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A DETERMINISTIC SMJLATION OF LOGGING TRUCK PERFORMANCE by YVES LEVESQUE B. A. Sc., Laval University, Quebec, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF ., • MASTER OF FORESTRY in the Faculty of FORESTRY We accept this thesis as conforniing to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Ap r i l , 1975 In presenting this thesis i n partial fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of B r i t i s h Columbia Vancouver 8, Canada i i i ABSTRACT A deterministic simulation model i s developed and programmed for a d i g i t a l computer to represent the movement of logging trucks for specified alignment (actual or proposed) and truck-parameters. The force accelerating the vehicle i s taken as the difference between transmission output wheel force and the resistance force at steady-state conditions at the instantaneous vehicle speed. The accelerating force i s taken as constant over a small incremented distance and results i n a vehicle speed with new loading conditions. The process i s repeated through each gear, and time-distance and time-speed data are obtained. ' The technique described can be used to build up a distance travelled-time consumption history for a vehicle on a defined route. Such prediction enables a meaningful evaluation to be made of the time of a specified t r i p . Such an approach produces results 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 in the form of fellow-ships by the Quebec Department of Lands and Forests and in 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 — i i i ACKNOWLEDGMENTS — — i v LIST OF FIGURES v i i i LIST OF TABLES ix Chapter 1 INTRODUCTION 1 1.1 The road engineering process 1 1.2 An approach to the problem : • 1 1.3 Objective of the study 3 1.4 Outline of the study 4 2 GENERAL ASPECT OF THE STUDY 5 2.1 Note on the modeling concept 5 2.2 Overview of the model • 5 2.21 General assumption • 9 2.3 The computer program r — 9 3 RELATIONSHIPS BETWEEN ROAD CONDITIONS AND THE SPEED OF VEHICLES 15 3.1 Introduction 15 3.2 Maximum permissible speed on curves 15 3.21 Assumptions 17 3.22 Centrifugal force as a speed control 18 3.221 Assumptions —• 20 3.23 Sight distance as a speed control 21 3.24 Comparaison of speed limits on curves with empir-i c a l values from a previous study 27 3.3 Maximum permissible speed as controlled by surface con-ditions 27 3.31 Previous study • — 29 3.32 Winter conditions 31 3.4 Speed limit on favorable grade - — 31 3.41 Sight distance as a speed control 31 3.42 Braking capacity as a speed control — 31 v i Chapter Page 3.5 Speed l i m i t on adverse grade : 32 3.6 The independent variables 32 3.7 Conclusion 34 4 RELATIONSHIPS BETWEEN VEHICLE CHARACTERISTICS AND SPEED 36 4.1 Introduction • 36 4.2 Manual transmission modeling • : 36 4.3 Torque-converter transmission modeling 40 4.4 Method of solution 42 4.41 Manual transmission procedure — . 42 4.42 Torque-converter transmission procedure — 44 4.5 Braking ; 44 4.6 The independent variables • 45 5 MODEL TESTING 47 5.1 Introduction 47 5.2 The test situation 47 5.3 Predicted versus measured times • 49 6 DISCUSSION AND CONCLUSIONS 53 6.1 Using the model to make decisions • 53 6.2 Areas of further investigation 53 6.3 Conclusion 54 BIBLIOGRAPHY 55 APPENDIX 1. ECONOMIC EQUATIONS OF ALTERNATIVE ROAD ALIGNMENTS 57 APPENDIX 2. EFFECTIVE ENGINE POWER . 6 2 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 76 A9.1 Travel empty • 76 A9.2 Travel loaded 78 v i i Page APPENDIX 10. TESTING FOR SIMILARITY OF SLOPES 80 A10.1 Travel loaded - • • 80 A10.2 Travel empty 82 APPENDIX 11. THE COMPUTER PROGRAM 83 A l l . 1 Input cards ; •— 83 All.2 Computation time requirements 86 All.3 FORTRAN listing of computer program — 87 v i i i LIST OF FIGURES Figure Page 2.1 Diagram of the model 6 2.2 Flow diagram of the program 12 3.1 Portion of a road divided into sections of uniform charac-t e r i s t i c s — • — 16 3.2 Cross section of a vehicle on a superelevated curve 18 3.3 Grade force acting on a vehicle 22 3.4 Geometry for determining sight distance when sight distance i s less than length of curve 24 3.5 Transversal position of parameters 25 3.6 Geometry for determining sight distance when sight distance i s greater than length of curve — 27 3.7 Comparaison of theoritical speed limits on curve with empir-i c a l values • ; ; 28 3.8 Maximum descent speeds assumed by the model when no engine brake i s used 33 4.1 Typical engine data • — • 38 4.2 Typical torque converter data — — 41 5.1 A comparaison of actual and predicted cumulative times for travel loaded 50 5.2 A comparaison of actual and predicted cumulative times for travel empty -• 51 A3.1 Grade resistance of a truck 65 A5.1 Projected frontal area of loaded and empty trucks 69 A8.1 Maxiimjm descent speed for 100% Jacobs engine brake control-Detroit diesel engine 73 A8.2 Maximum descent speed for 100% Jacobs engine brake control-(LXimmins engine 74 A8.3 Maximum descent speed for 100% Jacobs engine brake control-Mack engine 75 ix LIST OF TABLES Table 3.1 3.2 Page 3.1 MaxinMm speeds as controlled by surface 30 3.2 Coefficient of sliding friction (M ) • 34 4.1 Loaded tire radius in inches (off-nighway tread) 46 A2.1 Average barometric pressures for various altitudes above sea level • 63 A9.1 Observed times for travel empty 76 A9.2 Analysis of variance for travel empty 77 A9.3 Observed times for travel loaded 78 A9.4 Analysis of variance for travel loaded 79 A10.1 (IXimulative actual and predicted times for each section for travel loaded 80 A10.2 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 into account many things which have an important bearing on costs. In fact, he i s interested in analyzing a large number of alternative alignments i n order to most nearly optimize his f i n a l l o -cation from an economic standpoint. Basically he has to estimate the probable costs of a certain type of road for a certain service level and accordingly determine whether i t i s economically j u s t i f i e d (the reader i s referred to Appendix 1 for more details). To do so, the decision-maker needs information that w i l l help him assess the relative strengths and weaknesses of each alternative. Some of the d i f f i c u l t i e s i n his analysis are the many assumptions that must be made. These assumptions enter into the development of the hauling time, vehicle operating costs, hauling costs and road construction and maintenance costs. Differences i n the basic assumptions may throw the f i n a l result either way and therefore the computations are only as good as the i n i t i a l assumptions. . 1.2 An approach to the problem Suppose that a designer has a model or has gained experience in the 2 forecasting of road construction and maintenance costs. Gain of experience i n the forecasting of these costs could be j u s t i f i e d by the fact that one knows pretty well how much i t w i l l cost for additional miles after construc-ting many miles under the same conditions. Since road construction and maintenance costs are predicted, the remaining cost to predict i n order to evaluate alternative road designs i s the operating cost of vehicles (hauling cost). It i s very d i f f i c u l t for the road designer to predict operating cost since there are not two roads with the same alignment and profi l e and fuel consumption, t i r e wear o i l consumption and maintenance of vehicles are closely related to them. For example, grades affect particularly fuel consumption and t i r e wear. Steeper more frequent grades require extra energy (extra fuel) and extra traction ( t i r e wear) to ascend them. On curves extra t i r e wear and fuel consumption are due to the surface f r i c t i o n resistance produced by turning the steering against the direction of vehicle motion. Road surface conditions affect a l l running costs (fuel consumption, t i r e wear, o i l consumption, repair and maintenance). Compared to hard surfaces extra energy i s needed on gravel surfaces and tires are subject to the deteriorating effects of violent 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. Finally, truck maintenance cost i s affected by the roughness of the road surface on the suspension and by dust on the wear of cylinder walls. The change from an i n i t i a l speed to a lower speed followed by an acceleration to regain this i n i t i a l speed requires again extra fuel. These frequent speed changes are often due to curves or 3 insufficient road width for a certain t r a f f i c density causing interferences among vehicles. 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 traction wear during acceleration. Furthermore, maintenance cost i s increased by brake wear during deceleration and trans-mission wear during acceleration. On a mile basis, for an average truck these running costs may be as important as §0.61 for repairs and maintenance, §0.16 for fuel and lubricants and §0.32 for tires and tubes (Boyd and Young, 1969). The determination of operating costs as a function of road geometry characteristics, as described above, i s not known accurately yet. However, a l l costs involve a time element and most accounting systems record the direct operating cost as hourly costs. In other words, with those account-ing systems vehicles are wearing out tires, consuming fuel and accumulating other charges at a constant time rate (machine rate). Use of the machine rate and prediction of the travel time would therefore enable the close estimation of travel cost. 1.3 Objective of the study The aim of the study was to produce a simulation model that predicts travel times of logging trucks for specified alignment (actual or proposed) and truck parameters. It i s a deterministic simulation which w i l l output information on the speed and time for a logging truck to traverse sections of the road unaffected by t r a f f i c . Among the numerous factors included as independent variables i n the model are the alignment, grades, surface type, and vehicle characteristics such as horsepower (HP) versus revolutions per minute (RPM) of the engine, gear ratios and rear axle ratio. 4 It must be clear that no attempt i s made i n this study to predict travel cost, only travel time. The purpose of the previous explanation (discussed i n Sec. 1.2) was to show the po s s i b i l i t y of using machine rate times travel time to predict the travel cost u n t i l more accurate approach i s available. 1.4 Outline of the study Chapter 2 presents an overview of the model. In Chapter 3 rules and functional relation hips are developed to simulate vehicle behavior as a function of road geometry. The speed of the vehicle related to i t s drive-line characteristics constitutes the core of the simulation model and i s developed i n Chapter 4. Measured versus computed results along with the findings are the subject of 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 of 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 size and complexity of forest systems i s such that analytical models are needed. A model i s a representation of a set of essential relationships present i n a system. The word essential i s important because i n situations as complex as those encountered i n road engineering and t r a f f i c systems, one i s forced for practical considerations to try to reduce the number of vvariables included i n the model. The relationships, i f properly expressed, enable a model to react to a new environment i n a manner similar to that of the system by which the model i s validated. 2.2 Overview of the model Vehicle travel time i s a direct function of engine RPM, engine torque, gear ratios, and vehicle tractive effort (rimpull). The last i n turn i s directly related to certain road design characteristics such as vertical alignment or p r o f i l e , the unbalanced force caused by curves, surface type and operational restrictions . The model takes these design characteristics and a description of the trucks to mimic velocities, accelerations and decelerations by mathematical deterministic simulation. Schematically this could be reprensented by the diagram of Figure 2.1. 6 desired v e l o c i t y throttle. DRIVER ti o •iH •P (ti U. <u rH Q) O O at •H O O rH CD > _ •a POWERPLANT CD <u (0 Si ROAD GEOMETRY motion resistances VEHICLE DYNAMICS Figure 2.1 Diagram of the model The problem of expressing the performance i n terms of kinematics and engineering mechanics starts with the elementary concept of motion and natural laws which produce motion. The primary concern i s with a particular type of motion called translation which denotes a displacement along a straight line path. The conventional concepts of distance, time, velocity and acceleration are associated with translation. The differential equations defining the translatory motion of a vehicle can be expressed 7 as v = ds dt and a = dv = ds dt dt dv = v dv ds ds Therefore dv = a ds ...(2.1) v and dt = dv ...(2.2) a where t = time, sec s = distance, f t v = velocity, ft/sec 2 a = acceleration, ft/sec . In addition to the preceeding expressions for time and speed, the causes of motion and the associated concepts of force, mass and acceler-ation must be considered. The explanation i s found i n Newton's law of motion from which the familiar relationship Force = Mass times Acceleration (F=ma) i s derived. This expression provides the link relating the vehicle translatory motion to i t s cause-the net driving force at the wheels. This value for acceleration i s substitued i n the previous equations (2.1) and (2.2) to give dv = F(v) ds mv (2.3) and dt = m dv F(v) (2.4) 8 where F(v), the net driving force at the wheels, i s a function of velocity (developed i n Chapter 4). In the model the road i s divided into inany sections of uniform char-acteristics. 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 vehicle data (developed i n Chapter 3) . Then by dividing the sections into subsections of constant length (ds) the time to traverse from one subsection to the next and the new velocity at the end of each subsection, keeping the forces constant over this small increment, can be evaluated by v = 2 v ds f F(v)1 ...(2.5) » L m J and t = 2 dv r ml. ...(2.6) L F ( V ) J This process i s repeated u n t i l the maximum safe speed i s reached or de-celeration i s necessary. If the maximum safe speed i s reached then the simulated truck travels at constant speed u n t i l a new speed l i m i t i s imposed requiring acceleration or deceleration. Each time a new velocity i s computed the vehicle i s checked to determine i f i t i s i n the corresponding correct gear. If not, shifting i s made to the proper one. A check i s also made to determine i f braking should Start. Braking w i l l begin at the proper time and the simulated truck w i l l be decelerate to the correct speed at the end of the course or at the end of any interim section i f a lower speed restriction has been placed on the next section. The time to traverse each subsection i s accumulated leading to hauling time (travel empty and travel loaded) prediction unaffected by t r a f f i c . 9 2.21 General assumption The general assumption i s that whenever possible the vehicle i s assumed to travel at wide open throttle. This assumption i s j u s t i f i e d by the fact that a s k i l l f u l l driver w i l l generally achieve the maximum attainable speeds except when limited by t r a f f i c or operational speed restrictions on safe speed limits as controlled 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 of the mathematical relationships among the parameters and the amount of calculations required to scan a road led to the use of the computer for the estimation of travel time. The program i s written in FORTRAN TV language for 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. Basically the program works with three sets of input data. One of these describes the horizontal and ver t i c a l alignments of the road under study, from which the speed limits are computed, the stops that the truck i s to make and the average time i t i s to wait at each stop. The computation of speed limits as controlled by the road characteristics simulates the knowledge and judgment of the driver when travelling over the road. A second set of input defines the truck. Input truck data includes vehicle weight (loaded and empty), f u l l throttle HP points versus RPM, drive-wheel r o l l i n g radius, torque converter performance, gearbox and rear axle ratios. This information i s a l l readily available from manufacturers. From the truck data the tractive effort (rimpull) available at the wheels i s 10 computed for small velocity increments. Second degree polynomials were f i t t e d to the rimpull versus speed points for each gear. The third 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 velocities (empty and loaded). The second phase of the system consists of the simulation of vehicle 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 logical flow diagram showing, i n a simplified form, the general sequence of computational steps through which the computer goes at each subsection. The result of the model i s a l i s t i n g of the vehicle operating speeds and times. There are two levels of output available to the user. The lowest level gives: 1. Total length of the course. 2. Round t r i p time. 3. Travel empty and travel loaded time. 4. Time stopped. 5. Average velocity over the course, loaded and empty. The highest level gives more details for specified sections: 1. A resume of the geometry of the section. 2. The entry and exit speed for each subsection. 3. The time to traverse each subsection and the entire 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 level one. The input formats are described i n Appendix 11. 12 Vehicle data information supplied by user Road data Control data procedure carried out by program i n i t i a l l i z a t i o n and preparation Compute r i f i t 2nd polynomia] mpull and degree s for each ar Compute speed limits Compute resistances for instantaneous speed and section characteristics Find proper gear for the instantaneous speed Figure 2.2 Flow diagram of the program Net force = rimpull - resistances Figure 2.2 Flow diagram of the program - continued Yes Print section summary Print course summary Figure 2.2 Flow diagram of 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 driver j u s t i f i e d i n using a l l the speed provided i n his vehicle because of conditions of the road. In the model, the simulated truck w i l l enter any section of the road (a section i s of uniform characteristics) below or at a specified speed limit. This chapter explains how the speed limit of each section i s deteimined. The design elements affecting speed are the horizontal alignment (road width, shoulder width, horizontal sight distance, degree of curva-ture, superelevation), vertical alignment (vertical sight distance, percent of grade) and the type of surface. A thorough review of literature available led to proposals offered below to approximate the effects on travel speed of vehicles. A plan and pr o f i l e of a portion of a road i s shown i n Figure 3.1. It shows how the sections of uniform characteristics are determined from the plan and pr o f i l e of the road. 3.2 Maximum permissible speed on curves If a vehicle enters a curve too fast the centrifugal force could surpass the f r i c t i o n a l grip of the tires on the road causing i t to slide off the road or overturn. Once slipping 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 slight obstruction (Harkness, 1959 and Paterson, 1970). The driver controls the speed of his vehicle also to avoid hit t i n g objects or other vehicles. The controlling factor i n this case i s the safe stopping distance which i s a function of the sight distance. For these reasons, in 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 of the curve. 3.21 Assumptions In the present model i t i s assumed that driver behavior conforms to the following assumptions when confronted with curved courses: 1. Speeds on curves never exceed those at which the unbalanced cen-trifugal force makes the driver uncomfortable. 2. Speeds on curves do not exceed the li m i t to allow safe stopping within the available horizontal sight distance. 3. When the curve i s f l a t enough that neither centrifugal force nor safe horizontal sight distance cause the driver to reduce speed to traverse the curve, then the vehicle proceeds around the curve at the approach speed or obeyes some other rule. The approach speed i s influenced by numerous factors including grades, the proximity and sharpness of preceding curves, the a b i l i t y of a given vehicle to accelerate and the-type of road surface. In short, a driver approaching a curve w i l l reduce the speed Of his vehicle, i f necessary, to match to the appropriate safe stopping distance and centrifugal force assuring his comfort. 18 3.22 Centrifugal force as a speed control The maximum speed at which an horizontal curve may be negotiated, when centrifugal force i s the controlling factor, i s one i n which the tangential force applied through the centroid of the vehicle and i t s load i s exactly counterbalanced by the forces resisting tangential s l i p at the wheels or resisting overturning of the vehicle. Figure 3.2 shows the forces acting through the center of gravity of the vehicle. 19 Conditions for skid-free curve driving can be derived as follows 2 S = M (F + W ) max s y y where 2S = sum of the side-force reactions on a l l wheels, lb Hs = coefficient of sliding f r i c t i o n F = centrifugal force, lb W = vehicle weight, lb. The resultant force must not become larger than the maximum f r i c t i o n a l side-force reaction (F - W ) < M (F + W ) x x — s y y (F cos 6 - W sin 8 ) < u (F sin 6 + W cos 0 ) ... (3.1) s . since F = W v 2 gR where v = speed, ft/sec R = radius of curvature, f t 2 g = acceleration of gravity, ft/sec 8 - superelevation angle, deg. By replacing F i n equation (3.1) 'gR (tan 6 + Mg)" _(1 ~ M„ tan 8 ) _ v s , max = I U f t / s e c s gives the maximum speed on a curve as controlled by centrifugal force. As mentioned above, once slipping has occured, should the wheel encoun-tered even a very slight obstruction overturning could easily result. 3.221 Assumptions In the preceding equations, the vehicle i s assumed to be moving with constant speed, no accelerating or braking forces are present and the centrifugal force i s assumed to be distributed on axles as the static level axle weights. The assumption of constant speed permits the use of the coefficient of sliding f r i c t i o n (M )—^ instead of the coefficient of s f r i c t i o n adjusted for lateral sliding (also called lat e r a l ratio, unbalanced centrifugal ratio, cornering ratio, unbalanced side f r i c t i o n or side f r i c t i o n factor). The value of the side f r i c t i o n factor varies with each vehicle and depends principally upon the speed of the vehicle, the condition of the tires and the characteristics of the surface. There i s no simple relation available from which i t can be computed. The speed on a curved section w i l l be constant except, sometimes, at the beginning and at the end of a section. If the preceding section of uniform characteristics has a lower speed l i m i t than the present curved section then the vehicle w i l l accelerate up to the speed l i m i t of the curve i f enough power i s available. On the other hand, acceleration or deceleration at the end of the section w i l l be necessary i f the next section has a speed limit higher or lower tJhan the present section. The acceleration or deceleration w i l l be usually performed over short distance compared with the total length of the section which j u s t i f i e s the assumption. 1/ The coefficient of sliding f r i c t i o n i s defined by: ratio of the force necessary to move one surface over an other with uniform velocity 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 limited by the sight distance that permits two trucks approaching each other to stop without colliding, or one truck to stop without hitting an obstruction on the road. Sight distance i s assumed to be limited by back slope on the cut side of the road and by timber and brush at an equivalent distance from the centerline 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 vehicle from the instant the driver sights an object for which a stop i s necessary, to the instant the brakes are applied; and the other, the distance required to stop the vehicle after the brake application begins (AASHO, 1965). Distance required to stop a vehicle from a given speed on level grade i s derived as follows F = m a = W a  8 since a - M gg where a i s the deceleration. From the following equation 2 2 v = v + 2 a SD o a vehicle decelerating to a complete stop w i l l take the following distance on level grade 2 2 SD = v_ = v o o where SD = braking distance, f t V q = i n i t i a l speed, ft/sec u = coefficient of f r i c t i o n r s g = gravity acceleration. 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 for each driver i n order to stop would then be 2 SD = 2.5 v + V o ° 64.32 n s on level grade. I f the vehicle must be stopped on a grade, stopping distance w i l l be influenced positively or negatively by the grade force. From Figure 3.3, the grade force can be seen to be the component of the vehicle weight given by F = W sin 6 g Figure 3.3 Grade force acting on a vehicle 23 The maximum force that can be transmitted through the tires i s F = M W cos 6 s The summation of a l l forces gives and H W cos 6 + W sin $ = W a S — • g a = M g (cos $ + sin 0 ) Sight distance required i n order to stop would then be r 2 SD = 2.5 v + o 64.32 M (cos 8 + sin B ) ..(3.2) where (+) i s for adverse grade and (-) i s for favorable grade. The speed limit as a function of sight distance (SD) w i l l be found by solving equation (3.2) No consideration i s made for 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 of these effects would not add accuracy to the model and would require more data. The errors, at this stage, are not cumulative and the equations adopted constitute good approximations. The combined sight distance required for two drivers approaching each other i s expressed by K t r _l_ J i r ...(3.3) SD = 5 v + 2 v o o 64.32 M The grade of the road does not affect this combined distance because a favorable grade to one driver w i l l be generally adverse to the other. The combined sight distance could be used as controlling factor on a single lane road when no radio connnunication exists 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 of the road parameters. For curves having large central angles, minimum horizontal sight distances occur when both the driver's eye and the obstruction are positioned within the circular curve. Figure 3.4 shows this aspect. sight distance Figure 3.4 Geometry for determining sight distance when sight distance i s less than length of curve The AASHO standards prescribe that the line of sight for safe stopping distance combines the top of a six-^inch-high object and a driver's eye 3.75 feet above the roadway surface. In this study i t i s assumed that the line of sight intersects the backslope at a height of two feet. Figure 3.5 explains this aspect. 25 point at which line of sight intersects backslope later a l position of driver's eye (located at the center of the road) Figure 3.5 Transversal position of parameters For a lat e r a l position of driver's eye located at 10 feet 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 . It 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 relationship between the central angle, 26 R and M i s given by cos A = R - M R 2 therefore (3.5) Combining the previous equations (3.4) and (3.5) we get SD = 2 R cos -1 (^ ) The speed l i m i t as controlled 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 driver's eyes are both positioned on the tangents at equal distances from the curve ends. The reader i s referred to Figure 3.6. For this situation 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 following equation L = M - m where m i s given by m = R /1 - cos (0 whilst S i s given by S = R p Combining these expressions 27 and the f i n a l results are obtained by replacing SD i n equations (3.2) and (3.3) and solving them. sight distance Figure 3.6 Geometry for determining sight distance when sight distance i s greater than length of curve V* 3.24 Comparaison of speed limits on curves with empirical values  from a previous study A time-motion study of timber hauling conducted by Campbell and Van der Jagt (1969) gives empirical values for the maximum curve speed versus degree of curve. These values are compared with the maximum safe curve speeds con-trolled 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 theoretical values are reasonable. 3.3 Maximum permissible speed as controlled by surface conditions Road geometry i s not the only factor affecting speed; the physical state of the surface i s another. Such things as the type of surface, maintenance, t r a f f i c patterns and density, loads, weather conditions a l l notes: 1. n = 0.436 for a l l theoritical curves s 2. no grade effect was included on speed limits as controlled by sight distance 3. no superelevation i s included on speed limits as controlled by side f r i c t i o n no side slope i.e. as controlled by side f r i c t i o n , no superelevation 5 10 1000 2000 500 I 300 250 200 175 T 150 _1 125 I 100 i 1 r 75 80 85 90 degree of curve 75 64 r I 1500 800 400 Figure 3.7 Comparaison of theoritical speed limits on curve with empirical values curve radius (ft) 29 roust be considered as an integral part of the traction problem. Since i t i s impossible to control or isolate many ot these variables 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 travelling below i t s maximum speed due to other limiting conditions (gradients or curves) the effect of surface i s very slight. Probably, the way in which the road surface sets an overall maximum speed with l i t t l e or no effect on speeds already restricted 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 driver must reduce speed to maintain control i.e. surface contact with driving wheels. Drivers seem to drive by the seat of their pants, i n that, i f they remain more or less i n their seats they are satisfied that they have control and the truck is.not suffering unduly." Table 3.1, extracted from this study, shows the speed li m i t as con-trolled by surface conditions. These values are not used as they appear since sight distance and surface conditions are identified 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 of Table 3.1, 50 miles per hour was adopted as a f i r s t t r i a l for maximum speed on gravel road. On paved roads the speed l i m i t becomes, very often, more a regulation than a surface control. The maximum permissible speed due to surface conditions i s an input to the model and i s l e f t to the discretion of the user. 30 Table 3.1 Maximum speeds as controlled by surface Surface (gravel) Road width 8 f t bunk trucks 12 f t bunk trucks uphill-level downhill uphill-level downhill sight d >250ft ti stance < 500ft sight d] > 500ft Lstance < 500ft sight d >250ft istance <250ft sight c >500ft istance < 500ft Good hard smooth single lane 40 35 35 30 40 30 40 30 double lane 50 40 50 40 40 35 50 40 Fair f a i r l y loose rough single lane 40 35 35 30 30 25 30 30 double lane 45 40 45 40 30 30 30 30 Poor very loose rough single lane 35 25 25 20 20 15 20 20 double lane 35 35 35 30 25 20 25 20 notes: 1. the figures are rounded off to the nearest 5 mph, which i s a reasonable level of precision. 2. a paved surface (which approaches a perfect surface) exercises no significant restraint on maximum speeds. source: Campbell and Van der Jagt, Table 2, p 106 31 3.32 Winter conditions It was found, by Campbell and Van der Jagt (1969), on sections of alignment and sight distance, that i n winter trucks were able to attain 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 of the frozen surface which i s far less l i k e l y to deteriorate with t r a f f i c . However, for most of the sections speed w i l l be controlled by safe stopping sight distance since M takes a lower value i n winter s conditions. 3.4 Speed limit on favorable grade The mental attitude of the driver, the safe stopping distance and the roughness of the road surface are some of the major controlling factors of logging truck speed on favorable grade. 3.41 Sight distance as a speed control The speed li m i t as controlled by sight distance, on favorable grade, w i l l be determined by solving equation (3.2) as for curved sections. The value of SD is the length of the grade to the beginning of the curve where a curved section i s next. In many instances this speed limit 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 straight road ahead. 3.42 Braking capacity as a speed control Logging trucks are too heavy to be controlled on steep and long grades by their service brakes without excessive heating. Therefore, they are usually 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 for 100% engine brake without the use of service brakes may be found as a function of the grade and vehicle weight. These limiting speeds are input by the user and are used as maximum descent speeds by the model as controlled by braking capacity. If no limiting speed i s specified the model assumes the empirical values of Campbell and Van der Jagt (1969) shown in Figure 3.8. 3.5 Speed li m i t on adverse grade Most of the tine, on adverse grade speed w i l l not be limited by road geometry or surface but by engine power. The effect of up 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 position of driver's eye favors a safe sight distance and w i l l not affect the speed of the vehicle. 3.6 The independent variables Since the model i s intended as a designer's guide, the assumptions must be consistent with the independent variables available. The independent variables affecting speed limits as input i n the program are: 1. Section length, f t . 2. Radius of curvature (R), f t . 3. Superelevation, f t / f t . 4. Coefficient of sliding f r i c t i o n (M ) (for recommended coefficient s of f r i c t i o n , refer to Table 3.2) . 5. Grade (G), f t / f t . 6. Distance between driver's eye (assumed center of the roadway) and the point at which line of sight intersects backslope (M), f t . 7. Maximum descent speeds as controlled by engine brake, mph. 1_ , ! . — , , 1 — 1 \ 2 4 6 8 10 12 14 favorable grade (%) source: Campbell and Van der Jagt Fig. 3 p 104 Figure 3.8 Maximum descent speeds assumed by the model when no engine brake i s used 34 The expected value for speed limits on each section can be computed according to the different rules from the appropriate independent variables. The smallest value i s kept for the maximum permissible speed of the section. 3.7 Conclusion Determination of the speed limit of each section requires a-look-ahead feature i n the model. After each small increment of Table 3.2 Coefficient of sliding 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 start. At the proper time braking w i l l start and the vehicle w i l l be slowed down to the correct speed at the end of any interim section i f a speed restriction has been placed on the next section. It 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 limits as controlled by safe stopping distance. It i s f e l t that since we deal with 35 each section of the road separately the error i s not cumulative. Results of this approach should be accurate enough and at the same time reduce computer time. The determination of these speed limits i s i n fact simulation of the  knowledge and judgment of the driver when travelling over the road. After speed limits for each section have been determined i t i s possible to simulate the motion of the vehicle 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 incor-porate significant vehicle characteristics. The components which influence performance prediction to the greater extent are, of course, the engine, the torque converter ( i f dealing with a torque-converter transmission), and the mechanical transmission. These components provide and transmit power to the vehicle's drive axle(s). In this chapter each component i s considered seperately and the relationship of one of the other i s deter-mined. Fi n a l l y the overall picture of what the vehicle 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 ratio gearbox incapable of power-on shifts, with a driver-controlled clutch) and torque-converter (defined as a hydrodynamic torque converter i n series with a gearbox capable of power-on shifts). The latte r type of drive i s becoming most popular for heavy off-highway vehicles. 4.2 Manual transmission modeling The engine speed-vehicle speed relationship must be accurately deter-mined to express the net driving force function of vehicle velocity correctly. In order to do so, many forces must be accounted for such as the available rimpull (propulsive force), the resistances to motion (roll i n g resistance, 37 a i r resistance, grade resistance, curve resistance), and the masses to be accelerated (inertias). These requirements are easy to meet for a manual transmission since there i s a fixed relationship between the engine and vehicle speeds and acceleration i n each gear. The relationship between rimpull and vehicle speed i s developed from the installed engine horsepower-engine speed (RPM) curve obtained from manufacturers with allowance made for altitude effect and accessory losses (the reader i s referred to Appendix 2 for details). Figure 4.1 shows typical engine data as supplied by manufacturers. After allowance for losses, to each RPM corresponds a net engine torque value (Te). The net engine torque, as a single valued function of engine RPM, 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 related to engine torque by the equation F = Te Gr Ar yt ...(4.1) r and the engine RPM i s related to vehicle speed by the equation RPM = MPH (5280) (12) Ar Gr ...(4.2) (60) 2 w r As mentioned above to each RPM corresponds one Te. In the previous equations Te represents the net engine torque which i s multiplied by the transmission reduction (Gr), axle reduction (Ar), and the efficiency (-nt), and divided by the r o l l i n g radius (r) to give the rimpull available for the present engine RPM (or present vehicle speed). Transmission efficiency (-qt) normally depends on the gear i n use. In this study, i t i s assumed that transmission efficiency i s constant i n any given gear. A figure of 0.85 i s generally accepted as a good approximation. 38 Engine model: NTC-350 (335) Type: Turbocharged & Aftercooled CUMMINS ENGINE COMPANY Columbus, Indiana Curve number: CO-3189-A1 Bore: 5-§- i n . Stroke: 6 i n . No. of cylinders: 6 Displacement: 855 cu.in Date: By: IOOO H 900 -A 800 -J .400 .350 L350 .325 •300 L275 L250 -225 200 •P +-> o t-1 CU o —I 1 1 - i 1 r 1300 1500 1700 Engine speed-RPM 1900 2100 Figure 4.1 Typical engine data 39 The forces to be overcome include the component of vehicle weight resolved along the gradient (Rg) (the reader i s referred to Appendix 3 for details), 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 = Rg + Ra + Rr + Rc + My a ...(4.3) r where M7 i s referred to as the total effective mass of the vehicle (Appen-dix 7). Putting a = 0 i n this equation allows the rimpull at any constant speed to be calculated. Under certain circumstances the rimpull that can be developed may be limited by the adhesion between the driven tires and the road. I t i s assumed i n the model that whatever rimpull i s required for a certain performance can be produced at the t i r e s . It i s understood that there are limits to the rimpull and that the transmission of more power than i s necessary to develop can result i n wheel spin. However, this does not happen very often with logging trucks since they are very heavy, even when empty. Speed to distance and time to distance are readily calculated from equation (2.5) and (2.6) expanded as explained above. Methods of solving equations (2.5) and (2.6) are discussed later i n this chapter. If shifting time i s neglected, vehicle performance w i l l be over estimated. However shifting time and deceleration during shifting are 40 not included i n this model. 4.3 Torque-converter transmission modeling In the case of a torque converter i n series with a gearbox, the precise definition of this relationship 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 particular engine and a particular torque converter i s done i s described below. A relationship may be established only i f the performance of the torque converter is known. Manufacturers supply torque converter information. Figure 4.2 shows typical data as supplied by them. It has been demonstrated by Ott by Ishihara and Emori that i t i s permissible to assume quasi steady conditions for the operation of a torque converter. Hence, the input torque to the torque converter may be described by 2 T i = / Impeller rotational 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 ratio Figure 4.2 Typical torque converter data and the Torque converter K-factor = Input shaft speed . yj Input torque The K-factor of the torque converter i s a function of the torque converter speed ratio (Figure 4.2). The converter speed ratio i s defined as Converter speed ratio = 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 detail i n section (4.42). After the torque to the driveshaft i s available the equation of motion can be derived the same way as for the manual transmission. If the speed ratio, torque ratio, and K-factor points of the torque converter are not available, only output RPM and torque points to the torque converter may be input. In that case the program proceeds exactly as for manual transmission. 4.4 Method of solution Linear interpolation and curve f i t t i n g by method of least squares are carried out to adapt the engine and power train 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 this sort. 4.41 Manual transmission procedure 1. Read engine HP versus engine RPM points, correct HP for altitude, and compute the engine torque for each RPM point. 2. Beginning with the lowest gear, find the engine RPM for a certain 43 speed from equation (4.2) (an increment of 0.5 mph was adopted for the program). 3. For the RPM found i n (2) compute the corresponding engine torque by linear interpolation between points computed in (1). 4. For the engine torque found i n (3) compute the rimpull available to the wheel from equation (4.1). 5. Repeat (2), (3), and (4) u n t i l shifting point i s found. 6. I f shifting occurs repeat (2), (3), (4), and (5) with the next gear. 7. When the top speed i n the last gear i s attained f i t a second degree polynomial to the rimpull versus MPH for each gear. Two conditions dictate a gear change: 1. When the governed RPM i s attained for a certain speed and a partic-ular gear. 2. When the rimpull versus MPH for two adjacent gears intersect prior to governed RPM. The f i t t i n g of a second degree polynomial to the rimpull i s partic-ularly done to approximate the rimpull when slipping of the clutch occurs i n f i r s t gear. It also gives a smooth curve for the rimpull of each gear which i s used i n the simulation of vehicle motion. Without this f i t , rimpull at low speed for 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, for a certain speed and a particular section, the r o l l i n g , a i r , inertia, curve, and grade resistances are computed. Then for the actual speed the proper polynomial (proper gear) i s found and the available rimpull computed. The net force to accelerate climb a grade or traverse a curve i s then computed by substracting the resistances from the available rimpull. The numerical integration of equation (2.5) and (2.6) may then be performed knowing a l l the variables. 4.42 Torque-converter transmission procedure 1. Read engine HP versus engine RPM points, correct HP for altitude, and compute the engine torque for each RPM point. 2. Compute the engine K-factor for each torque versus RPM point from (1). 3. Read torque converter speed ratio, torque ratio, and their corre-sponding K-factor. 4. By linear interpolation find the engine RPM for which the engine and torque converter K-factors are matched. 5. Find the output RPM to the torque converter (Engine RPM X Speed ratio = Output RPM). 6. Find the output torque to the torque converter (Engine torque X Torque ratio = Output torque). 7. Proceed as for manual transmission beginning at (2). 4.5 Braking The equations used to predict power-on performance remain valid for braking, provided that the sign of Te and a i n equation 4.3 are reversed and that the transmission overall efficiency i s replaced by i t s inverse . to allow for the transmission losses that are helping to slow the vehicle The variable rate of deceleration experienced by a vehicle, can also 45 be represented by an average rate of deceleration. It i s advanced that 2 operator discomfort i s reaching an undesirable level at 8-12 ft/sec deceleration (Caterpillar Tractor Co., research department). For the 2 computer program a constant deceleration rate of 6 ft/sec i s conservatively assumed. 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 velocity, ft/sec s = distance to reduce the speed or stop the vehicle for the instantaneous speed, f t 2 (-12) = deceleration (2 X -6 ft/sec ). 4.6 The independent variables The engine and power train parameters are obtainable from the manu-facturers. They are l i s t e d below with details when necessary. 1. Horsepower versus RPM. 2. Main transmission gear ratios, auxiliary transmission ratios, and rear axle ratio. 3. Torque converter K-factor, speed ratio, and torque ratio, or i f the second option i s used, output shaft speed and output torque. 4. Tire r o l l i n g radius (see Table 4.1). Torque converter data such as torque ratios, speed ratios, 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 rimpull-velocity curve found on most equipment specification sheets i f the previous data are not available. Tire size Radius Tire size Radius 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 source: Kenworth Motor Truck Company Table 4.1 Loaded t i r e radius i n inches (off-highway tread) 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 variables a v a i l -able. The purpose of the study i s mainly to help decision-makers in regards to design of logging roads. This means that the model must predict times accurately enough to enable ranking of alternatives. The two following sections show how close the model i s to real i t y by comparing observed and predicted times. 5.2 The test situation The data used to validate the model were collected by the B.C. Forest Service. Porpaczy (1973) describes the data collection as follows: "The Prince George Di s t r i c t Time Studies Crew, in collaboration 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 off into sections with the physical measurements of 1/ the characteristics of each section taken by the Road Recorder. The timing procedure was to record the total time lapse between section markers. A l l haul time studies, almost singularly, were conducted i n isolation of extraneous factors, such as the relationship 1/ The B.C.F.S. Road Recorder i s an automatic vehicle-mounted system to record road geometry as the vehicle traverses i t . 48 of a particular t r i p to others; the relationship of round tr i p time to the working day, which may be more or less than 8 hours, and the sub-sequent driver freedom to allocate his 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 for making another tri p as the time i s not sufficient for a round tr i p , which then i s manifested i n a slackening of pace." The performance tests were conducted over 33 miles of road. The road width varied from 22 to 30 feet, a maximum gradient of 6.3% and a maximum curvature of 20° were also encountered. The road had a gravelled surface for i t s entire length. The route afforded a conglomerate of curvature, gradient, and restricted sight distances. Five vehicles of gross weights of 30,000 pounds were tested. An average loaded weight (vehicle weight plus the payload) of 110,000 pounds was recorded. The power developed by the engines ranged from 325 HP to 370 HP. A l l vehicles had a manual transmission. The drivers employed were a l l s k i l l e d professional drivers. The time study data were analyzed to investigate: 1. The consistency of driver performance within sections, 2. The comparison of performance between different trucks for the total course. Consistency of driver performance within section The coefficient of variation i n time for each section traversed seldom exceeds 10% with an average of 8%. This indicates that the performance of the drivers i s consistent. 49 Comparison of performance between different  trucks for the total course An analysis of variance was performed and the comparison of performance of the individual trucks for travel loaded indicated no difference between the five units studied even though they had different rated engine horsepower, transmission ratios and were of different ages. S t a t i s t i c a l l y there i s a difference between the travel empty mean of each unit. It i s suspected to be caused by a slackening of pace due to dispatching and interactions of vehicles. For more details on the analysis of variance refer to Appendix 9. Even with the difference for travel empty, i t was decided to use the characteristics of one of the observed trucks as a representative average to predict times with the model. 5.3 Predicted versus measured times The simulation model computes average times of a given truck for a given road. A comparison of the results 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 results. A perfect coincidence would have been represented by a 45° line from the origin. To verify i f the computer prediction and observed mean could be represented by a single regression a test of similarity of slopes was performed* The hypothesis of common slope was rejected for both travel empty and loaded. Refer to Appendix 10 for more details on the tes"t_.of similarity of slopes. However, the results obtained for travel loaded might be considered acceptably close. An error of 5% for the total course and an average error of 10% within each section existed i n comparison to the observed data. Predicted times for travel empty (Figure 5.2) were too low (the 50 70 _, l5 20 30 ~ 40 50 60~~ Cumulative predicted (computer) mean times, minutes Figure 5.1 A comparison 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 for travel empty 52 simulated vehicle travelling faster than the observed vehicles). An error of 19% on the total course and an average error of 20% within each section were detected. Something appears to affect travel empty whilst apparently not affecting travel loaded. It i s suspected that the n_aximura permissible empty speed i s controlled by surface conditions. As mentioned in section 3.31, a f i r s t t r i a l was made with a speed limit of 50 mph as controlled by surface conditions. A second t r i a l was performed with a speed li m i t of 40 mph which i s the average of Table 3.1 extracted from Campbell and Van der Jagt (1969). A closer estimation was obtained for travel empty whilst for travel loaded nothing has changed since the vehicle does not attain this speed due to the load constraint. It appears that 40 mph would be more reliable for speed li m i t as controlled by surface conditions. However, even with a speed l i m i t of 40 mph the times are underestimated. For travel loaded the load i s restraining the speed of the vehicle i n a way that the drivers do not have any choice but to use the f u l l potential of the engine. Empty, since the f u l l potential of the engine cannot be attained, the driver's choice may result i n variation. On a day-to-day basis the drivers do not operate their vehicles at their f u l l potential. 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 vehicle movement i s represented i n the model in 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 in certain input parameters. Because of the large number of parameters affecting the system performance this sensitivity may be limited to the major controllable parameters such as curves, grades, and surface type. Results obtained from the sensitivity tests between the vehicle and system parameters can be used to compare alternative designs of logging roads and the more economical alternative may be choosen. However, the adoption of this model i s not seen as the f i n a l answer. Indeed, i t should be developed and updated i n line with further research. 6.2 Areas of further investigation 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 this study and a stochastic simulation to generate t r a f f i c and to evaluate i t s effects on the travel 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 interactions among vehicles. Such a model would permit the evaluation of alternative road designs to predict their performance 54 for the anticipated use of the road (used for recreation, protection, and harvesting). The model was designed principally to handle the problem of alternatives in road location. It has been recognized however, that this i s only one type of problem. Among other p o s s i b i l i t i e s are: 1. To establish for certain future operations the production rate of trucks. The results of such prediction could be used to determine the most economical number of trucks to use i n the predicted situation. 2. To select equipment that best matches a given application. 3. To determine hauling costs for stumpage price appraisal. 6.3 Conclusion A simple model predicting truck performance on a defined route was developed. It produces results acceptably close to experimental data arid use of this model allows parametric study of alternatives. Such simulation has the advantage of replacing the real hardware by the computer. The measurements on trucks under test on actual terrain were recorded and analysed s t a t i s t i c a l l y . The performance of the complete vehicle system was then assessed and direct comparaison between the simulation and the actual test became possible. The simulation does not eliminate thorough road testing but insures that further research and expensive hardware construction and road testing be not undertaken u n t i l there i s a high probability that the result could be satisfactory. 55 BIBLIOGRAPHY American Association of State Highway O f f i c i a l s (AASHO), 1965. A policy on geometric design of rural highways. Washington, D.C., 650 pp. Anderson, J.W. , J.C., Firey, P.W., Ford, and W.C., Kieling, 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, main-tenance, inventory and repair policy for 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. 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Engrs. 1969-70, Vol. 184, Paper 37, 19 pp. McKenzie, R.D., W.M., Howell, andD.E., Skaar, 1968. Computerized evaluation of driver-vehicle-terrain system. SAE Transactions, Vol. 76:2, 12 pp. Oglesby, CH. , F. , Arias, and R.W. Clark, 1971. The effects of horizontal alignment on vehicle running costs and travel times. Program in Engineering-Economic Planning, Stanford University, report EEP37, 82 pp. 56 Ordorica, M.A., 1966. Vehicle performance prediction. SAE Transactions, Vol. 74:4, 10 pp. Ott, A., 1966. Calculation of driving performance with reference to torque converter and power changing. Eleventh FISITA Congr., Preprint No. A10. Paterson, W. G., 1971. Transport on forest roads-1980. Woodl. Sect. Index, Canad. Pulp Pap. Ass. No. 2597(B-8-b), 8 pp. Paterson, W. G. , H. W., McFarlane, and W. J., Dohaney, 1970. A proposed forest roads cl a s s i f i c a t i o n system. Pulp and Paper Research Institute 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, University of Stanford. Pike, J. N., Finning Tractor and Equipment Co. Ltd. (representing Caterpillar Tractor Co.), 555 Great Northern Bay, Vancouver 10, B.C.. June 14, 1972. Personal correspondence. Porpaczy, L. J., 1973. Log haul studies-1972. Unpublished report, B r i t i s h Columbia Forest Service, Enginnering Division. Roberts, P. 0., and J. H., Suhrbier, 1966. Highway location analysis: an example problem. MIT, Report No. 5. Taborek, J. J., 1957. Mechanics of vehicles. Machine Design, The Penton Publishing Co., Cleveland, 93 pp. Tangeman, R.J., 1971. A proposed model for estimating vehicle operating costs and characteristics on forest roads. Transportation System Planning Project, U.S. Forest Service, 151 pp. Waelti, H., B.C. Forest Service, Victoria, B.C.. June 13, 1972. Personal correspondence. Winfrey, R., 1970. Economic analysis of highways. International Textbook Co., Scranton, Pensyslvania. 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 alternative road alignments. It was also included to show that by predicting the travel time a big otep toward the application of this 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 of annual cost for alternative alignments i s based on the following equation relating i n i t i a l costs, user time and operating costs, and maintenance costs: TAC = ACC + AUC + AMC where TAC = total annual cost, $ ACC = annual capital 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 capital cost becomes ACC = tec (CRF) where tec = total construction cost, $ 58 and CRF = capital recovery factor tec = ec + sc + pc + rc + l c where ec = earthwork cost, $ sc = structures cost, $ pc = pavement cost, § dc = drainage cost, § rc = relocation cost, § l c = land and right-of-way cost, § CRF = i ( l + i ) n U + i ) n - l where i = interest rate and n = service l i f e , years This relation for annual construction cost holds only for the simple case where the service lives of the various components are the same and where there i s no salvage value. Where this additional refinement i s j u s t i f i e d , and i t frequently is, the annual construction cost i s the sum of the individual components: j ACC = X C R F k [ c c k + <svk> where j = total number of construction categories 59 k = category presently being considered CRF^ = capital recovery factor for the appropriate l i f e CC^ = construction cost category under consideration SV^ = salvage value of this construction category and PWF^ = present worth factor for the appropriate l i f e where PWF = i where EAT = equivalent annual t r a f f i c , vehicles/year and utc = user time cost, $/vehicle doc = direct operating cost, $/vehicle These can be further broken down as where vol = 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 Direct operating cost i s ( l + i ) n - l Annual user cost becomes AUC = EAT (doc + utc) EAT = vol + av + av - n (av) (CRF - i ) 1 1 j 60 where j = total number of vehicle classes = percentage of vehicles of class i f c ^ = fuel cost of class i vehicle, $/vehicle tr c ^ = t i r e cost of class i vehicle, ^/vehicle oc^ = o i l cost of class i vehicle, $/vehicle mtc^ = maintenance cost of a class i vehicle, S/vehicle and dpci = depreciation cost of a class i vehicle, $/vehicle For time cost, where t^ = time for a class i vehicle to travel the alignment, hours tc^ = time cost for a class i vehicle, $/hour and tur^ = cost of time u n r e l i a b i l i t y for a class i vehicle, $ I t i s assumed that the same number of trips are taken on each of alternative alignments under consideration. In cases where the assumption of a linear growth of t r a f f i c cannot be made, user operating and time costs may be computed for each individual year, then discounted to the present time and converted into annual cost as follows: j i=l where 61 atv\ = annual t r a f f i c volume during year i doc^ = direct operating cost during year i utc^ = user time cost during year i and PWE\ = present worth factor for year i Maintenance costs, the third 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 alternative, $/mile By combining the previous equations into a single equation for total annual cost: _ J TAC = CRF (cc + ac + pc + dc + rc + lc) + EAT T £ \ + t r c i + oc. + mtc. + dpc. + (t.) (tc.) + (tur.) + (mi) (mc) It i s recognized that tools discussed above are only a part of the analytical evaluation and other procedure are needed for the planning process such as scenic view and measurement of public interest. Until such procedures are developed the decision-maker must rely on less sophisticated techniques. 62 Appendix 2 EFFECTIVE ENGINE POWER The manufacturers of motor vehicles run extensive tests to determine the performance of their engine. Usually those tests are performed under the following stand£--d atmospheric conditions extablished by the SAE (Society of Automotive Engineers): temperature, T Q = 520 degree Rankine and barometric pressure, B Q = 29.92 inches of Hg (dry a i r ) . From the results 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 plotted against engine RPM. The term bare engine refers to an engine stripped of a l l accessory equipment not essential 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 effective power (P) developed under the present set of atmospheric conditions. The effective power developed for diesel engines can be calculated from P 8 8 P o ( B " V To B 0 T where P D = engine power under SAE standards ' B = prevailing barometric pressure under the hood 63 B v = part i a l pressure of water vapor i n the a i r i n inches of Hg ( i t i s usually neglected for practical case) T = ambient temperature in deg Rankine (air-intake temperature). Only diesel engine i s considered i n the program. Since barometric pressure decreases about 1 inch of Hg per 1000 f t increase i n altitude i t can be seen from the above expression that power losses due to atmospheric conditions can become substantial and should not be neglected. Table A2.1 gives the average barometric pressures for various altitudes above sea level. Altitude above sea level, f t Barometric pressure, in. Hg Altitude above sea level, f t Barometric pressure, in. 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 for various altitudes above sea level Installation and accessory losses (Pa) vary according to size and make of accessory used. For general purposes, an engine i s derated of 10% for normal accessories to determine net HP at the flywheel (Pe). The available engine torque (Me) i s related 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. 6 5 Appendix 3 GRADE RESISTANCE The resistance offered to movement of 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 vehicle through a height equal to that attained because of plus grade. The value of this resistance i s given by Rg = W sin 0 center of gravity Figure A3.1 Grade resistance of a truck 66 Appendix 4 ROLLING RESISTANCE There are many variables affecting r o l l i n g resistance such as the kind and size of ti r e s , inflation pressure, t i r e temperature, type of roadway surface, road speed of the vehicle and, the most important of a l l , the gross vehicle weight on the tir e s . The rol l i n g resistance (Rr) i s made up of the following elements: 1. Work to compress and deflect the roadway surface. 2. Work required to flex 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 inside of the t i r e , and outside a i r resistance. For general use, i t i s necessary to determine by theoritical or experimental work the percentage of the total Rr contributed by each of these elements. However what i s needed, i n this model, i s a good average Rr for typical vehicles and road surfaces. The information published to date indicates approximations of the r o l l i n g resistance that seem acceptable. Paterson et a l . (1970) used the following equation for the r o l l i n g resistance of trucks on gravel road Rr = (15.1 +0.088 V) W 1000 where Rr = r o l l i n g resistance, lb 67 V = vehicle speed, mph W = gross vehicle weight, lb. This approximation should be accurate enough and i s adopted in this model. The SAE recommends the following formula for paved surface Rr = (7.6 + 0.09 V) W . 1000 Appendix 5 AERODYNAMIC RESISTANCE The following three factors combine to account for the total a i r resistance: 1. Drag resistance as related to the outside shape and size of the vehicle. 2. The resistance to the a i r offered by surface of the body. 3. Flow of a i r through the vehicle for purposes of ventilating and cooling. The greatest single factor i n a i r resistance i s the projected frontal area of the vehicle. The formula for a i r resistance involves also a factor for the weight of the a i r , the drag and skin f r i c t i o n of the vehicle (Ca). From investigation conducted by Flynn and Kyropoulos (1962) and tests con-ducted at GMC (General Motors Corp.) the a i r drag coefficient (Ca) of a tractor-trailer combination i s in 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, lb A Ca • a i r drag coefficient, dimensionless 2 projected frontal area, f t V r speed of the vehicle relative to the a i r , mph. 69 This formula i s adopted in the model without consideration for wind velocity. Figure A5.1 shows the approximate frontal areas for loaded and empty trucks. These data are based on f i e l d measurements by Byrne et a l . (1970). |_ , ! _1 , , . | 20 40 60 80 100 120 140 Projected frontal area, f t Figure A5.1 Projected frontal area of loaded and empty trucks 70 Appendix 6 CURVE RESISTANCE In most vehicle performance studies curve resistance is not included. Tests at GMC have shown that curve resistance i s very high for certain tractor-trailer combinations. An empirical formula i s given which approxi-mates the curve resistance (Rc) of a 76000 lb tandem tractor-tandem t r a i l e r combination Rc = curve resistance, lb V = vehicle speed, mph R = radius of curve, f t E = Superelevation of curve, f t / f t W = gross vehicle weight, lb. This resistance i s subtracted from the available rimpull i n the model. where 71 Appendix 7 INERTIA RESISTANCE Probably the most important consideration in vehicle performance prediction i s acceleration. This i s d i f f i c u l t to calculate since the net force driving the vehicle not only accelerates the vehicle but also accelerates the rotating components encountered throughout the drive train. Rotating inertias include the engine flywheel, hydraulic torque converter, inertias associated with the driveshaft and axles, and with the wheels and tires of the vehicle. The apparent increase i n mass may be expressed as a mass factor. The mass factor i s defined as being equal to 1 plus the ratio of equivalent i n e r t i a to the gross vehicle weight. A good approximation to the mass factor i s (Ordorica, 1965) 2 7 = 1.04 + (0.05 X Reduction) . This approximation i s adopted i n the model. Appendix 8 NOMOGRAPHS ON ENGINE BRAKE DEVICE CD > i M SINGLE AXLE — =! 3 TO H-3 (D cr CD O O 3 r+ H r+ & CD co CD s TO H-3 CD o o 8 8 8 8 00 I • • • • I • . , • I . • . i I i . , , i i | n i . l 1 I i • • • I I i . I I I I I i I i I I 11 i J1111111 l l 111 111 111 GROSS VEHICLE WEIGHT.THOUSANDS OF POUN03 \ (X ENGINE 1 1 1 CO (Tt < < < < OP <n co ^ DUAL AXLE o 9 . CO TJ CD CD a o V* t--o o ^ • - \ P TURNING LINE o 8-CO '\5 CONCRETE OR ASPHALT T PER CENT GRADE , ! [ — , f . J ( | . ,. 1, 1, 1,1,1,1 __! GRAVEL OR HARD PACKEO DIRT <3 DESCENT SPEEO" MPM-95 SQ FT VAN • *» I C * if* OO O O I O O w» * ' r 4 f r L T Vw T wHtH . f t H . i t . 111 t — | — s s s J s ° " * OE SCENT SPEED - M P M- TANKERS . LOG RIGS > 00 a CD CO o fD 3 rt co (D <D a O O C-i P> o 8-CO 3 TO H -3 (D CT* H s-O o 3 rt 8 ^ I I L L I I I U U I U O I L. i _Li.j..i_i.l 11 n IniilimJ G R O S S V E H I C L E . 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 ENGINE SINGLE AXLE DUAL AXLE i l . M M i l u, VI S SS S S SS SS I ' \ \ I 1 S I PER CENT GRADE-TURNING LINE C O N C R E T E OR A S P H A L T O ffi -# t -t 1 i ' I H - r W r V r V C R A V E L O R HARD P A C K E D DIRT 3 ca CD 3 TO £? CD D E S C E N T S P E E D " M P H " 95 SO f T VAN • i f -r1 - rWr r |tttljtt H | H -HfH-H-f - t - ) - f - f -r S 6 D E S C E N T S P E E D - M P H - " J A N K E R S , LOG RIGS •s fl> o o o o o l - i . * . . . i , . i . J . _ _ , i , . i . i l l - - i i i i U - - - U - l - i i l J ^ CO GROSS -VEHICLE WEIGHT, THOUSANDS OF POUNDS i ^ \ TURNING LINE I CONCRETE OR ASPHALT I - ~ tM A t » 0 l " J < B O * CTl CO O » ». !< » 5 N ; i ; j GRAVt" L OK HARD PACKED DIRT I DESCENT S»EED " M PH - 95 SO FT VAN o o o o jo 5 o> * _» |Jf^Uw|4H|Hi|jtfftf4+f+-|-+--r-t-H—| \ \-O O o O 1 O v DF SCENT SPEED - M HH- TANKERS , LOG RI<_S Appendix 9 ANALYSIS OF VARIANCE A9.1 Travel empty units times^\. (minutes ) \ . 181 101 84 179 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 59.03 307.52 61.50 note: Unit 130 was excluded because only one t r i p was observed. Table A9.1 Observed times for travel empty 77 H o : V181 ~ y101 " y84 ~ y179 : at least two of the means are not equal a=0.05 c r i t i c a l region F > 3.20 Source of variations SS DF MS Computed F Columns means 100.90 3 33.63 5.5 Error 103.98 17 6.12 Total 204.88 20 Table A9.2 Analysis of variance for travel empty Conclusion: reject H 78 A9.2 Travel loaded >v units timesN. (minutes^v 181 101 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 64.69 66.85 66.07 63.90 Total Mean 549.23 68.65 290.36 72.59 286.73 71.68 279.40 69.85 217.12 72.37 Table A9.3 Observed times for travel loaded H o : W181 = *101 = w84 = v179 = v130 : at least two of the means are not equal cc = 0.05 c r i t i c a l region F > 2.93 79 Source of variations SS DF MS Computed F Columns means 62.47 4 15.62 .65 Error 431.28 18 23.99 Total 493.75 22 Table A9.4 Analysis of variance, for travel loaded Conclusion: Accept H 80 Appendix 10 TESTING FOR SIMILARITY OF SLOPES A10.1 Travel loaded Actual Predicted Actual Predicted Actual Predicted 6.677 6.00 24.357 25.63 49.920 48.22 9.395 8.94 30.145 31.59 53.186 50.54 11.850 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 Table A10.1 Cumulative actual and predicted times for each section for travel loaded A conditioned regression was fitted by imposing the restriction that the intercept is zero. The coefficient of regression (b^) obtained was 1.0219. The following test was then performed: . V b i " 1  H l : b l * 1 ^TRAf " b l - g l = 1-0219 - 1 = 2.408 1 B d s.e.O^) 0.0091 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 Predicted Actual Predicted 3.016 2.35 29.490 21.35 42.985 33.27 7.776 5.88 31.446 23.03 44.653 34.75 9.504 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 for each section for travel empty As for travel loaded a conditioned regression was fi t t e d by imposing the restriction that the intercept i s zero. The coefficient of regression (b-^ ) obtained was 1.2896. The following test was then performed: V b i = 1 T 18df b l " 31 = 1.2896 - 1 = 28.143 s . e . C b . ^ 0.0103 which i s significant at the level of 0,05. This implies that the hypothesis of common slope should be rejected. 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 at the beginning of the output. 2. The next card i s for the total number of gears i.e. main and auxil iary transmissions combined. For example a manual transmission with the following gear ratios gives 15 gear positions. 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 UD 2.09 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 positions. 3. The next card(s) i s (are) for the gear ratios i n decreasing order i.e. as shown i n 2. FORMAT(10F4.2). 4. The rear axle ratio 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 vehicle weight i n pounds, and the length of log (38 or 48 f t ) . FORMAT(F3.1,2F6.0,F2.0). 6. The next card read determines i f the program deals with a manual or a torque-converter transmission. FORMAT(ll). 0 i s entered for manual transmission 1 for torque converter when torque ratios, speed ratios, 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 or 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 idle RPM, and the barometric pressure due to altitude. If two (2) i s encountered see 11. FORMAT(I2,F4.0,F4.2) 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 for the number of ratios (NRATIO) input. If 0 was encountered GO TO 13. F0RMAT(l2). 10. The following NRATIO cards should contain the speed ratios, torque ratios, and K-factors of the torque converter. GO TO 13. F0RMAT(2F4.2, F5.2). 11. If a 2 was encountered the program expects to read the number (M) of RPM versus torque to the exit of the torque converter input, and the idle 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) of maximum descent speed points are input (when dealing with engine brake). If 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 controlled by surface conditions or regulation, and i f the truck are radio controlled or 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 of the section - section length i n feet - surface type (1 = paved, 2 = gravel) 86 - coefficient of f r i c t i o n - curve radius i n feet - superelevation i n feet/foot - distance between driver's eye and backslope i n feet - the grade for the loaded direction (+ = adverse, - = favorable). For the empty direction 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 for travel empty and loaded. FORMAT(13) 18. The following NSTOP cards determine, for travel 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 for travel empty. 20. The next card contains the following control data: i n i t i a l velocity loaded, i n i t i a l velocity empty, length of the subsection i n feet (ds), and the output level desired (1, or 2). The value ds should be smaller than or equal to the smallest section length. FORMAT(3F3.0,11). 21. If the output level 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 level i s 2, the following card(s) contain(s) the number of the section where output i s desired. F0RMAT(20l4). All.2 Computation time requirements The amount of computer time required for 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 for a ds of 100 feet, a level of output of 1, and 33 miles of road (one way). For level of output 2, the time i s increase by 3 times (output for 39 sections from 142 sections was requested). The computer time w i l l also increase with the length of the course. All.3 FORTRAN l i s t i n g of computer program (~- : $ C O M P I L E ~~ ~ i C T R U C < P E R F O R M A N C E S I M U L A T I O N O V E R A D E F I N E D P .OAO I C * * * < : * * * * * * * * * * * * * * * * * > { : * * * * * * i > t * * * * * * * * * * * * * * * . * * > £ * 1 c*** M A I N P R O G R A M ! ' 1 L O G I C A L A C C E L , T R A C E \ — 2_ I N T E G E R R C . S T Y P F . O U T L E V . S T A O U T . G ' 3 R E A L 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 , l N H P f J , M A X H P . 4 R£AL_LAS.I.i N R I V P , M A X V L E , M A X V , L T I M , L S T T I M , L A V 5 D I M E N S I O N G R P O S ( 3 0 ) , E R P M ( 4 0 I , B E H P ( 4 0 ) . N E T O R ( 4 0 ) , V M P H ( 2 0 0 ) , R I M P ( 2 0 0 11 , R S H I F T ( 3 0 ) , S H [ F T V ( 3 0 ) , G R A ( 2 5 ) , M D E S L ( 2 5 ) , M D E S E ( 2 5 ) fS D I M E N S I O N 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 D I M E N S I O N M A X V L E t 5 0 0 , 2 ) , M A X S P E f 5 0 0 ) , M A X S P L ( 5 0 0 ) , V O ( 2 ) 8 D I M E N S I O N I N F O ) . ( 2 0 ) , I N F 0 2 ( 2 0 ) , I N F 0 3 ( ' 2 0 ) , I N F 0 6 I 2 0 ) 9. D I M E N S I O N I S T O P ( 3 0 , 2 ) , A T ( 3 0 , 2 I . W A I T ( 3 0 , 2 ) . S T A O U T I 5 0 0 ) , I N F 0 4 ( I 2 , 3 0 ) 1, I N F 3 5 I 2 2 , 3 0 ) 10 n E Q U I V A L E N C E ( V A X S P L ( 1 ) , M A X V L E ( 1 , 1 ) ) » ( M A X S P E ( 1 ) , M A X V L E ( 1 , 2 ) ) E 01) W A L E N C E ( B E H P , N E T O R ) 12 D O U B L E P R E C I S I O N A N 13 C O M M O N / V A R / X ( 2 0 0 ) , Y ( 2 0 0 ) , N P , N D 14 C O M M P M / C O E F / A N I 3 0 , 3 ) , I I 15 C O M M C N / R O A O / N ( 5 0 0 ) , 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 1 M ( 5 0 0 ) , G R A O ( 5 0 0 ) T R U C K D A T A " R E P A R A T I O N T O B E U S E D - I N M O T I O N S I M U L A T I O N I N P U T D A T A F O R T R U C K D A T A P R E P A R A T I O N c B = B AR O M E T R I C P R E S S U R E ( I N O F HG) F O R P R E S E N T A I T I T U D E c B E H P = B R U T E N G I N E H O R S E P O W E R c E R P t = E N G I N E R F M c E V W = E M P T Y V E H I C L E W E I G H T c GRA=F A V O R A B L E G R A D E I N X ( T H E E N G I N E B R A K E D E V I C E I S R E P P E ^ F N T F D RY c 3 R A V S . M D E S G A N D M D E S L ) c G R P O S = G E A R P O S I T I O N R A T I O S c L V W = L 0 AD E D V E H I C L E W E I G H T c M = N U M B ER O F H P V S R P M I N P U T c M D E S E = M A X I M U M D E S C E N T S P E E D E M P T Y c M D E S L = MA X I MUM 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 OF G R A F O P T H I S c P A R T I C U L A R E N G I N E B R A K E D E V I C E c N E B R A K = N U M B E R O F E N G I N E B R A K E P O I N T S I N P U T ( T O B E U S E D I N R O A n c D A T A P R E P A R A T I O N ) c N E T O R = .NET E N G I N E T O R Q U E c N G E A R = N U M B E R C F G E A R S c RA D = R D L L I N G R A D I U S c R A X L E = R c A R A X L E R A T I O c R P M I D = I O L E R F M 16 R E A D ! 5 . 2 0 0 2 ) ( I N F O H I ) , 1 = 1 , 2 0 ) 17 R E A D ! 5 , 2 0 0 2 1 ( I N F 0 2 I I ) , 1 = 1 , 2 0 ) 18 R E A ) ( 5 , 2 0 0 2 ) ( I N F Q 3 ( I ) , 1 = 1 , 2 0 ) 1 9 R E A D ! 5 , 2 0 0 2 ) ( I N F 0 6 ( I ) . 1 = 1 , 2 0 ) 20 2002 F O R M A T ( 2 0 A 4 ) 21 R E A 0 ( 5 , 2 0 0 4 ) N G E AR ? ? ...2004 F O R M A T ( 1 2 ) 23 R E A ) ( 5 , 2 0 0 5 ) ( G R P O S ( I ) , 1 = 1 , N G E A R I '24 2005 F 0 R M A T Q 0 F 4 . 2 ) ?"? R E A D ! 5 . 2 0 0 6 1 R A X L E 26 2006 F C R ' I A T ( F 4 • 2 I 27 R E A D ! 5 , 2 0 0 7 ) R AD , E V W , 1 . V W , L O G 28 2007 F 0 R M A T ( F 3 . 1 , 2 F 6 . 0 , F 2 . 0 ) C D E T h R M I N E I F D E A L I N G W I T H T O R Q U E C O N V E R T E R 29 R E A C H 5 , 1 0 0 0 ) K T V ^0 1000 F O R M A T ( 1 1 ) . ; 89 C I F K T = 0 D E A L I N G W I T H M A N U A L T R A N S M I S S I O N C I F K T = 1 D E A L I N G W I T H T O R Q U E C O N V E R T E R A N D T O R Q U E R A T I O S , S P E E D C R A T I O S , A N D K - F A C TO R S A P. E A V A I L A B L E C I F K T = 2 D E A L I N G W I T H T O R Q U E C O N V E R T E R A N D O N L Y O U T P U T T O R Q U E C A N D O U T P U T R P M T O T H E T O F O U E C O N V F R T E R A R E A V A I L A B L E C. I N T H A T C A S E T H E I N P U T I S A S S U M E D TO H A V E B E E N C O R R E C T E D C F O R A L T I T U D E 3 1 I F ( K T . E Q . 2 ) G O T O 9 9 0 R E A T I 5 . 2 0 C 3 I M . P P M I D . B P 3 3 2 0 0 8 F O R M A T ! I 2 , F 4 . C , F 4 . 2 1 — : 3 4 2 0 0 9 , REACH 5 , 2 0 0 9 ) t E R F M I I ) , B E H P ( I ) , 1 = 1 , M l F O R M 4 T ( F 4 . 0 . F 5 . 1 ) 3 6 M A X H P - ^ E H P ( M ) 17... C F I N O I N G O F N E T O R F O R P R E S E N T A L T I T U D E A N D A T M O S P H E R I C D O ? 1 1 = 1 , M C O N D I T I O N S 3 8 P O - ^ E H P < I ) 3 9 H P O = P D ( B P , P O ) 4 0 N H P . l = H P r > *.,<» 4 1 4 2 2 1 C N E T O R ( I > = 5 2 5 2 . * N H P D / E R P M ( I ) I F I K T . E Q . O I G O T O 9 9 8 C O M P I J T F E N G I M F K - F A C T O R 4 3 D O 9 9 7 1 = 1 , * 4 4 4 5 9 9 7 E K F A C I I I = E R P M ( I ) / S Q R T ( N E T O R ( I ) ) C O N T I N U E C C N R A T I 0 = N U M B E R O F P O I N T S S P R = S P E E D R 4 T I 0 c T O R OR = T O P . 0 1 ) c R A T I O c C K F A C - C C N V E R T E R K - F A C T O R 4 6 c P R E F E R A B L E T O G E T A S M A N Y N R A T I O T H A N P P M V S H P P O I N T S R E A " ) ( 5 . 1 . 0 0 1 I N R A T I O 4 7 1 0 0 1 F C R ' 1 A T ( I 2 I 4 8 4 9 1 0 0 ? R E A D ! 5 , 1 0 0 2 ) I S P R ( I ) , T O R O R ( I ) , C K F A C < I ) , I =' , N P A T * 0 ) F a R ^ 4 T ( ? F 4 . 2 . F 5 . ? ) 5 0 c c L I N E A R I N T E R P C L AT I O N T O F I N D T H E O U T P U T R P M A N D O U T P U T T O R Q U E C O N V E R T E R E X I T M M = M - 1 T O R Q U F TO T H E 5 1 DO 9 3 6 1 =1 , N R A T I O . 5 2 D O 9 9 5 J = 1 , M M 5 3 • . , I F ( C < F A C ( . I ) , G E . E K F A C ( 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 QOL 5 4 5 5 5 6 9 9 4 D E K F A C = E K F A C ( J + 1 ) - E K F A C ( J ) D E R » M = F R P M ( . l + 1 1 - E R P M i . l ) 5 7 S L O ° E = Q E R P M / D F K F A C —.— : 5 8 C X R P - 1 = E R P M ( J ) + ( S L 0 P E * ( C K F A C ( I ) - E K F A C ( J I ) 1 _ E . I N T 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 5 9 6 0 D T O * = N E T C R < J * 1 > - N E T O R ( J ) • S L 0 ° E = D T 0 P 7 D E R P M 6 1 X T l ' R = N F T G P . ( J ) + ( S L O P E * ( X R ° M - E P . PM ( J ) 1 ) 6 2 9 9 5 C O N T I N U E 6 3 .... C O U T ° J T R P M T O T H E T O R Q U E C O N V E R T E R E X I T E R P ^ t I ) = S P R ( I ) * X R P M 6 4 6 5 C 9 9 6 O U T P U T T O R Q U E T C T H E T O R Q U E C O N V E R T E R E X I T N E T 1 R ( I ) = N E T O R ( 1 1 * T O R Q R ( I ) C C 1 N T I N U F 6 6 6 7 A a .... 9 9 0 3 0 0 0 I F ( K T . N E . 2 ) G 0 T 0 9 9 3 R E A M 5 , 3 0 0 0 ) M , R P M I D -£CMAiJ[ji,F4. 0 ) 6 9 7 0 • ^ 71 9 9 8 R E A K 5 . 2 C C 9 I ( E R P M f I ) , N E T O R ( L I , I = 1 , M | R E A T I 5 , 2 0 0 4 ) N E B R A K I F ( N F 3 R A K - F 0 . C l r , n T 0 2 0 7 2 R E A C H 5 , 2 0 0 1 M G R A t I I , M D E S L ( I I » M D E S E t I 1 , I = 1 , N E B R A K I 7 3 2 0 0 1 C F 0 R 1 A T ( F 3 . 2 , 2 F 4 , 1 I R I M P J L L A N D S H I F T I N G P O I N T C O M P U T A T I O N F O R S M A L L S P E E D I N C R E M E N T T O P S P = T Q P S P E E D I N H I G H E S T G E A R 7 4 2 0 T O P S ° = t E R P M ( M ) * 3 o l 4 1 5 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 ) . 7 5 1 = 1 7 6 S P = . 5 7 7 C K = l S H I = T V ( I l = S H I F T I N G V E L O C I T Y I N G E A R I : 1 = 1 . 2 . . . N G E A R C R S H I F T t I ) = R I M P U L L A T S H I F T I N G E A R I ; I = 1 , 2 . o . N G E A R 7 8 S H I F T V ( 1 ) = 0 . 7 9 R S H I F T t 1 l = ( N F T O R t I I * G R P O S ( I I * R A X I . E * „ 3 5 * 3 . 2 . I / R A O S O 2 G R 1 = G R P 0 S ( I ) 8 1 C G R 2 = G R P O S t I + 1 I E N G I N E R P M I N 0 F A R I A N D 1 + 1 8 2 3 R P M . l = ( S P * 5 2 8 0 . * ! 2 . * P . A X L E * G R l ) / ( 6 0 . * 2 „ * 3 . 3 . 4 1 5 9 * R AD I 8 3 R P M 2 = ( S P ^ 5 2 B 0 . * 1 2 o * R A X L E * G R 2 ) / ( 6 0 o * 2 o * 3 < > 1 4 1 5 9 * R A D ) 8 4 I F t R O M I . L T . R P M I O l G O T O 1 4 8 5 C M M = 1 - 1 L I Mr A R I N T E R P O L A T I O N B E T W E E N I N P U T P O I N T S 8 6 D O 4 .1=1 . M M 8 7 I F t M 2 . G T . E R F M ( J I „ A N D „ R P M 2 « , L E . E R P M ( J + 1 ) ) G O T O 5 8 8 G O T O 6 8 9 5 D T O < = N F T n R ( .1+3 ) - N F T O R (.] ) 9 0 D R P ' 1 = E F . P M ( J + l l - E R P M < J I 9 1 S L O P E = O T Q R / D R P M 9 2 X T O R = N F T O R ( .1) + ( S L O P E * ( R P M 2 - E R P M ( J ) ) ) 9 3 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 9 4 6 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 1 ) G O T O 7 9 5 G O T O 4 9 6 7 D T O R = N E T O R U + 3. I - N E T O R ( J I 9 7 D P P M = E R P M ( J + l l - E R P M ( J 1 9 8 S L O P E = D T O R / D P . P M 9 9 X T O ^ = N E T O R ( J 1 + ( S L O P E * ( R P M l - E R . P M ( J I I ) 1 0 0 R I M P 1 = ( X T 0 R * G R 1 * R A X L E * . 8 5 * 1 2 „ l / R A D 1 0 1 4 C O N T I N U E 1 0 2 G O T O 1 5 1 0 3 1 4 S P = S ° + o 5 1 0 4 R I M P 1 = 0 . 1 0 5 R I M P 2 = 0 o 1 0 6 G O T O 3 1 0 7 1 5 I F U P M 1 . G E . E R P M ( M ) ) G 0 T 0 9 1 0 8 C C I F ( R I M P 1 . L T . R I M F 2 ) G 0 T 0 8 V M P H t K I = V E L O C I T Y I N M P H ; V M P H = 0 . , o 5 , 1 . . . . T O P S P R I M P t K ) = R I M P U L L A V A I L A B L E A T V E L O C I T Y V M P H ( K ) 1 0 9 V M P H ( K ) = S P 1 1 0 R I M P t K I = R I M P 1 1 1 1 A = R I M P 1 1 1 2 B = R I M P 2 1 1 3 K = K + 1 114 S P = S P + . 5 1 1 5 C C G O T O 3 I F R I M P U L L V S M P H C U R V E S F O R T W O 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 T O G 1 V E R N F D R P M E N T E R H E R E 1 1 6 8 V M P H ( K ) = S P 1 1 7 R I M P I K ) = R I M P 2 1 1 8 S L 1 = ( R I M P 1 - A ) / ( V M P H t K l - V M P H I K - l I 1 1 1 9 C S L 2 = ( R I M P 2 - 3 ) / ( V M P H ( K ) - V M P H ( K - l I I R I M " J L L A T T H E S H I F T I N G P O I N T J U S T B E F O R E S H I F T I N G 1 2 0 R S H I F T t I + 1 I = ( ( A * V M P H ( K I - R I M P l * V M P H ( K - 1 I ) / ( R I M P 1 - A > - ( B * V M P H ( K ) ) / (P. I ( i 1 I 121 122 123 124 _ _ .. 91 1MP2-B )+ <R IMP2*VMPH(K-1) (/(RIMP2-B ) ) / ( ( S L 2 - S L 1 ) / ( S L 1 * S L 2 ) 1 SHI F TV ( I + 1 ) = ( (VMPH<K-1 )MRIMP1-RIMP2)-VMP H(K)*(A-B) )/(VMPHIK l-VMPH 1 I K - 1 ) ) 1 / ( S L 1 - S L 2 ) K=KU SP=SP+.5 GOTO i o r 125 C 9 • GOVERNED R P M CICT AT E JUMP TO NEXT GEAR ENTER HERE SHI^TVI 1 + 1 ) = < ERPMIM )*3ol4159*RAD*60.*2. ) / ( 5?80.*12.*PAXLE*GPPOS (I ) 1 ) 126 127 C 10 RIMPULL AT THE SHIFTING POINT JUST BEFORE SHIFTING RSHIF T( I + 1 ) = ( NETOP.I M)*GRPOS(I)*RAXLE*.8 5*12.)/RAD I = I M 128 129 C IF1 I+-1.LE.NCE AR 1G0T0 2 IF IM LAST GEAP FIND RIMPULL FROM SHIFTING POINT TO TOP SPFED NDSo=SP*?„ 130 131 13? NSP=T0PSP7.5 DO 11 JJ=NDSP,NSP n s p=.u 133 134 135 SP=DSP/2. RPM1=<SP*5280.*12.*GRP0S< NGE AR ) *P. A XL E) /(6 0.*'.*3.14159*PAD) DO 1? .1=1 .MM 136 137 C IF(RPM1.GT.5RPM(J).AND. PPrvl.LE.ERPM(J + l ) ) G O T O 13 GOTO 1 2 t IN"4R INTFRPCI AT ION 138 139 1 4 0 13 DT0R=NET0R(J+1) -NETOR {J.) DRPM=ERPM(J+1)-ERPM(J) SLOPE=DT0R/ORPM 141 142 143 XTO:< = NETOR ( J ) + ( SLOPE* (RPM1-ERPM( J )) ) RIMPI =(XT0R*GRPOS (N GE AR ) * R AXL E*. 85*1 2. ) /P. AD VMPHt K) = SP 144 145 146 RIMPIK)=RIMP1 K=K+1 GOTO 11 147 148 149 12 11 CONTINUE CONTINUE KMAX=K-1 150 C C FITTING OF A SECOND DEGREE POLYNOMIAL FOR RIMPULL BETWEEN EACH GFAR DATA PREPARATION BEFORE CALLING SUBROUTINE FIT K = l 151 152 C DO 19 II=1,NGEAR J = l X(1)=SHIFTING VELOCITY 153 1 5 4 . C Y(1)=RIMPULL JUST AFTER SHIFTING I F ( I I . E O . l ) Y ( J ) = R S H I F T ( I I ) I F ( I t . E O . l ) X ( J ) = S H I F T V ( I I ) 155 1 5 6 c IF< II .EC).1 (GOTO 23 X(JI = SHIFTVII I) RPM AT THE SHIFTING VELOCITY 1 5 7 158 c R P M = X ( J ) * 5 2 3 0 „ * 1 2 . * R A X L E * G R P O S ( I I)/(60.*2.*RAD*3. 14159) LINEAR INTERPOLATION TO FIND RIMPULL JUST AFTER SHIFTING DO 13 1=1.MM 1 5 9 160 161 17 IF(RPM.GT.EPFM( I ).AND.RPM.LE.ERPM( 1 + 1))GOTO 17 GOTO 1 8 DT0}=NFT0R(I+1)-NETOR(I) 162 163 164 . ORPn=ERPM(1+1 l-ERPMII I S L O°E=DTOR/ORPM XTO^= NFT.QS.(_I..l+i_SLQP E* ( RPM-ERPMI I ) ) ) 165 1 6 6 167 18 Y(J) = XTOR*GRPOS(I I ) * R A X L E *. 35 *12 . / R AD CONTINUE IF(II+1.GT.NCFARISHIFTVI I 1 + 1 )=VMPH(KMAX1 — — — : g? 1 6 8 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 169 2 3 I F ( V M P H ( K ) . G E . S HI FT V< I I + l ) . G O T O 2 2 1 7 0 J = J + 1 1 7 1 Y ( J ) = R I M P ( K ) 1 7 2 X ( J I = V M P H ( K ) \ 1 1 3 K=K+1 1 7 4 GOTO 2 3 1 7 5 22 J = J+1 1 7 6 NP= I 1 7 7 Y ( J ) = R S H I F T ( I I + l l 1 7 8 X ( J ) = S H I F T V ( I I + l ) -129, LU2£J 1 8 0 I F ( ? \ | P . E Q . 2 ) N D = 1 181 C A L L F I T 182 19 C O N T I N U E 1 8 3 W R I T E ( 6 , 2 0 1 2 ) 1 8 4 2 0 1 2 F O R M A T ( * 1 • , ' T R U C K P E R F O R M A N C E S I M U L A T I O N ' ) 1 8 5 WRITE I 6 . ;-:01 3 ) 1 8 6 201 3 FORMAT (1 X * * * * ^ f t * * * > i i , / / / ) 1 8 7 W R I T E ( 6 , 2 0 1 4 ) ( I N F O ! ( I ) , 1 = 1 , 2 0 ) 1 8 8 WRITE ( 6 , 2 0 1 4 ) ( I N F 0 2 I I ) , 1 = 1 , 2 0 ) 1 8 9 W R I T E ( 6 , 2 0 1 4 ) < I N F 0 3 ( I ) , 1 = 1 , 2 0 . 1 9 0 WRITE I 6 , 2 0 1 4 ) ( I N F 0 6 ( I ) , 1 = 1 , 2 0 ) 1 9 1 2 0 1 4 F O R M A T ( 1 X . 2 0 A 4 )  192 I F 1 K T . E Q . 2 ) G O T O 8 80 1 9 3 WRITE I 6 , 2 0 1 5 ) MA X H P , EP. PM( M ) 1 9 4 2 0 1 5 F O R M A T ( I P X . F 5 . 0 . 3 X . ' H O R S E P O W E R A T • , 3 X , F 6 . 0 , 3 X , ' F P M ( G O V E R N E D R P M ) ' 1 ) 1 9 5 8 8 0 W R I T E ( 6 , 2 0 1 6 ) E V V > , L V W , L 0 G 1 9 6 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 V E H I C L E WEIGHT 1 = ' , F 1 0 . 0 , 3 X , • L E N G T H OF L O G S = ' , F 6 . 0 , 3 X , ' F E E T ' ) 1 9 7 I F K T . E Q . 2 1 G 0 T 0 8 6 1 1 9 8 WRITE ( 6 . 2 0 1 9 ) BP 1 9 9 2 0 1 9 FOR 1 A T I 1 0 X , « ATMOSPHER IC C O N D I T I O N S : B A R O M E T R I C P R E S S U R E ^ , F P . . 2 , ^ X , 1 * OETE R MI NED FROM 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 ' ) 2 0 0 8 8 1 W R I T E ( 6 . 2 0 1 7 ) R A H 2 0 1 2 0 1 7 F 0 R M 4 T Q 0 X , • R O L L I N G R A D I U S = ' , F 7 . 1 , 3 X , ' I N C H E S ' ) 2 0 2 W R I T E ( 6 , 2 0 1 8 ) R A X L E 2 0 3 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 ) ' 2 0 4 W R I T E ( 6 , 2 0 2 2 ) 2 0 5 2 0 2 2 FORMA T ( / 1 O X , ' G F A R RAT 1 0 • , 2 0 X , • S H I FT ING V E L O C I T Y • / , 4 4 X , * C O M P U T E D • ) 2 0 6 • W R I T E ( 6 , 2 0 2 3 ) ( G F P O S ( I ) , S H I F T V ( ! ) , I = 1 , M G E A R )  2 0 7 2 0 2 3 F 0 R M A T U 0 X . F 7 . 2 , 2 3 X . F 1 0 . 2 ) C*** ROAO DATA P R E P A R A T I O N C*** S I M U L A T I O N OF KNOWLEDGE AND J U D G E M E N T OF T H E _ D R I V E R C * * * C O M P J T A T I O N OF 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 CA N G = C E N T R A L A N G L E C R A O = C U R V E . R A C I U S C E = S U ( , S R 5 L E V A T I O N , F T / F T C GRAD= G R 4 D E IN F T / F T J E LM=JI S T A N C E BETWEEN D R I V E R ' S EYE AND BACK S L O P E C M A X S P L = MAXIM!JM S P E E D L O A D E D C M A X S P E = M A X I M U M S P E E D E M P T Y C M C S P ^ M A X I M U M C U R V E S P E E D . MPH 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 C O N D I T I O N S C N=N'JM3ER OF THE S E C T I O N S _C ?JS..EC= NUMBER OF SECT T I N S C R C = I F 1 : R A D I O C O N T R O L L E D C 0 : NO R A D I O CONTROL OR G E N E R A L P U B L I C HAS A C C E S S - C S E C L = S E C T i r N I F N G T H . F T  r C S D = S I G H T D I S T A N C E M E A S U R E D A R O U N D T H E C U R V E C S M = S T A N D S F O R S M A L L M A S U S E D I N T H E T E X T • c S T Y P E = T Y P E O F S U R F A C E ( 1 = P A V E D , 2 = G R A V E L ) ! c U S = C O E F F I C I E N T O F F R I C T I O N i i 208 R E A O t 5 , 2 0 1 0 ) N S E C , M P S P , P . C \ ?09 2 0 1 0 F O R M A T ( I 4 , F 2 . 0 , 1 1 1 C R E A D R O A D D A T A O N L Y F O R L O A D E D D I R E C T I O N ; T H E G R A D E I S I N V E R S t D F O R C T R A V E L E M P T Y S P F E D L I M I T C O M P U T A T I O N 210 R E A D ! 5 , 2 0 1 1 ) < 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 2011 F O R M A T ( I 4 , F 5 . 0 , U , F 3 . 3 , F 4 . 0 , F 2 . 2 , F 2 . 0 , F 4 . ? ) C K E E P S M A L L E S T S P E E D A S M A X I M U M P E R M I S S I B L E 212 D O 30 I = 1 , N S E C 213 M A X S P L t I ) = M P S P 214 M A X S P E ( I ) = M P S 0 215 I F ( C * A D t I ) . E Q . O . ) G O T O 2 5 C S P E E D L I M I T A S C O N T R O L L E D 3 Y S I D E F R I C T I O N 2 1 6 V S F = S 3 R T C 3 2 . 1 6 * C R A D ( I ) * ( E ( I ) + U S ( I ) ) / < J . . - U S ( I ) * E < I ) ) ) 217 V S F = V S F * 3 6 0 0 . / 5 2 3 0 . 218 I F t V S F . L T . M A X S P L t I I ) M A X S P L ( I > = V S F 219 M A X S P E ( I ) = M A X S P L ( I ) c S P E F D L I M I T A S C O N T R O L L E D B Y S I G H T D I S T A N C E c S I G H T D I S T A N C E A S S U M E D T H E S A M E I N B O T H D I R E C T I O N 220 C A M G = S E C L ( I ) / C R A D ( I ) 221 T E T A = A T A N ( G R A C ( K ) ) 222 S M = C R A D < I ) * t l . - C Q S t C A N G / 2 . > ) 223 I F ( L M ( I I . L E . S M ) G O T O 2 6 224 L = ( L M ( I l - S M I / S I N ( C A N G / 2 . I 225 S D = S E C L < I ) + 2 . * L 226 G O T O 2 7 227 26 S D = 2 , * C R A D ( I ) * A R C O S ( t C R A D t I l - L M ( I ) ) / C R A D ( I ) ) 228 27 I F ( R C • E Q . 1 ) G O T O 2 3 229 V S D = ( S O R T t ( 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 * 164. 3 2 * U S ( I ) ) ) / 4 . 230 G O T O 2 9 231 2 8 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 < T 1 E T A 1 * ( U S t I H - G R A D t I ) > * S D ) ) - ( 2 . 5 * 6 4 . 3 2 * C 0 S ( T F T A ) * ( U S ( I ) + G R A D ( I ) ) ) ) / 2 232 2 9 c. % V S 0 = V S D * 3 6 0 0 . / 5 2 3 0 . 233 I F t V S D . L T . M A X S P L t I t ) M A X S P L ( I ) = V S D 234 M A X S P E ( I » = M A X S P L t I ) 235 25 I F t G R A D ( n . E O . O . J G O T D 3 0 C M A X I M U M D E S C E N T S P E E D D O W N H I L L 236 I F t N E B R A K . E Q o 0 1 G O T O 3 3 c L I N E A R I N T E R P O L A T I O N B F T W E E N E N G I N E B R A K E D A T A P O I N T S 237 I F I G ^ A D I I 1 . G T . O . ( G O T O 3 4 238 I F t G ^ A O t I ) . G T . G R A ( l ) ) G O T O 3 3 239 J = 0 240 35 J = J + 1 241 I F t J . E Q . N E B R A K ) G O T O 3 3 • 242 . I F I G * A D ( I ) . L E . G R A ( . | ) „ A N D , G R A D t I I . G T . G R A t J + U ( G O T O 3 6 243 G O T O 3 5 244 36 D G R A = A f l S t G R A t J + l ) l - A B S t G R A ( J ) ) 245 D D E S = M D F S t ( l + l l - M D E S L ( . ) ) 246 S L O f E = D D E S / D G R A 247 X D E S = H D E S L ( J > + < S L O P E * ( A B S ( G R A D I I ) 1 - A B S t G R M J ) i ) ) 248 I F t X I E S n L T . M A X S P L ( I 1 ) M A X S P L ( I ) = X D E S 249. G O T O 3 7 250 34 G R D = ( - G R A C ( I ) ) 251 .1 = 0 252 38 94 J = J+1 253 I F ( J . E Q . N E B R A K ) G O T O 3 3 -254 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 39 255 G O T O 3 3 256 39 0 G R A = A B S ( G R A ( J + l ) ) - A B S ( G R A ( J ) ) 257 D D E S = M D E S 5 ( J + 1 l - M D E S E ( J ) 258 S L 0 P E = D 0 E S / 0 G R A 259 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 ) ) ) ) 260 l F ( X Q E S . L T . M A X S P - ( I M M A X S P F ( I ) = X D E S 261 G O T O 3 7 262 33 C I F ( CA A O ( I ) . L T . O . 1 G O T O 4 0 I F N O E N G I N C B R A K E U S E C A M P 3 F L L £ V A N D E R J A G T C U R V E S F O R C D O W N H I L L S P E E D L I M I T S 263 M A X 0 E = 4 0 . ? 3 - 2 . 9 4 * < - G R A D ( I ) ) - . 1 1 * G R A D ( I I * * 2 + . 0 1 * ( - G R A D ( I ) ) * * 3 264 I F ( M A X D E , L T . M A X S P E ( I ) ) M A X S P E ( I ) = M A X D E 26 5 G O T O 3 7 266 40 M A X O E = 3 6 . 6 7 - . ! * G * A D ( I ) - . 2 2 * G R A D ( I ) * * 2 + . 0 1 * G R A D ( I ) * * 3 267 I F ( M A X D E . L T . M A X S P L ! I ) ) M A X S P L ( I ) = M A X P E C S P E E D L I M I T C O N T R O L L E D B Y S I G H T D I S T A N C E D O W N H I L L 268 37 I F I C * A O t I ) . G T . O . ) G O T O 4 1 269 I F ( ' ' J < I ) . E C . N S E O G O T O 41 270 I F t C R A O t I ) . E Q . 0 . . 4 N D . C P A Q < 1 + 1 ) , E 0 . 0 . ) S D = S E C L ( I l + S E C L ( 1 + 1 ) 271 I F t C ^ A D t 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 ) 272 41 I F ( N ( I l . E O o M S E C ) S O = S E C L ( I ) 273 I F t G ^ A D t I ) . L T . O . ( G O T O 4 2 274 V S D = ( S O R T ( I 2 o 5 * 6 4 . 3 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 . 275 V S D = V S D * 3 6 C 0 . / 5 2 3 0 . 276 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 277 G O T O • 3 0 278 42 V S D = t S O R T t t 2 . 5 * 6 4 . 3 2 * < U S ( 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 V S D = 7 S D * 3 6 0 0 . / 5 2 3 0 . 280 I F t V S D . L T . M A X S P L ( I ) ( M A X S P L ( I ) = V S D 281 30 C O N T I N U E R E A D A D M I N I S T R A T I V E A N D R E G U L A T I O N D A T A C N O S P E E D R E G U L A T I O N I S I N P U T S I N C E I T I S F E L T T H A T T H E Y A R E N O T c R E S P E C T E D B Y C R I V E R S c A T ( N S T , J T ) = 0 1 S T A N C E F R O M T H E B E G I N N I N G O F T H E S E C T I O N T H E S T O P c I S T O B E D O N E . c . D S = I N C R E M E N T I N D I S T A N C E W I T H 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 S M A L L E R c T H A N T H E S M A L L E S T S E C T I O N ) c I S T O * ( N S T , J T ) = S E C T I C N N U M B E R I N W H I C H T H E R E I S A S T O P c N S T O P = N U M B E R O F S T O P S ; A S S U M E D T H E S A M E F O R T R A V E L E M P T Y A N D L O A D E D • c ( R E M A R K S : M U S T H A V E A T L E A S T O M E S T O p L O A D E D A N D E M P T Y ; O N I Y CIM E c S T O P B Y S E C T I O N I S A C C E P T E D , I F M O R E T H A N O N F S T O P I S c N E C E S S A R Y C R E A T E A N O T H E R S E C T I O N W I T H T H E S A M E c C H A R A C T E R I S T I C S ) c N S T 0 J T = N U M 3 E R O F S T A T I O N S W H E R E O U T P U T I S R E Q U E S T E D c O U T L E V = O U T P U T L E V E L ( 1 , O R 2 ) c S T A O I l T d ) = S T A T I C N N U M B E R W H E R E O U T P U T I S R E Q U E S T E D ( R E Q U I R E D Q N t Y F O R c O U T P U T L E V E L 2 ) ( T H E P R O G R A M W I L L O U T P U T A T T H E S A M E S T A T I O N c F O R T R A V E L L O A D E D A N D E M P T Y ) c V 0 ( 1 ) = I N I T I A L V E L O C I T Y W H E N T R A V E L L I N G L O A D E D ( M P H ) c V 0 t 2 > - I N I T I A L V E L O C I T Y W H E N T R A V E L L I N G E M P T Y ( M P H ) c W A I T I N S T , J T » = W A I T I M G T I M E I N M I N U T E S 282 . R E A M 5 . 2 0 2 4 1 N S T O P 283 2024 F O R M A T ( 1 3 ) 284 DO -39 1 = 1, N S T O P 285 R E A O t 5.2 0 2 5 ) I S T O P ( I . 1 ) . A T I I , 1 ) , W A I T ( 1 , 1 ) , ( I N F 0 4 ( J , I ) , J = l , ? 2 ) 9 5 2 8 6 8 9 C O N T I N U E 2 8 7 0 0 1 0 0 1 = 1 , N S T O P 2 8 8 R E A C H 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 ) 2 8 9 1 0 0 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 9 1 R E A C H 5 , 2 0 2 6 ) V 0 < 1 ) , V 0 ( 2) , O S , O U T L E V 2 9 2 2 0 2 6 F O R M A T 1 3 F 3 . 0 , 1 1 1 2 9 3 R E A C H 5 , 2 0 2 7 I N S T O U T 2 9 4 2 0 2 7 F O R M A T ! 1 4 ) 2 9 5 • I F ! N S T O U T . E O . 0 1 G O T H 5 0 2 9 6 R E A C H 5 , 2 0 2 3 ) ( S T A O U T ( I ) , 1 = 1 , N S T O U T ) 2 9 7 2 0 2 8 F O R M A T { 2 0 1 4 ) S T A 3 T S I M U L A T I O N O F T H E V E H I C L E M O T I O N C A V = A V E R A G E V E L O C I T Y C J T = 1 F O R T R A V E L L O A D E D C 2 F O R T R A V E L E M P T Y C N A V = C O U N T E R C N S T = S T O P C O U N T E R C R E S = T O T A L R E S I S T A N C E A G A I N S T M O T I O N O F T H E V E H I C L E ( P O U N D S ) c S T Q P T M = C U M U L A T I V E S T O P P I N G T I M E ( M I N U T E S ) c • T O T ' O I S = T O T A L D I S T A N C E T R A V E R S E D A T T H E P R E S E N T T I M E ( F E E T ) c T O T T I M = T O T A L T I M E E L A P S E D S I N C E T H E B E G I N N I N G ( S E C O N D S 1 c T R A C E = L O G I C A L T O K E E P T R A C K B R A K I N G H A S O C C U R E D A T T H E B E G I N N I N G O F A N E W c S E C T I O N c I N I T I A L I Z A T I O N 2 9 8 5 0 T O T 0 I S = O . 2 9 9 T O 0 I S = 0 . 3 0 0 T O T T I M = 0 . 3 0 1 T O T I M = 0 . 3 0 2 S T O ^ T M = 0 . 3 0 3 R E S = 0 . 3 0 4 A V = 0 . 3 0 5 N A V = 0 3 0 6 N S T = 1 3 0 7 T P A C E = . T R U E . 3 0 8 J T = 1 c C O N S T A N T T O C O N V E R T F R O M M P H T O F T / S E C 3 0 9 C l = 5 2 3 0 . / 3 6 0 0 . c C O N S T A N T T O C O N V E R T F R O M F T / S E C T O M P H 3 1 0 C 2 = l . / C I 3 1 1 9 9 9 V = V O ( J T ) 3 1 ? 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 ) 3 1 5 2 0 4 6 F O R M A T ! / / / , ' T R A V E L L O A D = D ' / , • * * * * * * * * * * * * * ' ) 3 1 6 I F ! 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 ) . 3 1 7 2 0 4 7 F O R M A T ! ' 1 ' , ' T R A V E L E M P T Y ' / , ' * * * * * * * * * * * * ' ) 3 1 8 I F C U T L E V . G E . 2.) W R I T E ! 6 , 2 0 4 3 ) 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 I F ! 1 J T L E V . G E . 2 ) W R I T E ! 6 , 2 0 5 0 1 3 2 1 2 0 4 3 F O R M A T ! / / / . ' G E A R ' , 5 X , ' V E L O C I T Y - M P H ' , 8 X , ' D I S T A N C E ' , J 3 X , ' T I M E * , 1 . O X 1 ' R O L L I N G R E S I S T A N C E ' , 5 X , ' G R A D E R E S I S T A N C E ' , 5 X , ' C U R V E R E S I S T A N C E 1 ) 3 2 2 2 0 4 4 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 3 X , ' P O U N D S ' , 1 6 X , ' P O U N D S 1 ' 1 5 X . • P O U N D S ' I 3 2 3 2 0 5 0 F 0 R M 4 T 1 2 9 X , ' S E C T I O N - C O U R S E • , 2 X , ' S E C O N D S - M I N U T E S ' / 3 0 X , • F F E T 1 M I L E S ' / / ) C S C A N F O R T R A V E L L O A D E D F I R S T C" I F R A V E L L O A D E D V E H I C L E W E I G H T = L O A D E D V E H I C L E W E I G H T 3 2 4 I F ( . J T . E Q . 1 ) V W = L . V W c I F T R A V E L E M P T Y V E H I C L F W E I G H T = E M P T Y V E H I C L E W E I G H T 3 2 5 3 2 6 3 2 7 I F ( J T . E Q . 2 ) V W = E V W SCAM THE ROAD SECTION BY SECTION KEEPING FORCES CONSTANT OVER DS DO 4 5 I = 1 , N S E C I F t J T . E Q . 1 ) K = I FOR TRAVEL EMPTY START FROM L A S T SECTION AND GO TOWARD FIRST - a 6 _ 3 2 9 C C 1 0 8 FOR T R A V E L EMPTY INVERSE GRADE SIGN BECAUSE ROAD DATA READ FOR DIRECTION LOADED I F ( J T . F O „ ? ) G R A D ( K ) = t -GRAOtK) ) IN ARE 3 3 0 3 3 1 3 3 ? I Ft OUT L E V . L T . 2 ) G O T O 107 DO 109 J = 1 , N S T 0 U T IF( Ml K ) . FO.STAOtJTtJ ) ) WRITFI 6 . 20601 3 3 3 2 0 6 0 FORMA T t 1 X » 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . ; < * * * * * * * * * * 1 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * • 2 ) 3 3 4 3 3 5 2 0 4 5 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 l V L E t K . J T I F O R M A T ( 1 X . « * « . 1 1 8 X . , * , / , 1 X . « * ' . ? X . • S F C T I O N NUMBFR=• . I 6 . ? X . • SPOT ION 3 3 6 1 LENGTH= * , F 6 . 0 , 2 X , ' C U R V E R A Q I U S = ' , F 6 . 0 , 2 X , « G R A D E ( F T / F T ) = ' 2 , , S * E E D LIMIT (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 . 2060 ) , F 6 . 3,2X . 3 3 7 1 0 9 C r. CONTINUE DETERMINATION OF THE NUMBER OF SUBSECTIONS TO SCAN SECTION 1 OOK IF A STOP HAS TO BE MADF IN THAT SFCTION K 3 3 8 3 3 9 1 0 7 C IF( I S T O - M N S T , J T J - N l K) . EO. 0 ) GOTO 79 N S U 3 = S E C L ( K ) / O S LAST= DISTANCE REMAINING TO SCAN COMPLETELY THE SECTION K 3 4 0 3 4 1 3 4 ? 7 9 L A S T = S E C L t K ) - ( N S U B * D S ) GOTO 8 0 X S U B = S E C L ( K ) - A T ( M S T . . ) T ) 3 4 3 3 4 4 3 4 5 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= XSUB/DS LAST=XSU3- (NSLiB*DS) 3 4 6 3 4 7 8 1 C GOTO 3 0 LAST=XSUB SU3 = ACCUMIJLATF0 DISTANCE WITHIN A SECTION 3 4 8 3 4 9 3 5 0 8 0 I F t . N O T . T R A C E IGOTO 85 S U B = 0 . GOTO 86 - ' 3 5 1 3 5 2 3 5 3 8 5 TRACE = . T R U E . SUB = A>TtNST, JT ) I F ( 0 U T L E V . G E . 2 ) G 0 T 0 110 3 5 4 3 5 5 3 5 6 1 1 0 GOTO 111 DO 1 1 2 J = l t N S T O U T I F t N ( K ) . E O . S T A O U T t J ) ) W P I T E ( 6 , 2 0 4 2 ) K , S U B 3 5 7 3 5 8 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 ) I K K , M S T ) , K K = 1 , 2 2 ) 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 AITt N S T , J T ) , ( ! N F 0 4 ( , ( I N F O M 3 5 9 3 6 0 1 1 2 2 0 4 2 1 K K , M S T ) , K K = 1 , 2 2 ) CONTINUE 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 . 3 6 1 1 1 1 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 2 I S 0 ' ) NST=MST+1 E LOCITY 3 6 2 C C GOTO 6 3 I F F IRST SECTION AND VELOCITY IS GREATER THAN 0 GO TO TEST BRAKING IF SHOULD START 3 6 3 3 6 4 8 6 c 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 SFCTION IS COMPLETED CONTINUE WITH NEXT ONE 365 68 I F ( S . J B . E Q . S E C L ( K M G O T O - 45 C SCA ' - J F O R A N O T H E R S U B S E C T I O N 366 I F ( S U B + D S . G T . S C C L ( K ) ) G O T O 7 0 367 SUfS = S U B + O S 368 D O S = O S 369 G O T O 7 1 370 70 S U 3 = S U B + L A S T 371 D O S = L A S T C I F S P E E D I S L I M I T E D S C A N AT C O N S T A N T V E L O C I T Y 372 71 I F ( V . E Q . T O P S P ( G O T O 6 4 373 C I F ( V . E Q . M A X V L E ( K , J T ) ) G O T O 6 4 c c E N T E R H E R E I F A C C E L E R A T I N G c C O M M U T A T I O N O P R E S I S T A N C E S F O R P R E S E N T V E L O C I T Y ( C U R V E , R O L L I N G , c A N D G R A D E R E S I S T A N C E S ) 374 C A L L R E S I S T ( V , V W , K , R C U , R G . R R ) c E R O N T A L A R E A C O M P U T A T I O N ( A ) 375 53 I F ( J T . E Q . 2 ) A = 2 8 . 8 6 + . 8 2 * < V W / 1 0 0 0 . ) 376 I F ( J T . E Q . 1 . A N C . L O G . E Q . 3 8 . ) A = 2 9 o 3 5 + . 7 5 * ( V W / 1 0 0 0 . ) 377 I F ( J T . E Q . L A N D . L O G . E Q . 4 8 . ) A = 2 3 . 1 0 + . 5 * ( V W / 1 0 0 0 « ) . 378 R A = . 0 0 2 6 * . 7 * A * V * * 2 C S U M O F T H E R E S I S T A N C E S 379 • R E S = R C U * R G * P . R + R A C S E A R C H F O R T H E P R E S E N T G E A R ( F U N C T I O N O F S P E E D ) I N O R D E R T O C O M P U T E C T H E I N E R T I A R E S I S T A N C E I N C A S E O F A C C E L E R A T I O N A N D TO U S E T H E P R O P E R C P O L Y N O M I A L T O C O M P U T E T H E R I M P U L L 380 G=0 381 54 G=G+1 38? I F ( G o F Q » N G E A R 1 G 0 T 0 5 5 383 I F ( G + 1 . G T . N G E AR ) S H I F T V ( G +1 ) =T O P S P 384 I F ( V . G E . S H I F T V I G ) . A N D . V . L T . S H I F T V f G + l ) 1 G 0 T 0 5 5 . 385 G O T O 5 4 C A V A I L A B L E R I M P U L L I N P R E S E N T G E A R . 386 55 AR IMP = A N ( G , 1 ) + A N ( G , 2 ) * V + A N ( G , 3 ) * V * * 2 C N E T R I M P U L L T O A C C E L E R A T E T H E V E H I C L E 387 N R I V 1 P = A R I M P - R E S 388 I F I N R I M P . L T . 0 . 1 G O T O 5 6 c I N E R T I A R E S I S T A N C E F O R T H E " R E S E N T GEAP . P F P U C T I O N 389 R I = l o O 4 + ( . 0 5 * G R P O S ( G ) * R A X L E ) * * 2 390 A C C = N R I M P * 3 2 . 1 6 / ( V W * R I ) 391 G O T O 5 7 c IN O E C E L E R A T E D M O T I O N T H E I N E R T I A R E S I S T A N C E H E L P T O D E C E L E R A T E 392 56 RI = 1. 0 4 + ( . 0 5 * G R P 0 S ( G ) * R A X L E ) * * 2 393 R I = 1 . / R I 394 ACC = * J R I M P * 2 2 . 1 6 / ( V W * R I ) 39 5 57 A C C E L = . F A L S E . 396 I F ( V ) 5 3 , 5 9 , 5 3 C T I M E T O T R A V E R S E A S U B S E C T I O N ( U N A F F E C T E D B Y B R A K I N G ) 397 58 T I M = 0 0 ' S / ( V * C 1 ) 398 G O T O 6 0 399 59 T I M = S Q R T ( 2 . * D C S / A C C ) C . V I = I N I T I A L V E L O C I T Y A T T H E B E G I N N I N G O F T H E S U B S E C T I O N 400 60 V I = V C V E L O C I T Y A T T H E E N D O F T H E S U B S E C T I O N A N D A T T H E B E G I N N I N G O F T H E N E X T C N E 401 V=V+4CC*TIM*C2 c . T E S T I F T H E V E 1 0 C I T Y S H O U L D B E L I M I T E D TO T O P S P , OR M A X S P L , OR M A X S P E 402 I F ( V . G T . T O P S P . O R . V . G T . M A X V L E l K , J T ) ) G O T O 6 6 403 G O T O 63 r. O N F I T E R A T I O N T O F I N D O U T T H F A C C U R A T E T I M E I T T O O K TO T R A V E R S E 4 0 4 4 0 5 4 0 6 4 0 7 4 OR .. C 6 6 9 8 T H E S l J f l S E C T I O N IF(V.GT.TOPSP)V=TOPSP IF(V.GT.MAXVLEIK,JT)IV=MAXVLE(K,JT) T I M = (V-VI)*C1/ACC XSU3 = ( (V*C1 ) **2-< VI *C 11**2)/( 2.*ACC 1 XSUB=< v + v i )/2.*CI*TIM 4 0 9 4 1 0 4 1 1 RSU3=D0S-XSUB TIM=TIM+RSU3/(V*C1) GOTO 6 3 C C C ENTER HE RF IF TRAVFII IMG AT CONSTANT VELOCITY 4 1 2 4n c 6 4 TIME TO TRAVERSE A SUBSECTION AT CONSTANT VELOCITY T I M = D 0 S / ( V * C 1 ) VI = V 4 1 4 C c ACCEL = .TRUE. TEST I F BRAKING SHOULD START FIRST LOOK FOR STOP TO MAKE AHFAD c c c 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 c c c S=OISTANCE REQUIRED TO DECREASE THE PRESENT VELOCITY TO A STOP OR A SDFF.T L I M I T ST=THE DISTANCE BETWEEN THE PRESENT POSITION AND THE NEXT STOP PR SPEFP 4 1 5 4 1 6 c 6 3 LIMIT S= ( V * C 1 ) * * 2 / 1 ? „ STA=ISTOP<NST ,JT)-N(K ) 4 1 7 4 1 8 C NSTA= ABS(STA) L O O K FOR ONLY ONE SECTION AHEAD I F ( N S T A . E Q o O ) S T = ( ATU.'ST, J T)-SUB) 4 1 9 C c IFJNSTA..EQ.1 1 ST = ( SECL ( K ) - SUB)+AT<NST ,JT 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 4 2 0 c c 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 4 2 1 c c IF(S,GE.ST1G0T0 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 4 2 2 4 2 3 c I F IN T H E LAST SECTION TO SCAN THERE IS NO SPEED LIMIT AHFAD I F ( J T .EQ. 1 .AND.K+l.GT.NSEC.OR . J T .EQ.2.ANDo K-l . E Q o01G0T0 72 I F ( J T . E Q . 1 ) G O T O 84 4 2 4 4 2 5 4 2 6 8 4 8 8 G O T O 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 4 2 7 4 2 8 4 2 9 4 7 4 6 G O T O 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 4 3 0 C C IF THE DISTANCE BETWEEN THE PRESENT POSITION AND THE BEGINNING OF A LCWFR SPEED LIMIT IS GREATER THAN 1500 FT DO NOT TEST IF(ST.GT.1500.)GOTO 72 4 3 1 4 3 2 4 3 3 I F ( J T . E Q . 1 ) S = ( ( M A X V L E ( K + l . J T ) * C 1 ) * * 2 - ( V * C 1 ) * * 2 ) / I - 1 2 . 1 . I F ( J T . E Q . 2 ) S = ( ( M A X V L E ( K - l , J T ) * C l l * * 2 - ( V * C l ) * * 2 ) / ( - 1 2 . ) I F ( S . L T . S T I G O T O 72 4 3 4 IF(S.GT.ST)GOTO 73 C ENTER HERE THE VEHICLE HAS TO DECELERATE L ; -C • : C S=ST; DECREASE VELOCITY AND COMPUTE TIME TO DO IT JC DISTANCE. TIME. AND VELOCITY OF THE SUBSECTION JUST SCANNED ARE 4 3 5 4 3 6 4 3 7 4 3 8 4 3 9 C — — : : : 99 A C C U M U L A T E 0 T O T T I M = T O T T I M + T I M AV=A7+V NAV=NAV+1 T O T D I S = T 0 T 0 ! S + D D S I F I O J T L E V . L T . 2 ) G O T O 1 0 1 4 4 0 441 4 4 2 1 2 1 .. 0 0 1 2 1 J = l , N S T O U T I F ( N ( K ) . E Q . S T A O U T ( J )) GOTO 1 2 2 C O N T I N U E 4 4 3 4 4 4 4 4 5 122 GOTO 101 C A L L R E S 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 IWRITF (6 , 2 0 4 8 ) G , VI , V , SU B , TOD I S , TOT TI M , TOT I M . RR , R G . PCU 4 4 6 4 4 7 2 0 4 8 F O R M A T ! I X , I 3 . 6 X . F 5 . 2 , I X , • T O ' , l X , F 5 . 2 , 6 X , F 6 „ 0 , F 9 „ 2 , 4 X , F 7 . 1 , F 7 o 2 , 1 2 X l , F 6 . 1 , 1 5 X , F 7 . 1 , 1 5 X , F t > „ l ) ,...IF( S U B . E Q . D O S 1 G 0 T 0 1 0 1 4 4 8 4 4 9 45 0 2 0 5 5 I F( Vo E Q« V I ) GOTO 1 0 1 W R I T E ( 6 , 2 0 5 5 ) G , V I , V , S U B , T O T T I M , R R , R C U F O R M A T ( I X . 1 3 . 6 X . F 5 . 2 , I X , • T O ' . I X , F 5 . 2 , 6 X , F 6 . 0 , 9 X , 4 X , F 7 . 1 , 7 X , 1 2 X , F 6 . 4 5 1 4 5 2 1 0 1 1 1 , 1 6 X , 7 X , 1 5 X , F 6 . 1 ) I F ( J T . E Q . l I M A X V = M A X V L E ( K + 1 , J T ) I F ( J T . E 0 . 2 ) M A X V = M A X V L E ( K - 1 , J T ) 4 5 3 4 5 4 C V I = V 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 ) T I M = ( M A X V - V ) * C 1 / ( - 6 . ) 4 5 5 4 5 6 c I F ( J T . E Q . 1 ) V = M A X V L E ( K + 1 , J T ) I F ( J T . E Q . 2 ) V = M A X V L E ( K - 1 , J T ) A C C U M U L A T I O N 4 5 7 4 5 8 4 5 9 T O T T I M = T O T T I M + T I M T O T I M = T O T T I M / 6 0 . T O T T I S = T O T D I S + S T 4 6 0 4 6 1 4 6 2 T O D I S = T O T D I S / 5 2 9 0 . S U 3 - S E C H K ) I F ( 0 U T L E V . L T . 2 ) G 0 T 0 7 00 4 6 3 4 6 4 DO 12 3 J = 1 , N S T 0 U T I F I 0 J T L E V . G E . 2 . A N D . S T A O U T I J ) . E Q . N ( K ) 1 W R I T E ( 6 , 2 0 4 9 ) V I , V , S U B , T O O I S , T 1 0 T T I M . T 0 T I M 4 6 5 4 6 6 1 2 3 2 0 4 9 C O N T I N U E 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 , 1 2 ) 4 6 7 4 6 8 4 6 9 7 0 0 AV=AV+V NAV=NAV+1 GOTO 6 3 C c c 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 COMPUTE 4 7 0 c 7 3 C B R A K I N G T I M E 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 IN THE L A S T S U B S E C T I O N 4 7 1 4 7 2 C X S U B = S - S T 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 T I M = T I M - X S U B / ( V * C 1 ) 4 7 3 4 7 4 4 7 5 TOT TI M=T OTT I M + T I M . T O T D I S = T O T D I S + P D S - X S U 3 I F ( 0 J T L F V . L T . 2 ) G O T O 1 0 2 4 7 6 4 7 7 4 7 R 1 2 4 DO 1 2 4 J = l , N S T O U T I F ( N ( K > . E Q . S T A O U T ( J ) ) G C T O 1 2 5 C O N T I N U E 4 7 9 4 8 0 4B1 1 2 5 GOTO 102 S U B = S U B - X S U B C A M R F S I S T ( V • V W . K . R C U . R G . R R ) : loo 4 8 2 I F ( 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 I S , T O T T I M , T O T I M , R R , R G , R O D 4 8 3 1 0 2 AV=AV+V 4 8 4 4 8 5 4 8 6 ^ 4 8 7 NAV=NAV+1 I F t J T . E Q . 1 ) M A X V = M A X V L E ( K + 1 , J T ) I E < J T . E Q . 2 ) M A X V = M A X V L E ( K - 1 , J T 1 V I = V f 4 8 8 489 C 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 ) T I M = ( M A X V - V ) * C l / ( - 6 . ) T O T T I M = T O T T I M + T I M 4 9 0 1 4 9 1 4 9 ? ,,. T 0 T I M = T 0 T T I M / 6 0 . S U B = S E C L ( K ) T O T D I S = T O T D I S + S 4 9 3 4 9 4 4 9 5 . T O D I S = T O T D I S / 5 2 8 0 . I F ( J T . E Q . l ) V = M A X V L E ( K + l , J T ) I F ( J T . E Q . 2 ) V = M A X V L P ( K - l . J T ) 4 9 6 4 9 7 4 9 8 I F ( 0 J T L E V . L T . 2 ) G 0 T 0 7 0 1 DO 1 2 6 J = 1 , N S T 0 U T I F ( O U T L E V . G E . 2 . A N D . S T A O U T ( J ) . E O . N I K ) ) W R I T F ( 6 , 2 0 4 9 ) V I , V , S U B , T O n I S , T 4 9 9 5 0 0 1 2 6 7 0 1 1 0 T T I M . T 0 T I M C O N T I N U E AV=AV+V 5 0 1 5 0 2 r. NAV=NAV+1 GOTO 6 8 5 0 3 C C 7 6 THE V E H I C L E WAS A C C E L E R A T I N G IN THE L A S T S U B S E C T I O N A C C E L = „ T R U E . 5 0 4 5 0 5 C S U B D I V I D E THE S U B S E C T I O N INTO . 1 * D D S D D D S = D D S * . l V I O = V I 5 0 6 C c 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 S U 3 = S U B - D D S C O M P U T E A NEW V E L O C I T Y AT THE END OF EACH S U B - S U B S E C T I O N 5 0 7 5 0 8 5 0 9 82 SUB=SU3+DDDS T O T D I S = T O T D I S + D D D S V = ( S Q R T ( ( V I 0 * C 1 > * * 2 + 2 . * A C C * D D D S ) ) * C 2 5 1 0 511 5 1 2 V IO=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 . ) I F t J T . E Q . ? ) S = ( ( M A X V L E ( K - l , J T ) * C 1 I * * 2 - ( V * C 1 1 * * 2 ) / ( - 1 2 . ) 5 1 3 5 1 4 515 S T = S E C L ( K ) - S U B I F ( S . L T . S T ) G O T O 32 T I M = ( V - V I ) * C 1 / A C C 5 1 6 5 1 7 518 T O T T I M = T O T T I M + T I M I F I O U T L E V . L T . 2 1 G 0 T 0 1 0 3 DO 1 2 7 J = 1 . M S T 0 U T 5 1 9 5 2 0 5?1 1 2 7 I F ( N ( K ) . E Q . S T A O U T ( J ) ) G O T O 1 2 8 C O N T I N U E GOTO 1 0 3 5 2 2 5 2 3 524,.... 1 2 8 C A L L R E S I S T ( V , V W , K , P C U . R G , R R ) 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 I S , T O T T I M , T O T I M , R R , R G , R C U I F ( S J 3 . L E . D D S ) G 0 T 0 1 0 2 52 5 5 2 6 5 2 7 1 0 3 W R I T E ( 6 , 2 0 5 5 ) G , V I , V , S U B , T C T T I M , R R , R C U AV=A\ /+V NAV=NAV+1 5 2 8 C C ADD TO T I M B R A K I N G T I M E FROM P R E S E N T P O S I T I O N TO THE B E G I N N I N G OF THF NEXT S E C T I O N ( S P E E D L I M I T ) I F t J T . E Q . 1 ) M A X V = M A X V L F ( K + 1 , J T ) 5 2 9 I F t J T . E Q . 2 ) M A X V = M A X V L E ( K - 1 , J T ) 5 3 0 V I = V 53,1 T I H = S T / ( ( M A X V + V ) * C 1 / ? , ) 101 532 TOTTIM=TOTTIM+TIM 533 TOTIM=TOTTIM/60. 534 TOTQIS=T0T0IS+ST 535 TODIS=TOTDIS/5230. 536 SUB=SECL(K) 537 I Ft IT • FQ. 3 ,V=MAXVLE<K»1. JT) ; 538 IF(JT.EQ.2)V=MAXVLE(K-1,JT) 539 IF(0JTLEV.LT.2)G0T0 702 54Q 00 129 J=1,MST0UT , 541 IF(QUTLEV.GE.2.AND.STACUT< J).EQ.N(K)IWRITE(6,2049)VI,V,SUB,TOOIS,T 10TTIM.T0TIM 5.42 129 CONTINUE- : ' 543 AV=AV+V 544 702 AV=AV+V .,,545 . ... NA,V=N,AV_1 546 GOTO 63 C LL C THE VEHICLE HAS TO STOP ENTER HERE 547 48 IFIS.GT. STIGQTO 77 C S=ST: NO ITFRATfQN TO MA K F C ACCUMUi :ATEO I M F' A N D V E L 0 C I T Y 0 F T H E S U B S E C T I O N J U S T SXTNTTET) TRE~ -5__ TOTTIM=TOTTTM»TIM . 5*9 TOTOIS=TOTDIS+nOS 5 5 0 IF(0UTLEVoLT.2)G0T0 104 -551 00 130 .l = l.NSTnilT 552 553 130 CONTINUE 554 GOTO 1 04 IF(N( K)„ EO.STAOUTIJ))GOTO 131 555 131- CALL RES I ST<V , VW,K,PCU,RG,RR) 556 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 557 IFtS.lB.EQ.DDSIGQTO 104 ;  558 IFIV.EQ.VIIGOTO 104 559 WRITE (-6, 2 055 )-G, VI , V , SUB, TOTT I M ,RR , RCU 560 104 AV=AV+V  561 NAV=MAV+1 562 VI=V BRAKING 563 TIM=V*Cl/6. 564 TOTTIM=TOTTIM+TIM -5^5 , TOTT M = T O T T I M/ A O . 566 TOTOIS=TOTDIS+ST 567 TODIS=TOTDIS/5280. . 568 V=0.  569 NAV=NAV+1 570 STOPT M = STOPTM +W A 1T(NST,JT ) __7J IFINSTA.EQ.l ) TP ACE= . FAL SE . 572 IFI.NOTo TRACEJGOTO 45 573 SUB=AT(NST,JT) 5.74 IFfOUTl F V.I T.?IGOTO 7 03 575 00 132 J=1,NST0UT 576 ,r\tl',ir^'GE'2' A N D ' N ( K » « E Q . S T A O U T ( J) )WRITE(6,2049)VI ,SUB,TOOIS,T l 11r r T i . T Q T I M 5 7 7 , JF(0UTLEV.GE.2.AMD. JT.EQ.1.AND.STAOUT<J). EQ.M ( K ) ) WP, I TE ( 6 ,2051 ) WA I TKNST, JT) , ( INF04(JL,NST), JL = 1,22) 1 HI r F n C S ^ ; , ( , p I X ' , T I , , E S T O P P E D - , F 7 . 2 ; 3 x , 2 2 A 3 , r 581 N S T = N S T + 1 582 703 N S T = \ IST+1 583 C G O T O 68 C C S > S T : 0 0 O N E I T E R A T I O N T O F I N D W H E R E B R A K I N G H A D T O S T A R T A N D C O M P U T E r C B R A K I N G T I M E 584 77 I F ( . N O T . A C C E U G O T O 7 8 C S P C F Q 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 585 X S U B = S - S T C S U B T R A C T T I M E I T T O O K 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 586 T I M = T I M - X S U B / ( V * C 1 ) 587 T O T T I M = T O T T I M + T I M 588 T O T D I S = T O T D I S + D D S - X S U B 589 S U B = S U B - X S U B 590 I F t O U T L E V . L T . 2 ) G O T O 1 0 5 591 D O 133 J = 1 , N S T 0 U T 59 2 I F ( N ( K ) o E O „ S T A O U T ( J ) ) G O T O 1 3 4 593 133 C O N T I N U E . 594 G O T O 105 59 5 134 C A L L R E S I S T ( V , V W . K . R C U , R G i R R ) 596 I F t 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 597 105 A V = A V + V 598 N A V = N A V + 1 599 V I = V C B R A K I N G T I M E T O S T O P 600 T I M = V * C l / 6 . 601 T O T T I M - T O T T I M + T I M 602 T 0 T I M = T 0 T T I M / 6 0 . 603 T O T D I S = T 0 T D I S + S 604 T O D I S = T O T D I S / 5 2 8 0 . 605 V=0. 606 N A V = N A V + 1 607 S T O P T M = S T O P T M + W A I T t N S T , J T ) 608 I F t N S T A . E Q . l ) T P . A C E = . F A L S E , 609 I F ! . N O T . T R A C E 1 G 0 T 0 4 5 610 S U B = A T ( N S T , J T ) 611 I F t O U T L E V o I. T , 2 ) G O T O 7 0 4 612 D O 135 J = 1 , N S T 0 U T 613 I F t J 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 , S U R , T P D I S , 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 ) . E O . M ( K ) ) W R I T E ( 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 ) . E Q . N ( K ) ) W R I T F ( 6 , 2 0 5 1 ) W A IT K N S T . J T ) , ( I N F 0 5 t J L , N S T ) , J L = l , 2 2 ) 616 135 C O N T I N U E 617 704 N S T = N S T + 1 618 G O T O 6 3 C C C T H E V E H I C L E W A S 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 C S > S T ; D O O N E I T E R A T I O N T O F I N D W H E R E B R A K I N G H A D T O S T A R T AND.COMPUTE C 3 R A K I N G T I M E 619 78 A C C E L = . T R U E . 620 D D Q S = D D S * . l 621 V I O = V I 622 S U B = S U B - O D S 623 83 S U B = S U B + D C D S 624 T O T D I S = T O T D I S + D O D S 625 V = ( S Q R T ( t V I 0 * C 1 ) * * ? + 2 . * A C C * 0 D D S ) ) * C 2 > 626 627 628 629 630 631. 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 T o S T ) G O T O 8 3 T I M = ( V - V I ) * C 1 / A C C 632 633 634 T O T T I M =T O T T I M + T I M I F 1 0 U T L E V . L T . 2 ) G O T O 1 0 6 0 0 1 3 5 J = i , N S T O U T 635 636 637 136 I F ( N ( K ) . E Q . S T A O U T ( J ) ) G O T O 1 3 7 C O N T I N U E G O T O 1 0 6 638 639 640 137 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 , 2 0 4 8 ) G , V I , V , S U B , T O D I S , T O T T I M . T O T I M , R R , P G , R C U I F ( S J B . L E o D D S I G O T O 1 0 6 641 642 6 4 3 106 W R I T E ( 6 , 2 0 5 5 I G , V I , V , S U B , T G T T I M . R R . P . C U A V = A V + V N A V = \ I A V + 1 644 645 C V I = V A D D 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 T O T H E S T O P T I M = V * C l / 6 . 646 647 648 T O T T I M = T O T T I M + T I M T O T H = T O T T I M / 6 0 . T O T D I S = T O T D I S + S T 649 650 651 T O D I S = T O T D I S / 5 2 3 0 . V=0. N A V = N A V + 1 652 653 654 S T O P T M = S T O P T M + 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 4 5 655 656 657 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 0 5 0 0 1 3 8 J = l . N S T O U T 658 659 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 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 > ) W R I T E ( 6 , 2 0 5 1 ) W A I T 660 1 ( N S T , J T ) , ( I N F 0 4 ( J L , N S T ) , J L = l , 2 2 ) I F { Q U T L E V . G E . 2 . A N D . J T . E Q o 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 ) 661 662 663 138 705 C O N T I N U E N S T = N S T + 1 G O T O 6 3 C C C N O 3 R 4 K I N G N E C E S S A R Y E N T E R H E R E 664 665 C 72 D I S T A N C E , T I M E , A N D 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 + 1 666 667 663 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 1 4 1 D O 1 4 2 J = l , N S T O U T 669 670 671 142 I F ( N ( K ) . E Q . S T A O U T ( J ) ) G O T O 1 4 3 C O N T I N U E G O T O 1 4 1 672 673 674 143 141 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 . 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 I S , T O T T I M , T O T I M , R R , R G , R C U T 0 T I M = T 0 T T I M / 6 0 . 67 5 676 677 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 6 7 8 DO 1 3 9 J = 1 , N S T 0 U T 1 0 4 6 7 9 I F ( N ( K ) . E Q . S T A O U T t J ) ) G O T O 1 4 0 6 8 0 1 3 9 C O N T I N U E 6 8 1 G O T O 6 8 6 8 2 1 4 0 C A L L R E S I S T ( V , V W , K , R C U , R G , R R ) L E j L S J _8 .eQ .SECL I K ) ) W R I T F ( 6 , 2 0 4 8 ) G . V I . V . S U D < T O O I S . T OT T I M . T D T T M . R R .PG l.RC ' J ' 6 8 4 I F ( S O B « E Q . S E C L ( K ) 1 G 0 T 0 6 8 6 8 5 I F ( S U B . E Q . D D S I G O T O 68 6 8 6 I F ( V . E Q . V I ) G O T 0 6 8 6 8 7 W R I T E ( 6 , 2 0 5 5 ) G , V I , V , S U B , T O T T I M , R R , R C U 6 8 8 G O T O r , a 6 8 9 4 5 C O N T I N U E 6 9 0 c I F ( J T . 5 Q . 2 1 G 0 T 0 6 9 r\91 C C T R A V E L L O A D E D I S F I N I S H E D ; S A V E S T A T I S T I C * L T I M = T 0 T T I M / 6 0 -6 9 2 L S T T I M = S T O P T M 6 9 3 L A V = A V 6 9 4 _ L A V = N A V • 6 9 5 J T = 2 6 9 6 N S T = 1 6 9 7 G O T O 9 9 9 6 9 8 C T R A V E L E M P T Y I S F I N I S H E D A N D T H E C O U R S E H A S B E F N S C A N N E D 6 9 E T I M = T 0 T T I M / 6 0 . - L T I M 6 9 9 E S T T I M = S T O P T M - l S T T I M 7 0 0 E A V = A V - L A V 7 0 1 N E A V = N A V - N L A V 7 0 ? ' C O U R S E = T O T D I S / ? . 7 0 3 T O T T I M = T O T T I M / 6 0 . 7 0 4 W R I T E ( 6 , 2 0 4 1 ) 7 0 5 2 0 4 1 F 0 R 1 A T I / / / , * * * * * * * * * R E S U M F * * * * * * * * i . / / ) 7 0 6 W R I T . ( 6 , 2 0 3 1 ) C O U R S E 7 0 7 2 0 3 1 F O R M A T ( I X , ' T O T A L L E N G T H O F T H E C O U R S E O N E W A Y = ' , F 1 0 . 0 , 5 X • F E E T ' , F 1 . . 1 5 . 2 , 5 X . ' M I L F ( S ) ( T H I S D I S T A N C F I S T H E D I S T A N C E T R A V F R S F D B Y T H E V E 2 H I C L E • ) 7 0 8 W R I T E ( 6 , 2 0 3 2 ) T 0 T T I M 7 0 9 2 0 3 2 F O R M A T t l X , * R O U N D T R I P T I M E = ' , F I 0 . 2 , 5 X . • MI N t l T F S ' ) 7 1 0 W R I T E ( 6 , 2 0 3 3 ) E T I M : 7 1 1 2 0 3 3 F O R M A T ( 1 0 X , ' T R A V E L E M P T Y T I M E = « , F 1 0 . 2 , 5 X , ' M I N U T E S ' ) 7 1 ? W R I T E ( 6 , 2 0 3 4 ) L T I M 7 1 3 2 0 3 4 F O R M A T d O X , ' T R A V E L L O A D E D T I M E = • , F 1 0 . 2 , 5 X , ' M I N U T F S ' ) 7 1 4 W R I T E ( 6 , 2 0 3 5 ) S T 0 P T M 71 5 2 0 3 5 F O R M A T ( 1 O X , ' T O T A L T I M E S T O P P E D = • , F 1 0 . 2 , 5 X , • M I N U T F S ' 1 7 1 6 W R I T E ( 6 , 2 0 3 6 » E S T T I M :  7 1 7 2 0 3 6 F O R 1 A T ( 1 O X , * T I M E S T O P P E D W H E N E M P T Y = • , F 1 0 . 2 , 5 X , • M I N U T E S ' ) 7 1 3 W R I T E ( 6 , 2 0 3 ^ ) L S T T IM 7 1 9 2 0 3 7 F O R M A T ( 1 0 X , - T I M E - S T O P P E D W H E N L O A D E D = • , F 1 0 . 2 , 5 X , ' M I N U T E S • ) 7 2 0 A V = A V / N A V 7 2 1 L A V = L A V / N L A V 7 2 2 E A V = E A V / N E A V 7 2 3 W R I T E ( 6 , 2 0 3 3 ) A V 7 ? 4 2 0 3 8 F O R M A T t l X , • A V F R A G E V E L O C I T Y O V E R T H E C O U R S E ( B O T H W A Y ) - ' . F I 0 . 2 , 5 X , 1 • M P H ' ) 7 2 5 W R I T E ( 6 , 2 C 3 9 ) E A V 7 2 6 . 2 0 3 _ L _ F O R M A T ( 1 X , • A V F R A G E V E L O C I T Y E M P T Y = « , F I 0 . 2 , 5 X . • M P H ' I V 7 2 7 W R I T E ( 6 , 2 0 4 0 ) L A V 7 2 8 2 0 4 0 F 0 R 1 A T I 1 X , ' A V E R A G E V E L O C I T Y L O A D E D = • , F 1 0 . 2 , 5 X , • M P H ' I ^ 7 2 9 S T O P (• 7 3 0 luj E N D S U B R O U T I N E E I T A L E A S T S Q U A R E S A P P R O X I M A T I O N F O R A P O L Y N O M I A L O F D E G R E E N 7 3 1 S U B R O U T I N E F I T > :— 73? C O M M O N / V A R / X ( 2 0 0 ) . Y ( 2 0 0 ) . N P . N D f 7 3 3 D O U B L E P R E C I S I O N A N . B 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 5 C O M M E ' N / C O E - / A N ( 3 0 » 3 ) . I I c A N = C O E F F I C I E - N T S W A N T E D c B = A U G M E N T E D M A T R I X c N D = O F G R E E O F T H E P O L Y N O M I A L c N P = N L ) M B E R O F D A T A P O I N T S 7 3 6 N R 0 W = N 0 + 1 7 3 7 . N C 0 L = N D + 2 7 3 8 DO 1 1 = 1 , N R O W 7 3 9 DO 1 J = 1 , N C 0 L 7 4 0 1 R ( I , J ) = 0 . 7 4 1 DO 2 1 = 1 , N R O W 7 4 2 D O 2 J = l , N R O W 7 4 3 DO 2 K = l , N P c C O M P U T A T I O N A S S U M E 0 „ * * 0 = 1 . 7 4 4 I F ( X ( K I . G T . O . ( G O T O 6 7 4 5 I F ( X ( K ) „ L T . O o I G O T O 7 7 4 6 I F I I . G T . l o O R . J . G T . l ( G O T O 5 7 4 7 S = l . 7 4 3 G O T O 2 7 4 9 5 S = 0 . 7 5 0 G O T O 2 7 5 1 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 , M P 7 5 5 I F ( I o G T . 1 ( G O T O 4 7 5 6 I F ( X ( K I . G T . O . I G O T O 4 7 5 7 S S = Y ( K ) 7 5 8 G O T O 3 7 5 9 4 S S = X ( K ) * * . ( 1 - 1 ) * Y ( K ) 7 6 0 3 B ( I . ^ 0 + 2 ) = B < I . N D + 2 I + S S 7 6 1 C A L L G A U S S 7 6 2 G O T O . 8 7 6 3 7 W R I T E ( 6 . 2 0 3 0 ) 7 6 4 2 0 3 0 F O R M A T < 5 X , ' W A R M I N G : A N E G A T I V E V A L U E H A S B E E N E N C O U N T E R E D I N S U B R O 1 U T I N E F I T C H E C K T R U C K D A T A F O R N E G A T I V E V A L U E ' ) 7 6 5 S T O P 7 6 6 8 R E T U R N 7 6 7 E N O S U B R O U T I N E G A L ' S S G A U S S - J O R D A N E L I M I N A T I O N W I T H P I V O T E L E M E N T S N O R M A L I Z E D 7 6 8 S U B R O U T I N E G A U S S 7 6 9 D 0 U 3 L E P R E C I S I O N A N , B , C , D 7 7 0 C O M M C N / M A T R I X / P ( 3 , 4 ) , N R O W . N C O L . 771 O O M M r N / C O F F / A N ( 3 0 . 3 ) . I I 7 7 2 K = 0 7 7 3 4 K = K + 1 7 7 4 C = B K . K 1 7 7 5 0 0 1 J = l , N C O L 7 7 6 I F ( Jo L T o K ) G O T O 1 s. 777 B I K . J ) = P ( K . 1 ) / r 106 c 7 7 8 7 7 9 7 8 0 7 8 1 7 8 2 7 8 3 1 C O N T I N U E 0 0 2 1 = 1 i N R O W D = B ( I , K ) 0 0 2 J = l , N C O L I F ( I . E Q . K I G O T O 2 1 F t J . L T . K ) G O T O 2 > 7 8 4 7 8 5 7 8 6 2 B ( I , J ) = B ( I , . ) ) - ( D * B ( K , J ) ) C O N T I N U E I F t K . P Q . N P O W ) G O T O 3 7 8 7 7 8 8 7 8 9 3 5 G O T O 4 , 0 0 5 1 = 1 , M R O W A N t I I . I ) = B ( I . N C O L ) 7 9 0 7 9 1 R E T U R N END F U N C T I O N T O C O R R E C T H P D U E T O A L T I T U D E A N D T E M P E R A T U R E 7 9 2 C F U N C T I O N P D ( B P . P O ) T = 1 4 0 F A I R - I N T A K E T E M P F R A T U R E 7 9 3 7 9 4 7 9 5 T = 1 4 0 . B 0 = 2 9 . 9 2 T 0 = 5 ? 0 . 7 9 6 7 9 7 c 4 5 9 . 6 7 I S A C O N S T A N T T O T R A N S F O R M F R O M F T O R A N K I N E D E G R E E T R A N < = T + 4 5 9 . 6 7 P D = ( D 0 * 3 P / B 0 ) * ( T O / T P A N K ) 7 9 8 7 9 9 R E T U R N END S U B R O U T I N E C O M P U T I N G G R A D E , R O L L I N G , A N D C U R V E R E S I S T A N C E , T H E S E c c R E S I S T A N S E S A R E C O M P U T E D W I T H V , T H E V E L O C I T Y . A T T H E E N D 0 p T H E S U B S E C T I O N , A N D W I L L B E O U T P U T F O R O U T P U T L E V E L 2 8 0 0 8 0 1 S U B R O U T I N E R E S ! S T ( V , v w , K , R C U , P G , R R 1 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 ) , U S ( 5 0 0 ) , C R A D ( 5 0 0 ) , E ( 5 0 0 ) , L 1 M I 5 . M 0 ) . G R A D ( 5 0 0 ) 8 0 2 8 0 3 c C U R V E R E S I S T A N C E R C U = 0 . I F t C R A D t K l . E O . O . - C R . V . E O . O . ( G O T O 1 8 . 0 4 3 0 5 c 1 R C U = t t ( . 324»-. 0 0 1 4 * V * * 2 ) / C R A D t K ) ) - . 0 2 1 * E ( K ) ) * V W G R A D E R E S I S T A N C E R G = 0 . 8 0 6 8 0 7 8 0 8 I F ( G R A D ( K l o E Q . O . ( G O T O 2 T E T A = A T A N t G R A O t K ) ) R G = V W * S I N ( T E T A ) 8 0 9 8 1 0 c 2 R O L L I N G R E S I S T A N C E I F ( S T Y P _ ( K ) , E Q . 1 ) G 0 T 0 3 R R = ( 1 5 . 1 + . 0 8 8 * V ) * ( V W / 1 0 0 0 » > 8 1 1 8 1 2 8 1 3 3 4 G O T O 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 E N D *n A T A