / / / ) WRITE(6,2014)(INFO!(I),1=1,20) WRITE ( 6 , 2 0 1 4 ) ( I N F 0 2 I I ) , 1 = 1 , 2 0 ) W R I T E ( 6 , 2 0 1 4 ) < I N F 0 3 ( I ),1 = 1 , 2 0 . WRITE I 6 , 2 0 1 4 ) ( I N F 0 6 ( I ) , 1 = 1 , 2 0 ) 2 0 1 4 FORMAT(1X.20A4 ) IF1KT.EQ.2)GOTO 8 80 W R I T E I 6 , 2 0 1 5 ) MA X H P , EP. PM( M ) 2 0 1 5 FORMAT(IPX.F5.0.3X.'HORSEPOWER A T • , 3 X , F 6 . 0 , 3 X , ' F P M (GOVERNED R P M ) ' 1 ) 880 WRITE(6,2016)EVV>,LVW,L0G 2 0 1 6 F O R M A T ( 1 O X , ' E M P T Y V E H I C L E WE I G H T = ' , F 1 0 . 0 , 3 X , ' L O A D E Q VEHICLE WEIGHT 1 = ' , F 1 0 . 0 , 3 X , • LENGTH OF LOGS = ' , F 6 . 0 , 3 X , ' F E E T ' ) IFKT.EQ.21G0T0 861 WRITE ( 6 . 2 0 1 9 ) BP 2 0 1 9 FOR 1 A T I 1 0 X , « A T M O S P H E R I C C O N D I T I O N S : BAROMETRIC P R E S S U R E ^ , F P . . 2 , ^ X , 1 * OETE R MI NED F R O M T H E A V E R A G E A L T I T U D E OF O P E R A T I O N ' ) 881 WRITE(6.2017)RAH 2 0 1 7 F 0 R M 4 T Q 0 X , •ROLLING RADIUS = ' , F7. 1 , 3 X , ' INCHES' ) WRITE(6,2018)RAXLE 2 0 1 8 F O R M A T ( 1 O X , ' R E A R A X L E RAT 1 0 = ' , F 8 . 2 ) ' WRITE(6, 2022 ) 2022 FORMA T ( / 1 O X , ' G F A R RAT 1 0 • , 2 0 X , • S H I F T I N G V E L O C I T Y • / , 4 4 X , * C O M P U T E D • ) • WRITE(6,2023)(GFPOS(I ),SHIFTV(!),I=1,MGEAR ) 2023 F 0 R M A T U 0 X . F 7 . 2 , 23X.F10. 2) C*** ROAO D A T A P R E P A R A T I O N C*** S I M U L A T I O N OF K N O W L E D G E A N D J U D G E M E N T OF T H E _ D R I V E R *** C O M P J T A T I O N O F S P E E D L I M I T S AND S T O R A G E OF ROAD~ C H A R A C T E R I S T I C C CANG=CENTRAL ANGLE CRAO=CURVE.RACIUS C E = SU SR5LEVAT ION, FT/FT C GRAD= G R 4 D E I N F T / F T JE L M = J I S T A N C E B E T W E E N D R I V E R ' S E Y E AND B A C K S L O P E C MAXSPL = MAXIM!JM S P E E D LOADED C MAXSPE=MAXIMUM SPEED EMPTY C MCSP^MAXIMUM CURVE S P E E D . MPH C  ( ,  C C _C C C -C  MPS3=MAXIMijM P E R M I S S I B L E S P E E D AS C O N T R O L L E D BY S U R F A C E N=N'JM3ER OF T H E S E C T I O N S ?JS..EC= N U M B E R O F S E C T T I N S RC=IF 1 : RADIO CONTROLLED 0 : NO R A D I O C O N T R O L OR G E N E R A L P U B L I C H A S A C C E S S SECL=SECTirN I F N G T H . F T  CONDITIONS  r •  ! i i  \  208 ?09 210  C C c c 2 0 1 0  C C  S D = S I G H T SM=ST  D I S T A N C E  ANDS  M E A S U R E D  F O R S M A L L  S T Y P E = T Y P E  O F  M  A S  S U R F A C E  U S = C O E F F I C I E N T  OF  AROUND  U S E D  I N  ( 1 = P A V E D ,  T H E C U R V E T H E  T E X T  2= G R A V E L )  F R I C T I O N  REAOt 5 , 2 0 1 0 ) N S E C , M P S P ,P.C F O R M A T ( I 4 , F 2 . 0 , 1 1 1 R E A D  R O A D  D A T A  T R A V E L  E M P T Y  R E A D ! 5  , 2 0 1 1 ) <  O N L Y  F O R L O A D E D  S P F E D  L I M I T  D I R E C T I O N ;  T H E GRADE  I S  I N V E R S t D  F O R  C O M P U T A T I O N  N( I ) , S E C L ( I  ) , S T Y P E ( I )  , U S < I ) , C R A D t I ) , E t  I ) , L M (  I ) , G R A D ( I  1 ) , I = 1 , N S E C )  211 212 213 214 215 2 1 6  217 218 219 220 221 222 223 224 225 226 227 228 229  2011  F O R M A T ( I  C  K E E P DO  S P EE D  A S M A X I M U M  I = 1 , N S E C  30  M A X S P E ( I ) = MP S I F ( C * A D t  C  S P E E D  0  I ) . E Q . O . ) G O T O  L I M I T  V S F =S 3 R T C 3 2 . 1 6 * C R A D ( I  237 238 239 240 241 242 . 243 244 245 246 247 248 249. 250 251  3 Y  S I D E  F R I C T I O N  ) * ( E ( I ) + U S ( I ) ) / < J . .- U S ( I ) * E< I ) ) )  V S F = V S F * 3 6 0 0 . / 5 2 3 0 . I F t V S F . L T . M A X S P L t I I  c c  M A X S P E ( I  )=  ) M A X S P L ( I > = V S F  M A X S P L ( I )  S P E F D  L I M I T  SIGHT  D I S T A N C E  A S  C O N T R O L L E D A S S U M E D  B Y  S I G H T  T H E SAME  D I S T A N C E  I N  BOTH  D I R E C T I O N  C A M G = S E C L ( I ) / C R A D ( I ) T E T A= A T A N ( G R A C ( K ) ) S M = C R A D < I ) * t l . - C Q S t C A N G / 2 . > ) I F ( L M ( I I . L E . S M ) G O T O  2 6  L = ( L M ( I l - S M I / S I N ( C A N G / 2 . I S D = S E C L < I ) + 2 . * L GOTO  26 27  2 7  SD=2, * C R A D ( I ) * A R C O S ( t I F ( R C •  E Q . 1 ) G O T O  V S D = ( S O R T t 3 2 * U S (  GOTO 28  29  C R A D t  I l - L M ( I )  ) / C R A D (  I ) )  2 3  ( 2 . * 2 . 5 * 6  4 . 3 2 * U S U  ) 1 * * 2 + ( 4 . * 2 . *  6 4 . 3 2 * U S ( I ) * S D ) ) - f 2 . * ? . 5 *  I ) ) )/ 4 .  2 9  V S D =( S O R T !  <? „ 5 * 6 4 . : -  2 * C O S  ( T E T A  1 * ( U S ( I ) + G R A D ( I I ) ) * * 2 + t 4„ * 6 4 . 3 2 * C 0 S <  c. %  V S 0 = V S D * 3 6 0 0 . / 5 2 3 0 . I ) = V S D  M A X S P E ( I » = M A X S P L t I )  25  c  I F tG RAD( n . E O . O . J G O T D M A X I M U M D E S C E N T S P E E D I F tNEB R A K . E Q o 01 GOTO L I N E A R  3 0 D O W N H I L L  3 3  I N T E R P O L A T I O N  B F T W E E N  I F I G ^ A D I  I 1 . G T . O . ( G O T O  I F t G ^ A O t  I ) . G T . G R A ( l ) ) G O T O  E N G I N E  BRAKE  DATA  P O I N T S  3 4 3 3  J = 0  35  J = J + 1 I F tJ . E Q . N E B R A K ) G O T O I F I G * A D (  36  I ) . L E . G R A ( . |  3 3 • ) „ A N D , GRADt  GOTO  3 5  DGRA=  A f l S t G R A t J + l ) l - A B S t G R A ( J ) )  DDES=MDFSt  (  l+ l l - M D E S L  I I . G T . G R A t J +U  (GOTO  (.))  S L O f E = D D E S / D G R A X D E S = H D E S L ( J > + < I F t X I E GOTO  34  S  0  S L O P E * ( A B S (GRADI  L T . M A X S P L ( I  3 7  GRD = ( - G R .1 =  n  A C ( I ) )  T  > * S D ) ) - ( 2 . 5 * 6 4 . 3 2 * C 0 S ( T F T A ) * ( U S ( I ) + G R A D ( I ) ) ) ) / 2  I F tV S D . L T . M A X S P L t I t ) M A X S P L (  C  236  25  A S C O N T R O L L E D  1 E T A 1 * ( U S t I H - G R A D t I )  232 233 234 235  ? )  P E R M I S S I B L E  M A X S P L t I ) = M P S P  164.  230 231  4 , F 5 . 0 , U , F 3 . 3 , F 4 . 0 , F 2 . 2 , F 2 . 0 , F 4 .  S M A L L E S T  1 ) M A X S P L ( I )  I ) 1 - A B St G R M J ) i ) ) = X D E S  3 6  252 253 254 255 256 257 258 259 260 261 262 263 264 26 5 266 267 268 269 270 271 272 273 274 275 276 277 278  38  94  J = J+1 I F ( J . E Q . N E B R A K ) G O T O  3 3 -  I F( G R D ol_ E o G R A ( J ) . A N D o G R D . G T . G R A ( J + 1 ) ) G O T O GOTO  39  39  3 3  0 G R A = A B S ( G R A ( J + l ) ) - A B S ( G R A ( J ) ) D D E S = M D E S 5 ( J + 1 l - M D E S E ( J ) S L 0 P E = D 0 E S / 0 G R A X D E S = M O £ S E < J > + ( S L O P E * ( A B S ( G R D ) - A B S ( G R A ( J ) ) ) ) l F ( X Q E S . L T . M A X S P - ( GOTO  33 C C  I F ( CA A O ( I ) . L T . O . IF  NO  E N G I N  D O W N H I L L  I ) = X D E S  1GOTO  B R A K E  C  S P E E D  4 0  U S E C A M P 3 F L L  A D ( I ) ) - . 1 1 * G R  I F ( M A X D E , L T . M A X S P E (  ) M A X S P E (  I)  J A G T  C U R V E S  F O R  A D ( I I * * 2 + . 0 1* ( - G R A D ( I ) ) * * 3  3 7  MAXOE = 3 6 . 6 7 - .  C  S P E E D  37  I F I C * A O t  ! * G * A D ( I  ) - . 2 2 * G RA D ( I ) * * 2 +  L I M I T  C O N T R O L L E D  B Y  I ) . G T . O . ) G O T O  S I G H T  I ). E C . N S E O G O T O  I F t C R  AOt I ) . E Q . 0 . . 4 N D . C P A Q < 1 +  I F t C ^ A D t  . 0 1 * G R A D ( I ) * * 3  I ) = M A X P E D I S T A N C E  DOWNHILL  4 1  IF(''J<  I F ( N  V A N DER  I ) = M A X D E  I F ( M A X D E . L T . M A X S P L ! I ) ) M A X S P L (  41  £  L I M I T S  M A X 0 E = 4 0 . ? 3 - 2 . 9 4 * < - G R GOTO  40  I M M A X S P F (  3 7  41 1 ) , E 0 . 0 . ) S D = S E C L ( I l + S E C L ( 1 + 1 )  I I . E Q . O . . A N D . C R A D t 1 +  1 ) . G T . 0 . ) S D = S E C L ( I )  ( I l . E O o M S E C ) S O = S E C L ( I )  I F t G ^ A D t  I ) . L T . O . ( G O T O  VSD = ( S O R T ( I 2 o  5 * 6 4 . 3  4 2  2 * ( U S (  I ) - G P A D ( I  ) ) ) * * 2 + ( 4 . * 6 4 . 3 2 * ( U S ( I  ) - G R A  0 1 I ) )  l * S D ) ) - ( 2 o 5 * J 4 . 3 2 * ( U 5 ( I ) - G R A D ( I ) ) ) ) / 2 . V S D = V S D * 3 6 C 0 . / 5 2 3 0 . I F t V S D . L T . M A X S P E t I)  ) M A X S P E t I  ) = V S D  G O T O • 3 0  42  VSD=t  SORT  t t 2 . 5 * 6 4 . 3 2 * <US( I ) + G R A D ( I  ))  ) * * 2 + < 4 . * 6 4 . 3 2 * t U S ( I ) + G P A D t I )  )  1 * S D ) ) - ( 2 . 5 * 6 4 . 3 2 * t U S t I ) + G R A O ( I ) ) ) ) I Z ,  279 280 281  V S D = 7 S D * 3 6 0 0 . / 5 2 3 0 . I F t V S D . L T . M A X S P L( I)  30  C O N T I N U E  C  NO  R E A D  282 . 283 284 285  c c c c c c c c c c c c c c c c c c c 2024  ( M A X S P L ( I ) = V S D  A D M I N I S T R A T I V E  S P E E D  R E G U L A T I O N  R E S P E C T E D  B Y IS  . DS=INCREMENT T H E  DATA  I S  IT  I N P U T  S I N C E  I S  F E L T  T H A T  T H E Y  A R E N O T  C R I V E R S  A T ( N S T , J T ) = 0 1  T H A N  A N D R E G U L A T I O N  S T A N C E T O  F ROM  B E  I N  WITH  NUMBER  S T O P S ;  ( R E M A R K S :  OF  T H E  S E C T I O N  T H E  S T O P  F O R C E S  K E P T  C O N S T A N T  ( D S  S H O U L D  B E  SM A L L E R  SECT I O N )  I S T O * ( N S T , J T ) = S E C T I C N OF  B E G I N N I N G .  D I S T A N C E  S M A L L E S T  N S T O P = N UM B E R  T H E  DONE  I N  A S S U M E D  MUST  H A V E  S T O P  B Y  AT  WHICH T H E  L E A S T  S E C T I O N  N E C E S S A R Y  I S  C R E A T E  T H E R E  SAME OME  I S  F O R STO  p  S T O P E M P T Y  L O A D E D  A N D  A C C E P T E D ,  A N O T H E R  A  T R A V E L I F  MORE  S E C T I O N  WITH  A N D  L O A D E D  E M P T Y ;  THAN  ONI Y  O N F  T H E  STOP  • CIM E IS  SAME  C H A R A C T E R I S T I C S ) N S T 0 J T = N U M 3 E R  O F  O U T L E V = O U T P U T  L E V E L  S T A O I l T d  S T A T I O N S  ) = S T A T I C N O U T P U T FOR  NUMBER L E V E L  T R A V E L  WHERE  OR  (1,  O U T P U T  I S  R E Q U E S T E D  2)  WHERE  2 ) ( T H E  L O A D E D  O U T P U T P R O G R A M  A N D  I S  R E Q U E S T E D  W I L L  OUTPUT  V E L O C I T Y  WHEN  T R A V E L L I N G  L O A D E D  V 0 t 2 > - I N I T I A L  V E L O C I T Y  WHEN  T R A V E L L I N G  E M P T Y  R E A M  TIME  I N  T H E  SAME  E M P T Y )  V 0 ( 1 ) = I N I T I A L  W A I T I N S T , J T » = W A I T I M G  ( R E Q U I R E D AT  ( M P H ) ( M P H )  M I N U T E S  5 . 2 0 2 4 1 N S T O P  FORMAT(13) DO  -39  REAOt  1 = 1, 5.2  N S T O P  025)I S T O P ( I  . 1 ) . A TI I , 1 ) , W A I T ( 1 , 1 ) ,  ( I N F 0 4 ( J , I ) , J =l , ? 2 )  QNtY  FOR  S T A T I O N  95 2 8 6  89  C O N T I N U E  287  0 0  2 8 8  REACH 5 , 2 0 2 5 ) I S T O P ( I , 2 ) , A T ( I , 2 ) , W A I T ( I , 2 ) , ( I N F 0 5 ( J , I ) , J = 1 , 2 2 )  1 0 0  1 = 1 , N S T O P  2 8 9  100  C O N T I N U E  2 9 0  2 0 2 5  F O R M A T ! 1 4 , F 5 . 0 , F 5 . 2 , 2 2 A 3 )  2 0 2  6  F O R M A T 1 3 F 3 . 0 , 1 1 1  2 0 2  7  291 2 9 2  REACH REACH  2 9 3 2 9 4  5 , 2 0 2 6 5 , 2 0 2 7  I N S T O U T  8  STA3T  S I M U L A T I O N  AV= AV E R A G E JT=1 2  L O A D E D E M P T Y  R E S I S T A N C E  S T Q P T M = C U M U L A T I V E •TOT'OI S = T O T A L  A G A I N S T  S T O P P I N G  D I S T A N C E  T O T T I M = T O T A L  TIME  T R A C E = L O GI C A L  K E E P  V E H I C L E  ( P O U N D S )  T H E  B R A K I N G  T H E  P R E S E N T  B E G I N N I N G H A S  T I M E  ( F E E T )  ( S E C O N D S 1  O C C U R E D  A T  T H E  B E G I N N I N G  OF  I N I T I A L I Z A T I O N  T O T I M = 0 .  302  S T O ^ T M = 0 .  3 0 3  R E S = 0 .  3 0 4  A V = 0 .  3 0 5  NAV = 0  306  NST = 1  3 0 7  TP ACE = . T RUE . JT=1  c  C O N S T A N T  TO  C O N V E R T  FROM  M P H  TO  FROM  F T / S E C  F T / S E C  C l = 5 2 3 0 . / 3 6 0 0 .  c  C O N S T A N T  999  V = V O ( J T )  TO  C O N V E R T  TO  M P H  C 2 = l . / C I  31 ?  A V = A V + V  3 1 3  N A V = N A V + 1  3 1 4  I F U T . E Q . l . A N D o O U T L E V . G E . 2 > W R I T E < 6 , 2 0 4 6 ) F O R M A T ! / / / , ' T R A V E L LOAD = D ' / , • * * * * * * * * * * * *  2 0 4 6  I F !  3 1 6  I T . E Q . 2 . A N D . C U T L E V . G E . 2 ) W R I T E ( 6 , 2 0 4 7 )  F O R M A T ! ' 1 ' , ' T R A V E L  2 0 4 7  I F C U T L E V . G E . 2.) W R I T E !  3 1 9  I F ( 0 U T L E V o G E . 2 ) W R I T E ( 6 , 2 0 4 4 )  3 2 0  1 ' R O L L I N G 3 2 2  2 0 4 4  3 2 3  2 0 5 0  R E S I S T A N C E ' , 5 X , ' G R A D E  -  M P H ' , 8 X ,  • P O U N D S '  R E S  , 1 3 X , ' P O U N D S '  -  C O U R S E • , 2 X , ' S E C O N D S  -  MI  N U T E S ' / 3 0 X , • F F E T  M I L E S ' / / )  C C"  S C A N  c  IF  IF  F O R  R A V E L  T R A V E L  T R A V E L  L O A D E D  L O A D E D  I F ( . J T . E Q . 1 ) V W  I S T A N C E  V E H I C L E  F I R S T WE I G H T =  L O A D E D  V E H I C L E  WEIGHT  = L.VW  EMPTY  V E H I C L F  WE I G H T =  E M P T Y  V E H I C L E  W E I G H T  1  )  , 1 6 X , ' P O U N D S  I  F 0 R M 4 T 1 2 9 X , ' S E C T I O N 1  ' D I S T A N C E ' , J 3 X , ' T I M E * , 1.OX  R E S I S T A N C E ' , 5 X , ' C U R V E  F O R M A T ( 3 I X , ' A C C U M U L A T E D ' , 8 X , ' A C C U M U L A T E D ' 1 ' 1 5 X .  )  6 , 2 0 4 3 )  I F ! 1 J T L E V . G E . 2 ) W R I T E ! 6 , 2 0 5 0 1 F O R M A T ! / / / . ' G E A R ' , 5 X , ' V E L O C I T Y  3  *' .  E M P T Y ' / , ' * * * * * * * * * * * * ' )  318  3 2 4  T H E  T O T 0 I S = O .  5 0  204  AT  S I N C E  T R A C K  OF  ( M I N U T E S )  T R A V E R S E D  E L A P S E D  T O  MOTION  T I M E  S E C T I O N  301  321  M O T I O N  C O U N T E R  R E S= T O TA L  T O 0 I S = 0 .  3 1 7  V E H I C L E  OUNT ER  T O T T I M = 0 .  315  T H E  T R A V E L  299  311  OF  T R A V E L  3 0 0  310  1 , N S T O U T )  V E L O C I T Y  F O R  N S T = S T O P  C c c c c c c  ), 1=  F O R  NAV=C  C  309  5 0  FORMAT{2 0 1 4 )  C C C C  3 0 8  GOTH  REACH 5 , 2 0 2 3 ) ( S T A O U T ( I 202  , O S , O U T L E V  F O R M A T ! 1 4 )  296  2 9 8  ) V 0 < 1 ) , V 0 ( 2)  •I F ! N S T O U T . E O . 0 1  2 9 5 297  ..  A  NEW  325  IF(JT.EQ.2)VW=EVW SCAM THE ROAD S E C T I O N BY S E C T I O N DO 4 5 I = 1 , N S E C IFtJT.EQ.1)K=I FOR T R A V E L EMPTY START FROM L A S T  326  32 7  C  329 330 331 33? 333  C 108  2060  -a6_ KEEPING  FORCES  SECTION  AND  CONSTANT  GO TOWARD  OVER  DS  FIRST  FOR T R A V E L EMPTY INVERSE GRADE S I G N BECAUSE ROAD DATA READ FOR D I R E C T I O N LOADED I F ( J T . F O „ ? ) G R A D ( K ) = t-GRAOtK) ) I Ft OUT L E V . L T . 2 ) G O T O 107 DO 109 J=1,NST0UT IF( Ml K ) . F O . S T A O t J T t J ) ) WRITFI 6 . 20601 FORMA T t 1 X » * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . ; < * * * * * * * * * *  IN  ARE  1  1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * •  2) 334 335  I Ft N t K ) . E Q . S T A O U T t J ) ) W R I T E < 6 , 2 0 4 5 ) N ( K ) , S F C L ( K ) , C R A D ( K ) , G R A D t K ) , M A X lVLEtK.JTI 204 5 FORMAT(1X.«*«.118X. * /,1X.«*'.?X.•SFCTION NUMBFR=• . I 6 . ? X . • SPOT ION 1 LENGTH= * , F 6 . 0 , 2 X , ' C U R V E RAQIUS=',F6.0,2X,«GRADE ( F T / F T ) = ' , F6.3,2X . 2 , S * E E D L I M I T (MPH)=> , F 6 . 2 , 3 X , ' * ' / , 1 X , • * ' , U 8 X , ) I FtN< K l „ E O . S T A O U T t J ) ) W R I T E ( 6 . 2 0 6 0 ) 109 CONTINUE C D E T E R M I N A T I O N OF THE NUMBER OF S U B S E C T I O N S TO SCAN S E C T I O N K r. 1 OOK IF A STOP HAS TO BE MADF IN THAT SFCTION 107 I F ( I S T O - M N S T , J T J - N l K) . E O . 0 ) GOTO 79 NSU3=SECL(K)/OS C LAST= D I S T A N C E REMAINING TO SCAN C O M P L E T E L Y THE S E C T I O N K LAST=SECLtK)-(NSUB*DS) GOTO 8 0 79 XSUB=SECL(K)-AT(MST..)T) IFt X S U B . L T . D S 1 G 0 T 0 81 I F t X S U B . G E . D S )N Sl)B= X S U B / D S LAST=XSU3-(NSLiB*DS) GOTO 3 0 81 LAST=XSUB C SU3 = ACCUMIJLATF0 D I S T A N C E WITHIN A S E C T I O N 80 I F t . N O T . T R A C E IGOTO 85 SUB=0. GOTO 86 ' 85 TRACE = . T R U E . SUB = A>TtNST, J T ) IF(0UTLEV.GE.2)G0T0 110 GOTO 111 110 DO 1 1 2 J = l t N S T O U T IFtN(K).EO.STAOUTtJ))WPITE(6,2042)K,SUB I F t M ( K ) . E Q . S T A O U T ( J ) . A N D . J T . E Q . 1 ) W RI TE I 6, 2 051) W AI T( N ST , J T ) , ( ! N F 0 4 ( IKK,MST),KK=1,22) I F ( M ( K ) . E Q . S T A O U T t J ) o A N D . J T . E Q. 2 ) WR I TE ( 6 , 2 051 ) W A I T t N S T , J T ) , ( I N F O M 1KK,MST),KK=1,22) 112 CONTINUE 204 2 FORMA T (1 X , ' BR AK I NG OCCUP.ED AT THE . END OF THE LAST S F C T I O N , THE VE H . 1 I C L E IS NOW IN SECT I O N ' , 1 7 , 3 X , ' A T ' F 1 0 . 2 , 3 X , ' F E E T AND THE V E L O C I T Y ,  ,  ,  336 337  338 339 340 341 34? 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360  2IS 361  111  362 C  363  C 86  364 c  0 ' )  NST=MST+1 GOTO 6 3 I F F I R S T S E C T I O N AND V E L O C I T Y IS GREATER THAN 0 GO TO BRAKING I F t J T . E O . 1 . A N D . K . E O . l . A N D . V . G T . O , )GOTO 63 IFt J T . E Q . 2 . A N D . . K . E Q . M S E C . A N D . V . G T . O . I GOTO 63 I F THAT S F C T I O N IS COMPLETED CONTINUE WITH NEXT ONE  TEST  IF  SHOULD  START  365 366 367 368 369 370 371  68 C  I F ( S . J B . E Q . S E C L ( K M G O T O -45 SCA'-J F O R A N O T H E R SUBSECTION IF(SUB+DS.GT.SCCL(K))GOTO 70 SUfS = S U B + O S DOS=OS GOTO 71  70  SU3=SUB+LAST DOS=LAST  C  372 373  IF SPEED IS LIMITED S C A N AT C O N S T A N T IF(V. EQ.TOPSP(GOTO 64 I F ( V . E Q . M A X V L E ( K , J T ) ) G O T O 64  71  VELOCITY  C  374 375 376 377 378 379  c c c c  ENTER  386 387 388 389 390 391 392 393 394 39 5 396 397 398 399 400 401 402 403  IF  ACCELERATING FOR PRESENT  VELOCITY  (CURVE,  ROLLING,  CALL RESIST(V,VW,K,RCU,RG.RR) ERONTAL AREA COMPUTATION (A)  c53  IF(JT.EQ.2)A=28.86+.82*<VW/1000.) IF( J T . E Q . 1 . A N C . L O G . E Q . 3 8 . ) A = 2 9 3 5 + . 7 5 * ( V W / 1 0 0 0 . ) IF( JT.EQ. L A N D . LOG. E Q . 4 8 . ) A = 2 3 . 1 0 + . 5 * ( V W / 1 0 0 0 « ) . o  RA=.0026*.7*A*V**2 SUM OF T H E R E S I S T A N C E S  C  •RES=RCU*RG*P.R+RA SEARCH FOR THE PRESENT  C C C 380 381 38? 383 384 . 385  HERE  COMMUTATION OP RESISTANCES AND G R A D E RESISTANCES)  GEAR  (FUNCTION  THE I N E R T I A RESISTANCE IN CASE OF POLYNOMIAL TO COMPUTE THE RIMPULL  OF  SPEED)  ACCELERATION  IN  ORDER  TO  COMPUTE  AND TO U S E T H E  PROPER  G=0  54  G=G+1 I F(Go FQ» N G E A R 1 G 0 T 0 55 I F ( G + 1 . G T . N G E A R ) S H I F T V ( G +1 ) =T O P S P IF(V.GE.SHIFTVIG).AND.V.LT.SHIFTVfG+l)1G0T0 GOTO 5 4  C 55 C  AVAILABLE  RIMPULL  IN  PRESENT  55  GEAR.  ARIMP = A N ( G , 1 ) + A N ( G , 2 ) * V + A N ( G , 3 ) * V * * 2 NET R I M P U L L TO ACCELERATE THE VEHICLE NRI 1P = A R I M P - R E S IFINRIMP.LT.0.1GOTO V  c  INERTIA  RESISTANCE  IN O E C E L E R A T E D M O T I O N THE INERTIA RI = 1. 0 4 + ( . 0 5 * G R P 0 S ( G ) * R A X L E ) * * 2 RI = 1./RI ACC = * J R I M P * 2 2 . 1 6 / ( V W * R I )  56 57  ACCEL=.FALSE. IF(V)53,59,53  C 58  TIME  c r.  GEAP.  PFPUCTION  RI=loO4+(.05*GRPOS(G)*RAXLE)**2 ACC=NRIMP*32.16/(VW*RI) GOTO 5 7  c  59 C 60 C  56 FOR T H E "RESENT  TO T R A V E R S E  A  SUBSECTION  RESISTANCE  (UNAFFECTED  BY  HELP  TO  DECELERATE  BRAKING)  TIM =00'S/(V*C1 ) GOTO 6 0 TIM=SQRT(2.*DCS/ACC . VI=INITIAL VI = V VELOCITY  VELOCITY  ) AT THE BEGINNING  OF T H E  AT T H E END O F T H E S U B S E C T I O N  AND AT  SUBSECTION THE BEGINNING  OF  THE NEXT  V=V+4CC*TIM*C2 .  TEST IF THE VE10CITY SHOULD BE L I M I T E D TO T O P S P , IF(V.GT.TOPSP.OR.V.GT.MAXVLElK,JT))GOTO 66 G O T O 63 ONF  ITERATION  TO FIND  OUT THF ACCURATE  TIME  IT  OR  TOOK  MAXSPL,  TO  OR  TRAVERSE  MAXSPE  CNE  C 4 0 4  6 6  4 0 5 4 0 6 4 0 7 4  OR ..  4 0 9 4 1 0 411  C C C  4 1 2  4n  4 1 4  4 1 5 4 1 6 4 1 7  c  6 4  C cc c c c c c c  63  C  4 1 8 4 1 9  4 2 0  4 2 1  4 2 2  C c c c c c c  4 2 3 4 2 4  98 THE  IF(V.GT.TOPSP)V=TOPSP IF(V.GT.MAXVLEIK,JT)IV=MAXVLE(K,JT) T I M = (V-VI)*C1/ACC XSU3 = ( ( V * C 1 ) **2-< VI *C 11**2)/( 2.*ACC 1 XSUB=< v + v i )/2.*CI*TIM RSU3=D0S-XSUB TIM=TIM+RSU3/(V*C1) GOTO 6 3 ENTER HE RF IF TRAVFII IMG AT CONSTANT VELOCITY TIME TO TRAVERSE A SUBSECTION AT CONSTANT VELOCITY TIM=D0S/(V*C1) VI = V ACCEL = .TRUE. TEST I F BRAKING SHOULD START FIRST LOOK FOR STOP TO MAKE AHFAD ISTOP = TH.E SECTION NUMBER IN WHICH THE NEXT STOP IS SITUATED NSTA= THE NUMBER OF SECTION<S) THE NEXT STOP IS FAR AWAY FROMTHF PRESENT POSITION S=OISTANCE REQUIRED TO DECREASE THE PRESENT VELOCITY TO A STOP OR A S FF.T D  L I M I T  ST=THE DISTANCE BETWEEN THE PRESENT POSITION AND THE NEXT STOP PR SPEFP LIMIT S=(V*C1)**2/1?„ STA=ISTOP<NST,JT)-N(K ) NSTA= ABS(STA) LOOK FOR ONLY ONE SECTION AHEAD I F ( N S T A . E Q o O ) S T = ( ATU.'ST, J T ) - S U B ) IFJNSTA..EQ.1 1 ST = ( SECL ( K ) - S U B ) + A T < N S T , J T 1 I F THE NEXT STOP IS MOT IN THE NEXT SECTION THE VALUE OF ST IS J U S T ASSUMED A LARGE NUMBER I F ( NS T A. GT. 1 ) ST =1. E 06 I F THE DISTANCE REQUIRED TO STOP IS GREATER THAN OR EQUAL To THE DISTANCE BETWEEN THE PRESENT POSITION AND THE NEXT STOP, BRAKF I F ( S , G E . S T 1 G 0 T 0 43 I F T H E VEHICLE DOES NOT HAVE TO STOP, TEST IF ITS VELOCITY SHOULD DECREASE DUE T O A LOWER SPEED LIMIT AHEAD I F IN T H E LAST SECTION TO SCAN THERE IS NO SPEED LIMIT AHFAD I F ( J T . E Q . 1 . A N D . K + l . G T . N S E C . O R . J T . E Q . 2 . A N D o K - l . E Q o 0 1 G 0 T 0 72 I F ( J T . E Q . 1 ) G O T O 84 GOTO  4 2 5  84  4 2 6  88  4 2 7 4 7  4 2 9  4 6  C C  4 3 0 4 3 1 4 3 2 4 3 3 4 3 4  C  L C  C JC  8 8  I F ( M A X V L E ( K U , J T ) . G E . M A X V L E ( K , J T ) )GOTO 72 IF{JT.EQ.21G0T0 47 GOTO  4 2 8  S l J f l S E C T I O N  4 6  I F ( M A X V L E ( K - 1 , J T ) . G E . M A X V L E ( K , J T ) 1 G 0 T 0 72 ST=SECL«Kl-SUB IF THE DISTANCE BETWEEN THE PRESENT POSITION AND THE BEGINNING OF A LCWFR SPEED LIMIT IS GREATER THAN 1 5 0 0 FT DO NOT TEST IF(ST.GT.1500.)GOTO 72 IF(JT.EQ.1)S=((MAXVLE(K+l.JT)*C1)**2-(V*C1)**2)/I-12.1 . IF(JT.EQ.2)S=((MAXVLE(K-l,JT)*Cll**2-(V*Cl)**2)/(-12.) I F ( S . L T . S T I G O T O 72 IF(S.GT.ST)GOTO 73 ENTER HERE THE VEHICLE HAS TO DECELERATE  ;  •  -  :  S=ST; DECREASE VELOCITY AND COMPUTE TIME TO DO IT DISTANCE. TIME. AND VELOCITY OF THE SUBSECTION JUST SCANNED ARE  435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 45 0 451 452 453 454 455 456 457 458 459 460 461 462 463 464 46 5 466 467 468 469  ——  :  :  :  99  ACCUMULATE 0 TOTTIM=TOTTIM + TIM AV=A7+V NAV=NAV+1 TOTDIS=T0T0!S+DDS IFIOJTLEV.LT.2)GOTO 101 00 121 J=l,NSTOUT I F ( N ( K ) . E Q . S T A O U T ( J )) GOTO 1 2 2 1 2 1 .. C O N T I N U E GOTO 1 0 1 122 CALL RES I S T I V , V W , K , R C U , R G , R R ) I F t S U 3 . E Q . D D S I W R I T F ( 6 , 2 0 4 8 ) G , V I , V , SU B , TOD I S , TOT TI M , TOT I M . RR , R G . P C U 2048 FORMAT!IX,I3.6X.F5.2,IX,•TO',lX,F5.2,6X,F6„0,F9„2,4X,F7.1,F7o2,12X l,F6.1,15X,F7.1,15X,Ft>„l) ,...IF( S U B . E Q . D O S 1 G 0 T 0 1 0 1 I F( Vo E Q« V I ) GOTO 1 0 1 WRITE(6,2 055)G,VI,V,SUB,TOTTIM,RR,RCU 2055 FORMAT(IX.13.6X.F5.2,IX,•TO'. IX,F5.2 ,6X,F6.0,9X,4X,F7.1,7X,12X,F6. 11,16X,7X,15X,F6.1) 101 I F ( J T . E Q . l I M A X V = M A X V L E(K + 1 , J T ) IF(JT.E0.2)MAXV=MAXVLE(K-1,JT) VI = V C B R A K I N G T I M E TO D E C E L E R A T E TO M A X V L E ( K + 1 , J T ) OR TO M A X V L E ( K - 5 , J T ) TIM=(MAXV-V)*C1/(-6.) IF(JT.EQ.1)V=MAXVLE(K+1,JT) IF(JT.EQ.2)V=MAXVLE(K-1,JT) c ACCUMULATION TOTTIM=TOTTIM+TIM TOTIM=TOTTIM/60. TOTTIS=TOTDIS+ST TODIS=TOTDIS/5290. SU3-SECHK) I F ( 0 U T L E V . L T . 2 ) G 0 T 0 7 00 DO 12 3 J = 1 , N S T 0 U T IFI0JTLEV.GE.2.AND.STAOUTIJ).EQ.N(K) 1WRITE(6,2049)VI,V,SUB,TOO IS,T 10TTIM.T0TIM 123 CONTINUE 2049 F O R M A T ( I X , • B R A K E ' , 4 X , F 5 . 2 , 1 X , ' T O ' , 1 X , F 5 . 2 , 6X , F6 . 0 , F 9 . 2 , 4 X , F 7 . 1 , F 7 , 12) 700 AV=AV+V NAV=NAV+1 GOTO 6 3  C  C  470 471 472 473 474 475 476 477 47R 479 480 4B1  c c c  73  C C  124 125  S > S T : DO ONE I T E R A T I O N TO F I N D WHERE B R A K I N G HAD TO S T A R T AND BRAKING TIME I F I . N 1 0 T . A C C E L )GGTO 76 S P E E D WAS C O N S T A N T I N THE L A S T S U B S E C T I O N XSUB=S-ST S U B T R A C T T I M E \j TOOK TO T R A V E R S E X S U B AT C O N S T A N T V E L O C I T Y TIM=TIM-XSUB/(V*C1) TOT TI M=T OTT I M + T I M . TOTDIS=TOTDIS+PDS-XSU3 IF(0JTLFV.LT.2)GOTO 102 DO 1 2 4 J = l , N S T O U T IF(N(K>.EQ.STAOUT(J))GCTO 125 CONTINUE GOTO 1 0 2 SUB=SUB-XSUB CAM RFSIST(V •VW.K.RCU.RG.RR)  COMPUTE  ^ f  1  482 483 484 485 486 487 488 489 490 491 4 9 ? ,,. 493 494 495 . 496 497 498 499 500 501 502  503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 5?1 522 523 524,.... 52 5 526 527  528 529 530 53,1  :  102  C  126 701 r.  C C  76  C C c 82  127 128  103  C C  loo  IF( S J 3 . L E . D O S ) W R I T E ( 6 , 2 0 4 8 ) G , V I , V , S U B , T O D IS,TOTTIM,TOT IM,RR,RG,ROD AV=AV+V NAV=NAV+1 IFtJT.EQ.1)MAXV=MAXVLE(K+1 ,JT) IE<JT.EQ.2)MAXV=MAXVLE(K-1,JT1 VI=V B R A K I N G T I M E TO D E C E L E R A T E TO MA X V L E { K + l , J T ) OR TO M A X V L E < K — 1 , J T ) TIM=(MAXV-V)*Cl/(-6.) TOTTIM=TOTTIM+TIM T0TIM=T0TTIM/60. SUB=SECL(K) TOTDIS=TOTDIS+S TODIS=TOTDIS/5280. IF(JT.EQ.l)V=MAXVLE(K+l,JT) IF(JT.EQ.2)V=MAXVLP(K-l.JT) IF(0JTLEV.LT.2)G0T0 701 DO 1 2 6 J=1,NST0UT IF(OUTLE V.GE.2.AND.STAOUT ( J ) . E O . N I K ) ) W R I T F ( 6 , 2 0 4 9 ) V I,V,SUB,TOnIS,T 10TTIM.T0TIM CONTINUE AV=AV+V NAV=NAV+1 GOTO 6 8  THE V E H I C L E WAS A C C E L E R A T I N G I N T H E L A S T S U B S E C T I O N ACCEL = „T R U E . S U B D I V I D E T H E S U B S E C T I O N INTO .1*DDS DDDS=DDS*.l VIO=VI R E S T A R T AT T H E B E G I N N I N G OF T H E S U B S E C T I O N SU3=SUB-DDS C O M P U T E A NEW V E L O C I T Y AT T H E END OF E A C H S U B - S U B S E C T I O N SUB=SU3+DDDS TOTDIS=TOTDIS+DDDS V=(SQRT((VI0*C1>**2+2.*ACC*DDDS))*C2 VIO=V I F( J T . E Q . 1 ) S = ( ( M A X V L E 1 K + l , J T ) * C 1 ) * * ? - ( V * C 1 I * * 2 ) / ( - 1 2 . ) IFt JT.EQ.?)S=((MAXVLE(K-l,JT)*C1I**2-(V*C11**2)/(-12.) ST=SECL(K)-SUB IF(S.LT.ST)GOTO 32 TIM=(V-VI)*C1/ACC TOTTIM=TOTTIM+TIM IFIOUTLEV.LT.21G0T0 103 DO 1 2 7 J = 1 . M S T 0 U T IF(N(K).EQ.STAOUT(J))GOTO 128 CONTINUE GOTO 1 0 3 CALL R E S I S T ( V , V W , K , P C U . R G ,RR) I F ( S J B . L E . D O S ) W R I T E ( 6 , 2 0 4 8 ) G , V I , V , S U B , T O P IS,TOTTIM,TOT IM,RR,RG,RCU IF(SJ3.LE.DDS)G0T0 102 WRITE(6,205 5)G,VI,V,SUB,TCTTIM,RR,RCU AV=A\/+V NAV=NAV+1 ADD T O T I M B R A K I N G T I M E F R O M P R E S E N T P O S I T I O N TO T H E B E G I N N I N G OF THF NEXT S E C T I O N ( S P E E D LIMIT) IFtJT.EQ.1)MAXV=MAXVLF(K+1,JT) IFtJT.EQ.2)MAXV=MAXVLE(K-1,JT) VI=V TIH=ST/( (MAXV+V)*C1 / ? , )  532 533 534 535 536 537 538 539 54Q 541 5.42 129 543 544 702 .,,545 . ... 546 C LL C 547 48 C C -5__ 5*9 5  5  0  -551 552 553 554 555 556 557 558 559 560 561 562  130 131-  566 567 . 568 569 570 __7J 572 573 5.74 575 576 5  7  7  :  THE VEHICLE HAS TO STOP ENTER HERE IFIS.GT. STIGQTO 77 S=ST: NO ITFRATfQN TO MA K F ACCUMUi ATEO :  IMF  '  A  N  D  V  E  L  0  C  I  T  Y  0  F  T  H  S U B S E C T I O N  E  J U S T  SXTNTTET)  TRE~  TOTTIM=TOTTTM»TIM . TOTOIS=TOTDIS+nOS IF(0UTLEVoLT.2)G0T0 104 00 130 .l = l . N S T n i l T IF(N( K)„ EO.STAOUTIJ))GOTO 131 CONTINUE GOTO 1 04 CALL RES I ST<V , VW,K,PCU,RG,RR) I F! SJ3. E Q. OD 5 ) WRI TE ( 6 ,2043 ) G , VI , V , SUB , TOD I S , TOTT I M , TOT I M, P.R , P G, P.CU IFtS.lB.EQ.DDSIGQTO 104 IFIV.EQ.VIIGOTO 104 WRITE (-6, 2 055 )-G, VI , V , SUB, TOTT I M ,RR , RCU AV=AV+V NAV=MAV+1 VI=V BRAKING TIM=V*Cl/6. TOTTIM=TOTTIM+TIM ;  104  563 564 -5^5  101 TOTTIM=TOTTIM+TIM TOTIM=TOTTIM/60. TOTQIS=T0T0IS+ST TODIS=TOTDIS/5230. SUB=SECL(K) I Ft IT • FQ. 3 ,V=MAXVLE<K»1. JT) ; IF(JT.EQ.2)V=MAXVLE(K-1,JT) IF(0JTLEV.LT.2)G0T0 702 00 129 J=1,MST0UT , IF(QUTLEV.GE.2.AND.STACUT< J).EQ.N(K)IWRITE(6,2049)VI,V,SUB,TOOIS,T 10TTIM.T0TIM CONTINUE' AV=AV+V AV=AV+V NA,V=N,AV_1 GOTO 63  ,  TOTT M = T O T T I M/ A O .  TOTOIS=TOTDIS+ST TODIS=TOTDIS/5280.  V=0. NAV=NAV+1 STOPT M = STOPTM +W A 1T(NST,JT ) IFINSTA.EQ.l ) TP ACE= . FAL SE . IFI.NOTo TRACEJGOTO 45 SUB=AT(NST,JT) IFfOUTl F V . I T.?IGOTO 7 03 00 132 J=1,NST0UT r GE 2 ' » « E Q . S T A O U T ( J) )WRITE(6,2049)VI ,SUB,TOOIS,T  ,r\tl',i ^' ' ' l 11r r T i . T Q T I M  A N D  N ( K  , JF(0UTLEV.GE.2.AMD. JT.EQ.1.AND.STAOUT<J). EQ.M ( K ) ) WP, I TE ( 6 ,2051 K N S T , JT) , ( INF04(JL,NST), JL = 1,22) 1  HI  r n S^;, ,p F  C  (  I X  '  , T I , , E  STOPPED-,F7. ; x,2 A3, 2  3  2  ) WA I  T  r  581 582 583  r 584 585 586 587 588 589 590 591 59 2 593 594 59 5 596 597 598 599  NST=NST+1  703  N S T = \IST+1 GOTO  C C C C 77 C  68  S > S T :  0 0 O N E I T E R A T I O N  B R A K I N G IF( S P  . N O T .A C C E U G O T O C  F Q  T O F I N D  WHERE  B R A K I N G  H A DT O S T A R T  A N D COMPUTE  T I M E 7 8  W A S C O N S T A N T  I N T H E L A S T  S U B S F C T I O M  X S U B = S - S T  C  S U B T R A C T  TIME  I T TOOK  T O T R A V E R S E  X S U B  A T C O N S T A N T  V E L O C I T Y  T I M = T I M - X S U B / ( V * C 1 ) TOT T I M= T O T T I M + T I M T O T D I S = T O T D I S + D D S - X S U B S U B = S U B - X S U B I F t O U T L E V . L T . 2 ) G O T O DO  1 0 5  J = 1 , N S T 0 U T  133  I F ( N ( K ) o E O „ S T A O U T ( J  133  C O N T I N U E  134  C A L L  GOTO I F t  105  ) ) G O T O  1 3 4  .  105 R E SI  S T ( V , V W . K . R C U , R G i R R )  S J B . L E .  D O S ) W R I T E ( 6 , 2 0 4 8 ) G , V I , V , S U B , T C P I S , T O T T I M , T O T IM , RR , P 0 , F C IJ  AV=AV+V N A V = N A V + 1 VI = V  C 600 601 602 603 604 605 606 607 608 609 610 611 612 613  B R A K I N G  TIME  T O S T O P  T I M = V * C l / 6 . T O T T I M - T O T T I M + T I M T 0 T I M = T 0 T T I M / 6 0 . TOTDIS=T0TDIS+S T O D I S = T O T D I S / 5 2 8 0 .  V=0.  NAV=NAV+1 S T O P T M =S T O P T M + W A I T t N S T , J T I F t N S T A .  )  E Q . l ) T P . A C E = . F A L S E ,  I F ! . N O T . T R A C E 1 G 0 T 0  4 5  S U B =A T ( N S T , J T ) I F t O U T L E V o I. T , 2 ) G O T O DO  7 0 4  J = 1 , N S T 0 U T  135  I F tJ J T L E V . G E . 2 . A N D . S T A O U T ( J ) . E Q . N ( K ) ) W P I T E < 6 , 2 0 4 9 ) V I  , V ,SUR,TPDIS,T  1 0 T T I M . T 0 T I M  614  I F ( O U T L S V . G E . 2 . A N D . J T . E Q . 1  0  A M D o S T A O U T t  J ) . EO.M(K))WRITE( 6 , 2 0 5 3  (WAIT  1 t N S T , J T ) , ( I N F 0 4 ( J L , N S T ) , J L = 1 , 2 2 >  615  I F ( 0 U T L E V . G E . 2 . A N D . J T . E O . 2 . A N D . S T A O U T ( J ) . K N S T .  616 617 618  619 620 621 622 623 624 625  135 704  C O N T I N U E NST=NST+1 GOTO  C C C C C 78  THE  6 3  V E H I C L E  S > S T ;  W A S A C C E L E R A T I N G  DO O N E I T E R A T I O N  3 R A K I N G  I N T H E L A S T  T O F I N D  WHERE  T I M E  ACCEL = . T R U E . D D Q S = D D S * . l V I O = V I S U B = S U B - O D S  83  E Q . N ( K ) ) W R I T F ( 6 , 2 0 5 1 ) W A IT  J T ) , ( I N F 0 5 t J L , N S T ) , J L =l , 2 2 )  S U B = S U B + D C D S T O T D I S = T O T D I S + D O D S V = ( S Q R T ( t V I 0 * C 1 ) * * ? + 2 . * A C C * 0 D D S ) ) * C 2  S U B S E C T I O N  B R A K I N G  H A DT O S T A R T  AND.COMPUTE  >  626 627 628 629 630 631. 632 633 634 635 636 637 638 639 640 641 642  V I 0 = V S = < V * C 1 ) * * 2 / ( 1 2 . ) I F I N S T A . E Q . 0 ) S T = ( A T ( M S T , J T ) - S U R ) I F ( N S T A . E Q . l ) S T = < S E C L ( K I - S U 3 ) + A T I N S T , J T ) I F ( j , L To S T ) G O T O T I M = (  83  V - V I ) * C 1 / A C C  T O T T I M  =T O T T I M + T  IM  I F 1 0 U T L E V . L T . 2 ) G O T O  0 0  1 3 5  1 0 6  J=i,NSTOUT  I F ( N ( K ) . E Q . S T A O U T ( J  ) ) G O T O  1 3 7  136  C O N T I N U E GOTO  1 0 6  137  C A L L  R E S I S T ! V , V W , K , R C U , R G , R R )  I F ( S J B . L E . D D S ) W R I T E ( 6 I F ( S J B . L E o D D S I G O T O  106  WRI  TE ( 6 ,  205 5 I G, VI  NAV = \IAV + 1  644  V I = V  C  I S ,  T O T T I M . T O T I M , R R , P G , R C U  , V , S U B , T G T T  I M . R R . P . C U  A V = A V + V  6 4 3  645 646 647 648 649 650 651 652 653 654 655 656 657 658  ,2 0 4 8 ) G , V I , V , S U B , T O D 1 0 6  ADD  TO  T I M  B R A K I N G  T I M E  F R O M  P R E S E N T  P O S I T I O N  TO  THE  S T O P  T I M = V * C l / 6 . T O T T I M = T O T T I M + T I M TOT H  = TOTT  I M / 6 0 .  T O T D I S = T O T D I S + S T T O D I S = T O T D I S / 5 2  V=0.  3 0 .  N A V = N A V + 1 S TOPT M= S TOPTM+W  A I T ( N S T , J T )  I F I N S T A . E O o l ) T R A C E = . F A L S E . I F ( . N O T . T R A C E ) G O T O  45  S U 3 = A T ( N S T , J T ) I F I O U T L E V . L T . 2 ( G O T O  7  05  0 0  1 3 8  J = l . N S T O U T  I  F ( Q U T L E V . G E . 2 . A N D . S T A O U T I J ) . E O . N I K ) ) W R I T E ( 6 , 2 0 4 9 ) V I , V , S U B , T C D I S , T  1 0 T T I M . T 0 T I M  659  I F t Q U T L E V . G E . 2 . A N D . J T . E O . 1 . A M D . S T A O U T ( J ) . E Q . N ( K 1 ( N S T , J T)  660  , ( I N F  0 4 ( J L , N S T ) ,  I F { Q U T L E V . G E . 2 . A N D . J T . E Q o  J L = l , 2 2  > ) W R I T E ( 6 , 2 0 5 1 ) W A I T  )  2 . A N D . S T A O U T t  J ) . E Q . N ( K ) ) W R I T E ( 6 ,  2 0 5 1 ) W A I T  1 ( N S T , J T ) , ( I N F C 5 ( J L . N S T ) , J L = 1 , 2 2 )  661 662 663  664 665 666 667 663 669 670 671 672 673 674 67 5 676 677  138 705  C O N T I N U E N S T = N S T + 1 GOTO  C C C C 72  NO  6 3  3 R 4 K I N G  D I S T A N C E ,  N E C E S S A R Y T I M E ,  AND  E N T E R  H E R E  V E L O C I T Y  A C C U M U L A T I O N  A V = W + V N A V = N A V + 1 T O T T I M = T O T T I M + T I M I F ( ' ' J U T L E V . L T . 2 ) G 0 T 0 DO  1 4 2  1 4 1  J = l , N S T O U T  I F ( N ( K ) . E Q . S T A O U T ( J ) ) G O T O  142  GOTO  143  1 4 3  C O N T I N U E C A L L  141 RES  I S T ( V  , V W , K , R C U . R G . R R )  I F ( S J B . E Q . O O S ) W R I T E ( 6 , 2 0 4 8 ) G , V I , V , S U B , T O D  141  T 0 T I M = T 0 T T I M / 6 0 . T Q T O I S = T O T D I S + D D S T O D I S = T 0 T D I S / 5 2 3 0 . I F l 0 U T L E V . L T . 2 I G 0 T 0  6 8  I S , T O T T I M , T O T  I M , R R , R G , R C U  678  DO  139  104  J=1,NST0UT  679 680 681  139  IF(N(K).EQ.STAOUTtJ))GOTO CONTINUE GOTO 6 8  682  140  CALL  140  RESIST(V,VW,K,RCU,RG,RR)  LEjLSJ_8.eQ.SECL I K ) ) W R I T F ( 6 , 2 0 4 8 ) G . V I . V . S U D  l.RC'J  684  IF(SOB«EQ.SECL(K)1G0T0  685 686 687 688 689  45  CONTINUE IF( J T . 5 Q . 2 1 G 0 T 0  c  C C  696 697  C  '  703 704  STATISTIC*  2041 2031  AND THE COURSE  HAS BEFN  SCANNED  NEAV=N A V - N LAV COURSE=TOTDIS/?. TOTTIM=TOTTIM/6 0. WRITE(6,2041) F 0 R 1 A T I / / / , * * * * * * * * *  RESUMF  * * * * * * * * i . / / )  WRIT.(6,2031)COURSE FORMAT(IX,'TOTAL LENGTH OF T H E COURSE ONE W A Y = ' , F 1 0 . 0 , 5 X ..15.2,5X.'MILF(S) (THIS DI S T A N C F I S T H E D I S T A N C E TRAVFRSFD 2HICLE•)  •FEET', F 1 THE V E  BY  708 709  203 2  710 711  203 3  71? 713  203 4  714 71 5  203 5  716 717  203 6  713 719  FOR 1 A T ( 1O X , * T I M E S T O P P E D W R I T E ( 6 , 2 0 3 ^ ) L S TT IM  WHEN  EMPTY=•,F10.2,5X,•MINUTES')  203 7  720 721  FORMAT(10X,-TIME-STOPPED AV=AV/NAV LAV=LAV/NLAV  WHEN  LOADED=•,F10.2,5X,'MINUTES• )  722 723  WRITE(6,2033)AV  7?4  WRITE(6,2032)T0TTIM FORMATtlX,*ROUND WRITE(6,2033)ETIM  TRIP  T I M E =' , F I 0 . 2 , 5 X . • MI N t l T F S ' )  FORMAT(10X,'TRAVEL WRITE(6,2034)LTIM  EMPTY  FORMA T d O X , ' T R A V E L WRITE(6,2035)ST0PTM  LOADED  FORMAT(1 OX, 'TOTAL TIME WRITE(6,2036»ESTTIM  T I ME= • , F 1 0 . 2 , 5 X , ' M I N U T F S ' )  STOPPED=•,F10.2,5X,•MINUTFS' 1  203 8  FORMATtlX, •AVFRAGE 1•MPH' )  VELOCITY  OVER  THE COURSE  (BOTH  W A Y ) - ' . F I 0 . 2 , 5 X,  WRITE(6,2C39) EAV  726 727  . 203_L_  VEL O C I T Y  EMPTY=«,FI0.2,5X.•MPH'I  728  FORMA T ( 1 X , • A V FRAGE WRITE(6,2040)LAV  204 0  F 0 R 1 A T I 1 X , ' A V E R AGE STOP  VELOCITY  LOADED=•,F10.2,5X,•MPH'  729  :  TIME=«,F10.2,5X,'MINUTES')  EAV=E A V / N E A V  725  ^  SAVE  •  TRAVEL EMPTY IS F I N I S H E D ETIM=T0TTIM/6 0 . - L T I M E STTIM=STOPTM-l STTIM EAV=AV-LAV  69  700 701 70?  705  FINISHED;  LAV=AV _LAV=NAV JT=2 NST = 1 GOTO 9 99  69 5  706 707  69  TRAVEL LOADED IS LTIM=T0TTIM/60L STTIM = S TOPTM  692 693 694  698 699  '  68  IF(SUB.EQ.DDSIGOTO 68 IF(V.EQ.VI)GOT0 68 WRITE(6, 2055)G,VI,V,SUB,TOTTIM,RR,RCU G O T O r,a  690  r\91  < T O O I S . T O T T I M . T D T T M . R R .PG  V I  :  (•  7 3 0  A 731  > f  :—  luj  END S U B R O U T I N E L E A S T  E I T  S Q U A R E S  S U B R O U T I N E  73? 733 7 3 4  C O M M 0 N / M 4 T R I X / B ( 3 , 4 ) , N R O W , N C O L  7 3 6 7 3 7  COMME' N / C O E - /  c c c c  A N = C O E F F  A N( 3 0 »3 ) .  IC IE-NTS  B = A U G M E N T E D  T H E  NP=NL)MBER  OF  DATA  1  1 = 1 , N R O W  1  J = 1 , N C 0 L  1  DO  2  1 = 1 , N R O W  7 4 2  DO  2  J = l , N R O W  DO  2  K=l,NP  . N P . N D  II  P O L Y N O M I A L P O I N T S  c  C O M P U T A T I O N  A S S U M E  0 „ * * 0 = 1 .  I F ( X ( K I . G T . O . ( G O T O  6  7 4 5  I F ( X (  7  7 4 6  I F I I . G T . l o O R . J . G T . l ( G O T O  7 4 7  S = l .  7 4 3  GOTO 5  K ) „ L T . O o I G O T O  7 5 0  2  GOTO  2  6  S = X ( < ) * * ( 1 - 1 ) * X ( K ) * * ( J - l )  7 5 2  2  B ( I , J ) = B ( I , J ) + S  7 5 3  0 0  3  I = 1 , N R O W  7 5 4  0 0  3  K=1,MP  7 5 5  IF(  Io G T . 1 ( G O T O  7 5 6  I F ( X ( K I . G T . O . I G O T O  7 5 7  S S = Y ( K )  7 5 8  GOTO  4 4  3  7 5 9  4  S S = X( K )**.(  7 6 0  3  B ( I . ^ 0 + 2 ) = B < I . N D + 2 I + S S  761  C A L L  7 6 2  GOTO  7 6 3  7  7 6 4  203  1 - 1  ) * Y ( K )  G A U S S .8  W R I T E ( 6 . 2 0 3 0 ) 0  F O R M A T < 5 X , ' W A R M I N G : 1 U T I N E  7 6 5  5  S=0.  751  F I T  C H E C K  A  T R U C K  N E G A T I V E  V A L U E  DATA  N E G A T I V E  F O R  H A S  B E E N  E N C O U N T E R E D  V A L U E ' )  STOP 8  7 6 7  R E T U R N ENO S U B R O U T I N E  GAL'S S  G A U S S - J O R D A N  E L I M I N A T I O N  7 6 8  S U B R O U T I N E  7 6 9  D 0 U 3 L E  7 7 0  COMMC  771  O O M M r N / C O F F / A N ( 3 0 . 3 ) .  7 7 2 7 7 3  N  R ( I , J ) = 0 .  741  7 6 6  D E G R E E  N C 0 L = N D + 2  .  DO  7 4 9  OF  NR0W=N0+1  7 3 9  7 4 4  P O L Y N O M I A L  M A T R I X  O F  DO  7 4 3  A  WANTED  ND=OF GRE E  7 3 8 7 4 0  F O R  F I T  C O M M O N / V A R / X ( 2 0 0 ) . Y ( 2 0 0 ) D O U B L E P R E C I S I O N A N . B  73 5  s.  A P P R O X I M A T I O N  P I V O T  G A U S S  P R E C I S I O N  A N , B , C , D  N / M A T R I X / P ( 3 , 4 ) , N R O W . N C O L  K=0 4  W I T H  K=K+1  7 7 4  C =  B K . K 1  77 5  0 0  1  7 7 6  I F ( Jo L T o K ) G O T O  777  B I K . J ) = P ( K .  J = l , N C O L 1  )/r  1  I I  .  E L E M E N T S  N O R M A L I Z E D  I N  SUBRO  c >  106 7 7 8  C O N T I N U E  1  7 7 9  0 0  7 8 0  D = B ( I , K )  7 8 1  0 0  7 8 2  I F ( I . E Q . K I G O T O  2  7 8 3  1 F t J . L T . K ) G O T O  2  7 8 4  B ( I , J ) = B (  7 8 5  2  1=1  2  iNROW  J = l  , N C O L  I , . ) ) - ( D * B (  K, J )  )  C O N T I N U E  2  7 8 6  I F t K . P Q . N P O W ) G O T O  7 8 7  GOTO  7 8 8  3  0 0  7 8 9  5  3  4  5  ,  1=1,MROW  A N t I I . I ) = B ( I . N C O L ) R E T U R N  7 9 0  END  7 9 1  F U N C T I O N  TO  F U N C T I O N  7 9 2  T = 1 4 0  C 7 9 3  F  C O R R E C T  HP  DUE  TO  A L T I T U D E  AND  T E M P E R A T U R E  P D ( B P . P O ) A I R - I N T A K E  TE MPFR ATUR  E  T = 1 4 0 .  7 9 4  B 0 = 2 9 . 9 2  7 9 5  T 0 = 5 ? 0 .  c  7 9 6  4 5 9 . 6 7  I S  A  C O N S T A N T  TO  T R A N S F O R M  FROM  F  TO  R A N K INE  D E G R E E  T R A N < = T + 4 5 9 . 6 7  7 9 7  P D = (  7 9 8  R E T U R N  D  0 * 3 P / B 0 ) * ( T O / T P A N K )  END  7 9 9  S U B R O U T I N E  c c  C O M P U T I N G  G R A D E ,  R E S I S T A N SE S  ARE  C O M P U T E D  S U B S E C T I O N ,  AND  W I L L  BE  R O L L I N G ,  WITH  V ,  O U T P U T  THE  FOR  AND  O U T P U T  8 0 0  S U B R O U T I N E  801  C O M M O N / R O A O / N t 5 0 0 ) , S E C L I 5 0 0 ) , S T Y P E t 5 0 0 )  I F t C R A D t K l . E O . O . - C R . V . E O . O . ( G O T O RCU = t t  (.  GRADE  R E S I S T A N C E  c  324»-.  R G = 0 .  1  I F ( G R A D ( K l o E Q . O . ( G O T O  8 0 7  T E T A = A T A N t G R A O t K ) ) R O L L I N G  3  81  4  3  GOTO  4  R R = 1 7 . 6 < - . 0 9 * V ) M V W / 1 0 0 0 . R E T U R N  8 1 4  END  *n  3  R R = ( 1 5 . 1 + . 0 8 8 * V ) * ( V W / 1 0 0 0 » >  8 1 0 8 1 2  R E S I S T A N C E  I F ( S T Y P _ ( K ) , E Q . 1 ) G 0 T 0  2  811  2  R G = V W * S I N ( T E T A )  c  A  TA  1  0 0 1 4 * V * * 2 ) / C R ADt K) ) - .  8 0 6  8 0 9  , U S ( 5 0 0 )  R C U = 0 .  8.04  8 0 8  L E V E L  THE  END  0  T H E S E p  T H E  2  R E S ! S T ( V , v w , K , R C U , P G , R R 1  8 0 3  3 0 5  R E S I S T A N C E , AT  1 M I 5 . M 0 ) . G R A D ( 5 0 0 ) C U R V E R E S I S T A N C E  c  8 0 2  C U R V E  V E L O C I T Y .  )  0 2 1 * E  (K )  )*VW  , C R A D ( 5 0 0 ) , E ( 5 0 0 ) , L  

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