UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

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

Item Metadata

Download

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

Full Text

A DYNAMIC PROGRAMMING MODEL FOR SELECTION OF OPTIMUM LOGGING ROAD SURFACE  by HAROLD A . JOLLIFFE B.S.F.,  University of B r i t i s h  Columbia,  1968  A THESIS SUBMITTED I N P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY  in THE FACULTY OF FORESTRY  We a c c e p t to  this  thesis  the r e q u i r e d  as  standard  THE U N I V E R S I T Y OF B R I T I S H September,  (5)  conforming  COLUMBIA  1976  H a r o l d A l f r e d J o l l i f f e , 1976  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the U n i v e r s i t y of  the  British  Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference  and  study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e  c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may head of my  Department or h i s r e p r e s e n t a t i v e s .  be  granted by  I t i s understood  the that  copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not allowed w i t h o u t my  written  permission.  Faculty The  of  Forestry  U n i v e r s i t y of B r i t i s h  Vancouver,  B.C  Canada  Columbia  be  ABSTRACT The studied.  s e l e c t i o n o f optimum road s u r f a c i n g f o r l o g g i n g  A dynamic program model t h a t s i m u l a t e s  roads i s  d i f f e r e n t road  surfaces,  over the l e n g t h o f the r o a d , i s developed to a r r i v e a t the optimum combination o f road The  surfaces.  model s i m u l a t e s  types over the road.  the t r a v e l , o f up to three d i f f e r e n t  The p h y s i c a l c h a r a c t e r i s t i c s o f the road, the road  s u r f a c e and the v e h i c l e s a r e used to determine t r a v e l speeds. speed and v e h i c l e o p e r a t i n g to the road s u r f a c e .  vehicle  Travel  c o s t s a r e used to f i n d v e h i c l e c o s t s  These c o s t s a r e combined w i t h s u r f a c e  relative  construction  and maintenance c o s t s t o f i n d the optimum combination o f s u r f a c e s . T e s t i n g o f the model r e v e a l e d importance than road g r a d i e n t combination o f road  surfaces.  t h a t volume o f wood was o f l e s s  i n the d e t e r m i n a t i o n  o f the optimum  )  -  i i  -  TABLE OF CONTENTS Page ABSTRACT  i  TABLE OF CONTENTS  .  •  L I S T OF TABLES  iv  L I S T OF FIGURES  .  .  .  .  .  v  ACKNOWLEDGMENTS CHAPTER  vi  I  INTRODUCTION 1.1 Road s t a n d a r d and s u r f a c e s e l e c t i o n . 1.2 Another approach to the problem . . 1.3 O b j e c t i v e s of the study . . . CHAPTER  .  .  1 1 2 3  .  . .  . .  . .  II  DYNAMIC PROGRAMMING MODEL 2.1 G e n e r a l dynamic programming f o r m u l a t i o n 2.2 I n t r o d u c t i o n of road s u r f a c i n g problem 2.3 Formulation of road surfacing problem 2.4 Comments on t h e s t a t e o f t h e s y s t e m . CHAPTER  i i  . . .  . . .  .  4 4 5 6 7  . . . .  .  III  COST 3.1 3.2 3.3  CALCULATIONS AND V A R I A B L E S C o n s t r u c t i o n and M a i n t e n a n c e c o s t s . . . V e h i c l e o p e r a t i n g , t i r e and maintenance c o s t s . V e h i c l e s u r f a c e , and a l i g n m e n t v a r i a b l e s . .  . . .  11 11 11 12  CHAPTER I V PROGRAMMING THE MODEL 4.1 General assumption . 4.2 Computer Program . . 4.3 Speed f u n c t i o n s . . 4.3.1 Maximum s a f e c u r v e 4.3.2 Maximum s a f e s p e e d 4.3.3 Maximum s a f e s p e e d 4.3.4 Maximum a v a i l a b l e 4.3.5 S o l u t i o n of cubic 4.4 Program output . .  .  . . .  . . .  . . .  . . .  !4 14 14 15 15 15 21 21 21 21  . . .  . . speed . . . . for stopping . . of descent . . . speed o f v e h i c l e . . relationships . . . . . . .  . . . . . .  CHAPTER V MODEL RESULTS 5.1 H y p o t h e t i c a l problem  2  .  .  .  .  .  .  .  3  23  5.2 5.3 5.4 5.5  i i i -  Length of minor sections Significant results I m p o r t a n c e o f number o f v e h i c l e s Changing surfaces along the road  CHAPTER V I DISCUSSION AND CONCLUSIONS 6.1 Areas of further i n v e s t i g a t i o n 6.2 Conclusion .  BIBLIOGRAPHY  .  APPENDIX 1  Maximum s a f e  curve speed  .  APPENDIX 2  Maximum s a f e s p e e d  for  APPENDIX 3  Maximum s a f e s p e e d  of descent  APPENDIX 4  Maximum a v a i l a b l e s p e e d o f  APPENDIX 5  Solution of cubic  APPENDIX 6  The c o m p u t e r  APPENDIX 7  Sample o f a program  APPENDIX 8  Data f o r h y p o t h e t i c a l  stopping .  vehicle  equation  program output problem  .  - iv -  LIST OF TABLES  TABLE I  Vehicle  variables  TABLE I I  Surface v a r i a b l e s  TABLE I I I Alignment  variables  LIST OF FIGURES  FIGURE  211  G e n e r a t i o n of s t a t e s i n s i m p l i f i e d problem  FIGURE  4.1  Flow diagram o f the program  FIGURE  5.1  E f f e c t of t r a f f i c density surface . . .  .  .  .  .  and grade on optimum . . . . .  FIGURE A l . l  Cross-^section superelevated  o f v e h i c l e i n t i p p i n g c o n d i t i o n on curve . . . . .  FIGURE A l . 2  C r o s s - s e c t i o n o f v e h i c l e i n s l i p p i n g c o n d i t i o n on a s u p e r e l e v a t e d curve . . . .  - vi-  ACKNOWLEDGEMENTS I wish to express my g r a t i t u d e to A s s i s t a n t  Professor  G.G. Young, F a c u l t y o f F o r e s t r y , who a s s i s t e d i n the f o r m u l a t i o n o f the problem and under whose d i r e c t i o n t h i s study was undertaken. H i s a s s i s t a n c e and c o n s t r u c t i v e c r i t i c i s m were o f g r e a t  benefit.  The t h e s i s was reviewed by Dr. D.D. Munro, and by Dr. D. Haley. T h e i r comments  and s u g g e s t i o n s were g r e a t l y  appreciated.  F i n a n c i a l a s s i s t a n c e was granted the author i n the form o f teaching  a s s i s t a n t s h i p s by the U n i v e r s i t y o f B r i t i s h  Columbia.  - 1 -  CHAPTER I INTRODUCTION 1.1  Road s t a n d a r d and s u r f a c e s e l e c t i o n A road s t a n d a r d s t a t e s the l i m i t s p l a c e d on alignment  and o t h e r  p h y s i c a l c h a r a c t e r i s t i c s of a road, i n c l u d i n g s u r f a c i n g , and u s u a l l y s p e c i f i e s the d e s i g n speed.  The s e l e c t i o n of the optimum road  standard  f o r a l o g g i n g road i n v o l v e s the a c c o u n t i n g f o r , and e s t i m a t i o n o f a l l f a c t o r s t h a t have a b e a r i n g on c o s t s .  T h i s i s g e n e r a l l y accomplished by  the e s t i m a t i o n o f u n i t c o s t s f o r , h a u l i n g , c o n s t r u c t i o n and maintenance, and  the e s t i m a t i o n o f the t o t a l volume to be h a u l e d over the road.  The  c o s t s e s t i m a t e d r e l a t e t o average p h y s i c a l c h a r a c t e r i s t i c s o f the road, and do not vary w i t h alignment w i t h i n a s t a n d a r d s p e c i f i e d .  There i s  always a unique s t a n d a r d t h a t produces lowest c o s t on a s e c t i o n o f road where the volume o f wood to be t r a n s p o r t e d i s c o n s t a n t .  A higher  standard  would be optimum o n l y i f t h e r e i s an i n c r e a s e i n volume, which r e s u l t s i n a lower t o t a l c o s t p e r u n i t . i s decreased enough to j u s t i f y  T h i s w i l l occur i f the h a u l i n g c o s t per u n i t the i n c r e a s e i n c o n s t r u c t i o n and maintenance  c o s t r e q u i r e d f o r the h i g h e r s t a n d a r d .  The road s u r f a c e i s s p e c i f i e d by  the road s t a n d a r d , thus, the s e l e c t i o n o f road s t a n d a r d r e s u l t s i n the s u r f a c e a l s o b e i n g s e l e c t e d , and t h e r e b e i n g a unique s u r f a c e i f volume i s constant. The  d e c i s i o n to upgrade the s u r f a c e on an e x i s t i n g road i s  g e n e r a l l y made on the b a s i s o f a t o t a l c o s t a n a l y s i s .  To determine what  p o r t i o n o f the e n t i r e road s h o u l d be upgraded the road i s d i v i d e d s e c t i o n s dependent on volume o f wood to be t r a n s p o r t e d .  into  F o r example, a  - 2 mainline  road would be  d i v i d e d i n t o s e c t i o n s having  the d i s t a n c e s between spur r o a d s . s t u d i e d i s determined by willing  The  the l e n g t h s  minimum l e n g t h o f s e c t i o n to  section.  Most  i n some a r e a s , where t h e r e i s v e r y poor alignment,  t h a t a change to a lower q u a l i t y s u r f a c e w i t h i n a s e c t i o n may The  be  A g a i n the method of s o l v i n g the problem  g i v e s a s o l u t i o n where t h e r e i s a unique s u r f a c e on any admit,that  to  the minimum l e n g t h f o r which a c o n t r a c t o r i s  to s e t up h i s equipment.  designers  equal  main problem w i t h  be  justified.  the above methods of d e t e r m i n i n g  road s u r f a c e i s the d e t e r m i n a t i o n  of h a u l i n g c o s t s .  Hauling  optimum  costs  may  be determined by u s i n g average h i s t o r i c a l c o s t s on s i m i l a r r o a d s . H i s t o r i c a l c o s t s may  a l s o be  combined w i t h  a r r i v e at h a u l i n g c o s t s on new  roads.  t r a v e l time e s t i m a t e s  to  T r a v e l times are based e i t h e r on  h i s t o r i c a l data f o r s i m i l a r roads o r on the d e s i g n speed. s h o u l d be based on the i n t e r a c t i o n of v e h i c l e and  road  T r a v e l time  characteristics.  Another problem i s t h a t s u r f a c e s e l e c t i o n i s based on the l o g g i n g  truck  alone  for  and  t h e r e i s no  c o n s i d e r a t i o n of o t h e r  example, crew busses and  1.2  t r a f f i c on the road,  service vehicles.  Another approach to the problem G e t t i n g away from the u n i t c o s t concept p o p u l a r i z e d  Matthews (1942) i s d i f f i c u l t but  can be j u s t i f i e d by  the use  Levesque (1975) developed a s i m u l a t i o n model t h a t determines  by of  computers.  travel  times f o r l o g g i n g t r u c k s r e l a t i v e to the p h y s i c a l c h a r a c t e r i s t i c s of road.  He  suggested the use o f these t r a v e l times to determine the  of a l t e r n a t e road a l i g n m e n t s . h a u l i n g c o s t s and  This allows  one  best  to get away from u n i t  r e l a t e the c o s t s more d i r e c t l y  to the p h y s i c a l  the  - 3 c h a r a c t e r i s t i c s o f the road.  The approach however, s t i l l has  the  drawback t h a t i t c o n s i d e r s a u n i f o r m s u r f a c e over the l e n g t h of road  and  does not a l l o w f o r changing s u r f a c e s . The development of a dynamic programming model a l l o w s the changing o f road s u r f a c e , ~ s u c h t h a t a lower q u a l i t y s u r f a c e may  be  considered f o r a s e c t i o n a f t e r a s e c t i o n with a higher q u a l i t y surface.  1.3  O b j e c t i v e s of the study The aim of the study i s t w o f o l d .  First,  to develop a dynamic pro  gramming.model t h a t w i l l s i m u l a t e d i f f e r e n t road s u r f a c e s , over the e n t i r e l e n g t h o f road, to a r r i v e a t the optimum combination a g i v e n road alignment.  Secondly,  meters on optimum road s u r f a c e .  o f road s u r f a c e , f o r  to study the e f f e c t o f the road p a r a -  -4-  CHAPTER  II  DYNAMIC PROGRAM MODEL 2.1  General dynamic programming f o r m u l a t i o n Dynamic programming i s a o p e r a t i o n s r e s e a r c h technique,  makes use o f a s e q u e n t i a l d e c i s i o n p r o c e s s based optimality.  The p r i n c i p l e was f i r s t  that  on the p r i n c i p l e o f  s t a t e d by Bellman  (1957) and  r e s t a t e d by Wagner(1969) a s : "An o p t i m a l p o l i c y must have the p r o p e r t y t h a t r e g a r d l e s s o f the r o u t e taken t o e n t e r a p a r t i c u l a r s t a t e , the remaining that  d e c i s i o n s must c o n s t i t u t e an o p t i m a l p o l i c y f o r l e a v i n g  state"  1  All  dynamic programming problems must be decomposable  stages w i t h a p o l i c y d e c i s i o n t o be made a t each stage.  The v a r i o u s  p o l i c y d e c i s i o n s , w i t h the s t a t e s o f a p a r t i c u l a r stage, w i l l i n v a r i o u s s t a t e s a s s o c i a t e d w i t h the next stage. one  result  To s o l v e the problem  begins by f i n d i n g the o p t i m a l p o l i c y f o r each s t a t e o f the l a s t  T h i s one-stage  problem i s u s u a l l y t r i v i a l ,  decisions with a s i n g l e input state.  the combination  Beyond t h e one-stage  p a r t i c u l a r s i t u a t i o n being studied. w i t h n stages remaining  problem a t o f i t the  The o p t i m a l p o l i c y f o r each s t a t e  i s i d e n t i f i e d w i t h the r e c u r s i v e r e l a t i o n s h i p  g i v e n the o p t i m a l p o l i c i e s f o r each s t a t e w i t h n-1 stages S t a r t i n g w i t h the s t a t e i n f o r m a t i o n f o r the l a s t s o l v e d moving backward stage by stage, u n t i l the o p t i m a l . p o l i c y o f the f i r s t  '''Wagner, H.M.  stage.  of a l l possible  r e c u r s i v e r e l a t i o n s h i p i s formulated w i t h e q u a t i o n s developed  and  into  remaining.  stage the problem i s  the i n i t i a l  stage i s reached  stage i s found.  1969. P r i n c i p l e s o f O p e r a t i o n s R e s e a r c h , P r e n t i c e  Inc., New J e r s e y , p. 257.  Hall,  -  2.2  I n t r o d u c t i o n o f road  5  -  s u r f a c i n g problem  Four items used i n the s o l u t i o n o f the problem need a b r i e f introduction types,  a t t h i s point to avoid l a t e r confusion.  traffic  d e n s i t y , road  s e c t i o n s , and road  surfaces.  Three d i f f e r e n t v e h i c l e types a r e allowed just  the l o g g i n g t r u c k .  They a r e , v e h i c l e  for, rather  T h i s p e r m i t s the i n c l u s i o n o f c o s t s and b e n e f i t s  r e l a t e d to v e h i c l e s o t h e r  than l o g g i n g t r u c k s  that are using  the roads.  For example, crew busses can t r a v e l f a s t e r on good q u a l i t y road and  than  surface,  consequently t h e r e w i l l be l e s s t r a v e l time allowances p a i d to  employees.  The i n i t i a l  i n c l u s i o n of logging  i d e a of t h r e e types o f v e h i c l e s was f o r the  t r u c k s , crew busses, and s e r v i c e v e h i c l e s .  f o r m u l a t i o n o f the problem the t h r e e v e h i c l e types a r e a l l o w e d making the s t a t e s a t any stage a v e c t o r .  The t h r e e  In the f o r by  components o f the  v e c t o r a r e r e l a t e d t o the speeds o f the t h r e e v e h i c l e s . T r a f f i c d e n s i t y i s used i n the c a l c u l a t i o n s r a t h e r than u s i n g volume o f wood d i r e c t l y .  The t r a f f i c  the number o f t r i p s t h a t v e h i c l e w i l l the case o f l o g g i n g  d e n s i t y o f each v e h i c l e type i s make over the road  each y e a r .  t r u c k s the number o f t r i p s i s simply  the y e a r l y  volume o f wood d i v i d e d by the average l o a d s i z e . traffic  for  The o t h e r v e h i c l e  d e n s i t i e s may be found from the number o f o p e r a t i n g  y e a r and number of t r i p s p e r day. each y e a r o f the p l a n n i n g  The t r a f f i c  In  days p e r  d e n s i t i e s must be found  period, allowing f o r v a r i a t i o n i n density  over time. The with  constant  discussed  road b e i n g traffic  studied i s f i r s t  densities.  d i v i d e d i n t o main s e c t i o n s ,  This i s equivalent  to the s e c t i o n s  e a r l i e r i n t h e i n t r o d u c t i o n , as b e i n g p i e c e s o f road between  j u n c t i o n s , where the amount of wood to be hauled  over the road  remains  - 6 constant.  Secondly,  the road i s d i v i d e d i n t o s u b s e c t i o n s .  The s u b s e c t i o n s  are p i e c e s o f road where the p h y s i c a l c h a r a c t e r i s t i c s remain c o n s t a n t , i.e.,  the alignment  variables l i s t e d  i n T a b l e I I I a r e c o n s t a n t over a  subsection. Road s u r f a c e s a r e the r u n n i n g s u r f a c e s o f the road, t h a t p a r t of  the road i n c o n t a c t w i t h the wheels o f the v e h i c l e s .  Different  s u r f a c e s make i t h a r d e r o r e a s i e r to r o l l a wheel over the s u r f a c e . f r i c t i o n between road s u r f a c e and wheels, determines t r a c t i o n and s t o p p i n g e f f o r t t h a t can be generated  the l i m i t s  The  t o the  by the v e h i c l e .  In  the h y p o t h e t i c a l problem i n Chapter V the three s u r f a c e s used were e a r t h , g r a v e l , and pavement. speed  limit,  conditions.  determined  The type of s u r f a c e a l s o has a b e a r i n g on the by smoothness o f r i d e o r v i s i b i l i t y  i n dusty  Road s u r f a c e type a l s o has a l a r g e e f f e c t on both v e h i c l e .  and road maintenance c o s t s .  2.3  F o r m u l a t i o n o f road s u r f a c i n g problem Road s u r f a c i n g i s t o be a p p l i e d i n stages t o each s u b s e c t i o n  of  the road, i . e . , t h e s h o r t s e c t i o n o f road o f u n i f o r m  characteristics  w i l l be t h e s t a g e . The p a r t i c u l a r s u r f a c e a p p l i e d i n any stage i s t h e decision.  The s t a t e o f the system w i l l be the r e s u l t i n g speed o f the  loaded v e h i c l e s l e a v i n g the s u b s e c t i o n o f road.  I t i s noted t h a t  d e t e r m i n a t i o n o f the s t a t e o f the system does n o t i n c l u d e the speed o f the empty v e h i c l e s and i s e x p l a i n e d and j u s t i f i e d o p t i m a l combination  i n S e c t i o n 2.4.  The  o f s u r f a c e s i s found by s i m u l a t i n g the t r a v e l o f  v e h i c l e s from the l o a d i n g end o f the road to the dump o r d e l i v e r y end of  t h e road.  The r e c u r s i v e formula d e r i v e d i s :  - 7-  f  (S ) = minimum {C_ „. + f , (S.. )} n , „ S K n-1 n-1  n  f o r n = 1, 2, 3,  (S _ K) n  r  where f  (S ) = the minimum t o t a l c o s t to complete s u b s e c t i o n n, n  n  and  a l l previous  subsections, with  of s u b s e c t i o n n r e p r e s e n t e d S  by  the output .  = t h e s t a t e o f the system, an i n t e g e r valued  n  speed  found from the speed o f the loaded  vector  vehicles leaving  s u b s e c t i o n n.  K  = the d e c i s i o n v a r i a b l e (road s u r f a c e type) used on s u b s e c t i o n n.  C 'S K n n  v  = the c o s t to c o n s t r u c t , m a i n t a i n  and operate  over  s u b s e c t i o n n w i t h s u r f a c e K and s t a t e S_ .  The  stage  coupling function i s : S = F (S , r , v, k) n n-1  where the a c t u a l output are used w i t h  by S _^, n  the road alignment ( r ) , v e h i c l e c h a r a c t e r i s t i c s ( v ) and the  surface properties  (k) o f s u r f a c e K, to compute the output  subsection n represented  2.4  speeds f o r s u b s e c t i o n n-1, r e p r e s e n t e d  by  speeds o f  .  Comments on the s t a t e o f the system The  number o f p o s s i b l e s t a t e s (loaded speeds) f o r any stage  ( s u b s e c t i o n o f road) i s n o t known a t the o u t s e t .  There w i l l o f t e n be  -8more than one way t o o b t a i n  the same s t a t e a t a g i v e n stage.  It i s  n e c e s s a r y t o c a l c u l a t e the r e s u l t i n g s t a t e obtained by the use of each surface  w i t h each f e a s i b l e i n p u t  state, to find  new s t a t e .  A simplified version  2.1, u s i n g  a maximum o f 5 s t a t e s and 2 p o s s i b l e  the minimum c o s t  o f the problem i s , i l l u s t r a t e d  o f each  i n Figure  surfaces.  C a l c u l a t i o n of the s t a t e numbers f o r each stage was reduced to a maximum o f 15 per v e h i c l e type.  I n the case o f t h r e e v e h i c l e  types  3 t h i s r e s u l t s i n a maximum o f 15  states.  To get the g r e a t e s t  number of  s t a t e s , and f o r the most e f f i c i e n t use of s t o r a g e , i n d i c e s were c a l c u l a t e d for  each v e h i c l e f o r each stage.  The i n d i c e s at each stage were  calculated  from the loaded speeds r e s u l t i n g from the combination o f the lowest state vector  (lowest input  i n d i c e s were s e t such t h a t gave a s t a t e v e c t o r  speed) and the lowest q u a l i t y s u r f a c e . the r e s u l t i n g speeds from t h i s f i r s t  of (2,2,2).  to integer valued state vectors.  that  s t a t e , i f not the a c t u a l v e h i c l e  necessary information The the  s t a t e s and road  a lower cost  To f i n d a t r u e  speeds and a l l o t h e r  i n d i c a t o r o f the empty speed, the empty  of road must be known, t o be a b l e  a c c e l e r a t i o n or d e c e l e r a t i o n  resistance.  To c a l c u l a t e empty speed the i n i t i a l  to f i n d  T h i s was found t o be  i m p o s s i b l e and s t i l l m a i n t a i n a dynamic programming approach  subsection  policy  speed of the empty v e h i c l e was not c o n s i d e r e d i n c a l c u l a t i n g  s t a t e number.  problem.  was  was saved.  speed i n the next s u b s e c t i o n the  combination  As each new s t a t e v e c t o r  determined i t was checked t o see i f there was a l r e a d y to o b t a i n  The  The i n d i c e s were used t o c o n v e r t the loaded  speeds, r e s u l t i n g from the remaining combinations of i n p u t surface,  input  t o the  speed a t the end o f the  was assumed to be one m i l e per hour (m.p.h.).  This  assumption  - 9 -  _o  X  o-  X -oo  >-  X  o.  X FEASIBLE STATE  X  o  •o • X  NUMBERS  o. X  n+1  n-1  STAGE ( S u b s e c t i o n number o f road)  LEGEND: Feasible states Surface 1 Surface 2 L e a s t c o s t r o u t e to s t a t e  F i g u r e 2.1  O  Generation of s t a t e s i n s i m p l i f i e d  O  problem.  -  10  -  makes the empty speed independent o f t h e f o l l o w i n g s u b s e c t i o n , t h e r e i s no c a r r y - o v e r  hence,  e f f e c t a s s o c i a t e d w i t h empty speed and no r e a s o n  to i n c o r p o r a t e i t i n t o c a l c u l a t i o n o f the s t a t e number.  The i n i t i a l  speed i s used i n o n l y one o f the f i v e speed f u n c t i o n s and i s o n l y i n the c r i t i c a l f u n c t i o n about one t e n t h o f the time. compensated f o r i n two ways.  First,  The a s s o c i a t e d e r r o r i s  the t r a v e l time i s c a l c u l a t e d from  the maximum empty speed over the s e c t i o n r a t h e r than t h e average speed. Second,  the empty v e h i c l e must stop o r slowdown when a p p r o a c h i n g a loaded  v e h i c l e on a l o g g i n g road. A s i t u a t i o n which puts the v e h i c l e i n the assumed s t a t e q u i t e  frequently.  - 11  -  CHAPTER I I I COST CALCULATIONS AND 3.1  Construction The  VARIABLES  and maintenance  costs  construction cost i s subdivided  i n t o f o u r components.  The  b a s i c s u r f a c i n g c o s t of each s u r f a c e , i s the c o s t to b u i l d a u n i t l e n g t h o f s u r f a c e , on l e v e l grade, when the s u r f a c i n g m a t e r i a l i s w i t h i n one  mile.  The  second component a l l o w s  r e l a t i v e to each s u c c e s s i v e  f i v e per  component i s to a l l o w f o r i n c r e a s e d m a t e r i a l source.  The  an i n c r e a s e i n s u r f a c i n g c o s t  cent i n c r e a s e i n grade. c o s t due  l a s t component a l l o w s  The  third  to i n c r e a s e i n d i s t a n c e  to  f o r a saving i n surfacing  c o s t i f t h e r e i s a l r e a d y a lower q u a l i t y s u r f a c e i n p l a c e . The components.  c o s t of m a i n t a i n i n g The  y e a r , w i t h a minimum t r a f f i c  Maintenance c o s t s are i n c r e a s e d by  3.2  into  three  b a s i c maintenance c o s t i s the c o s t to m a i n t a i n a u n i t  l e n g t h of the s u r f a c e , f o r one  All  the s u r f a c e i s s u b d i v i d e d  i n c r e a s i n g grade and  f u t u r e maintenance c o s t s are d i s c o u n t e d  Vehicle operating,  t i r e and maintenance  to p r e s e n t  load.  traffic dollar  density.  values.  costs  O p e r a t i n g c o s t s are c a l c u l a t e d from v e h i c l e r a t e s which g i v e the o p e r a t i n g  c o s t per u n i t time.  The  c o s t s o f t i r e s and  maintenance,  which are mainly dependent on d i s t a n c e , s h o u l d not be i n c l u d e d i n the vehicle rate. and  The  v e h i c l e r a t e must i n c l u d e the pay  the a s s o c i a t e d overhead c o s t s .  r a t e of the operato  In the case of crew t r a n s p o r t a t i o n  v e h i c l e s , the t r a v e l time allowances of the employees r i d i n g the v e h i c l e and  a s s o c i a t e d overhead must be  incorporated  i n t o the machine r a t e .  The  - 12 a l l o w a n c e s , t h a t a r e r e l a t i v e to time spent on the v e h i c l e , p a i d to passengers must be i n c o r p o r a t e d  into operating  c o s t s , so t h a t an i n c r e a s e  i n v e h i c l e speed r e f l e c t s the b e n e f i t o f l e s s t r a v e l time c o s t . t o t a l operating and  c o s t i s then the product of t r i p  v e h i c l e rate a l l discounted The  distance  travelled basis.  lower q u a l i t y s u r f a c e . of distance, t r a f f i c  density  dollars.  v e h i c l e maintenance and t i r e  c o s t i s c a l c u l a t e d on a u n i t  The c o s t s must be a r r i v e d a t f o r each v e h i c l e  t r a v e l l i n g on each s u r f a c e ,  the h i g h e r  costs being  a s s o c i a t e d w i t h the  T i r e and maintenance c o s t then a r e the product  d e n s i t y and c o s t per u n i t d i s t a n c e .  then must be d i s c o u n t e d  3.3  to p r e s e n t  time, t r a f f i c  The  The t o t a l  costs  to p r e s e n t d o l l a r s .  V e h i c l e , s u r f a c e and alignment v a r i a b l e s The  i n p u t v a r i a b l e s used to s o l v e the problem a r e l i s t e d i n  T a b l e s I, I I and I I I . Table I .  Vehicle  Variables  Units  Variable  Symbol WE  Empty weight  tons  WL  Loaded weight  tons  WR  Rotating  tons  HE  Height to c e n t e r of g r a v i t y empty  feet  HL  Height to c e n t e r  feet  0  P r o j e c t e d d i s t a n c e from c e n t e r of g r a v i t y to o u t s i d e wheels  feet  FAE  F r o n t a l area  empty  sq.ft.  FAL  F r o n t a l area  loaded  sq.ft.  BHP  Brake Horse Power  h o r s e power  BC  Braking  per cent  weight  capacity  of g r a v i t y  loaded  (BHP)  -  Table I I .  Symbol  13  -  Surface  Variables  Variable  Units  SPLIM  Speed l i m i t  m.p.h.  R  Rolling resistance  pounds p e r ton  F  C o e f f i c i e n t of f r i c t i o n  pounds per pound  Table I I I .  Variable  Symbol G  Alignment V a r i a b l e s  Grade (+  favourable)  (- adverse)  Units per  cent  per  cent  feet  SL  Section length  SDE  Sight distance  empty  feet  SDL  Sight distance  loaded  feet  CR  Curve  BETA  Superelevation  degrees  PK  Existing  —  radius  Surface  feet  - 14 -  CHAPTER IV PROGRAMMING THE MODEL 4.1  G e n e r a l Assumption The g e n e r a l assumption  i s t h a t , as t h e loaded v e h i c l e s w i l l be  more a f f e c t e d by the p h y s i c a l c h a r a c t e r i s t i c s o f the road alignment and surface  than t h e empty v e h i c l e s , t h e optimum p o l i c y f o r the problem w i l l  be determined  by t h e l o a d e d v e h i c l e s and n o t the empty v e h i c l e s .  G e n e r a t i o n o f an optimum p o l i c y i n the d i r e c t i o n o f t r a v e l o f the l o a d e d v e h i c l e does n o t n e c e s s a r i l y mean the p o l i c y w i l l be optimum f o r the empty v e h i c l e or f o r the e n t i r e system.  The o v e r a l l optimum would be  the optimum f o r the combined system of loaded and empty v e h i c l e s where both a r e i n f l u e n c e d by t h e i n p u t  speed  from t h e p r e v i o u s s e c t i o n s .  An  a r e a o f f u r t h e r i n v e s t i g a t i o n may be to t r y by some i t e r a t i v e p r o c e s s to combine o p t i m a l o r suboptimal p o l i c i e s f o r loaded and empty v e h i c l e s to f i n d the t r u e o p t i m a l p o l i c y . I t must be s t r e s s e d a c y c l i c network. one  without  changing  t h e assumptions o r  used i n the model.  Computer program The number o f c a l c u l a t i o n s n e c e s s a r y  s t a t e s a r e generated, for  i s a type o f  An a c y c l i c network i s one t h a t has an o p t i m a l p o l i c y i n  d i r e c t i o n and cannot be r e v e r s e d  conditions  4.2  t h a t t h e model as developed  to ensure  that a l l p o s s i b l e  and the o p t i m a l s t a t e f o r each s e c t i o n i s a v a i l a b l e  the backward pass, l e d to t h e use o f the computer to c a l c u l a t e a l l  the s t a t e v a l u e s and c o s t s .  The program i s w r i t t e n  i n FORTRAN IV language  for  a n I B M 370  input  4.3  o u t l i n e d i n the  The p r o g r a m i s  Speed  flow diagram of  l i s t e d i n A p p e n d i x 6 w i t h an e x p l a n a t i o n  of  functions functions  generate the  limiting  vehicle  times  trip  vehicle operating functions  i n the  are  the model.  These  speeds on each s e c t i o n and from the  speeds  curve speed  is  for solution:  depending  on t h e  Maximum s a f e s p e e d  an o b s t r u c t i o n  sliding  for  speed to  on t h e  to  the  developed  are  used  used f o r  the  to o b t a i n the  the  speed  outside  a vehicle  or t i p p i n g  i n A p p e n d i x 1. the  can over.  The  following  w h e r e H i s HE o r H L ,  considered.  stopping for  stopping i s  stop s a f e l y before road,  v e h i c l e or o b s t r u c t i o n .  after  the  t h e maximum s p e e d  The r e l a t i o n s h i p s  The f u n c t i o n s u b p r o g r a m  the  of f r i c t i o n  and s i g h t  at which  h i t t i n g another v e h i c l e ,  operator  i n Appendix 2. coefficient  are  t h e maximum s p e e d  CR, F , BETA, H , 0 ;  case being  able  times  c a l l e d SLIDE and r e q u i r e d  variables  a vehicle is  is  i n v o l v e d are  subprogram  Maximum s a f e  The t r i p  functions  speed  negotiate a curve without  function  heart of  program.  curve  The r e l a t i o n s h i p s  the  F u n c t i o n s subprograms  computer  Maximum s a f e  are  calculated.  costs.  Maximum s a f e  4.3.2  conceptual  formatting.  The s p e e d  4.3.1  -  computer.  The p r o g r a m i s Figure 4.1.  15  is  has  observed  i n v o l v e d are  for  the  developed  c a l l e d STOP a n d  distance  or  requires  solution.  INITIALIZE 1. A l l o l d s t a t e t o t a l c o s t to maximum c o s t { f ( S ) = MAX} 0  1  0  2. Set one o l d s t a t e to zero c o s t { f ( l ) = 0.0} 0  INPUT Main s e c t i o n data  (road s e c t i o n  with constant t r a f f i c  density)  INPUT S u b s e c t i o n road parameters  F i g u r e 4.1  Flow diagram o f the program.  f o r s i m p l i c i t y the s t a t e v e c t o r s used i n the f l o w diagram are one-dimensioal "making the v e c t o r s t h r e e - d i m e n s i o n a l o n l y i n c r e a s e s the number o f l o o p s .  - 17 -  * COMPUTE The c o s t s t h a t a r e independent o f speed f o r each p o s s i b l e  surface  I INITIALIZE 1. Set a l l new s t a t e t o t a l c o s t s to maximum c o s t { f ( S ) n  n  = MAX}  2. Set s t a t u s = 0.0  F i g u r e 4.1  Flow diagram o f the program -  continued.  - 18 -  COMPUTE 1. Loaded and empty speeds of a l l vehicles 2. P r e s e n t all  F i g u r e 4.1  discounted  cost of  future operating  costs  Flow diagram of the program -  continued.  - 19  -  1. T o t a l a l l c o s t s of new 2. Add  states  c o s t of i n p u t o l d s t a t e  for  testing  {TEST = C  s  K  f^CS^i)}  +  Yes  1. I t i s a lower c o s t route to a new  state  2. T r a n s f e r a l l i n f o r m a t i o n of new  state {including  f (S )  = TEST}  n  n  0  F i g u r e 4.1  ©  Flow diagram of the program - c o n t i n u e d .  F i g u r e 4.1  Flow diagram of the program - c o n t i n u e d .  4.3.3  21  -  Maximum s a f e speed o f descent Maximum s a f e speed o f descent i s the c o n s t a n t speed a t which the b r a k i n g c a p a c i t y forces  of the v e h i c l e ' s  a r e e x a c t l y b a l a n c e d by the f o r c e o f g r a v i t y p u l l i n g t h e  v e h i c l e down the grade. i n Appendix 3. the  engine and the r e s i s t a n c e  The r e l a t i o n s h i p s i n v o l v e d  The f u n c t i o n  following variables  a r e developed  subprogram i s c a l l e d SPEED and r e q u i r e s  for solution:  R, W, G, BHP, BC, FA; where  W = WE o r WL and FA = FAE o r FAL.  4.3.4  Maximum a v a i l a b l e speed o f v e h i c l e Maximum a v a i l a b l e speed i s the speed l i m i t e d by the a b i l i t y o f the engine to generate t r a c t i v e e f f o r t . are  developed i n Appendix 4 .  The r e l a t i o n s h i p s  There a r e two f u n c t i o n  involved  subprograms,  POMPHF f o r the l o a d e d v e h i c l e and POMPHI f o r the empty v e h i c l e . d i f f e r e n c e between the two b e i n g t h a t of one m.p.h.  The  the second uses an i n p u t  speed  The v a r i a b l e s n e c e s s a r y f o r s o l u t i o n o t h e r than  input  speed a r e : R, W, G, SL, BHP, FA, CC; where CC i s the f a c t o r used f o r a c c e l e r a t i o n and d e c e l e r a t i o n  4.3.5  S o l u t i o n of c u b i c The  4.4  as e x p l a i n e d  i n Appendix 4 .  relationships  r e l a t i o n s h i p s developed f o r the f u n c t i o n s  and  4.3.4 resulted i n cubic  The  s o l u t i o n of the c u b i c e q u a t i o n s i s e x p l a i n e d  i n Section  e q u a t i o n s i n the unknown v a r i a b l e  4.3.3 speed.  i n Appendix 5.  Program Output A sample of the program output i s g i v e n i n Appendix 7. A l l  feasible states  f o r each s e c t i o n a r e l i s t e d  can be made to f i n d the o p t i m a l p o l i c y .  such t h a t  the backward pass  -  The f i r s t ALT  22 -  l i n e f o r each s t a t e g i v e s t h e f o l l o w i n g :  s t a t e number which connects t h e p r e s e n t s e c t i o n o f road w i t h the f o l l o w i n g  s e c t i o n f o r backward pass  DOLRMC  t o t a l accumulated road maintenance  DOLRCC  t o t a l accumulated road s u r f a c i n g  DOLTOT  t o t a l accumulated  SURFACE  s u r f a c e used on the p r e s e n t s e c t i o n  cost  cost  cost  OLD ALTERNATIVE s t a t e number from the p r e v i o u s s e c t i o n which r e s u l t e d i n the present state  ( I f t h e p r e s e n t s t a t e i s p a r t of the optimum  p o l i c y then the o l d a l t e r n a t i v e i s a l s o optimum),  The second and s u c c e e d i n g l i n e s f o r each s t a t e g i v e the following  i n f o r m a t i o n f o r each v e h i c l e type:  VEHICLE  v e h i c l e number  EMPTY MPH Empty speed a t s t a r t o f s e c t i o n LOADED MPH  Loaded speed a t end o f s e c t i o n  TRIP TIME T o t a l accumulated t r a v e l time i n minutes DOLOP  T o t a l accumulated o p e r a t i n g  cost  DOLTIR  T o t a l accumulated t i r e  DOLMAV  T o t a l accumulated v e h i c l e maintenance  cost cost.  - 23 -  CHAPTER V MODEL RESULTS 5.1  Hypotehtical  problem  The h y p o t h e t i c a l problem was made up u s i n g t h r e e v e h i c l e types and  t h r e e road s u r f a c e s .  The v e h i c l e s used were highway l o g g i n g  18 passenger crew busses and 3-ton s e r v i c e v e h i c l e s .  Operating  were based on c u r r e n t IWA wage r a t e s and c o s t s p u b l i s h e d News (March, 1976). Current  trucks, rates  i n B.C. Logging  The t h r e e s u r f a c e s were d i r t , , g r a v e l and pavement.  t i r e costs r e l a t i v e to the three surfaces are not a v a i l a b l e , but  c o s t s f o r the l a t e 1950's a r e g i v e n i n t h e Logging Road Handbook by Byrne (1960).  Current  t i r e c o s t s f o r g r a v e l s u r f a c e s were taken from  B.C. Logging News (March, 1976). inflated  T i r e costs f o r d i r t  and pavement were  to c u r r e n t c o s t s p r o p o r t i o n a l t o t h e i n c r e a s e i n t i r e c o s t s f o r  gravel surfaces.  A t e n year a m o r t i z a t i o n p e r i o d w i t h an i n t e r e s t r a t e o f  ten p e r cent was used. The road alignment was made up from p e r s o n a l author i n road  l a y o u t and c o n s t r u c t i o n .  (adverse) and +15% ( f a v o r a b l e ) , b e i n g constructed  i n the f o r e s t i n d u s t r y .  experience  of the  Road grade was v a r i e d between -6%  r e p r e s e n t a t i v e o f system roads  being  The number o f t r i p s p e r y e a r f o r  l o g g i n g t r u c k s were v a r i e d from 1 to 24 thousand p e r year,  e q u i v a l e n t to  a p p r o x i m a t e l y 1 to 24 m i l l i o n c u b i c f e e t o f wood p e r y e a r .  The t r a f f i c  d e n s i t i e s f o r crew busses was 10% o f l o g g i n g t r u c k d e n s i t i e s , and s e r v i c e v e h i c l e s were 10% o f crew bus d e n s i t i e s .  -23-  CHAPTER V MODEL RESULTS 5.1  Hypothetical The  and  problem  h y p o t h e t i c a l problem was made up u s i n g t h r e e v e h i c l e types  three road  surfaces.  The v e h i c l e s used were highway l o g g i n g  18 passenger crew busses and 3-ton s e r v i c e v e h i c l e s . were based on c u r r e n t News (March, 19 76). Current  tire  IWA wage r a t e s and c o s t s p u b l i s h e d The t h r e e  s u r f a c e s were d i r t , 1  c o s t s r e l a t i v e t o the t h r e e  c o s t f o r the l a t e 1950's were g i v e n Byrne (1960).  Current  tire  gravel  to current  surfaces  rates  i n B.C. Logging  g r a v e l and pavement.  a r e not a v a i l a b l e , but  i n The Logging Road Handbook by  c o s t s f o r g r a v e l s u r f a c e s were taken from  B.C. Logging News (March, 1976). inflated  Operating  trucks,  T i r e costs f o r the other  s u r f a c e s were  c o s t s p r o p o r t i o n a l t o the i n c r e a s e i n t i r e  costs f o r  surfaces. The  c a p i t a l c o s t o f the road  a t e n year p e r i o d . to d i s c o u n t  author i n road  road  over  To do t h i s an i n t e r e s t r a t e o f t e n per cent was used  f u t u r e c o s t s , o f s u r f a c e maintenance and v e h i c l e The  alignment was made up from p e r s o n a l  l a y o u t and c o n s t r u c t i o n .  ( a d v e r s e ) and +15% ( f a v o r a b l e ) , being constructed  s u r f a c e was t o be amotrized  i n the f o r e s t i n d u s t r y .  operation.  experience  o f the  Road g r a d i e n t was v a r i e d between -  r e p r e s e n t a t i v e o f system roads  being  The number o f t r i p s per year f o r  l o g g i n g t r u c k s were v a r i e d from 1 t o 24 thousand per year,  equivalent to  a p p r o x i m a t e l y 1 t o 24 m i l l i o n c u b i c f e e t o f wood p e r year.  The t r a f f i c  d e n s i t i e s f o r crew busses was 10% o f l o g g i n g were 107 o f crew bus--densities. o  '''native c l a y and rock mixture.  t r u c k s , and s e r v i c e v e h i c l e s  The c o s t s used a r e g i v e n i n Appendix 8  - 24 5.2  Length o f s u b s e c t i o n s The  u n t i l near  importance  o f the l e n g t h o f the s u b s e c t i o n s was n o t r e a l i z e d  the end o f the study and almost  the dynamic program model.  caused a complete f a i l u r e o f  I f the l e n g t h o f a l l the s u b s e c t i o n s a r e over 150  f e e t , the dynamic program model w i l l  g i v e the same r e s u l t as a s i m p l e  model t h a t o n l y c a l c u l a t e s the c o s t s f o r the t h r e e s u r f a c e s u s i n g the minimum c o s t a l t e r n a t i v e from the p r e v i o u s s e c t i o n .  T h i s o c c u r s because  i n a l o n g s e c t i o n the v e h i c l e s a r e a b l e to reach a maximum speed not determined  by the a c c e l e r a t i o n or d e c e l e r a t i o n r e s i s t a n c e .  o c c u r s the optimum i s independent  o f i n p u t speed.  When t h i s  T h e r e f o r e , t h e r e i s no  i n c e n t i v e t o spend e x t r a d o l l a r s on the p r e s e n t s e c t i o n , t o i n c r e a s e the i n p u t speed  to the next s e c t i o n , because i t w i l l have no e f f e c t on the  f i n a l speed i n t h e next s e c t i o n .  When t h i s o c c u r s the o p t i m a l p o l i c y i s  to use the minimum c o s t s t a t e i n a l l s u b s e c t i o n s .  5.3  Significant  results  Two s i g n i f i c a n t r e s u l t s arose from the h y p o t h e t i c a l problem. First,  the e f f e c t of t r a f f i c d e n s i t y (volume o f wood) on o p t i m a l p o l i c y  was c o m p a r a t i v e l y s m a l l .  Second, the e f f e c t of grade on o p t i m a l p o l i c y  was c o m p a r a t i v e l y l a r g e .  These r e s u l t s a r e the o p p o s i t e o f what was  expected The  a f t e r a review o f t h e l i t e r a t u r e r e g a r d i n g road s t a n d a r d  l i t e r a t u r e on road standards  emphasizes the use o f volume o f wood  h a u l e d o r t r a f f i c d e n s i t y to determine  the optimum road s t a n d a r d .  standards o n l y p l a c e an upper and lower l i m i t Although it  selection.  Road  on grade f o r each s t a n d a r d .  s u r f a c e s e l e c t i o n i s n o t the same problem as s t a n d a r d  selection  i s one o f t h e main f a c t o r s i n c o r p o r a t e d i n t o s t a n d a r d s e l e c t i o n .  The  - 25 r e l a t i v e e f f e c t s o f t r a f f i c d e n s i t y and grade on o p t i m a l s u r f a c e a r e shown i n F i g u r e 5.1.  5.4  Importance o f d i f f e r e n t  types o f v e h i c l e s  The v a l u e o f u s i n g t h r e e v e h i c l e types able. The  i n the model i s q u e s t i o n -  The h y p o t h e t i c a l problem was r e r u n u s i n g o n l y the l o g g i n g  r e s u l t s were the same a l t h o u g h  truck.  the s e c t i o n s where the s u r f a c e was about  to change d i d have much s m a l l e r m a r g i n a l  c o s t s between a l t e r n a t i v e  There i s a danger, however, when u s i n g one v e h i c l e type q u a l i t y s u r f a c e i s n o t chosen soon enough.  surfaces.  t h a t the h i g h e r  Two o r more v e h i c l e  types  s h o u l d be used when secondary v e h i c l e s comprise a major p o r t i o n o f t o t a l transportation costs.  5.5  Changing s u r f a c e s along  the road  There i s no allowance made i n the program.for the e x t r a c o s t i n v o l v e d by changing from one s u r f a c e to another.  I t i s obvious from the  r e s u l t s t h a t i n cases where t h e r e a r e d i f f e r e n t s u s t a i n e d grades w i t h d i f f e r e n t o p t i m a l s u r f a c e s t h a t the e x t r a t r a n s i t i o n c o s t would be o v e r come.  - 26 24  \\ \\ \\ \\ \\ \\ \\ \\ \\ \  12  \  \  \  \  \  \  \  \  N  ^1  2 1 -6  -4  -2  +0  +2  +4 PER  Legend:  Surface 1  +6  CENT  +8  +10  +12  GRADE  (dirt)  Surface 2 (gravel) \  F i g u r e 5.1  Effect  >  \'\^  > s  \  Surface 3  (pavement)  of t r a f f i c d e n s i t y and grade on optimum s u r f a c e .  +14  -27-  CHAPTER VI DISCUSSION AND CONCLUSIONS 6.1 Areas o f f u r t h e r i n v e s t i g a t i o n This  study frought  investigated further. be  c a r r i e d out.  t o l i g h t many q u e s t i o n s  There a r e two main c a t e g o r i e s  F i r s t , modifications  of research  be that  could  t o the model and second, e x t e n s i o n o f  the technique beyond the problem o f road Modifications  t h a t should  surfaces.  t o the model  Improvement o f the model c o u l d  p o s s i b l e be made by a d d i t i o n t o  or m o d i f i c a t i o n o f the model i n the f o l l o w i n g ways: 1.  Incorporation  o f curve r e s i s t a n c e i n t o the model.  2.  The use o f speed p r o f i l e s f o r e s t i m a t i o n  o f speed o f v e h i c l e s as  used by Roberts (1966) and Levesque (1975). 3.  Consideration  o f changing weather and i t s e f f e c t s on road  surface  characteristics. 4.  Allowance f o f improved morale and j o b e f f i c i e n c y o f employees as a r e s u l t o f h i g h e r  5.  Consideration  q u a l i t y surfaces.  to t r a f f i c  i n t e r a c t i o n and d e l a y  maintenance as a f u n c t i o n o f t r a f f i c 6. Extension  times f o r s u r f a c e  d e n s i t y and s u r f a c e  type.  V a r i a t i o n i n load s i z e o f v e h i c l e s w i t h season. o f Technique There i s a p o s s i b i l i t y o f e x t e n d i n g the technique developed  i n t o the f i e l d  o f road standards, t o be used f o r d e f i n i n g as w e l l as  choosing optimum road standards. for extension  The technique a l s o has p o s s i b i l i t i e s  i n t o the woods, p o s s i b l y t o study y a r d i n g  optimization.  -286.2  Conclusion A dynamic programming model was developed t o s e l e c t the optimum  road  s u r f a c e f o r an e x i s t i n g l o g g i n g road.  from t e s t i n g of the model on a h y p o t h e t i c a l 1.  Road g r a d i e n t  road.  surface.  T r a f f i c d e n s i t y o r volume o f wood t o be t r a n s p o r t e d importance next to g r a d i e n t  i f the road  Greater  roads be b u i l t  a constant  road  surface.  change over the The p r a c t i c e  s u r f a c e r e g a r d l e s s of  demand f o r wood and l e s s a c c e s s i b l e timber, d i c t a t e t h a t  i n more rugged t e r r a i n , ^ a n d  v a r i a t i o n i n grades. look a t road  s u r f a c i n g should  has a l a r g e v a r i a t i o n i n grade.  i n the f o r e s t i n d u s t r y i s to m a i n t a i n gradient.  i s of minor  i n s e l e c t i o n o f optimum road  The p r o j e c t i n d i c a t e s t h a t road l e n g t h of a road,  arose  i s the most important c r i t e r i a f o r s e l e c t i o n  of optimum road 2.  Two main c o n c l u s i o n s  Therefore,  t h a t t h e r e w i l l be a wider  i n d u s t r y and government should  take a new  s u r f a c i n g , so t h a t more v a r i a t i o n over the l e n g t h of road i s  possible. The model does g i v e some s h o r t s e c t i o n s of v a r y i n g These are v a l i d  surfaces.  i n the case when the a l t e r n a t e s u r f a c e s are d i r t and  g r a v e l , as g r a v e l can e a s i l y be a p p l i e d to s h o r t s e c t i o n s o f road.  In  the case where the v a r i a t i o n i s between g r a v e l and pavement, the t e c h n i c a l problems o f c o n s t r u c t i n g s h o r t s e c t i o n s o f pavement and the problems o f joining  the s u r f a c e s , ^ t h e  s h o r t s e c t i o n s should  l a t t e r case the same o p t i m a l  be e l i m i n a t e d .  p o l i c y can be a r r i v e d at u s i n g a  model t h a t takes the minimum c o s t f o r each s u b s e c t i o n o f road dynamic programming model i s not n e c e s s a r y . decide  I n the simple and the  The model can be used t o  the s u r f a c i n g p o l i c y when two or t h r e e d i f f e r e n t q u a l i t y g r a v e l  s u r f a c e s are to be a p p l i e d t o a g i v e n  road.  - 29 -  BIBLIOGRAPHY Adamovich,  L. 1968. L e c t u r e on t r a c t i v e e f f o r t . Given to F o r e s t H a r v e s t i n g c l a s s a t U n i v e r s i t y of B r i t i s h Columbia. . 1974. Road network and r o a d s p a c i n g p l a n n i n g . Paper p r e s e n t e d f o r Seminar.New Requirements i n f o r e s t road e n g i n e e r i n g FP2406 U n i v e r s i t y of B r i t i s h Columbia, F a c u l t y o f F o r e s t r y and Centre f o r C o n t i n u i n g E d u c a t i o n . 11pp.  American A s s o c i a t i o n of S t a t e Highway O f f i c i a l s (AASHO). 1965. A p o l i c y on geometric d e s i g n o f r u r a l highways. Washington, D . C , 650 pp. Bellman, R.E. New B.C.  1957. Dynamic programming, Jersey. 342 pp.  Logging News, March. 1976. Vancouver, B.C. l p .  Boyd, C.W.  Princeton University Press,  Highway c o a s t a l l o g t r u c k  rates,  and G.G. Young. 1969. A study on equipment replacement, maintenance, i n v e n t o r y and r e p a i r p o l i c y f o r one c l a s s of vehicles. U n p u b l i s h e d r e p o r t , F a c u l t y of F o r e s t r y , U n i v e r s i t y of B r i t i s h Columbia, 62 pp.  Byrne, J . J . , R.J. N e l s o n and P.H. Googins. 1960. Logging road handbook: the e f f e c t of road d e s i g n on h a u l i n g c o s t s . U.S. Department o f A g r i c u l t u r e , A g r i c u l t u r e Handbook 183, 65 pp. Harkness, W.D. 1959. Truck performance and minimum road s t a n d a r d s . Woodl. S e c t . Index, Canadian Pulp and Paper A s s o c . No. 1981 (B-8-a), 10 pp. Hay, W.W.  1961. An i n t r o d u c t i o n to t r a n s p o r t a t i o n e n g i n e e r i n g . W i l e y & Sons I n c . , New York. 505 pp.  John  Hennes, R.G. and M. Ekse. 1969. Fundamentals of t r a n s p o r t a t i o n e n g i n e e r i n g . McGraw-Hill, I n c . , New York. 613 pp. Hillier,  F.S. and G.J. Lieberman. 1967. I n t r o d u c t i o n to o p e r a t i o n s r e s e a r c h . Holden-Day, I n c . , San F r a n c i s c o . 639 pp.  Levesque, Y. 1975. A d e t e r m i n i s t i c s i m u l a t i o n model of l o g g i n g t r u c k performance. U n p u b l i s h e d t h e s i s , U n i v e r s i t y of B r i t i s h Columbia. 107 pp. • Matthews, D.M. 1942. Cost c o n t r o l i n the l o g g i n g i n d u s t r y . Inc., New York. 374 pp.  McGraw-Hill,  N i k o l i c , S. 1972. T h e o r e t i c a l b a s i s f o r d e t e r m i n i n g the optimum d e n s i t y of a f o r e s t road network. Sumanstuo, B e o g n u l l , Y u g o s l a v i a T r a n s l a t i o n from Environment Canada. 17 pp.  Paterson,  Perrin,  -  W.G. et a l . 1970. A proposed forest road c l a s s i f i c a t i o n system. P u l p and Paper R e s e a r c h I n s t i t u t e o f Canada, P o i n t e C l a i r e , P . Q . , Woodlands Paper N o . 20. 45 p p .  P . Y . 1968. P r a c t i c a l m e t h o d o f n e t w o r k o p t i m i z a t i o n f o r wood t r a n s p o r t a t i o n by t r u c k . Laval University, Quebec. 10 p p .  Peurifoy,  Riggs,  30  R . L . 1970. McGraw-Hill,  J.L. 1975. science.  C o n s t r u c t i o n p l a n n i n g , equipment, I n c . , New Y o r k . 696 p p .  Introduction McGraw-Hill,  and  methods.  t o o p e r a t i o n s r e s e a r c h a n d management I n c . , New Y o r k . 497 p p .  Roberts,  P . O . , and J . H . S u h r b i e r . 1966. Highway l o c a t i o n a n a l y s i s : example p r o b l e m . MIT, Report No. 5.  Taborek,  J.J. 1957. Mechanics of v e h i c l e s . Publishing Co., Cleveland. 93 p p .  Wagner,  Weast,  H . M . 1969. P r i n c i p l e s of operations I n c . , New J e r s e y . 937 p p .  M a c h i n e D e s i g n , The  research,  an  Penton  Prentice-Hall,  R . C . et a l . 1964. M a t h e m a t i c a l t a b l e s from handbook o f c h e m i s t r y and p h y s i c s . The C h e m i c a l R u b b e r C o . , C l e v e l a n d , O h i o . 458 p p .  -  31  -  APPENDIX  1  MAXIMUM SAFE CURVE SPEED The c e n t r i f u g a l of  t h e v e h i c l e i n one o f  or  t h e v e h i c l e may s l i p  the  resultant  the  grade l i n e at  wheels force  and the  force,  is  on a v e h i c l e i n a curve l i m i t s the  two w a y s . to  force vector  E x c e s s i v e s p e e d may r e s u l t  the o u t s i d e  of  a c t i n g on the  the  ground  (Figure A l . l ) .  acting  e x c e e d e d by t h e  a c t i n g away f r o m t h e  towards  center of  of contact  center of  the  of  the  and the  curve a l o n g the  when  outside frictional  Cross-section of a vehicle i n tipping c o n d i t i o n on a s u p e r e l e v a t e d c u r v e .  the  centrifugal  ground  A1.2).  Figure A l . l  tipping  intersects  curve along  of v e h i c l e weight the  in  speed  Tipping occurs  S l i p p i n g o c c u r s when t h e  the  resultant  curve.  center of gravity  a p o i n t beyond the p o i n t  on the wheels  ground,  force  (Figure  Conditions of  t h e moments  R  x  32  -  f o r n o n - t i p p i n g d r i v i n g c a n be d e r i v e d by e q u i l i b r i u m  about A ( F i g . A l . l ) as  follows:  H = R 0 y  (Al.l)  where R  = resultant  in x-direction lb.  = resultant  in y-direction lb.  H  = height  center  0  = projected  R  x y  to  of g r a v i t y  distance  ft.  from c e n t e r  to o u t s i d e wheels,  of  gravity  ft.  since W v g CR 2  C  =  '  R  x  = C cosg - W sinf  R  y  = C sing + W cosf  where C  = centrifugal  force,  W  = weight of v e h i c l e s ,  v  = speed,  lb. lb.  ft/sec. 2  g  = a c c e l e r a t i o n of g r a v i t y ,  CR = r a d i u s  of curvature,  ft/sec.  ft.  g = angle of s u p e r e l e v a t i o n , deg. By r e p l a c i n g C , R a n d R i n e q u a t i o n x y  V  m  a  X  =  {  . g CR (0 + H tang) , } (H - 0 tang)  2  c f t  (Al.l)  , '/seC"  gives hour  t h e maximum s p e e d the  equation  33  -  on a curve p r i o r  to  tipping.  r CR (0 + H t a n g ) , { ^ o' t a n g ) " *  • m.p.h.  Changing to m i l e s  per  becomes,  c to S , max = 3 . 9  S l i p p a g e o c c u r s when  Figure A1.2  EFF -  (C  - W )  Cross-section of a v e h i c l e i n s l i p p i n g c o n d i t i o n on a s u p e r elevated curve.  (A1.2)  Conditions equilibrium of the  the  road surface.  v  s'  for  skid-free  frictional, Levesque  34  -  curve  d r i v i n g can be d e r i v e d  centrifugal  (1975)  derived  the  forces  parallel  to  following:  h  g CR ( t a n g + y ) rz — T ^ T (1 - y tang) s  , max = {  and w e i g h t  by  }  ft./sec.  (A1.3)  where v u  , max = maximum s p e e d o n c u r v e p r i o r = coefficient  s  of s l i d i n g  to  slipping  friction,  E q u a t i o n A 1 . 3 can be m o d i f i e d by e x p r e s s i n g coefficient  u  also  i n terms o f  s  the  frictional  the  frictional  angle  = tan$  converting  to m i l e s per  hour  i,  S , max = 3 . 9  '2  { CR tan(.3+ 0) }  The maximum s a f e force  is  S , max  the  smaller  (A1.4).  of  curve  s p e e d as  t i p p i n g speed S  t >  m.p.h.  c o n t r o l l e d by max  (A1.4)  centrifugal  ( A 1 . 2 ) and s l i p p i n g  speed  -  35  -  APPENDIX 2 MAXIMUM SAFE SPEED FOR STOPPING The  safe  speed i s l i m i t e d by the  sight distance which allows  room to s t o p b e f o r e h i t t i n g an o b s t r u c t i o n on t h e r o a d . where t h e r e i s n o t enough room t o p a s s , react The  and a p p l y t h e b r a k e s  time a d r i v e r s i g h t s brakes.  an o b j e c t  Braking distance  is  the d i s t a n c e  r e q u i r i n g a stop u n t i l  the  distance  to  collision.  t h e sum o f r e a c t i o n d i s t a n c e  Reaction distance i s  roads,  b o t h d r i v e r s must h a v e t i m e  t o come t o a c o m p l e t e s t o p b e f o r e  stopping distance of a v e h i c l e i s  braking distance.  On l o g g i n g  and  t r a v e l l e d from he has  travelled while  the  applied  the  the brakes  are  applied. A r e a c t i o n time o f 2.5 seconds b e t w e e n . s i g h t i n g an and  a p p l y i n g the brakes  distance  i s recommended b y t h e AASHO ( 1 9 6 5 ) .  obstacle Reaction  r e q u i r e d f o r each d r i v e r to a p p l y the brakes would then  RD = 2 . 5 x 1 . 4 7  S = 3.67 S f t .  be  (A2.1)  where RD = r e a c t i o n d i s t a n c e , S  = speed,  ft.  m.p.h.  B r a k i n g d i s t a n c e on l e v e l  grade r e q u i r e d to stop a v e h i c l e  a g i v e n s p e e d was d e r i v e d b y L e v e s q u e ( 1 9 7 5 )  BD =  f  64.32 v  s  t  V  to  be,  < '> A2  2  from  -  36  -  where BD = b r a k i n g d i s t a n c e , v y  = speed, s  D  ft/sec.  = c o e f f i c i e n t of s l i d i n g  Converting equation  B  ft.  '  (A2.2)  to speed,  friction  s,  i n m i l e s per  hour,  29 9M S  < A 2  -  3 )  s the e f f e c t opposite  of grade  on b r a k i n g d i s t a n c e  direction for  for both drivers  is  the  two t i m e s  Maximum s a f e (SD) a n d t h e and  two d r i v e r s ,  speed  the  is  c o n s i d e r e d t o be e q u a l b u t  therefore,  distance  the b r a k i n g  r e q u i r e d on l e v e l  distance  grade.  f o r s t o p p i n g as a f u n c t i o n o f s i g h t  c o e f f i c i e n t of f r i c t i o n  is  found by a d d i n g e q u a t i o n s  ( A 2 . 3 ) m u l t i p l y i n g b y two a n d s o l v i n g t h e  resulting  distance (A2.1)  quadratic  equation for S  S  2  59.8 u  s  + 7.34  S- -  SD = 0  of  (A2.4)  -  37  -  APPENDIX 3 MAXIMUM SAFE SPEED OF DESCENT The maximum s a f e  speed o f a l o g g i n g t r u c k i s a l s o c o n t r o l l e d  by t h e b r a k i n g c a p a c i t y o f t h e  truck.  excessive heating of service brakes, e q u i p p e d w i t h some s o r t  Long steep grades r e s u l t therefore,  most l o g g i n g t r u c k s  o f r e t a r d i n g d e v i c e s u c h as a J a c o b s  brake.  The c a p a c i t y o f e n g i n e r e t a r d e r s  percent  o f b r a k e h o r s e p o w e r a n d c a n be e x p r e s s e d  BE =  3  7  5  ;  C  B  H  in  i s u s u a l l y expressed  are  engine as  a  as a f u n c t i o n o f  speed.  (A3.1)  P  where BE = b r a k i n g e f f o r t ,  lb.  BC = b r a k i n g c a p a c i t y , % BHP= b r a k e h o r s e S  = speed,  power  m.p.h.  The t o t a l b r a k i n g f o r c e i n c l u d e s a i r r e s i s t a n c e resistance. by T a b o r e k  A i r resistance  is  g i v e n by the  following  and  rolling  equation developed  (1957).  R  a  = C  a  0.01 A S  (A3.2)  2  where R C A  a a  = air resistance, = a i r resistance = f r o n t a l area,  lb. coefficient, lb-sec sq.ft.  2  -ft  -4  Using a value of 0.3, coefficient  R  s e l e c t e d from Taborek  for logging  trucks equation  = 0.003 A S  a  Rolling resistance  3  7  5  (A3.2)  for  the a i r  resistance  becomes,  (A3.3)  2  ton of v e h i c l e weight.  the v e h i c l e then  B =  (1957),  i s d i r e c t l y p r o p o r t i o n a l t o v e h i c l e w e i g h t and  e x p r e s s e d as pounds p e r to stop  38 -  ^  C  B  H  P  The t o t a l f o r c e s  is tending  are,  + 0.003 A S  2  + R W  (A3.4)  where B  = total braking forces,  R  = rolling  W  = vehicle weight,  resistance,  To m a i n t a i n a c o n s t a n t b r a k i n g f o r c e s must b a l a n c e vehicle.  The g r a d e  the  lb.  lb./ton  tons  or c o n t r o l l e d speed of descent  grade f o r c e t e n d i n g to a c c e l e r a t e  force i s expressed  GF = - 2 0 W G  the  above  the  as,  (A3.5)  where GF = g r a d e G  force,  lb.  = g r a d e as p e r c e n t ,  n e g a t i v e when v e h i c l e t r a v e l l i n g  downhill.  F o r m u l a A 3 . 5 i s an a p p r o x i m a t e r e l a t i o n s h i p and h o l d s t r u e o n l y f o r less  t h a n 15%.  grades  -  Combining equations  (A3.4)  375 BC BHP  simplified  into  cubic  +  0  i  0  and  0  A S  3  +  t h e maximum s a f e (A3.7)  as  -  (A3.5)  + R W + 2 0 W G = 0  2  (A3.6)  f o r m i n t e r m s o f S , A 3 . 6 becomes  3 , W (R + 20 G) S  39  0.003 A  S  +  375 BC BHP 0.003 A " °  speed of descent  shown i n A p p e n d i x  5.  i s found  by s o l v i n g  , {  the  A  cubic  . 5  '  7  )  equation  -  40  -  APPENDIX 4 MAXIMUM A V A I L A B L E SPEED OF V E H I C L E The the  engine.  resistance The  speed o f a v e h i c l e i s  a v a i l a b l e power o f  The p o w e r o f t h e v e h i c l e m u s t b e a b l e to m o t i o n caused b y : r o l l i n g ,  air,  to overcome  grade  f o r c e a v a i l a b l e to overcome t h e s e r e s i s t a n c e s  and c a n be found from the and  l i m i t e d by t h e  and  the  acceleration.  i s measured as  r e l a t i o n s h i p between brake h o r s e power,  rimpull speed  rimpull.  RP  EE 375 BHP S  (A4.1)  where RP = r i m p u l l ,  lb.  EE = e f f i c i e n c y t o be 85%  o f v e h i c l e power t r a i n u s u a l l y  BHP= b r a k e h o r s e S  = speed,  power  m.p.h.  Rolling resistance of  a i r and grade  are  considered  is  g i v e n i n A p p e n d i x 3 and t h e  g i v e n by e q u a t i o n s  acceleration resistance  is  g i v e n by the  and  following  (A3.5).  66.8 W ( S SL  SI )  AR  a c c e l e r a t i o n or d e c e l e r a t i o n resistance  SI  initial  SL  distance  2  (A4.2)  where  speed,  The  e q u a t i o n . f r o m Hay  AR  2  -  (A3.3)  resistances  lb.  m.p.h.  to a c c e l e r a t e  or decelerate,  ft.  (1961).  Equation  (A4.2)  does n o t  parts of v e h i c l e s . for  by m o d i f y i n g  41  account for  the  a c c e l e r a t i o n of  A c c o r d i n g to Adamovich the  factor  CC = 6 6 . 8 + 6 6 . 8  66.8  as  (1968)  this  the  rotating  c a n be  accounted  follows.  (A4.3)  w  where CC = m o d i f i e d  factor  WR = w e i g h t o f  for  equation  rotating parts,  (A4.2)  tons.  C o m b i n i n g r o l l i n g r e s i s t a n c e and e q u a t i o n s : (A4.3)  and e q u a t i n g t o  equation  R W + 0.003 A S I  2  (A4.1)  (A3.3),  (A3.5),  (A4.2)  and  yields,  + 20 WG +  C  C  ^  W  "  S  I  ^  = °-  8  5  3  7  5  B  M  >  (A4.4) Simplifying  S  into  3  +  cubic  form i n terms of  { W ( 2 0 G+R) -  SI  3 1 8 . 7 5 BHP SL CC w  Equation  equation  (A4.5)  as  it  shown i n A p p e n d i x  must d e c e l e r a t e ,  sufficient or  2  -z^zz } S  =  The maximum a v a i l a b l e  When t h e r e i s n o t vehicle  + 0.003 A S I  2  v  A 4 . 5 assumes t h a t S i s g r e a t e r  accelerating.  S,  remain  than S I ,  speed i s  i.e.,  found  the  vehicle  by s o l v i n g  the  is cubic  5. power a v a i l a b l e . t o at  accelerate  constant v e l o c i t y .  the  Following  the  above p r o c e d u r e the  following  42  -  cubic equation  for  deceleration  can  be  derived:  S  3  +  {W(20G+R) + ^ f ^  +  3 1 8 . 7 5 BHP SL CC W  E q u a t i o n A 4 . 6 assumes t h a t decelerating. of  the  S will  SI  2  =  as  2  ^ T ^ >  S  Q  be l e s s  The maximum a v a i l a b l e  cubic equation  + 0.003 A S I  than S I ,  speed i s  shown i n A p p e n d i x 5 .  again  i.e.,  the  vehicle  found by the  is  solution  -  SOLUTION OF CUBIC  3  -  APPENDIX  5  roots  the  EQUATIONS  The s o l u t i o n o f  x  43  the  of  c u b i c equations i n the  form  + ax + b = 0  where  is  x  = unknown  a  = coefficient  b  = constant  g i v e n by Weast  solution let,  then  the values  x  j.  = A +  I  f  1  1  If  T>  B,  3  i 2 b_ 4  3 a_ 27  ^  +  %  first  power  term  -  of x w i l l  be g i v e n b y ,  A + B . A - B  I  =-  A + B  — 2 — V  ~  '  2  ^ —  i 2  o f unknown t o  (1964).  "For  A  variable  +  there w i l l roots.  '  <0,  b e one r e a l  A - By  r-  2 * ~  root  a n d two c o n j u g a t e  imaginary  t h e r e w i l l be are e q u a l .  three r e a l  r o o t s o f w h i c h two a t  there w i l l  three r e a l  and unequal  be  roots."  least  1  Weast, R . C . et a l . 1964, M a t h e m a t i c a l T a b l e s from Handbook o f C h e m i s t r y and P h y s i c s . The C h e m i c a l R u b b e r C o . , C l e v e l a n d , O h i o . p . 3 2 0 .  The i m p o r t a n t f a c t o r  44  -  (T) i n d e t e r m i n a t i o n o f t h e  type of r o o t s  to expect  is,  (A5.1)  The v a l u e o f T i s p o s i t i v e i n m o s t c a s e s when s o l v i n g e q u a t i o n s (A4.5)  and  (A4.6),  and the o n l y r e a l r o o t  (A3.7),  i s given by,  (A5.2)  In the case o f equation zero,  (A3.7)  a n d t h e maximum s a f e  limits  of the  (A4.5)  and  three roots  T becomes n e g a t i v e when t h e  speed o f descent  road surfaces.  increases  grade  beyond the  T becomes n e g a t i v e i n t h e  cases  of  approaches speed equations  ( A 4 . 6 ) when t h e r e i s a s m a l l a c c e l e r a t i o n o r d e c e l e r a t i o n . t h a t o c c u r i n a l l t h r e e e q u a t i o n s when T i s n e g a t i v e  c h a r a c t e r i z e d as  large,  negative  large,  positive  small,  positive  the  cannot be the c o r r e c t r o o t , c a l l y be o v e r c o m e b y t h e  a small excess s m a l l change i n  are  follows:  The c o r r e c t r o o t i s S ^ ,  p o s i t i v e speed,  The  smallest positive real root, as any l a r g e r e s i s t a n c e  because  or f o r c e can  t r a c t i v e power o r d r a g p r o d u c e d a t  a n d S£ c a n n o t b e t h e  correct  root,  because  a low there i s  o f t r a c t i v e power o r d r a g a v a i l a b l e and hence o n l y speed.  theoreti-  a  only  The t h r e e r e a l r o o t s g i v e n by Weast  45  -  c a n be f o u n d from the  (1964),  as  "Compute t h e v a l u e o f t h e  trigonometric  relationship  follows: angle 0 i n the  expression,  -  cos 0 = -  then x w i l l  have the  following values.  -  2 V ^ | c o s f ,  l\j ^~% r  l\l  - f  cos ( | + 1 2 0 ° ) ,  cos  (| + 2 4 0 ° )  .  u  l  Weast, R . C . et a l . 1964. M a t h e m a t i c a l T a b l e s from Handbook o f C h e m i s t r y and P h y s i c s . The C h e m i c a l R u b b e r C o . , C l e v e l a n d , O h i o . p . 320.  -  46  -  APPENDIX 6 THE COMPUTER PROGRAM A6.1  Input  Cards  The  input cards  e x p e c t e d by the program a r e  i n the  following  order: 1.  The f i r s t  surfacing vehicle  The except 2. the  costs,  (up t o  sections  card  format used f o r a l l the  f o r one c o n t r o l c a r d  surfaces  starting with  next  card.  The n e x t  resistance  the  (pounds p e r  ($ p e r s t a t i o n " ' " ) ,  the  is(are) ton),  four values are  the  lower q u a l i t y surface.  the  f o r each of  the  speeds of v e h i c l e s approaching  the  for  the  the  entered  road.  surfacing factors  c o e f f i c i e n t of f r i c t i o n , maintenance  g i v e n f o r each surface  information for  10F8.2  on  In the  third  of  basic cost  i n turn starting  case of 3 s u r f a c e s ,  card would c o n t a i n the i n f o r m a t i o n f o r 2 surfaces, c a r d the  is  F10.5).  surface.  loaded v e h i c l e s are  and b a s i c s u r f a c e  The  cards  i n m.p.h.  lowest q u a l i t y  f r o m t h e woods e n d o f  card(s)  per  number o f m a i n  FORMAT ( 5 1 1 0 ,  remaining input  speed l i m i t  speeds o f the  The s p e e d s a r e  road under study  the  (18) f o r e a c h m a i n s e c t i o n .  card g i v e s the  The i n i t i a l  cost  surfaces,  and t h e d i s c o u n t r a t e a s a d e c i m a l .  The n e x t  to amortize  number o f v e h i c l e s , maximum number o f s t a t e s  1 5 ) , number o f d i f f e r e n t  3.  4.  g i v e t h e number o f y e a r s  the  and the  rolling surfacing ($/sta.). from first second  surface.  "*" S t a t i o n i s a u n i t o f l e n g t h o f one h u n d r e d f e e t  a b b r e v i a t e d STA.  5..  The s a v i n g s i n s u r f a c i n g c o s t  surface  r e s u l t i n g from a l o w e r q u a l i t y  already being i n place are  g i v e n on t h e n e x t  sequence b e i n g the s a v i n g s i f s u r f a c e the  last  place,  surface  and t h e  is  t o be b u i l t ,  third  1 is  card.  The  i n p l a c e and s u r f a c e  t h e s e c o n d i s when s u r f a c e  i f there are  first  three surfaces  1  2 is  when s u r f a c e  to in  3 is  in  place. 6.  The n e x t s e r i e s  ($/STA.) grade.  of cards  and s u r f a c e maintenance The p r o g r a m e x p e c t s  increased surfacing costs surface  the  for increases  i n surfacing  cost  due t o  first  f o r each s u r f a c e  are  T w e n t y v a l u e s o n two c a r d s  twenty  The same p r o c e d u r e  followed  surface  for  traffic  density.  9.  10.  the  The n e x t  empty,  increased  p e r c e n t jumps i n g r a d e  to  is  cost  due t o  miles. for  the  twenty v a l u e s f o r ($/STA.)  due t o  I n s e q u e n c e o n one c a r d t h e  projected  to c e n t e r  distance  each  increased  the v e h i c l e weights i n tons g i v i n g  l o a d e d and r o t a t i n g w e i g h t s f o r each v e h i c l e i n  The h e i g h t  are  distance  f r o n t a l a r e a empty  of g r a v i t y  from c e n t e r  (feet)  (square  feet) input.  empty a n d l o a d e d a n d  o f g r a v i t y to o u t s i d e o f wheels  on the n e x t c a r d f o r each v e h i c l e i n  the  turn.  and l o a d e d , as w e l l as b r a k e h o r s e power f o r each v e h i c l e i s 11.  for  maintenance.  i n sequence  ($/STA.)  increase i n surfacing cost  card contains  for  follow.  f o r each surface  t o m a t e r i a l s o u r c e o f up t o  cost  c a r d to have seven v a l u e s  due t o f i v e  expected to g i v e surface maintenance  8.  ($/STA.)  1 and t h e second seven s i m i l a r v a l u e s f o r s u r f a c e  Two more c a r d s 7.  is  sequence.  is  card contains  48  -  12.  The n e x t  cent  o f b r a k e h o r s e power, and the o p e r a t i n g c o s t  minute f o r each v e h i c l e i n 13.  T i r e maintenance  For each s u r f a c e on the 14.  in dollars  per  sequence.  costs  i n d o l l a r s per mile are  i n t u r n the  tire  costs  on the n e x t  f o r a l l v e h i c l e s are  card.  entered  card.  Similarly  on t h e n e x t 15.  the b r a k i n g c a p a c i t y as a d e c i m a l p e r  the v e h i c l e maintenance  costs  i n d o l l a r s per m i l e  are  card.  The f o l l o w i n g  sets of cards  f r o m 16 t o 19 a r e  required for  each  main s e c t i o n . 16.  The n e x t  vehicle  t h e number o f t r i p s  Similarly  densities 18.  contains  the  type f o r each year of the  density is 17.  card(s)  a different  other v e h i c l e s  card i s  format.  the  the  amortization period.  per year  a d d i t i o n a l input cards  o f the  The n e x t  traffic density for  first  Traffic  f o r each v e h i c l e  are used to e n t e r  type. the  traffic  types.  c o n t r o l c a r d from the main s e c t i o n u s i n g  The number o f s u b s e c t i o n s  i n the  current  s e c t i o n and t h e d i s t a n c e i n m i l e s t o t h e m a t e r i a l s o u r c e f o r surface 19.  is given.  FORMAT ( 1 8 ,  (feet),  the f o l l o w i n g  Sight distance  Radius of curvature Superelevation  i n f o r m a t i o n : Grade  empty  (feet),  (degrees).  each  7F8.2).  T h e r e i s one c a r d f o r e a c h s u b s e c t i o n , w i t h i n  containing  main  (feet), Present  (per  cent),  Sight distance surface  the main s e c t i o n , Section length  loaded  (real format),  (feet), and  A6.2  Computation time  49  -  requirements  The amount o f t i m e r e q u i r e d f o r a p r o g r a m r u n d e p e n d s  on  three  things: 1.  the  t o t a l number o f  subsections,  2.  t h e number o f v e h i c l e t y p e s  3.  t h e number o f s t a t e s two a r e  program.  The c o m p l e t e r u n w i t h requires  more l i m i t i n g  surfaces,  found f o r each  The f i r s t  grades,  and  section.  c o n t r o l l e d by the u s e r and the  about  grades  The same r u n o n  r e d u c e d by l e s s  D r o p p i n g f r o m t h r e e t o one v e h i c l e r e q u i r e s  A6.3  t h e r u n t o o k 61 s e c o n d s  FORTRAN l i s t i n g  o f computer program  (See f o l l o w i n g  11  pages).  of  the  on low steeper because  speed v a r i a t i o n .  about o n e - f i f t h the  On a two m i l e s e c t i o n o f r o a d w i t h 110 s u b s e c t i o n s , grades  a result  o n l y about 0.25 seconds per s e c t i o n ,  t h e number o f s t a t e s p e r s e c t i o n i s  and moderate  is  t h r e e v e h i c l e s and t h r e e s u r f a c e s ,  0.75 seconds per s e c t i o n .  requires  third  time.  3 vehicles, 3  o f computer  time.  surfaces  -  50  -  DIMENSION T I M E ( 3 , 1 5 , 1 5 , 1 5 ) , D 0 L 0 P ( 3 , 1 5 , 1 5 , 1 5 3 1, J O L D U 5 , 1 5 , 1 5 ) ,DOLRCC( 1 5 , 1 5 , 1 5 ) ,DOLRMC ( 1 5 , 1 5 , 15 3 2, D O L T O T ( 1 5 , 1 5 , 1 5 ) , S P L C 3 , 1 5 , 1 5 , 1 5 ) , S P E 1 3 , 1 5 , 1 5 , 1 5 ) 3, J O L D N ( 1 5 , 1 5 , 1 5 ) , I S U R N C 1 5 , 1 5 , 1 5 3 . D O L R M N C 1 5 , 1 5 , 1 5 ) 4 , DLORCNU 5 , 1 5 , 1 5 3 ,SPEN( 3,15,15,15.) , S P L N ( 3 , 1 5 , 1 5 , 1 5 ) 5, T I M E N ( 3 , 1 5 , 1 5 , 1 5 ) , D 0 L 0 P N C 3 , 1 5 , 1 5 , 1 5 3 DIMENSION D 0 L M A N ( 3 , 1 5 , 1 5 , 1 5 ) , D O L R C N U 5 , 1 5 , 1 5 3 1, DTN{.15,15,15) ,DDLMAV ( 3 , 1 5 , 1 5 , 1 5 ) , ISUR { 15 , 15,153 2, D Q L T I R ( 3 , 1 5 , 1 5 , 1 5 ) , D C L T I N ( 3 , 1 5 , 1 5 , 1 5 3 DIMENSION S P L I M I 3 ) , R ( 3 ) , F( 3) , B A S U R C O ) ,BASURMl 3) 1 , S C I G ( 3 , 7 ) , W E ( 3 ) , S M I G ( 3 , 7 ) , S M I 0 ( 3 , 2 0 3 , SCI DIS{ 3 , 2 0 3 2, F A E ( 3 ) , F A L C 3 3 , P D R C < 3 3 , P D R M l 3 1 , P D T ( 3 , 3 3 , P D M ( 3 , 3 3 3, DOPN(33, S E ( 3 ) , S L L ( 3 ) , H £ ( 3 ) , H L ( 3 ) , 0 0 ( 3 3 , S A V 4 3 . 3 ) 4, BHP(3),BC{3),VEHOPC(3),VEHTIR(3,33,VEMC(3,3),CE(33 5, T R A D E N ( 3 , 2 5 ) , D M S ( 3 ) , W L ( 3 3 , W R { 3 ) , C L ( 3 3 , T ( 3 3 C INITIALIZATION DO 1 J 3 = l , 1 5 DO 1 J2=l,.15 DO 1 J l = l , 1 5 DOLRCClJl,J2,J33=0.0 DOLRMCCJl,J2,J3)=0.0 D O L T O T ( J l , J 2 »J33 =9.E10 DO 1 1 - 1 * 3 TIME (I,Jl,J2,J33=0.0 DOLOP ( I , J 1 , J 2 , J 3 3 = 0 . 0 DOLT I R ( I , J l , J 2 , J 3 3 =0.0 1 D0LMAV(I,J1,J2,J3)=0.0 READ ( 5 , 5 0 1 3 NYEARS,IM,JN,KM,NOMASE,RI NT 501 FORMAT ( 5 1 1 0 , F 1 0 . 5 3 READ (5 ,5023 (S P L I M ( K ) , K = l , K M 3 502 FORMAT (1OF 8,23 READ ( 5 , 5 0 2 ) ( S P L ( I , 1 , 1 , 1 ) ,1=1,IM) DOLTOT(1,1,13=0.0 C READ SURFACES READ ( 5 , 5 0 2 3 ( R ( K 3 , F ( K 3 , B A S U R C { K 3 , B A S U R M l K 3 , K = 1 , K M 3 READ ( 5 , 5 0 2 3 ( ( S A V ( K , K K 3 , K = 1 , K M ) , K K = 1 , K M 3 DO 2 K=1,KM READ ( 5, 5023 ( S C I G ( K , K 1 3 , K 1 = 1,7) 2 READ ( 5 , 5 0 2 3 ( S M I G ( K , K l 3 , K l = 1 , 7 3 READ ( 5 , 5 0 2 3 (JSMIDtK,KD3,KD=1,203,K=1,KM3 READ ( 5 , 5 0 2 ) ( ( S e i D I S ( K , K D ) ,KD=1,203 ,K=1,KM 3 C READ VEHICLES READ(5,5023 C H E ( 1 3 , H L ( 1 3 , 0 0 ( I ) , 1 = 1 , I M 3 READ ( 5,5021 ( W E ( 1 3 , W L ( 1 3 , WR(13,1 = 1 , 1 M J READ ( 5,5023 (FAE< I ) , F A l ( I ) , B H P ( I ) ,1 = 1,IM) READ ( 5 , 5 0 2 ) ( B C ( I 3 , V E H O P C ( 1 3 , 1 = 1,IM) • READ ( 5 , 5 0 2 ) i(VEHTIR(!,K3 ,1=1,1M3,K=1,KM 3 READ ( 5 , 5 0 2 ) ( ( V E M C ( I , K ) , I = 1 , I M 3 , K = 1 , K M 3 C CALCULATE CL( 13 AND C E ( I ) DO 3 I=1,IM CL( 13 = 6 6 . 8 + 6 6 . 8 * { W R ( I 3/WLI 1 3 3 3 CE(13=66.8+66.8*(WR(I3/WE(I)3  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52  C  51  -  START READING S E C T I O N A L INFORMATION (MA I N j DO 111 NM=1,NOMASE DO 4 I = 1,IM 4 READ ( 5 , 5 0 2 1 ( T R A D E N ( I , 1 I ) , 1 1 = 1 , N Y E A R S ) READ ( 5 , 5 0 3 1 NOSEC,(DMS<K),K=1,KM) 503 FORMAT ( I 8 . 7 F 8 . 2 ) C START READING I N D I V I D U A L S E C T I O N A L INFORMATION DO 222 NS = 1,NOSEC READ ( 5 , 5 0 2 ) G , S L , S D H , S D L , C R . P K , B E T A KK = PK C START O P T I M I Z A T I O N WITH MINOR S E C T I O N S STATUS=0.0 KI = l + A B S ( G / 5 . J, FL1=SL/100. FL2=SL/5280. DO 8 K = l , K M KS=DMS(K) P D R C ( K ) = F L 1 * ( 8 A S U R C ( K ) - S A V ( K , K K ) + SCIG(K,K I) 1 +SCIDIS(K,KS)) FACT=0.0 DO 9 I Y = 1 , N Y E A R S RKD=0.0 DO 10 1=1,1M 10 RKD=RKD+TRADEN(I»IY)*(WL(I)+WE(I))/70000. KD=RKD+1 I F ( K D . G T . 2 0 ) KD=20 9 FACT=(8ASURM(K)+SMIGCK.KI)+SMID(K,KD))/U.+RINT) 1**1Y + F A C T PDRM(K)=FL1*FACT DO 11 1=1,IM FACT=0.0 FACT1=0.0 DO 12 I Y = l , N Y E A R S FACT=FACT+VEHTIR(I,K)*TRADEN(I ,IY)/(1.+RINT)** I Y 12 FACT1=FACT1+VEMC(I,K)*TRADEN<I , I Y ) / 1 1 . + R I N T ) * * I Y PDT(I »K)=FL2*FACT 11 PDM(I,K)=FL2*FACT1 8 CONTINUE DO 13 J 3 = l J M DO 13 J 2 = 1 , J M DO 13 J 1 = 1 , J M 13 DTN(Jl,J2,J3)=9.E10 DO 333 K=1,KM SUM=0.0 . DO 14 I = 1 » I M .. 14 SUM=SUM+PDT(I» K)+PDMCI»K) S UM=SUM + P D R C ( K ) + P D R M ( K ) DO 4 4 4 J 3 = 1 , J M DO 4 4 4 J2=1,JM DO 4 4 4 J l = l , J M DON=0.0 I F ( D O L T O T { J 1 , J 2 , J 3 ) . G E . 9 . E 1 0 ) GO TO 555 f  53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104  -  52  -  GG=G*t-1.0J RR = R C'K) FB=F(K3 DO  15  1=1,IM  WW=WL(I)  30 15  98  SS = S P L ( I , J 1 , J 2 , J 3 ) BB=BHP(I) FF=FAL(I3 CA=Cl_m 3A=BC(I3 WA=WE(I3 FC=FAE(I) CD=CEU) SLL(I3=POMPHF(RR,WW,GG,SS,SL,BB,N,FF,CA3 S-S PEED(RR,WW,GG,B B,BA,F F,N 3 I F ( S L U I 3 . G T . S 3 S L t ( 1 3 =S S=ST0P(FB,SDL3 IF ( S L L ( I ) . G T . S ) S L L ( n = S H=HL{ I ) 0=00(1) S = SL I D E ( C R , F B » B E T A » H» 0 ) IF ( S L L ( I ) - G T . S J S L L ( I J = S I F ( S L L { I 3 . G T . S P L I M C K 3 3 S L L ( I 3=SPLIM{K3 IF ( S L L ( I ) . L T . l . O ) S L L ( I ) = 1 . 0 S£(I)=SPLIM(K3 S=SPEED(RR,WA,G,BB,8A,FC,N) IF ( S E ( I ) . G T . S ) S E ( I ) = S S = S T O P ( F B » SDE) IF ( S E ( I ) . G T . S 3 S E ( I ) = S H=HE(I')' S=SLIDE{CR,F8,BETA,H,Q) I F ( S E ( IJ.GT-.S) S E ( I J=S S = POMPHI (RR,WA,G,SS,SL,BB,i\l,FC,CD) IF ( S E ( I ) . G T . S ) SE(I3=S I F ( S E ( 13 . L T . 1 . 0 3 S E ( I ) = 1 * 0 T(IJ=SL/<88.*SE(I))+SL/(88.*SLL(13) DOPN ( I ) = T { I ) # V E H Q P C ( I ) * T R A D E N ( 1 , 1 ) DO 30 I Y E = 2 , N Y E A R S DOPN(I)=DOPN(I)+T(!3*VEHOPC(I)*TRADEN(I,IYE)/(1.+ 1RINT)**IY£ D0N=DGN + D O P N ( I 3 IF { S T A T U S . N E . O . O ) GO TO 98 STATUS=l-0 JAF1=SLL(13-2 JAF2=SlL(2}-2 JAF3=SLU33-2 JN1=2 JN2=2 JN3=2 GO TO 9 9 CONTINUE  105 106 107 103 109  11-0 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155  -  99  20 555 444 333  22  53  -  JN1=SLL(1)/1.5-JAF1 JN2 = S L U 2 ) / 1 . 5 - J A F 2 JN3=SLL(3)/1.5-JAF3 IF(JN1.GT.JM) JN1=JM IF{JN2.GT.JMJ JN2=JM I F { J N 3 . G T . J M ) JN3=JM IF ( J N 1 . L T . 1 ) JN1 = 1 I F ( J N 2 . L T . 1 ) JN2=1 I F ( J N 3 . L T . 1 1 JN3=1 CONTINUE SCJ=SUM+DON+DOLTOT(Jl,J2,J3) IF (SCJ.GT.DTN(JN1,JN2,JN3)) GO TO 555 DTN (JN1,JN2,JN3J= SCJ ISURN ( J N 1 , J N 2 , J N 3 ) = K DOLRMN(JNI,JN2,JN3)= PDRM(K) D O L R C N l J N I , J N 2 , J N 3 1 = PORC(K) JOLDN ( J N I , J N 2 » J N 3 ) = J 3 + J 2 * 1 0 0 + J I * 1 0 0 0 0 DO 20 1=1,IM SPEN (I,JN1,JN2,JN3)= SE(I) SPLN (I,JN1,JN2,JN3)= SLL(I) T I M E N ( I » J N I , J N 2 » JN3 ) = T ( I ) DOLOPNCI,JNI,JN2,JN3)= DOPN(I) DOLTINtI,JN1,JN2,JN33 = PDTtl.K) OOLMANII,JNI,JN2,JN3)= POM(I,K) CONTINUE CONTINUE CONTINUE DO 21 J 3 = 1 , J M DO 21 J 2 = l , J M DO 21 J 1 = 1 , J M DOLTOT ( J 1 » J 2 » J 3 ) = D T N i J 1 , J 2 , J 3 J I F ( D T N U l , J 2 , J 3 3 . G E . 9 . E 1 0 ) GO TO 21 ISURJJl,J2,J3)=ISURN(Jl,J2,J3) JOLD(Jl,J2,J3)=J0LDN(Jl,J2,J3) ' JJI=JOLDN(Jl,J2,J3)/10000 JJ2=J0LDN(Ji,J2,J3)7100-JJ1*100 JJ3=J0LDN(Jl,J2,J3)-JJ2*100-JJ1*10000 DOLRCN(J1,J2,J3)=D0LRCC(JJ1.JJ2,JJ3)+D0LRCN(Jl,J2, 1J3) DOLRMNtJl,J2,J3)=D0LRMC{JJ1,JJ2,JJ3)+D0LRMN(Jl,J 2, 1J3) DO 22 1=1,IM SPE ( I , J 1 , J 2 , J 3 ) =SPENU » J 1 , J2, J3) SPL ( I , J 1 , J 2 , J 3 ) =SPLN(I,J1,J2,J3) TIMEN ( I , J 1 , J 2 , J 3 J = TIME (I , J J 1 » J J 2 , J J 3 ) + T I M E N ( I 1,J1,J2,J3) D O L O P N U , J l , J 2 , J 3 ) = DOLOP ( I » J J i , J J 2 , J J 3 )+DOLOPN( I 1,J1,J2,J3) DOLTINCI,J1,J2,J3) = DOLTIR(I,JJl,JJ2,JJ3)+DQLTIN(I 1,J1,J2,J3) D O L M A N ( I , J l , J 2 » J 3 ) = D O L M A V C I , J J 1 , J J 2 , J J 3 J+Q.OLMAN ( I 1,J1,J2,J33  156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207  -  54  -  21 CONTINUE C O U T P U T STAGE HEADING WRITE ( 6 , 6 0 2 ) NM,NS 602 FORMAT!//' MAIN S E C T I O N N U M B E R ' , 1 4 , 5 X , ' S U B S E C T I O N * I t ' NUMBER ' , 1 43 DO 25 J 3 = 1 , J M DO 25 J 2 = 1 , J M DO 25 J 1 = 1 , J M I F ( D T N ( J l , J 2 , J 3 3 . G E . 9 . E 1 0 ) GO TO 23 DOLRCCtJl,J2,J3)=00LRCN(Jl,J2,J3 3 DOlRMCtJl,J2,J3)=D0LRMN(Jl,J2,J3) DO 24 1 = 1 , I M TIME ( I , J l , J 2 , J 3 ) = TIMEN ( I , J 1 , J 2 , J 3 ) DOLOP ( I , J l , J 2 , J 3 ) = D O L O P N U , J l , J 2 , J 3 ) D O L T I R ( I , J 1 , J 2 , J 3 3= DOLT I N ( I , J 1 , J 2 , J 3 ) 24 DOLMAV(I Jl,J2,J33= DOLMAN(I,J1,J2,J33 WRITE ( 6 , 6 0 3 ) J l , J 2 , J 3 , D 0 L R M C ( J 1 , , J 2 , J 3 ) ,DGLRCC i J 1 , J 2 1, J 3 3 , D 0 L T 0 T ( J l , J 2 , J 3 3 , I S U R C J l , J 2 , J 3 3 , J O L D I J l , J 2 , J 3 ) 603 FORMAT (/' A L T ',31 3,4X,'DOLRMC = ' , F 1 0 . 2 , 4 X , • D O L R C * l ' C =•,F10.2,5X,'DQLTQT =',F10.2,5X,'SURFACE =',I3 2,5X,'OLD A L T E R N A T I V E = ' , I 7 ) DO 4 4 1=1,IM 44 WRITE ( 6 , 6 0 4 ) I , S P E ( I , J 1 , J 2 , J 3 ) , S P L { I , J 1 , J 2 , J 3 3 1» T I M E ( I , J 1 , J 2 , J 3 ) , D O L O P ( I » J 1 , J 2 , J 3 ) 2, D 0 L T I R ( I , J 1 , J 2 , J 3 ) , D 0 L M A V ( I , J 1 , J 2 , J 3 ) 604 F O R M A K I X ,* V E H I C L E ' , 13 ,3X, • EMPTY MPH = * , F 5 . 2 , 3 X , 1 * LOADED MPH = • , F 5 . 2 , 3 X , ' T R I P TIME = • , F 6 . 1 , 3 X , 2'DOLOP = • , F 9 . 2 , 3 X , ' D 0 L T I R =•,F3.2,3X,•DOLMAV =' 3, F 8 . 2 ) 23 CONTINUE 25 CONTINUE 222 CONTINUE 111 CONTINUE STOP END r  208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242  -  55 -  F U N C T I O N POMPHF ( R , W , G , S I , S L , B H P , N » F A , C C J C C R = C O E F F I C I E N T OF R O L L I N G R E S I S T A N C E POUNDS PER TON OF C V E H I C L E WEIGHT C • W=VEHICLE WEIGHT IN TONS C POMPHF=MAXIMUM S P E E D ( F I N A L } AS L I M I T E D BY THE POWER OF C THE V E H I C L E C G=GRADE AS A P E R C E N T C S 1 = S P E E D WHEN E N T E R I N G THE S E C T I O N C S L = L E N G T H OF T H E S E C T I O N IN F E E T C BHP=BRAKE HORSE POWER OF V E H I C L E C FA=FRONTAL AREA OF V E H I C L E IN SQUARE F E E T C C C = C O R R E C T I Q N FACTOR FOR T H E TWO T Y P E S OF MASS IN A C MOVING V E H I C L E C NOTE A L L S P E E D S E X P R E S S E D AS M I L E S PER HOUR IF CSI.EQ.O.O) SI=0.1  RP=318.75*BHP/SI  10  1 2  3 4 5  TR=0.003*FA*SI*SI+R*W+20.*W*G IF (TR.GT.RP) C C = C C * ( - 1 . 0 i XB=BHP*(-318.750)/ICC*W/SL) XA={W*{20.#G+R)-CC*W/SL*SI*SI +0.003*FA*SI*SIJ/(CC* 1W/SL) T=XB*XB/4.0+XA**3/27.0 I F ( T . G E . O . O ) GO TO 10 PHI=ARC0SCXB/(-2.)/(SQRT(XA**3/{-2 7 . ) ) ) J / 3 . Z=2.*SQRT<XA/{-3.)) P1=Z*C0S(PHI+4.1888) P3=Z*C0S(PHI+2.0944) P2=Z*C0S(PHI) IF ( P l . L E . O . O ) P l = 8 0 . I F ( P 2 . L E . 0 . 0 ) P2=80. IF C P 3 . L S . 0 . Q ) P3=80. I F ( P 2 . L T . P I ) P1=P2 IF i P 3 . L T . P 1 3 P1=P3 POMPHF=PI GO TO 5 YA=SQRT i T) YB=XB*(-1.0)/2.0 SP=Y8+YA SN=YB-YA IF { SP.GE.O.O.) GO TO 1 A = i(ABS(SPJ-}**ll./3-))*(-l-0) GO TO 2 A=SP**(1./3.3 I F ( S N . G E . O . O ) GO TO 3 8 = { ( A B S ( S N ) ) * * i l . / 3 . .) ) * ( - 1 . 0 ) GO TO 4 B=SN**ll./3.) POMPHF=A+B I F { P O M P H F . L E . 1 . 0 ) P0MPHF=1.11 IF ITR.GT.RPi CC=CC*(-1.0) RETURN END  243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258  259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295  FUNCTION  -  C C C C C  R = C Q E F F I C I E N T OF R O L L I N G R E S I S T A N C E P O U N D S P E R T O N O F V E H I C L E WEIGHT W = V E H I C L E WEIGHT IN T O N S P O M P H I = M I N I M U M S P E E D ( I N IT I A L ) AS L I M I T E D BY T H E P O W E R  296 297 298 299 300 301  C C C C C  THE V E H I C L E G = G R A D £ AS A P E R C E N T S L = L E N G T H OF T H E S E C T I O N IN F E E T BHP= B R A K E H O R S E POWER OF V E H I C L E FA = F R O N T A L A R E A O F V E H I C L E IN S Q U A R E  302 303 304 305 306  C C C  C C = C O R R E C T I O N F A C T O R FOR T H E TWO T Y P E S O F M A S S I N A MOVING V E H I C L E N O T E A L L S P E E D S E X P R E S S E D AS M I L E S P E R HOUR SI=1.0 RP=318.75*BHP/SI TR=0.003*FA*S I*SI+R*W+20.*W*G IF (TR.GT.RPi CC=CC*(-1.0) XA=(W*(20.*G+R)-CC*W/SL+0.003#FA)/(CC*W/SL) XB=BHP*(~318.750)/(CC*W/SL) T=XB*XB/4.0+XA**3/27.0  IF  10  1  2  POMPHI  56  (T.GE.O.O)  (R , W, G , S I , S I , BHP , N , FA , C C )  FEET  GO T O 1 0  307 308 309 310 311 312 313 314 315 316  317  P H I = A R C 0 S ( X 3 / { - 2 . ) /"tSORTC X A * * 3 / C - 2 7 . i ) ) ) / 3 . Z=2.*SQRT(XA/(-3.)) P1=Z*C0S(PHI+4.1888J P3=Z*C0S(PHI+2.0944) P2=Z*C0S{PHI) IF {Pl.LE.O.O) Pl=80. IF ( P 2 . L E . 0 . 0 ) P2=80. IF (P3.LE.0.0) P3=80. IF (P2.LT-P13 P1=P2 IF (P3.LT.P13 P1=P3 POMPHI=P1 GO T O 5 Y A = S Q R T <T) YB=XB*(-1.0)/2.0 SP=YB+YA SN=YB-YA  318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333  IF  (SP.GE.O.O)  334  A=  {(ABS(SP))**(l./3.)>  GO T O 1 *(-1.0)  GO T O 2 A=SP**(1./3.J  336 337  I F ( S N . G E . O . O ) GO T O 3 B= GO  335  {{ABS(SNJJ**C1./3.)J TO 4  338. *(-1.0)  339 340  3 4  B=SN*#(1./3.) POMPHI=A+B IF (POMPHI.LE.1.0)P0MPHI=1.22  341 342 343  5  IF (TR.GT.RP3 RETURN END  344 345 346  CC=CC*(-1.0)  - 57 F U N C T I O N S P E E D ( R , W , G , B H P , B C , F A , N3 c C R = C O E F F I C I E N T OF R O L L I N G R E S I S T A N C E POUNDS P E R TON OF C V E H I C L E WEIGHT c w= WEIGHT OF V E N I C L E IN TONS C G= GRADE AS A P E R C E N T C BHP = BRAKE HORSE POWER C FA = FRONTAL AREA I N SQUARE F E E T C SPE ED= THE CONSTANT S P E E D OF DESCENT IN M I L E S PER HOUR C I F ( G . G E . O . O ) GO TO 10 XB=BC*BHP*37500./FA/0-3 XA=W*(20.*G+R) / 0 . 0 0 3 / F A Z= X 8 * X B / 4 . 0 + X A * * 3 / 2 7 . Q I F ( Z . L E . O . O J GO TO 5 YA=SQRT(Z) YB=XB*(-1.0 3/2.0 SP=YB+YA SN=YB-YA I F ( S P . G E . 0 . 0 3 GO TO 1 A= ( ( A B S ( S P ) ) * * < ! . / 3 . J ) *(-1.0) GO TO 2 1 A=SP**(l./3.) I F ( S N . G E . O . O J GO TO 3 2 B= ( ( - A B S ( S N ) ) * * C 1 . / 3 . ) J *<-1.0) GO TO 4 3 B= SN**(1./3. ) SPEED=A+B ' 4 IF ( S P E E D . L T . 0 . 0 3 SPE£D=69.00 IF ( S P E E D . L E . 5 . 0 3 SPEED=5.0 GO TO 2 0 5 CONTINUE PHI=ARC0S(XB/(-2.3/(SQRT(XA**3/( -27 . 3 ) ) 3 / 3 . Z=2.*SQRT(XA/(-3.3) P l - Z * C O S t P H 1 + 4 . 1 8 88 3 P 3 = Z * C 0 S ( P H 1+2 . 0 9 4 4 3 P2=Z*C0S(PHI 3 IF ( P l . L E . O . O ) Pl=80. IF ( P 2 . L E . 0 . 0 ) P2=80. IF ( P 3 . L E . 0 . 0 3 P3=80. I F ( P 2 . L T . P 1 ) P1=P2 I F ( P 3 . L T . P 1 3 P1=P3 SPEED=P1 GO TO 2 0 SPEED=70.00 10 20 CONTINUE RETURN END  347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 3 70 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394  -  58  -  FUNCTION S T O P ( F , S I G H T D 3 C C F= C O E F F I C I E N T OF F R I C T I O N C SIGHTD= SIGHT D I S T A N C E IN F E E T C STOP= THE S P E E D AS L I M I T E D 8Y THE S T O P P I N G C NOTE S P E E D I S IN M I L E S PER HOUR C A=1.0/59.8/F B=7.34 C = S IGHTD*(-1.1 CALL -SOLVEQIA,B,C,Y,Z) IF ( Y . E Q . - 1 0 0 0 . ) GO TO 1 STOP=Y I F ( Y . L E . O . ) STOP=Z RETURN 1 STOP=0.0 RETURN END  DISTANCE  395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412  -  c c c c c c c c c 5 6 7  59 -  SUBROUTINE S O L V £ Q ( A , B , C ,Y ,Z) A= C O E F F I C I E N T OF T H E SQUARED TERM B= C O E F F I C I E N T OF THE TERM TO THE F I R S T POWER C= CONSTANT TERM Z = F I R S T ROOT Y= SECOND ROOT NOTE I F ROOTS ARE COMPLEX Y I S S E T AT -1000 AND Z AT 1000 D I S C = B*B-4.*A*C IF(0ISC3 5,6,7  Y = -1000. Z = +1000. RETURN  Y =  ;  -B/(2.0*A3  Z = -B/(Z.O^A) RETURN S = SQRTIDISC) Y = l-B+S)/(2.0*A) Z = (-B-S)/(2.0*A3 RETURN END  -  413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435  FUNCTION C C C C C C C C C C C  1  SLIDE  60 -  (CR» F , B E T A  »H»0)  H= 0=  HEIGHT OF C E N T E R OF GRAVITY P R O J E C T E D D I S T A N C E FROM CENTER OF GRAVITY TO O U T S I D E WHEELS S= T I P P I N G S P E E D MPH CR= RADIUS OF CURVATURE F E E T F= C O E F F I C I E N T OF F R I C T I O N (ROAD S U R F A C E ) S L I D E = MAXIMUM S P E E D IN M I L E S PER HOUR AT WHICH P O S S I B L E TO TRAVEL AROUND A CURVE B £ T A = S U P E R E L E V A T I O N IN DEG. ' • IF ( C R . G E . 1 0 0 0 . ) GO TO 1 FTAN=F*0.616 B=BETA*3.1415927/180. C=ATAN(FTAN ) A=CR*TAN(B+C) SLIDE=3.90*SQRTCA) S=3.9*SQRT(CR*(0+H*TAN(B))/(H-0*TAN{B))) IF (S.LT.SLIDE) SLIDE'S RETURN SLIDE=70. RETURN END  IT  IS  436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 45i 452 453 454 455 456 457 458 459  -  61 -  APPENDIX 7 SAMPLE OF PROGRAM OUTPUT The standard excerpt  following  15 i n c h b y 11 i n c h c o m p u t e r o u t p u t .  i s not  3 t o be t h e  optimum p o l i c y w h i l e  section is alternative  that  t h e minimum c o s t  The d y n a m i c p r o g r a m b a c k w a r d p a s s r e v e a l s  with surface  6-5-7 w i t h surface  is  an and  chosen by  state for  alternative  t h e minimum c o s t 2.  the  using three vehicles  i s an example o f an a l t e r n a t i v e  dynamic program model t h a t  section.  the  It  i s reduced from  The s e c t i o n 3 - 1 i s  from a program r u n w i t h 5 main s e c t i o n s  three surfaces. the  sample o f program output  the 9-8-9  state  for  VEHICLE VEHICLE VEHICLE  I 2 3  EMPTY EMPTY EMPTY  M P H = 19.12 MPH » 2 3 . 0 7 «PH = 2 1 . 6 6  I pATED MpH = 1 7 . 2 9 LPADEO MPH " 4 0 . 9 7 LOADED MPH = 3 9 . 4 9  TRIP TRIP TRIP  TIME>= TIMt" TI ME =  DOLOP OOLOP DDLOP  8.6 4.5 4. 8  » 297211. 37 « 2082.76 = 110.72  DOLTIP 00LT1P DOLTIR  = * =  11 7 5 . 3 8 26.77 3.99  DOLMAV DOLMAV DOLMAV  =  770.40 26.77 3.85  a  »  VEHICLE VEHICLE  10 14 OCLtVC = 11686.'=3 1 EMPTY M P H = 1 9 . 1 2 LOADED LCAPED EMPTY M P H = 2 3 . 0 7 2 LPAOEJ EMPTY « " H = 2 1 . 6 6 3  OCLRCC « 23010.00 DOLTOT M P H =17.46 T R I P T I ME = B. 7 4.6 TRIP TIME= MPH =38.47 TRIP T1ME= 4.8 M P H =40.55  69104.63 SURFACE = 3 DOLOP = 3 0 2 6 0 . 9 4 OOLTi P. = DOLT1R 2182.32 DOLOP 112.89 DOLT1R DOLOP  ALT 10 VEHICLE VtHICLE  13 1 2  VEHICLE  DCLRwc"= 12123.19 EMPTY M P H = 1 9 . 1 2 LCAOEO E ^ P T Y M P H = 2 3 . 07 LPAPEO LCADED EMPTY MPH = 2 1 . 6 6  DQLRCC = 19460.00 DOLTOT MPH = 1 7 . 6 1 TRIP TIME= 8.5 MPH = 4 2 . 1 6 T R I P TIME= 4.5 T R I P TIME= 4.8 MPH =40.55  64983.33 SURFACE = 3 OLD A L T E R N A T I V E OOLOP = 2 9 2 4 6 . 1 0 DOLT IR = 1 1 5 2 . 1 1 DOLMAV = DOLOP = 2 0 7 4 . 78 POL Tl R = 2 6 . 30 POLMAV = 3.96 OOLMAV = OOLTIR = 110.34 DOLOP =  = 81213 756.43 26.30 3.78  ALT 10 VEHICLE VEHICLE VEHICLE  14 15 OCLRMC = 11742.23 1 EMPTY MPH = 1 9 . 1 2 LOADED 2 EMPTY " P H = 2 3 . 0 7 LOADED 3 EMPTY MPH = 2 1 . 6 6 LPAPED  PCLPCC = 21380.00 DOLTOT MPH = 1 7 . 3 2 T R I P TIME= 8.5 MPH = 4 4 . 7 7 T R I P TIME= 4.4 MPH = 4 3 . 1 3 T R I P T IM E = 4.7  ' 66328.38 • SURFACE = 3 "DOLOP = 2 9 1 5 1 . 78 OOLTIR = DOLOP = 2052.79 DOL T i R = DOLOP = 109.23 DOLTIR =  OLD A L T E R N A T I V E 1105.56 OOLMAV = 25.37 DOLMAV = 3.89 DOLMAV =  = 81415 728.50 25.37 3. 64  ALT ID VEHICLE VEHICLE VEHICLE  15 15 OCLBMC = 11551.75 1 EMPTY WPH = 1 9 . 1 2 L PADED 2 'FMPTY "PH = 2 3 . 0 7 LOADED 3 EMPTY M P H = 2 1 . 6 6 LPAPED  OCLRCC = 22340.00 DOLTOT MPH = 1 7 . 4 6 T R I P T IM E = 8.4 MPH = 4 6 . 1 7 T R I P TIME= 4.4 MPH = 4 4 . 6 4 . T R I P TI ME = 4.7  66686.31 SURFACE = 3 OLD A L T E R N A T I V E DOLOP = 2 8 7 9 2 . 8 9 DPLTIR = 1 0 8 2 . 2 8 DOLMAV = OOLOP = 2039.08 DOLTIR = 24.90 OOLMAV = OOLOP = 108.52 DOLTIR = 3.85 OOLMAV =  = 81515 714.54 24.90 3.57  ALT 10 VEHICLE  MAIN ALT  14  SECT ION 1  KUVrtER  na.PMC =  1  EMPTY  VEHICLE  _yjri_IC_LE_  __£ i^FTY EMPTY  V EHIC LE ALT  5  1  VEHICLE VEHICLE VEHICLE  2  ALT 5 VEHICLE VEHICLE VEHICLE "ALT'""" 7 VEHICLE VEHICLE VEHICLE ALT VEHICLE VEHICLE VEHICLE . ALT 7 VEHICLE ~VE"iiiCLE VEHICLE ALT 6 VEHICLE VEHICLE  13536.44  MPH =11.31  LOADED  DCLRCC  MPH =  = 3.36  14460.00 TRIP  9.2  vPH =lfe.!7  LCAPED  MPH = 9.34  TRIP  T IM E=  4.7  LCADEO  MPH =  TRIP  T I ME=  5.0  7.71  68260.25 SURFACE = 2 DOLOP = 3 5 4 9 8 . 9 0 DOLTIR . DOLOP = 2387.56 OOLTIR « DOLOP = 128.09 DOLTIR =  = 13763.7P DCL °CC = 14070.00 DOLTOT =lo.92 IPAnEO M P H = 9 . 3 8 T R I P T I ME = 9.4 " P H =21.23 LOADED MPH = 2 5 . 1 6 TRIP TI ME = 4.8 «PH = 1 9 . 7 0 LOADED MPH = 2 3 . 0 2 T R I P TIME= 5.1  MPH  OCl^C = 1 3 2 9 6 . BO EMPTY MPH = 1 9 . 1 2 LOADED EMPTY MPH = 2 3 . 07 LCAPEO EMPTY MPH = 2 1 . 6 6 LOAOED  3 nriRMC = 13561.PI _E M P TY M ? H = 1 9 . 1 2 LPAPED EMPTY M P H = 23.~07 LCADEO EMPTY M P H = 2 1 . 6 6 IPAPEO  3 1 2  .  PCLPCC = 15030.00 DOLTOT M ° H = 1 2 . 7 5. J RIP TI M E«_ 9.4 MPH = 2 7 . 0 2 T R I P TI ME= 4.8 MPH = 2 4 . 9 7 TRIP TIME« 5.1  OCL MC = 13499.57DOLRCC = 14460.00 DOLTOT EMPTY ' ' P H =1(J.92 LOAPEO MPH = 1 1 . 0 1 T R I P TIME= 9.2 EMPTY M P H = 2 1 . 2 3 LCAPED MPH = 2 7 . 9 2 T R I P T1 ME= 4.7 c  *  2C202  91 9 . 3 6 31.  77  4.60  = 10101 865.83 3 C . C2 4.33  =  OLD A L T E R N A T I V E = 1010_1 SURFACE = 1 70221 . 1 9 942.63 OOLOP = 3 7 3 0 9 . 6 3 OOLTIR = 1 4 6 6 . 3 2 OOLMAV = 32.47 DOLOP = 2427.08 DOLTIR = 32.47 D0LM1V = 4.71 DOLOP.= 130.48 DOLTIP .=• . 4.71 DOLMAV =  =  68331.25 SURFACE = 3 DOLOP » 3 4 9 4 2.. .1.4 DOLTIP DOLOP = 2373.83 DOLTIR DOLOP * 1 2 7 . 24 DOLTIR  E M P T Y  3 1_ 2 3  OLD A L T E R N A T I V E 1419.77 DOLMAV = 31.77 OOLMAV = 4.60. DOLMAV =  67424.25 SURFACE = 3 0 LD' ALTER NAT IVF DOLOP = 3 3 9 6 8 . 5 5 DOLTIR = 1 3 2 6 . 6 7 OOLMAV = DOLOP = 2351.84 DOLTIR = 30.02 DOLMAV = DOLOP = 125.72 DPLTIR = 4.43 DOLMAV =  J'lLPCC = 15420.00 DOLTOT MPH = 1 2 . 6 7 TRIP TI ME= 9.2 MPH = 2 4 . 2 4 T R I P TI ME = 4.7 MPH = 2 2 . 5 2 " T R I P TIME= 5.0  DOLTOT DCLRCC = 14070.00 13800.65 OPLPMC "PH = 1 1 . 3 1 L P A O f J MPh = 3 . 9 b T R I P TIME = 9.4 F M P T Y WPH =16.17 ICAPEO MPH = 1 7 . 2 0 T R I P TIME= 4.8 e ^ P T Y MPH = 1 4 . 4 3 LOADED MpH = 1 5 . 1 5 T R I P TIME = 5.1  2_ 1 2 3  10101. 67359.38 SURFACE = 2 . OLD A L T E R N A T I V E = 907.72 DOLOP = 3 4 5 2 9 . 8 9 OOLTIR = 1 3 9 6 . 4 9 DOLMAV = 31.42 OOLOP = 2367.09 DOLTIR * 31.42 DOLMAV = 4. 54 DOLOP = 126.66 OOLTIR = 4,54 POJLMAV_=_.  DCl^C EMPTY EMPTY  80913 712.21 2 4 . 79 3.56  69919.38 SURFACE = 1 OLD A L T E R N A T I V E DOLOP = 3 6 8 7 3 . 6 9 DOLTIR = 1 4 4 3 . 0 4 DOLMAV = OOLOP = 246 8 . 4 6 DOLTIR = 32.12 DOLMAV = 4.65 DOLMAV OOLOP = 133.18 OOLTIR  DOLTOT  TIME=  MPH  =14.43  •  NUMBER  DCLFMC = 13499.57 DOLRCC = 14460.00 DOLTOT EMPTY MPH = 1 6 . 9 2 LCA TFD MPH = 9 . 3 2 T R I P TIME = 9.2 EMPTY MPH = 2 1 . 2 3 L C A P E D MPH = 2 2 . 3 9 T R I P TIME= 4.7 E M P TY vPH = 1 9 . 7 0 LPAPED M°H = 2 0 . 5 5 T R I P T I ME = 5.1  E M P T Y  1 2 1 Z 3  SUeSECTION  OLD A L T E R N A T I V E 1082 . 2 8 DOLMAV = OOLMAV = 24.79 DOLMAV = 3.88  20202 OLD A L T E R N A T I V E " » 1349.94 O.0,kMA.V..,?_ J 7 _ 7 . 4 6 _ 30. 3 7 = 30.37 OOLMAV = 4.3 9 = 4.49 DOLMAV »  67140.94 SURFACE = 2 OLD A L T E R N A T I V E DOLOP » 3 4 3 1 9 . 6 8 OOLTIR - 1 3 9 6 . 4 9 DOLMAV = DOLOP = 2359.22 OOLTIR •= 31.42 DOLMAV =  » 50101 907.72 31.42  EMFTY  V E H I C L E  3  ALT 6 VEHICLE VEHICLE VEHICLE  4 1 2 3  ALT 7 VEHICLE VEHICLE .VEHICLE  1 2 3  ALT 8 VEHICLE VEHICLE VEHICLE  4 1 2 3  5  '--PH = I S . 7 0 '  OPLRMC FJ.PTY  "PH  E M P T Y  M P H  5VPTY  MPH  O C L P C C  L O A D E D  MPH  L C A P E D  MPH  L O A D E D  MPH  *  TRIP  TIME =  14070.00  =11.03 =29.49 =27.18  T R I P T R I P T R I P  5.1 OOLTC'T .  = T I M E = TI M E= T I ME  9.4 4.8 5.1  EMPTY  "P.H  2  E M P T Y  MPH  3  EMPTY  "OH  6  D C L PCC 1 13573.30 L I M P E D MPH = 1 2 . 8 4 L P A O E O MPH = 3 0 . 0 0 = 2 1 . 2 3 LOADED MPH = 2 8 . 4 7 =19.70 =  = 1 6 . 9 2  CPLPMC = 13499.57 FMI-TY " P H = 1 6 . 9 2 LOADF D LPAPED EMPTY VPH •21.23 LCADEO EMPTY MPH •• 1 9 . 7 0  TRIP TRIP TRIP  T IME= TIME= TIM£=  OOLRCC = 14460.00 OOLTOT I'PH = 1 1 . 6 0 T R I P T I ME= 9.2 4.7 T R I P TIME= MPH = 3 0 . 0 0 5.1 TRIP TIME= MPH = 2 8 . 9 2  5 1 2 3  6  OCLRMC = 13106.32 E M P T Y ".'PH = 1 9 . 1 2 10ADE0 E M F T Y " P H " = 2 3 . 0 7 L CAE ED EMFTY " P H = 2 1 . 6 6 LOAPF.O  OOLRCC = 16380.00 DOLTOT MPH = 1 6 . 2 9 T R I P TI M E = ^ " 5 . 1 M P H = 3 0 . 81 T R I P T I ME = 4.7 MPH = 2 0 . 3 9 T R I P T I ME= 5.1  5  7  0CL MC = 1 2 8 5 4 . 39 EMPTY M P H = 1 6 . 9 2 LOADED EMPTY MPH = 2 1 . 2 3 LCAPED EMPTY MPH = 1 9 . 7 0 L O A O E O  DOLRCC = 1 6 7 / 0 . 00 DOLTCT MPH = 5 . 7 4 T R I P TIME= 9.0 MPH = 3 0 . O C TRIP TIM£= 4.6 M P H = 3 0 . 0 0 " T R I P T I ME = 4.9  3  V E H I C L E V E H I C L E  CMPTY  2  E M P T Y  3  F M P T Y  2 3 5 "l 2 3  5 I  7  V E H I C L E  ?  V E H I C L E  ALT""  b'  1 3 5 6 1 .  01  MPH  D O L R C C  L PA P E D  M PH  MPH  = 2 3 . 0 7  L O A D E D  i-'PH  = 2 1 . 6 6  L P A P E D  P  a  =29.7-,  =  T R I P  TI ME=  1 5 0 3 0 . 0 0  = 14. 52  T R I P  MpH  = 3 1 . 2 4  MPH  = 2 9 . 0 4  5.1  D O L T O T T IME=  9 . 4  T R I P  TIME=  4 . 8  T R I P  T 1ME =  5.1  p  V E H I C L E  V E H I C L E  =  L O A D E D  = 1 9 . 1 2  M  H  = 1 9 . 7 0  7_ J>C1 " " £ _ « _ 13044.87 OCLPCC = 15610.00 _DOLTPT_ " E M P I Y MPII = l o . 9 * 2 LOADED MPH = 6 . 9 0 T R T P f t M " E ' . " ~9T6 E M P T Y MPH - 2 1 . 2 3 LPAPF.D «PH » 3 0 . 0 0 TRIP TIME" 4.6 EMFTY " H = 1 9 . 7 0 . . L O A D E D M P H . =3 0 . 0 0 .T'R 1 P . T l'ME= 4.9 7  5  V E H I C L E  MPH  na°MC  6  5 1 2 3  ALT  On " M C " = i3309.09 OOLRCC = 15420.00 DOLTOT EMPTY MPH = 1 6 . 9 2 LOADED MPH = 1 2 . 3 7 TRIP TIME* 9.1 EMFTY MPH = 2 1 . 2 3 L P A P E D MPH = 3 0 . 0 0 T R I P TIME= 4.7  1  I  VEH'IC'LE  4 . 54  OLD A L T E R N A T I V E = 50102 1419.77 OOLMAV = 919.36 31.77 OOLMAV = 31.77 4.60 DOLMAV = 4.60  OLD A L T E R N A T I V E = 70203 SURFACE = 2 DOLTOT = 68419.44 DOLTIR = 1 3 9 6 . 4 9 DOLMAV = 905. 39 DOLOP = 3 4 9 3 6 . 6 4 .9.4 D O L T I R = 3 1 . 3 0 O O L M A V = 3 1 .30 OOLOP = 2378.34 4.8 DOLTIR = 4.56 DOLMAV = 4.53 DOLOP = 127.53 5.1  ALT 9 VEHICLE VEHICLE VEHICLE  ALT  o  5 0 3 0 . 0 0  5  '  DOLMAV =  67313.44 "SURFACE = 3 OLD A L T E R N A T I V E = 5 C 1 0 1 DOLOP = 3 3 8 6 3 . 1 4 DOLTIF = 1 3 2 6 . 6 7 OOLMAV = 865.83 DOLOP = 2346.65 DOLTIR = 30.02 OOLMAV = 30.02 DOLOP = 125.54 DOLTIR = 4.43 DOLMAV = 4.33  E M P T Y  V E H I C L E  68085.75 SURFACE « 2. DOLOP = 3 5 3 2 7 . 8 8 DOLTIR = OOLOP = 2 3 8 4 . 19 DOLTIP = DO L O P = 127.99 DOLTI£ =  4.54  CPHKC = 13296.80 DCLRCC = 15420.00 DOLTOT EMPTY MPH = 1 9 . 1 2 LEADED MPH = 1 4 . 5 0 T R I P TIME= 9.2 EMPTY " P H = 2 3 . 0 7 L T A P E D MPH = 2 9 . 7 0 T R I P TIME= 4.7 EMPTY " P H " = 2 1 . 6 6 L C A D E O MPH = 2 7 . 7 1 T R I P T I ME= 5.1  ALT S VE H i ; LE VEHICLE VEHICLE  V E H I C L E  =  5  2  2  DOLTIR  OLD A L T E R N A T I V E = 7 C 1 0 1 67471.88 SURFACE = 2 OOLMAV = 393.76 DOLOP = 3 3 9 2 7 . 9 1 DOLTIR = 1 3 7 3 . 2 2 30.96 OOLMAV = 30.96 DOLOP « 2351.16 DOLTIR = 4.50 OOLMAV = 4.47 OOLOP = 125.81 DOLTIP. =  5 1  ALT  126.31  DOLRCC = 15420.00 DOLTOT MPH = 1 2 . 8 . ? T R I P T I ME= 9.2 MPH = 2 9 . 0 5 T R I P T I ME= 4.7 MPH = 2 7 . 0 1 T R I P T I ME = 5.1  ALT 7 VEHICLE VEHIC LE VEHICLE  V E H I C L E  DOLOP =  VriBfC. = 133C9.09 tNPTY " P H =16.92 LOADED r i - ' P l y I'PH = 2 1 . 2 3 LPAPFO EMPTY MPH = 1 9 . 7 0 LCAPED  1  5 1  13763 .78  =16.92 =21.23 =19.70  MPH = 2 5 . 8 1  5  OrLPMC  ALT. VEHICLE VEHICLE VEHICLE  =  LCAPED  DCLPMf. = 12854.39 EMPTY " P H = 1 6 . 9 2 LOADED E M P T Y  MPH  = 2 1 . 2 3  L O A O E O  E  MPH  = 1 9 . 7 0  L O A D E D  OCLPCC = 16770.00 ' OOLTOT M H =10.33 T R I P T I ME= 8.9 4.6 TRIP TIME= MPH = 3 0 . 0 0 T R I P TIMe = 4.9 MPH = 3 0 . 0 0  OCL»MC = 13235.35 E M P T Y >'PH = 1 6 . 9 2 LOADED EMPTY MPH = 2 1 . 2 3 LPAPEO  OOLRCC = 14850.00 DOLTOT MPH =11.80 TRIP TIME8.9 MPH = 3 0 . 0 0 T R I P T1ME= 4.6  V  P T Y  P  67055.63 DOLOP "DULOP OOLOP  SURFACE  * 3 4 2 3 3_. 4 6 = 2360.15 = 126.32  67414.56  DOL  =  TI  2  O L D ALTERNATIVE  = 1396 . 4 9 = 31.42 = 4.54  P  DOLTIR D O L T I R  =  00 l>iAV_= DOLMAV = DOLMAV =  60303  9 0 7 . 7 2 ,., 31.42 4.54  OLD A L T E R N A T I V E = 60404 = 2 DOLMAV = 893.76 DOLTIP = 1373.22 30.96 OOLMAV = 30.96 D O L T 1R -• 4.47 4.50 OOLMAV = DOLTIR =  SURFACE  DOLOP = 3 3 8 6 7 . 7 0 _D0 L OP = 2354.0 8 125.84 DOLOP =  68259.69 SURFACE = 3 ' DOLOP = 3 4 8 7 2 . 18 DOLT I R = DOLOP = 2372.15 DOLTIR = DOLOP = 1 2 7 . 25 D O L T I R -•  O L D A L T E R N A T I V E .= 50102 1349.94 OOLMAV = 877.46 30.37 DOLMAV = 30.37 4.49 DOLMAV = 4 . 39  67728.03 SURFACE = 3 DOLOP = 3 3 5 5 4 . 5 9 DOLTIR = "DOLOP = 2 3 3 8 . 9 8 ' DOLTIR = DOLOP = 125.07 DOLTIR =  OLD A L T E R N A T I V E = 70101 1303.39 DOLMAV = . 8 5 1 . 3 6 29.56 OOLMAV = " 2 9 . 5 6 4.40 DOLMAV = 4.26  68325.25 SURFACE = 2 OLD A L T E R N A T I V E = 9 1 0 1 1 DOLOP = 3 4 0 4 9 . 17 DOLTIR = 1 3 2 6 . 6 7 OOLMAV = 8 6 8 . 15 DPLOP = 2267.50 DOLTIP = 30.14 D O L M A V » .. 3 0 . 1 4 DOLOP = 1 2 0 . 3 1 " DOLTIR = 4.41 DOLMAV = 4.34 67365.81 SURFACE = 2 _ O L P ALTERNATIVE « 80809 "DOLOP'""=""" 3Ta"i 3". 7 2 OOL T I?~='"'1"34T''94 OOLMAV = 6 8 2.1 k~ DOLOP « 2274.41 DOLTIR • 30.61 DOLMAV = 30.61 DOLOP « 120.66 DOLTIR = 4.45 D P L M A V =. .. . 4 . 4 1 67232.30  DOLOP OOLOP DOLOP  ""65835.75 DOLOP DOLOP  SURFACE  = 32954.85 = 2268.86 = 120.39  SURFACE  » 33008.73 = 2280.29  =  2  DOLTIP. = DOLTIR DOLTIR •  DOLTIR D O L T I R  2  OLD A L T E R N A T I V E 1326.67 DCLMAV  O L D ALTERNATIVE  » 1373.22 = 31.07  OOLMAV OOLMAV  « *  •  «  40507 8 6 8 . 15  60507  896.08 31.07  EMPTY " P H =19.70  LOADED MPH =30.00  TRIP TIME=  4.9  OOLOP =  120.96  DOLTIR =  4.48  DOLMAV =  4.48  VEHICLE  3  ALT Z__ VEHICLE VEHICLE VEHICLE  5_ 7. 0CLRMC_ = 13044__87 DOLRCC _= .15810.00 D OLTOT __r.__66197.25__ SURFACE = 2 OLD ALTERNATI VE_____ 70507 l '" EMPTY "PH " = T 6 . 9 2 ~ L O A D E D MPH =12.81 TRl"p~T"lME= ' - 32644.5 5 DOLTIR = 1349.94 DOLMAV = 8 8 2 . 12 2 EMPTY MPH =21.23 LOADED MPH =30.00 TRIP TIME= 4.6 DOLOP = 2275.00 DOLTIR = 30.61 DOLMAV = 30.61 3 EMPTY MPH =19.70 LOADED MPH =30.00 TRIP TIM.E= 4.9 DOLOP = 120.69 DOLTIR = 4.45 OOLMAV = 4.41  ALT 9 VEHICLE_ VEHICLE VEHICLE  6 1 2 3  7  ALT  8  7  9  VEHICLE  D  OCLRMC = 13296.80 EMPTY MPH_=19. 12 J.OADE0 "EMPTY « P H =23. 07 " LOADED EMPTY M P H =21.66 LOADED  1  DOLPMC EMPTY  M°H  =  12584.03  = 1 9 . 1 2  VEHICLE  2  EMPTY  M P H ^ 2 3 . 0 7  "VEHICLE  3  EMPTY  MPH  ALT  9  VEHICLE  7  8  I  OPLRMC EMPTY  MOH  =21.66 =  DOLRCC  =  MPH  LOADED  MPH_ = 3 4 . 7 2  13106.32  =19.12  l  Q  p  DOLRCC = 15420.00 DOLTOT = 6 7 2 5 6 . 2 5 SURFACE = 3 OLD ALTERNATIVE = 60303 MPH =15.09 TRIP_TIME= 9.2 DOLOP =_33806.64 DOLTIR = 1326.67 DOLMAV = 865.83 MPH =32.93 TRIP 1I ME = 4.7 DGLOP = 2345.85 DOLTIR = 30.02 DOLMAV = 30.02 MPH =30.74 T R I P TIME= 5.1 OOLOP = 125.61 DOLTIR = 4.43 DOLMAV = 4.33  LOADED "LCAOED  Q  MPH  18890.00  =15.32  TRIP _  = 3 0 . 7 3 "  DOLRCC  =  LCAPED  MPH  =15.88 =33.67  VEHICLE  2  EMPTY  MOH  =23.07  LCAPED  MPH  VEHICLE  3  EMPTY  MPH  =21.66  LOADED  MPH_ = 3 1 . 5 3  ALT 10 VEHICLE VEHICLE VEHICLE  7 1 2 3  OOLTOT  =  6 7 7 7 5 . 9 4  T IM E=  8.8  DOLOP  TRIP  TIME=  4.6  DOLOP  =  TRIP  TIME =  5.0  DOLOP  =  16380.00  OOLTOT  TRIP  T I ME=  9.1  TRIP  TIME=  4.7  _ T R I P__T I M E = _ _ 5 . 1  =  =  SURFACE  3 1 8 2 2 . 13  =  3  OLD  DOLTIR  =  1 2 3 3 . 5 7  _2244.76__  DOLTIR  =  124.21  DOLTIR  =  =  1 3 0 3 . 3 9  67649.88  "  SURFACE  =  3  DOLTIP  ALTERNATIVE  =  60503  DOLMAV  =  8 1 2 . 2 9  2 8 . 2 8  DOLMAV  =  28.28  4 . 2 7  DOLMAV  =  4 . 0 6  OLD  DOLOP  =  33476.97  OOLOP  =  2338.36  OOLTIR  =  29.56  _ _ DOLOP„ =  125.15  DOLTIR  =  4 . 4 0  ALTERNATIVE DOLMAV  =  60404  =  851.86  OOLMAV  =  29.56  DOLMAV  = _._  4 . 2 6  8 OCLPMC = 13106.32 EMPTY M P H =19.12 LOADED EMPTY M P H =23.07 LOADED EMPTY MPH =21.66 LOADED  DCLRCC = 1 6 3 8 0 . 0 0 DOLTOT = 6 7 6 9 3 . 1 9 SURFACE = 3 OLD ALTERNATIVE = 80405 M P H =17.13 TRIP TI ME= 9.1 OOLOP = 33519.34 DOLTIP = 1303 .39 DOLMAV = 851.36 MPH =34.16 TRIP TI ME= 4.7 DOLOP = 2339.25 DOLTIR = 29.56 DOLMAV = 29.56 MPH =32.07 T R I P TIME= 5.1 OOLOP = 125.21 OOLTIR = 4.40 DOLMAV = 4.26  ALT" 9 " 6 VEHICLE 1 VEHICLE 2 VEHICLE 3  8  DOLPMC = 129C3.55 EMPTY M P H =19.12 LOADED EMPTY M P H =23.07 LCAPED EMPTY M P H =21.66 LOADED  DCLRCC = 16870.00 DOLTOT = 6 6 8 1 6 . 5 0 SURFACE = 3 OLD ALTERNATIVE = 60505 MPH =15.28 TRIP TIME= 8.9 OOLOP = 32473.20 DOLTIR = 1280.12 OOLMAV = 8 4 0 . 2 2 M P H =34.72 TRIP TI ME= 4.6 DOLOP = 2258.25 DOLTIR = 29.21 OOLMAV = 29.21 MPH =32.73 TRIP TIME= 5.0 DOLOP = 124.17 DOLTIR = 4.34 DOLMAV = 4.20  ALT 10 VEHICLE VEHICLE VEHICLE  8 1 2 3  8  DCLPMC_ = 13370_.53 EMPTY MPH=l"9.12 LOADED EMPTY MPH =23.07 LOADED EMPTY V P H =21.66 LPAPED  DCL RCC_ = _15_990.00 D0LI0T_ = _ 6 8 6 9 0 . 13 SURFACE = 3_ . OLD ALTERNATIVE.?. 8 0 5 0 5 MPH~=17.14 T R I P TI ME= 9.4 DOLOP = 34576.86 DOLTIR = 1326.67 DOLMAV = 863.50 MPH =35.13 TRIP TIME= 4.8 OOLOP = 2366.94 DOLTIP = 29.91 DOLMAV = 29.91 MPH =32 .39 T R I P TIME= 5.1 DOLOP = 127.05 DOLTIR = 4.46 DOLMAV = 4.32  ALT 11 VEHICLE VEHICLE VEHICLE  8 1 2 3  8  OCLPMC = 1 2 9 1 5 . 84 EMPTY M P H =19.12 LOADED EMPTY P H =23. 07" LOADED EMPTY MPH =21.66 LOADED  OCLRCC = 17340.00 OOLTOT = 6 8 1 1 2 . 9 4 SURFACE = 3 OLD ALTERNATIVE « 90505 MPH_=18.13 TRIP_TIME=_ 9.1 DOLOP = 33215.57 DOLTIR = 1280.12 DOLMAV = 837.90 MPH =34.92 T R I P TI ME = 4. 7 DOLOP = 2331.98 DOLTIR = 29.09 OOLMAV = 29.09 MPH =32.88 TRIP TIME= 5.0 DOLOP = 124.76 DOLTIR = 4.36 DOLMAV = 4.19  ALT  10  10  W  8  OCLPMC  VEHICLE  1  V E H I C LS _  2  EMPTY  MPH  VEHICLE  3 "  EMPTY  MPH  ALT  11  12  EMPTY  8  MPH  DPI  PMC-  =  12393.55  =19.12 =23.07  LCADEO  MPH_= 3 8 . 2 6  TRIP  T I ME=  =21.66  L O A C E D M P H  TRIP"  TIM_ =  =  12203.07  MPH  =19.12  M.PH  EMPTY  3  EMPTY "PH  ALT  8  8  9  0CL°MC  DOLTOT  TRIP  EMPTY  2  19850.00  =17.43  1  VEHICLE  =  MPH  VEHICLE  _V.EH_I.C_LE  DCLRCC  LOADED  =32.06  OCLRCC  =  LCAPED  MPH  =18.65  =23.07  LCAPED  MPH  =40.65  =21.66.  LCADEO MPH =32.87  =  12713.07  DOLRCC  =  TIME=  2 0 8 1 0 . 0 0 TIME=  TRIP  TI ME=  TRIP TIME' 17830.00  5,6 =  8.7 4.6 5.0 DOLTOT  6 8 2 1 5 . 5 6 DOLOP  _ 4 . 6 _  DOLTOT  TRIP  =  8.7  =  SURFACE  =  =  31542.47  DPLTIR  DOLOP  =  _2233.22  ...DOLTIR.  DOLOP  =  123.81  68647.31 =  31253.67  DOLOP  =  2223.02  _P_OIO.P__=  1.23.36.  67311. 56  OLD = .=_  ALTERNATIVE  1210.29  DOLMAV  =  80805  =  7 9 8 . 3 3  27.81  DOLMAV  =  .27.81  »  4 . 2 4  OOLMAV  =  3.99  DOLTIR  =  1187.02  DOLTIP.  =  2 7 . 3 5  OOLTIR  SURFACE  OOLOP  3  =  3  OLD  DOLTIR.. =  SURFACE  =  3  ALTERNATIVE  4 . 20.. OLD  =  91005  DOLMAV  =  7 8 4 . 3 6  OOLMAV  =  2 7 . 3 5  D O L M A V . .=  3.92  ALTERNATIVE  =  50507  VEHICLE  1  EMPTY  MPH  = 1 9 . 1 2  LOADED  MPH  =14.98  TRIP  T1 M E =  8.8  DOLOP  "  3 2 2 4 7 . 2 9  DOLTIR  =  1256.64  DOLMAV  =  VEHICLE  2  EMPTY  M°H  =23.07  LOADED  MPH  =34.72  TRIP  TIME=  4.6  OOLCP  =  2252.62  DOLTIR  =  2 8 . 7 4  DOLMAV  =  2 8 . 7 4  VEHICLE  3  EMPTY  MPH  =21.66  LOADED  MPH  =34.11  TRIP  TIM£=  4.9  DOLOP  =  119.56  DOLTIP.  =  4 . 3 1  DOLMAV  =  4 . 1 3  A"LT  9  VEHICLE VEHICLE  8 1 2  9  DCLRMC EMPTY  MPH  EMPTY  MPH  = 1 3 0 3 2 . 58 =19.12 LPAPED =23.07 LCAPED  DOLRCC MPH MPH  =  =15.30 =34.72  15810.00  OOLTOT  TRIP  TIME=  TRIP  TIME=  8.9 4.6  =  66042.50 SURFACE = 3 = 32591.63 DOLTIR = DOLOP = 2262.66 DOLTIR =  DOLOP  OLD  1303.39 29.6e  ALTERNATIVE OOLMAV  =  OOLMAV  =  326.  =  26  60507 854.19 29.68  VEHICLE  3  ALT  6  11  VEHICLE  EMPTY 9  M P  =21.66  H  0CL»MC  =  LCAPED  13180.05  ..  MPH  =34.11  OOLRCC  .= .  EMPTY  "PH  =19.12  LOADED  VEHICLE  2  EMPTY  "PH  =23.07  LOADED  MPH  =35.98  TRIP  VEHICLE  3  EMPTY  MPH  =21.66  LOADED  MPH  =33.80  TRIP  ALT  9  10  9  DOLRMC  VEHICLE  1  j  VEnlCLE  2  EMPTY  VEHICLE  3  EMPTY  ALT  10  10  EMPTY  9  =  MPH  131C6.3?  MPH  = 17.?:i  TRIP  "PH  =23.07  LOADED  MPH  =36.26  MPH  =21.66  LOADED  MPH  =34.02  OCLRMC  =  12713.C7  EMPTY  " P H  =19.12  VEHICLE  2  EMPTY  " P H  VEHICLE  3  EMPTY  " P H  ALT  c  IQ  1  QCL E M C EMPTY  DCLRCC  =  =36.79  MPH  =23.07  LCAPED  MPH  " P H  =21.66  LOADED  MPH =34.5 8  ALT  11  9  E  1  EMPTY  VEHICLE  2  EMPTY  " P H  =23.07  VEHICLE  .3  EMPTY  MPH  =21.66  ALT"  1 0 1 0  VEHICLE  1  V E H K  2 3  LE  VEHICLE ALT  11  VEHICLE  10  10  10  OCL"MC  DCL'^C EMPTY  10  1  " P H  =  12915.84  =19.12  =  DCLRCC  LPAPED  29.44  DOLMAV  =  29.44  =  4.42  OOLMAV  =  4.25  DOLTOT TIME=  9.1  TRIP  TIME=  TRIP  TIME=  17830.00  =  2340.93  DPLTIR  =  29.56  DOLMAV  ='"  =  125.43  DOLTIR  =  4.40  DOLMAV  =  '=  1256.84  2246.70  DOLTIP  =  2R.74  DOLMAV  = .  123.80  DOLTIR  »  4.31  DOLMAV  =  DOLTIP.  =  1 2 8 0 . 12  DOLMAV  DOLTIR  =  29.09 4.36  TIME=  4.7  TR IP  TI ME=  .5.1  DOLTOT  TRIP  T I ME =  4.7  TRIP  TIME=  5.1  " P H  =23.07  .^^.~Zt>  LQArEO  MPH =37.64  TRIP  T I ME=  LCAPED  M>H  TRIP  T"lME =  12725.36 LOADED  =35. 2 7  DGLRCC  =  =  9.1  =37.18  MPH  DOLOP  DOLTOT  =  =  33185.97  DOLOP  =  2333.41  DOLOP  =  124.97  68127.19  3 3_2 2 7 . 1 2  DOLOP  =  OOLOP  =  VEHICLE  2  EMPTY  " P H '= 2 3 . 0 7 L O A D E D  " P H  VEHICLE  3  EMPTY  " P H  MPH  ALT  11  VEHICLE  l->  10  1  DPL°MC E ." F T Y  "PH  =21.66 =  LPADEO  12522.59  =19,12  LOADED LCAPED  VEHICLE  2  EMPTY  MPH  =23.07  VEHICLE"  3  EMPTY  MPH  = 2 1 . 6 6 L O A D E D  A LT  11  13  VEnlCLE  1  VEHICLE  2  VEHICLE  3  ALT  10  VEHICLE  10  10  DPL MC C  =  12332.1 1  EMPTY  MPH  =19.12  EMPTY  MPH  =23.07  _E.MPT Y _ M P K _ _ = 2 1 , 6 6 11  DCl=MC  =  TIME =  =3 9 . 9 1  TR IP  T IM E = 4 . 7 D O L O P  =  =35.09  TRIP  TIM£=  =  OOLRCC  =  MPri  =19,56  MPH  T I ME =  8.8  =40.65  TRIP  T I ME=  4.6  M P H = 3 5 . 09  TRIP  T I " . £ = 5 . 0  DCLRCC  =  =  DOLOP  =  2236 .5 1  DOLOP  =  LTADEO  MPH  =42.27  TRIP  TIME=  4.6  DOLOP  =  5.0  DOLOP.  =  12842.10  OOLRCC  =  VEHICLE  2  EMFTY  MPH  =23. 07  LOADED  MPH  =38.26  VEHICLE  3  EMPTY  MPH  =21.66  LOADED  MPH  =37.32  12915.84  =17.40  DOLRCC  =  T RI P__fl_M.E= 16770.00 TRIP  OOLTCT  =  8.9  OOLOP  TRIP  T1ME=  4.6  TRIP  T IME=  4.9 OOLTOT  =  =  2227.43 __l  5  32311.33  DOLOP  =  2251.1 1  DOLOP  =  119.48  OLD  29.0 9 4.19  ALTERNATIVE OOLMAV  ALTERNATIVE  80708 851.86 29.16  "V.Zb  = =  1007C8  =  823, 93  OOLMAV  =  28.63  DOLMAV  =  4.12  ALTERNATIVE DOLMAV  =  =  2 6 . 77  DOLMAV  =  4.19  OOLMAV  =  =  1233.57  OOLTIR. = .  =  DPLMAV_= "OOLMAV  =  OLD  _  =  = 3  ALTERNATIVE  90907 7 6 8 . 0?  '  26.77 3.84  =  91007  DOLMAV  =  812.29  2 0 . 28  DOLMAV  =  28.28  =  4.27  OOLMAV  =  4.06  DOLTIR  =  1210.29  DOLTIR  =  27.81  DOLTIP =  3  CLP  O O L T I R_.=  SURFACE'=  =  68136.06  =  DOLTIR  S UPFACE  31585.59  66481.38  TIME=  17340.00  123.40  68090.56 DOLOP  3  DOLTIR  SURFACE  31901.02.  8.7  J . P . A r E D _ M P H _ = 3 5... 7 0  125.95  =  TIME=  =  DOLTIR  2 3 3 8 . 7 3 D O L T I P .  67684.31  TRIP  MPH  =  " "  SURFACE  32769.05  OOLOP  =19.13  LOADED  DOLRMC  DOLTPT  =  MPH  =19.12  11  19750.0_0  DOLOP  =  LOADED  "PH  10  DOLTO'T  TRIP  EMPTY  11  1 8 7 9 0 . 00  DOLOP  5.1  124.5 0  71653.38  TRIP  1  ALT  =  9.0  = =  1163.74  =  OOLTOT  OOLMAV OOLMAV  =  =  DOLOP  90707 83 7^9 0  4.33  OOLOP  5.0  =  =  28.63  4.7  TIME=  22340. 00  DOLMAV  =  T I ME =  TRIP  =  OLD  ALTERNATIVE  =  TRIP  M P H =18.58  3  4.19  DOLTIP  =37.74  OOLRCC  =  '4.~40  29.09  OOLTIR  MPH  MPH = 35.60  LPAPED  SURFACE  29.56 .  =  2327.08  LOADED  1 2 0 8 6 . 32  = =  g 06 07  =  DOLMAV  LPAPED  =  D O L T I P. D O L f 1R  OLD  =  DOLMAV  1 2 5 6 . 84  =23.07  =19.12  ~  4.13  OOLMAV  =  =21.66  " P H  3  28.74  837^90  DOLTIR  " P H  DPLR"C  125'.50"  =  DnLTIR  80806 8 2 6 . 26  =  32909.30  MPH  EMPTY  1303.39  SURFACE  =  A L T F RN A T I V E  =  EMPTY  10  =  "  68532.81 DOLOP  FMPTY  1  4.36  2339.67  2  11  2 9 . 09  =  =  3  11  =  67701 .75  VEHICLE ALT  DOLTIR  OOLOP  =  OLD  OOLTIR  DOLOP"»  9.0  3  125.03  4.7  DOLTOT  =  '2334.43  5.1  f'lME=  DOLTIP, = .  1280 .12  33527.23  TRIP  0 LP  =  =  =19.01  3  DOLTIR  OOLOP  MPH  =  SURFACE  =  VEHICLE  VEHICLE  SURFAC E  =  DO L OP  9.1  18300.00  68 0 8 4 . 9 4 DOLOP  DOLMAV  =  =  MPH  EMPTY  ALTERNATIVE  =  5.0  "  OLD  . 4 . 6 _ . 0 0 L 0 P  TRIP  TIME=  3  4.26  DOLTIR  OOLTOT  TRIP  =  29.56  32192.24  T I ME=  = 1 6 3 8 0 . 0 0  SURFACE  80606 851.86  =  TRIP  =17.39  67254.88  =  DOLOP  M P H =35.01  EMPTY  =  DOLOP DOLOP =  DOLMAV  =  5.1  LCAPED  MPH  ALTERNATIVE  4.7  LCAPED  DOLRCC  OLD 1303.39  9.1  ""  3 =  TIME=  LOADED  =  DOLTIR  8.9  17340,00  SURFACE  33519.77  TRIP  13106.32  " ° H =19.12  =  67695.50 =  DOLTOT  17340.00  _  =  OOLOP  =18.52  =19.12  OCL^MC  =  DOLTIR  " P H  " P H  E " PT Y  DOLTIR  126.62  TIME=  EMPTY  90606  2360.01  TIME=  EMPTY  8 4 9 . 53  =  =  TRIP  2  =  =  TRIP  3  DOLMAV  ALTERNATIVE  OOLOP  MPH =34.09  VEHICLE  4.27.  DOLOP  MPH =38.26  =  1303.39  OLD  =  4.8  LCAPED  =17.66  =  3  DOLTIR  DOLMAV  5.1  LCAPED  " P H  =  4.38  T I ME=  =21.66  POL" CC  SURFACE  =  TIME=  =23.07  LPAPED  69110.50  DOLTIR  34273.34  TIME=  1 2 9 1 5 . 84  120.05  =  TRIP  =  =  =  DOLOP  =17.38  =19.12  DOLOP  9.3  MPH  VEHICLE  V E H I C L  DGLTOT T I ME=  LOADED  MPH  4.9  16380.00  LOADED  1  13  =  TRIP  =19.12  VEHICLE  VEHICLE  =18.14  OOLRCC  TIME=  16950.00  1  j  MPH  TRIP  4.24  3  OLD  ALTERNATIVE  =  101108  OOLMAV  =  798.33  DOLMAV  =  27.81  D O L M A . V ..= ALTFRNATIVE  3 . 9 9 ... =  80809  OOLTIR  =  1280.12  OOLMAV  =  840.22  DOLTJ R  =  29.21  OOLMAV  =  29.21  DOLTIR  =  4.34  DOLMAV  =  4.20  SURFA~CF  =  3  OLD  ALTERNATIVE  •  90808  VEHICLE  1  EMPTY  MPH  =19.12  LOADED  MPH  =18.59  TRIP  TIME*  9.1  DOLOP  =  33236.72  OOLTIR  =  1280.12  DOLMAV  =  837.90  VEHICLE  2  EMPTY  " P  =23.07  LCAPED  VPH  =38.62  TRIP  TIME=  4.7  OOLOP  =  2333.60  OOLTIR  =  29.09  OOLMAV  =  29.09  H  E*FTY MPH =21.66  VEHICLE  LCADEO MPH =36.33  TP.IP TIM_ =  5.1  OOLOP =  125.13  DOLTIR  4.36  4. 19  CCLMAv  OLD A L T E R N A T I V E = 90909 1280.12 DOLMAV = 637.9029.09 OOLMAV = 29. 09 _4_. J6 0.0 L MA V _____ 4. 19  VEHICLE  11 11 DCLP^C = 1 291 5. 84 DOLRCC = 17340.00 DOLTOT 1 EMPTY MPH =19.12 LOADED MPH = l f l . 6 1 T R I P T1ME= 9.1 2 EMPTY =22.07 LCADED MPH =39.70 TRIP TIME= 4.7 E M P T Y MPH =21.66 LOADED M P H =37.32 T R I P T I M E " 5. 1  68136.00 SURFACE = 3 DOLOP = 3 3 2 4 1 . 3 8 OOLTIP = DOLOP = 2329.02 DOLTIR = J}0L0P___ _124.9?_ DOLJJJL  ALT U VEHICLE VEHICLE VEHICLE  12 11 DCl ?MC = 1 2 5 3 4 . 68 DCLRCC = 1 9 2 6 0 . 00 DOLTOT 1 EMPTY MPH =19.12 LOADED MPH =18.59 TRIP TI ME = 9.0 2 EMPTY »PH =23.07 LOADED MPH =40.65 TRIP T IME= 4.7 3 EMPTY M P H =21.66 LCADED MPH =36.34 T R I P TIME= 5.2  69240.25 SURFACE = 3 DOLOP = 3 2 9 1 8 . 1 9 DOLTIR = DOLOP = 2291.07 DOLTIR = DOLOP = 127.92 OOLTIR =  OLD A L T E R N A T I V E 1233.57 DOLMAV = 28.16 DOLMAV = 4.29 DOLMAV =  ALT 11 VEHICLE VEHICLE VEHICLE  13 11 OOLPMC = 12344.39 DCLRCC = 20220.00 DOLTOT 1 EMPTY M P H =19.12 LOADED M P H =19.19 TRIP T I M E ' 9.0 2 EMPTY MPH =23.07 LOADED M P H =42. 27 T R I P TI ME = 4.7 3 EMPTY M P =21.66 L DA DEO MPH =37.10 TRIP TIME= 5.1  69648.69 SURFACE = 3 DOLOP = 3 2 6 0 4 . 8 9 DOLTIR = OOLOP = 2202.00 DOLTIP = DOLOP = 127.52 OOLTIR =  OLD A L T E R N A T I V E = 1 0 1 1 0 9 1210.29 DOLMAV = 796.00 27.70 00 L M A V = 27.70 4.26 DOLMAV = 3.98  ALT 11 VEHICLE VEHICLE VEHICLE  11 1 2 3  12  ALT  11  12  12  V E H I C  LE  ALT 11 VEHICLE VEHICLE  h  DCLPMC EMPTY  MPH  E M P T Y  MPH  EMPTY  MPH  D C - L B MC C MPTY  1  VEHICLE VEHIC LE  MPH  E M F T Y  MPH  EMPTY  MPH  OOLTOT DOLRCC 12725.36 1 8 3 0 0 . 00 =19.12 LCADEO M P H =19.22 TRIP TIME= 9.0 =23.07 LOADED M P H =40.47 TRIP TIME = 4.7 =21.66 LOADED M P H =38.15 T R I P TIME= 5.1  SURFACE = 68548.44 DOLOP = 3 2 9 2 9 . 1 4 DOLTIR DOLOP = 2322.8 1 DOLTIR DOLOP = 124.61 . D O L T I P  •  OLD A L T E R N A T I V E = 1256 .84 DOLMAV = = 28.63 DOLMAV = = . 4.33 DOLMAV =  100910 8 2 3 . 93 28.63 4.12  67920.50 SURFACE = 3 OLD A L T E R N A T I V E = 91010 12915.84 DOLRCC = 17340.00 DOLTOT 12 LOA-OfO MPH =1B.6Q TRIP T IM E___ .9 ._0_ _0_OLOP__= _330_33.78 DOLTIR = 1280.12 DOLM AV___ 837. 90 _ DOLOP = 2321 .38 DOLTIP = 2 9 . 09 DOLMAV = 29.09 =23.07 T R I P T l ME = LOADED M P H =40.61 4". 7 DOLOP= 124.70 DOLTIR = 4.36 OOLMAV = 4.19 LOADED M P H =38.13 =21.66 TRIP TIME = 5.1 =  = 19 ,  70201.94 SURFACE = 3 CLD A L T E R N A T I V E ALT 11 13 12 DDL PMC = 1 2 2 1 5 . 3 6 DOLRCC « 2 1 2 6 0 . 0 0 DOLTOI DOLOP = 3 2 2 7 3 . 7 9 OOLTIR = 1187.02 DOLMAV = VEHICLE 1 EMPTY M P H =19.12 LOADED M O H =19.42 TRIP TIME = 8.9 27 .23 P0LMAV__= VEHICLE_2 __F PTY_'-PH_=2___.C7 LEAPED M P H =43_.33 TR \ P__T I ME_= 4.6.. DOLOP =__2274 . 10 _ 0 O L T I R _ « "DOLOP"" 12 7.06 ~D0i.fi'p "= " 4.2 2"" " 0 O L M A v " LCADED MPH =37.54 T R I P T 1 ME = 5.1 " V E ' H EMPTY T C M;: L Y=21.66 "  =  V  11 13 OCLPMC = 12215.36 1 FMPTY M P H = 1 9 . 1 2 LOADED 2 EMPTY M P H = 2 3 . 0 7 LCADED 3 EMPTY M P H = 2 1 . 6 6 LOADED  101209 782.04 _2 7 . 2 3  " 3.91 "  h  ALT u VEHICLE VEHICLE _V E ______ L E  91008 809. 97 28. 16 4.05  DOLPCC = 21280.00 DOLTOT M P H =18.61 TRIP TIME= 9.0 MPH = 3 9 . 6 3 TRIP T I M E = 4.8 MPH =39 .49 TRIP T I ME= 5.0  7 0 8 8 2 . 13 SURFACE = 3 OLE A L T E R N A T I V E = 9091 1 DOLOP = 3 2 8 8 6 . 96 DOLTIR = 1 1 8 7 . 02 DOLMAV = 702.04 OOLOP = 2346.65 OOLTIP. = 27.23 OOLMAV = 27.23 OOLOP = 121.52 DOLTIR = 4.2.2 DOLMAV = 3.91  ALT 11 VEHICLE VEHICLE VEHICLE  12 13 DGLRMf. = 1 2 6 5 1 . 62 DCLRCC = 1 7 7 3 0 . 00 DOLTOT 1 E M P T Y MPH =19.12 LOADED MPH =18.61 TRIP TIME= 8,8 2 EMPTY MPH =23.07 L CADED MPH = 4 0 . 6 5 T R I P TIME= 4.6 3 EMPTY MPH =21.66 LOADED MPH =39.49 TRIP TIME= 4.9  66911.88 SURFACE = 3 OLD A L T E R N A T I V E = 91011 DOLOP = 3 2 0 2 1 . 3 4 DOLTIR = 1 2 5 6 . 8 4 DOLMAV = 826.26 DOLOP = 2240.92 DOLTIR = 28.74. DOLMAV = . 28.74 DOLOP = 118.97 DOLTIR = 4.31 OOLMAV = 4.13  ALT 11 VEHICLE VEHICLE VEHICLE  13  DOLRCC = 1 8 3 0 0 . 0 0 DOLTOT LOADED MPH =19.22 TRIP TJME= 9.0 LCADED MPH =42.27 TRIP TIME= 4.7 LOADED MPH =39.84 TRIP TIME= 5.0  60454.50 SURFACE = 3 OLD A L T E R N A T I V E = 101111 DOLOP = 3 2 8 5 3 . 2 1 OOLTIP = 1 2 5 6 . 6 4 OOLMAV = 823.93' OOLOP = 2305.56 DOLTIP = 28.63 OOLMAV = . 2 8 . 6 3 OOLOP = 123.87 DOLTIR = 4.33 DOLMAV = 4.12  ALT 12 VEHICLE VEHICLE VEHICLE  14 1 2 3  1 2  13  3 13  DrL  c u  r.  =  1 2 7 2 5 . 36  EMPTY MPH =19.12 EMPTY M P H =23.07 EMPTY MPH =21.66"  OOLTOT = 71521.94 SURFACF OfL^MC = 12160.C6 DOLRCC = 2 2 9 1 0 . 0 0 DOLOP = 3 2 0 9 2 . 8 1 DOLTIR EMPTY MPH =19. 12 LOADED MPH =19,61 TRIP TIME= 8.8 OOLOP = 2242.26 OOLTIR LOADED MPH =44.34 T R I P TIME= 4.6 EMPTY MPH =23.07 DOLOP = 125.97 DOLTIR LPAPED "PH =39.04 TRIP TI-ME= 5.1 .v F TY " H =21.66 p  OLD A L T E R N A T I V E = 101311 = 1163.74 DOLMAV = 765.74 = 26.65 DOLMAV = 26.65 * 4.21 UOLMAV » 3.83  - 71294.38 SURFACE = 3 CLP A L T E R N A T I V E ALT 11 11 14 .OCL'MC = 12024.88 OCLRCC = 22240.00 OOLTOT _0nLOP_= 32574. 6.__ D01.T1 R _=_J.J 63, 74 POL AV_. VrH ICLE 1 EM P T Y M P H _=_19 _J 2 LCAOFO M P H =19. ?_ T_R [ P_T J M,f, » 8, 9_ DOLOP = 2 3 4 0 . 4 2 DOLT 1R = 2 6 . 77 OOLMAV = TEHFC'LE 2 EMPTY ? P H - 2 T . 0 7 I f A t E O "MPH =40.39 TRIP T I M E * 4.7 DOLOP * 121.09 DOLTIR = 4.19 DOLMAV « VEHICLE 3 EMPTY MPH =21.66 LOADED MPH =40.93 TRIP T1ME= 4.9 M  11  12  V E H I C L E  ALT  1  14  EMPTY  D C L P M C MPH  = 1 9 . 1 2  =  1 1 8 9 5 . 8 4 L P A D E O  MPH  P O L R C C  = 1 9 . 4 9  =  2 3 3 0 0 . 0 0 T R I P  TI  ME=  D O L T O T 8 . 9  Y E H 1 C L F  2  E M P T Y  MPH  = 2 3 . 0 7  L P A P E D  MPH  = 4 0 . 9 4  T R I P  T1ME=  4 . 7  =  100912 7.<.i),.0.7__ 26.77 3.84  71S51.69 SURFACE = 3 OLD A L T E R N A T I V E = 1 0 1 0 1 3 DOLOP- » 3 2 2 4 6 . 4 3 DOLTIR * 1140.47 COLMAV = 7 5 4 . 11 DOLOP » 2333.64 DOLTIR = 26___.Q Q_3.LM.Ay__; 2i..iCL_  r  VEHICLE ALT_  3  11 _ 1 3  VEHICLE  1  VEHICLE  2  VEHICLE  3  ALT  EMPTY 14  MPH  DCLPMC_= EMPTY  15  =21.66  LOADED  12461.14  _  MPH  =41.81  DOLRCC„=  TRIP 18690.00  _  DOLTOT  LOADED  MPH  EMPTY  MPH = 2 3 . 0 7  LOADED  MPH  =42.27  TRIP  T I ME =  4.6  EMPTY  MPH  LOADED  MPH  =40.93  TRIP  TIME=  4.9  12  12  VEHICLE  I  EMPTY  DCLCMC "PH  =19.12  =  11766.81  VEHICLE  2  EMPTY  " P H  VEHICLE  3  EMPTY  MPH  •  OCLPCC  =  TRIP  4.9  MPH = 1 9 . 1 2 =21.66  =19.22  TIME =  TIME=  24360.00  OOLOP =  8.8  DOLTOT T I ME= _  =  OLD ALTERNATIVE  DOLOP  =  2231.84  DOLTIR  =  OOLOP  =  118.54  DOLTIR  =  =  1117.19  DOLMAV  =  25.84  DOLMAV  =  4.12  DOLMAV  =  72397.63  =41.26  TRIP  TIME*  4.7  DOLOP  = "2325.97  D O L T I R" =  =42.72  TRIP  TIME=  4.9  DOLOP  =  DOLTIR  =  =  68268.13 SURFACE = 3 D O L O P = 3 0 8 8 8 . 28 OOLTIR = _DOLOP^ 2214.85_ DOLTIR = DOLOP = ~ 117.74 OOLTIR = 69619.69 SURFACE = 3 DOLOP = 3 0 8 0 2 . 8 7 DOLTIR = DOLOP = 2190.56 DOLTIR = DOLOP = 116.50 DOLTIR =  3.77 =  1C1112  DOLMAV  =  812.29  28 . 2 8  DOLMAV  =  28.28  4.27  DOLMAV  =  4.06  OLD  MPH  120.29  OOLTIR  3  MPH  I DCLPMC = 13619.09 .EM?TY_'.'PH^=i0.67_ LPA PED EMPTY " P H = 1 5 . 5 2 LPAOEO E M P T Y MPH = 1 3 . 7 7 LPAPED  31907.76  =  LOADED  SUBSECTION  =  SURFACE  LOADED  NUMBER  ALT 5 1 1 VEHICLE 1 VEHICLE _ 2 VEHICLE 3  1233.57  =21.66  MJM8EF.  1 1 2 3  =  3  =  31709.03  =23. 07  DOLRCC = 22.730.00 DOLTQT = MPH = 1 9 . 5 1 T R I P TIME= 8.'6 MPH = 4 6 . 5 7 T R I P TIME= 4.5 MPH_= 4 4 . 9 8 _ _ T R I P T I M E * __4. 8  ALT 1 VEHICLt_ VEHICLE VEHICLE  DOLTIP.  _SURFACE_=  DOLMAV  =  DOLOP  0CIR"C 11622. 11 EMPTY " P H = 1 9 . 1 2 LOADED EMPTY " P H = 2 3 . 0 7 LCAPED EMFTY_ M P H _ = 2 1 . 6 6 _ LPAPED  3  4.15  T RIP  ALT 12 15 VEHICLE 1 VEHICLE 2 VEHICLE_ 3  SECTION  =  M P H = 19 . 6 1 _ _  DOLRCC = 20810.00 DOLTOT MPH = 1 9 . 7 3 TRIP TIME= 8.6 MPH = 4 4 . 3 4 . _ T R I P TIME = 4.5 MPH = 4 2 . 7 2 TRIP T I M E " 4.8  MAIN  _  DOLTIP  LOADED  ALT 12 14 1 5 OCLRMC = 12203.07 VEHICLE 1 E M P T Y MPH = 1 9 . 1 2 LOADED .VEHICLE_2. EMPTY M P H = 23.0_7_ LOADED VEHICLE. 3 EMPTY « P H = 2 1 . 6 6 LOADED 15  120.72  67321.31 DOLOP  8 . _8  =  ALTERNATIVE  =  101014 7 4 0 . 14  '  25.64 3.70  OLD A L T E R N A T I V E 1187.02 DOLMAV"= 27.35 DOLMAV = ~ 4.20 DOL MA V =  =  101314 734.36 27.35 " " 3.92  OLD A L T E R N A T I V E 1140.47 DOLMAV = 26.42 DOLMAV = _ 4 . 1 3 _ OOLMAV =  =  101415 756.43 26.42 3.78  2  OCLPCC = 14350.00 -DOLTOT M P H _ = _ 3 . 5_6 I R 1_P J L L E = 9.4 MPH = 9 . 7 6 TRIP TIME* 4.8 MPH = 8 . 0 5 T R I P TIME= 5.1  =  73058.44 SURFACE = 1 OLD A L T E R N A T I V E DOLOP = 3 8 9 8 5 . 0 8 DOL TI R _ = _ 1 5 4 7 . 7 8 _ DOLMAV = DOLOP = 2634.70 D O L T I R~ = " " 3 4 . 5 6 " " " C O L M A v " = DOLOP = 141.88 DOLTIP = 5.00 DOLMAV =  = 60507 1 0 0 0 . 82 34.56 5.00  OCI.PMC = 13819.09 Er'PTY M P H =16.03 LOADED EMPTY " P H = 2 0 . 4 7 L C A DED_ EMPTY M P = 1 8 . 9 0 ' LCATEO  OOLRCC = 14850.00 DOLTOT MPH = 1 0 . 6 3 T R I P T I ME= 9.4 MPH_ = 2 3 . 16 TRIP TI ME= _4.8 MPH = 2 1 . 3 7 tRIP f IM fc= 5 . 2  =  73473.13 SURFACE = 2 OLD A L T E R N A T I V E DOLOP = 3 9 3 6 8 . 4 7 " DOLTIR = 1 5 4 7 . 7 8 OOLMAV = O G L O P _=__ _ 2 6 6 4 . 0 9 OOLTIR. = 34.56 OOLMAV = DOLOP = " ~ 1 4 3 . 7 8 "00LTI>.~« ' ' 5.00 ~ 0 O L " A \ ' " «  = 10101 1 0 0 0 . 82 _ 3 4 . 56. " 5.00"  DOLRCC = 15810.00 DOLTOT MPH =14.10 T R I P TIME= 9.4 MPH = 2 5 . 0 1 T R I P TIME= 4.8 MPH = 2 3 . 3 3 T R I P _TJ.ME= 5.1  H  M  ALT 7 VEHICLE VEHICLE V_EHICLE_  1 1 2 3  2  DCL MC = 13616.32 EMPTY M P H = 1 8 . 2 0 LPAPED EMPTY MPH, = 2 2 . 3 0 LCAPED E M P T Y MPH = 2 0 , . 8 4 LPAPED  =  7 3 6 1 1 . 13 SURFACE = 3 DOLOP = 3 8 8 8 0 . 3 0 OOLTIR = DOLOP = 2648.76 DOLTIR = DOLO_P_ = 1 4 2 . 8.4 0OLTiR_=  OLO A L T E R N A T I V E 1477.96 DOLMAV = 33.17 DOLMAV = 4 .90 OOLMAV =  ALT 2 VEHICLE VEHICLE VEHICLE  2 1 2 3  2  OH. " C = 14120.17 OOLRCC = 14460.00 OOLTOT = E M P T Y MPH = 1 0 . 6 7 L C A P E D MPH = 4 . 3 6 T R I P TIM,E= 9.6 EMPTY " P H = 1 5 . 5 2 L C A P E D MPH = 1 7 . 9 0 TP. IP T IM E= 4."9 EMPTY « P H = 1 3 . 7 7 LOADED M P H = 1 5 . 8 6 TRIP TIM£= 5.2  • 76210.44 SURFACE = 1 OOLOP = 4 2 0 2 3 . 5 8 OOLTIR = OOLOP = 2 7 2 4 . 17 DOLTIP = DOLOP = 147.60 DOLTIR =  OLD A L T E R N A T I V E = 10101 1617.60 00 LMAV = 1035.73 35.61 OOLMAV = 35.61 5.18 OOLMAV = 5.13  ALT v "' VEHICLE VEHICL E VEHICLE  2 1 2 3  2  P.-1-.MC = 14C83.3C EMPTY M H = 1 6 . 0 3 LOADED EMPTY M P H =20. 47 LPAOEO EMPTY " ° H =18.90 LPAPED  g  C  C  P?l. FCC = 1446 0 . 0 0 DOLTOT MPH = 1 0 . 7 3 TRIP TIME= 9.6 MPH = 2 5 . 9 9 TR I P T I ME= 4.9 MPH = 2 3 . 8 6 T R I P TIME= 5.2  = 7 3 7 4 9 DOLOP OOLOP DOLOP  =  10101 958.93 33.17 4.79  . 7 5 S U R F A C E = 2 = 39789.72 DOLTIR = = 2612.71 OOLTIR = = 140.56 DOLTIR =  OLD A L T E R N A T [VE""= 20202 1571.05 DOLMAV = 1012.46 34.91 OOIMAV = 34.91 5.06 DOLMAV = 5.06  ALT 7_ 3 VEHICLE" " 1 VEHICLE 2 VEHICLE 3  4__ OPL°MC_=__ 1 3 3 8 0 . 5 3 _ E»PT Y MPH = 1 6 . 2 0 " " L O A D E O E M P T Y M P H = 2 2 . 30 LCA E D E M P T Y MPH = 2 0 . 6 4 LOADED  D C L RCC _= _ 1 _ 5 4 2 0 . 0 0 _ _ 0 O L T O T _ = _ 7 3 8 9 5 . 2 5 . _ S U R f A C E._=... .3 " P H " =14721" "f R l > T I K E * 9.6 DOLOP = 3 9 3 0 7 . 5 2 OOLHR = M PH = 2 7 . 8 1 TRIP TIME= 4.9 DOLOP = 2 5 9 8 . 83 DOLTIR = MPH = 2 5 . 8 0 T R I P TIME= 5.2 DOLOP = 139.70 DOLTIR =  OLD A L T E R N A T I V E * 20202 1501.23 DOLMAV = 970.56 33.52 DOLMAV = 33.52 4.96 POLMAV = 4.85  ALT 6 VEHICLE^ VEHICLE VEHICLE  4  DOLRCC = 14850.00 DOLTOT = 70673.06 SURFACE = 2 MPH_ = 1 2 . 4 7 „ T R J P T1 ME=_ __?_._4 DOLOP_= 3 6 8 0 3 . 3 1 OOLTIR_= MPH = 2 8 . 73 TRIP TIME* " 4 . 8 OOLOP = " " 2 5 4 4 . 9 4 DOLTI R = MPH = 2 6 . 6 5 TRIP TIME* 5.2 OOLOP = 136.28 OOLTIR =  OLD A L T E R N A T I V E 1501.23 _ DOLMAV = 33.86 DOLMAV = 4.89 OOLMAV =  4 I 2 3  -  n  OCLRMC = 13782.21 EMPTY M P H _=16.03_ LOADED E M P T Y MPH = 2 0 . 4 7 LOADED FKPTY MPH = 1 8 . 9 0 LOADEO  =  50101 977.55 " 33.86' 4.39  -68-  APPENDIX 8 COST DATA FOR HYPOTHETICAL PROBLEM Road s u r f a c i n g c o s t s v a r i e d w i t h s u r f a c e as  grade  follows: Surface  type  Basic cost  Additional  $/s.ta  0-5%  for increased  6-10%  0  0  0  gravel  500  0  0  10  1000  0  100  100  c o s t o f m a i n t a i n i n g the  r o a d g r a d e and t r a f f i c  d e n s i t y as  grade  11-157,  250  The type,  cost  dirt  pavement  road surface v a r i e d w i t h  surface  follows:  Surface  Basic cost  Additional  type  $/sta  cost  Additional  cost  i n c r e a s e d grade  increased  traffic  0-5%  density multiples  6-10%  for  11-15%  1  2  6  12  for  24  dirt  80  0  0  0  0  10  gravel  40  0  0  5  0  5  25  50  95  pavement  10  0  10  10  0  2  10  22  38  The and  t y p e and r o a d  $0.50/min.  respectively.  50 110 190  d i r e c t v e h i c l e o p e r a t i n g c o s t s were $ 0 . 7 5 / m i n . , for logging trucks, The t i r e  crew busses  $1.00/min.  and s e r v i c e v e h i c l e s  costs varied with vehicle  t y p e and s u r f a c e  as  follows: Surface  type  V e h i c l e .type logging truck  crew bus  service vehicle  $/mile  $/mile  $/mile  dirt  0.50  0.10  0.15  gravel  0;30  0.07  0.10  pavement  0.10  0.03  0.07  In favorable  or  the above c o s t s  adverse.  t h e g r a d e s w e r e t a k e n t o be  either  -69V e h i c l e maintenance  costs  as a f f e c t e d  by s u r f a c e  type are  as  follows: Surface  type  Vehicle  type  logging truck  c r e w bus  service  vehicle  $/mile  $/mile  $/mile  dirt  0.30  0.10  0.15  gravel  0.20  0.07  0.10  pavement  0.08  0.03  0.04  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

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

Comment

Related Items