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Speed and the probability of a collision Kwan, Thomas Yan Wa 2001

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Speed and the Probability o f a Collision by Thomas Y a n W a K w a n B A . S c , The University of British Columbia, 2000  A THESIS SUBMITTED I N P A R T I A L F U L F I L M E N T OF T H E REQUIREMENTS F O R T H E D E G R E E OF M A S T E R OF APPLIED  SCIENCE  T H E F A C U L T Y OF G R A D U A T E STUDIES (Department o f Civil Engineering; Transportation) We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A April 2001 © T h o m a s Y a n W a Kwan, 2001  In presenting this thesis in partial fulfilment o f the requirements for an advanced degree at the University o f British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying o f this thesis for scholarly purposes may be granted by the head o f my department or by his or her representatives. It is understood that copying or publication o f this thesis for financial gain shall not be allowed without my written permission.  Department o f The University o f British Columbia Vancouver, Canada  ABSTRACT  ABSTRACT Speed related automobile accidents account for about one-third o f all vehicle accidents in the United States and in the province o f British Columbia.  The estimated  economic cost o f speeding-related vehicle accidents in the U S is $27.7 billions U S D (1994 dollars).  Researchers have different views on the role that speed plays as a  causative factor in automobile collisions. The purpose o f this research is to develop an equation between speed and the probability o f a collision using a risk approach.  Risk is defined as the product o f the  exposure, the probability, and the consequence o f an event.  B y using published data  from the province o f Saskatchewan, an equation to estimate the probability o f a collision as a function o f speed is developed. This probability equation is a function o f the average vehicle travelling speed raised to an exponent, in which the exponent is also a function o f average vehicle speed. From the literature, the consequence o f a fatal or serious injury collision is the fourth power function o f the collision speed.  Thus the equation for  fatality risk for an individual travelling on a road is a fairly complex function o f the operating speed.  Additional analysis o f traffic accident and speed data on U S rural  highways and data for Bangkok urban expressways were used to estimate risk. This research found that not only does speed increase the severity o f a collision, but it also increases the probability o f a collision.  ii  Thomas Y . W . K w a n  T A B L E OF C O N T E N T  TABLE OF CONTENT ABSTRACT  ii  LIST OF TABLES  vi  LIST OF FIGURES  vii  ACKNOWLEDGEMENTS  ix  CHAPTER 1 INTRODUCTION AND OVERVIEW  1  CHAPTER 2 LITERATURE REVIEWS  3  2.1  INTRODUCTION  3  2.2  SPEED A N D ACCIDENT I N V O L V E M E N T  3  2.2.1  Solomon  4  2.2.2  MUARC  6  2.2.3  Australia Study  2.2.4  Liu and Popoff.  8  2.2.5  UK Experience  9  2.3  7  SPEED A N D ACCIDENT SEVERITY  10  2.3.1  Solomon  10  2.3.2  Joksch  12  2.4  T H E O R Y OF RISK  14  2.5  CONCLUSION  16  CHAPTER 3 DATA COLLECTION  iii  17  Thomas Y . W . K w a n  TABLE OF CONTENT 3.1 INTRODUCTION  17  3.2 DATA COLLECTION IN BRITISH COLUMBIA  18  3.3 DATA COLLECTION IN BANGKOK  21  3.4 CONCLUSION  31  CHAPTER 4 A NEW RISK THEORY  33  4.1 INTRODUCTION  33  4.2 THEORY  33  4.3 THE SPEED-COLLISION PROBABILITY EQUATION  34  4.4 THE SPEED-COLLISION RISK EQUATION  40  4.5 CONCLUSION  43  CHAPTER 5 APPLICATION OF THE NEW RISK THEORY  44  5.1 INTRODUCTION  44  5.2 SOLOMON'S DATA  44  5.3 BANGKOK EXPRESSWAYS  48  5.4 CONCLUSION  52  CHAPTER 6 ADDITIONAL RESEARCH  53  6.1 INTRODUCTION  53  6.2 MORE QUALITY DATA  53  6.3 SPEED VARIANCE-COLLISION PROBABILITY RELATIONSHIP  54  6.4 CONCLUSION  56  iv  Thomas Y.W. Kwan  T A B L E OF CONTENT  CHAPTER 7 CONCLUSION  57  BIBLIOGRAPHY  59  APPENDICES  62  APPENDIX 3-A  Sample Database of Hong Kong Expressways and Bangkok Highways  63  APPENDIX 3-B  BC MOTH Collision Report  71  APPENDIX 3-C  Speed Loop Locations  in  British Columbia  Provincial Highways  72  APPENDIX 3-D  Average Travelling Speed in Bangkok  74  APPENDIX 3-E  Traffic Accident Statistics in Thailand  75  APPENDIX 3-F  ETA Accident Database  76  APPENDIX 3-G  ETA's Traffic Speed, Volume, and Accident Data in 1999 77  APPENDIX 4-A  Sample Calculations of Speed-Collision Probability Equation  79  V  Thomas Y.W. Kwan  LIST OF TABLES LIST OF TABLES Table 3-1 Bangkok Expressways Characteristics  26  Table 4-1 Saskatchewan Rural Highway Speed and Collision Data  35  Table 4-2 Controlling Exponent at Different Speed  37  Table 5-1 Traffic Accident and Speed on Bangkok Expressways  48  Table 5-2 Comparisons of Results of Hypothetical Example  51  vi  Thomas Y . W . Kwan  LIST OF FIGURES LIST OF FIGURES Figure 2-1 Accident Involvement Rate by Variation F r o m Average Speed (Solomon 1964)  5  Figure 2-2 Involvement Rate A n d Speed Difference ( M U A R C 1993)  7  Figure 2-3 Relative R i s k vs. Speed in Australia (Risk =1 @ 60km/hr; K l o e d e n 1997) 8 Figure 2-4 Person Injured per 100 Accident-Involved Vehicles (Solomon 1964)  11  Figure 2-5 Property Damage per Accident-Involved Vehicle vs. T r a v e l Speed C u r v e (Solomon 1964)  12  Figure 2-6 Fatality R i s k vs. Delta Speed C u r v e (Joksch 1983)  13  Figure 3-1 M a p of B C Provincial Highways  19  Figure 3-2 Vehicle Travelling Speed vs. Posted Speed L i m i t in B C  20  Figure 3-3 M a p of T h a i l a n d  21  Figure 3-4 Motorization Trends in T h a i l a n d and Bangkok  23  Figure 3-5 Traffic Accident Trends in T h a i l a n d  24  Figure 3-6 Responsibilities of Thailand's U r b a n T r a n s p o r t Administrations  25  Figure 3-7 M a p of Expressway System in Bangkok  27  Figure 3-8 Expressway Networks in Downtown B a n g k o k  28  Figure 3-9 Traffic Accident Trends on B a n g k o k Expressways  29  Figure 3-10 Accident Rate on Bangkok Expressways  29  Figure 3-11 Causes of Traffic Accidents on Bangkok Expressways  30  Figure 4-1 Collision Probability vs. Speed Based on L i u and P o p o f f s D a t a  35  Figure 4-2 C o m p a r i s o n of Exponents vs. Speed Curves  38  vii  Thomas Y.W. Kwan  LIST OF FIGURES Figure 4-3 Involvement Rate vs. Average Travelling Speed (50 to 150 km/hr)  39  Figure 4-4 Unit Fatality Risk vs. Average Travelling Speed (50to 150km/hr)  42  Figure 5-1 Exponents vs. Speed For Solomon's Data  45  Figure 5-2 Comparison of Involvement Rate vs. Average Travelling Speed for US 46  and Saskatchewan Rural Highways Figure 5-3 Unit Fatality Risk vs. Average Travelling Speed for Solomon's Data  47  Figure 5-4 Exponents vs. Average Travelling Speed for Bangkok Expressways  49  Figure 5-5 Involvement Rate vs. Average Travelling Speed on Bangkok 50  Expressways Figure 5-6 Unit Fatality Risk vs. Average Travelling Speed for Bangkok  51  Expressways Figure 6-1 Average Speed, Speed Variance, and Involvement Rate Plane  viii  55  Thomas Y.W. Kwan  ACKNOWLEDGEMENTS  ACKNOWLEDGEMENTS Completing my Master degree is a major achievement in my life and I could not have achieved this goal without the help o f my family, my friends, and my colleagues. First o f all I want to express my greatest gratitude to my supervisor, D r . Frank Navin. H e spent countless hours talking to me and teaching me, not only about the research materials, but also about how to be a leader, a critical thinker, and a successful engineer. I would like to thank the Natural Science and Engineering Research Council o f Canada, the Insurance Corporation o f British Columbia's S M A R T Program, and the Canadian University Consortium ( C U C ) at the Asian Institute o f Technology (Bangkok, Thailand), supported by the Canadian International Development Agency ( C I D A ) .  They  all contributed to the funding o f this research. Next I would like to thank my beloved family for all the support that they have given me throughout the course o f my study. I am really proud o f being a member o f this family and I am sure my parent, brothers, and sister are also proud o f my achievement. Then I would also like to thank my girlfriend for going through the Master program with me.  She has been giving me confidence and moral support and has been  spending a lot o f her time reviewing my thesis. T H A N K Y O U . Special thanks go to the staff at the C U C office at A I T for helping me collect the data in Thailand. Also I would like to thank M r . Arthit o f the Expressways and Rapid Transit Authority o f Thailand ( A I T ) for his help collecting the accident and speed data.  ix  Thomas Y . W . K w a n  INTRODUCTION AND OVERVIEW  CHAPTER 1 INTRODUCTION AND OVERVIEW One o f the leading causes o f road accidents is speeding. Speeding is defined as "Exceeding the posted speed limit or driving too fast for conditions."  Speed related  accidents account for about thirty percent o f all road accidents in the U S and in British Columbia. In 1998, 12477 o f the 41471 deaths, roughly thirty percent, on U S roads were speed related ( N H T S A 1999). O f those 12477 deaths, 64 percent occurred in rural areas and 36 percent in urban areas.  The estimated economic cost o f speeding-related vehicle  accidents is $27.7 billions U S D (1994 dollars). In British Columbia, about 34 percent o f fatal crashes and 16 percent o f injury crashes have speeding involved. Speeding is a road safety issue that causes many difficulties for road safety professionals and political decision makers.  The debate is characterized by strong  personal opinion, poor data and no consistent theory. Groups who support a higher speed limit for better mobility have challenged the slogan "Speed K i l l s " because there have been few studies that can fully address the relationship between the chance o f getting into a traffic accident and the driving speed.  O n the other hand, the relationship between  driving speed and accident severity is well known.  Furthermore, another debate is  whether it is the speed variance or the average travelling speed on the road that is causing the traffic accidents. One method to study speeding is the Probabilistic Risk Approach ( P R A ) .  This  approach develops a relationship between speed and the probability o f a crash.  The  definition o f risk is the product o f the exposure to an event, the probability o f an event, and the consequence o f the event. The first problem tackled in this study is to develop a probability equation o f vehicle accidents as a function o f the average vehicle travelling  1  Thomas Y . W . K w a n  INTRODUCTION AND OVERVIEW  speed. From the literature, the consequence equation o f a fatal or serious injury collision is shown to be the fourth power function o f collision speed. Thus, combining these two equations will give the relationship between the unit risk o f a fatal accident for an individual travelling on a road. This thesis has o f seven chapters. Chapter two provides a literature review o f the relationship between speed and accident rate, speed and accident severity, and the theory of risk.  Chapter three describes the data collection process o f the accident and speed  data o f B C provincial highways and Bangkok expressways. Chapter four introduces the new risk theory and uses L i u and Popoff s data to develop a new average speed-collision probability equation ( L i u & Popoff 1997).  The probability equation is then combined  with a known consequence equation from literature to form the new average speedcollision risk equation.  Chapter five presents the application o f the risk-speed theory  using Solomon's data and data obtained from Bangkok.  Chapter six provides  suggestions for future research. Finally, Chapter seven provides a conclusion to end this thesis.  2  Thomas Y . W . K w a n  LITERATURE REVIEWS  CHAPTER 2 LITERATURE REVIEWS 2.1  INTRODUCTION A  new risk approach to quantify the relationship between average vehicle  travelling speed and vehicle crashes is being investigated in this thesis.  A literature  review was carried out to find what has been done in defining the relationship between speed and vehicle accidents. This chapter reviews international studies on speed and vehicle crashes. Section 2.2 presents studies on the relationship between the average travelling speed and vehicle crashes.  Section 2.3 deals with the relationship between the vehicle travelling speed and  accident severity. Section 2.4 then presents previous studies on the theory o f risk.  2.2  SPEED AND ACCDDENT INVOLVEMENT There have been many reported studies to determine the relationship between the  vehicle travelling speed and vehicle accidents. Many o f these studies tried to quantify the chance o f having an accident by a relationship with the vehicle speed and/or the variation of vehicle speed on a road.  There are debates and arguments as to whether it is the  vehicle travelling speed or the variation o f speed on the road that is causing accidents. The Transportation Research Board published a special report in 1998 titled "Managing S P E E D , Review o f Current Practice for Setting and Enforcing Speed Limits," presented a detail review on the topic o f speed and traffic accidents. Other reports by Baruaya and Kloeden et. al. also provided a thorough overview o f previous studies on speed and traffic accidents.  This section presents a few o f the earlier major studies in this field and the  latest reports published on the relationship between speed and traffic accidents.  3  Thomas Y . W . K w a n  LITERATURE REVIEWS  2.2.1  Solomon Early research in the United States regarding the relationship between crash  involvement and speed was reported by Solomon (Solomon 1964).  In the study,  Solomon defined a relationship between collision involvements by average vehicle speed and speed variance. H e examined accident records o f almost 10000 drivers across 600 miles o f 2-lane and 4-lane rural highways from 1954 to 1958, covering a total o f 35 sections o f the rural highways in a 11 states. The average length o f the sections was 27.3 km (17 miles) and the daytime speed limit for 28 sections was 88 km/hr to 112 km/hr (55mph to 70mph). Vehicle speed data were collected along the chosen two-lane and four-lane roadways. In addition to the speed data, traffic volume and crash records along the study roadways were analyzed by location, and vehicle crash involvement rates were calculated for various roadway sections.  Solomon defined vehicle crash involvement rate as the  number o f accidents per 100 million vehicle-miles. H e also defined speed variance,  which was the difference of the section's average speed from the collision speed of each accident. The crash involvement rates o f specific locations were then compared to the sections' speed variance, and gave the curve shown in Figure 2-1.  4  Thomas Y . W . K w a n  LITERATURE REVIEWS  r40  -30 -tO VAftlATtOti  -80 0 +10 AVERAGE SP££Q, M.« H.  *30  Figure 2-1 Accident Involvement Rate by Variation From Average Speed (Solomon 1964).  Solomon's curve in Figure 2-1 showed that crash involvement and speed difference along the study roadways formed a "U-shaped curve".  Based on the  relationship, the lowest involvement rate along the study roadways occurred along sections at a speed variance of around +8mph. The involvement rate at zero speed variance represented the experience of the route operating at a constant average speed. The relationship also indicated that as the speed variance deviated either positively or  5  Thomas Y.W. Kwan  LITERATURE REVIEWS  negatively, the likelihood o f crash involvement increased.  Solomon concluded that  "regardless o f the average speed on a main rural highway, the greater the driver's deviation from this average speed, the greater his chance o f being involved in an accident."  What Solomon's curve suggested was that speeds, both slower and higher  than the average speed, cause traffic accidents.  In order to reduce the number of  accidents, one must have all vehicles travel at a similar speed.  2.2.2  MUARC Fields, Rumbold, and Leening o f the Monash University Accident Research  Centre ( M U A R C , 1993) also studied the relationship between collision involvement and speed variance.  MUARC  studied the speed variance relationship using Australian  collision data on two-lane rural roadways.  Their findings indicated that at speeds faster  than the average speed, the collision involvement increased. the finding described in Solomon's study.  This result was similar to  However, instead o f a U-shaped curve,  M U A R C obtained a linear relationship between collision rate and speed variance.  In  other words, rather than higher collisions rates at speeds lower than the average speed, lower collision rates were observed. See Figure 2-2. The relationship derived from M U A R C data generally indicates that at speeds higher than the mean speed the collision involvements increase and at speeds lower than the mean speed the collision involvements decrease.  This graph also shows that driving  near the mean speed on the road does not result in the lowest collision involvement rate.  6  Thomas Y . W . K w a n  LITERATURE REVIEWS  E  -40  .30  -20  -10  m  c  a  n  1«  2  0  3  0  VARIATIONS FROM MEAN TRAFFIC SPEED (m.p.h.)  Figure 2-2 Involvement Rate And Speed Difference (MUARC 1993). 2.2.3  Australia Study Kloeden et. al. studied 151 accidents that involved injury and fatality in the  Adelaide Metropolitan area (Kloeden 1997). His team calculated the pre-crash speed o f each accident by an accident reconstruction simulation program ( M - S M A C ) .  With the  pre-crash speed and the mean travelling speed, Kloeden was able to calculate the relative risk o f injury and fatal accidents relative to the 60km/hr speed zone. They found that at speeds above 60km/hr there is an exponential increase in risk and that the risk doubles with each 5km/hr increase in travelling speed.  Figure 2-3 shows a plot o f Kloeden's  result and the curve shows an exponential function.  7  Thomas Y . W . K w a n  LITERATURE REVIEWS  Relative Risk vs. Travelling Speed 60.0 50.0  • M  40.0  PH  cu  .>  CU  30.0 20.0 10.0 0.0 4 0  20  40  60  80  100  Speed (km/hr) Figure 2-3 Relative Risk vs. Speed in Australia (Risk =1 @ 60km/hr; Kloeden 1997) 2.2.4  Liu and Popoff L i u and Popoff studied the relationship between speed and traffic safety on  Saskatchewan provincial highways ( L i u & Popoff 1997). Nine major speed surveys on provincial highways with a speed limit o f lOOkm/hr had been conducted from 1969 to the time o f this study.  They developed a linear regression relationship between average  vehicular speed and casualty rate and a multivariable relationship between  average  vehicular speed, speed differential, and casualty rate. These equations are: CasualtyRate = -17126.1 + 190.71v  (R = 0.85)  (2-3)  CasualtyRate = -0.0298v + 0 . 0 4 0 5 D / ^ - 3 . 3 6 6  (R = 0.94)  (2-4)  2  2  where Casualty Rate  -  people injured or killed per 1 million veh-km  8  Thomas Y . W . K w a n  LITERATURE REVIEWS v  =  average speed, km/hr  Diff  =  85 percentile speed minus 15 percentile speed, km/hr th  th  They showed that for every 1 km/hr reduction in the mean travelling speed there will be a 7 percent decrease in casualties. The equations suggested that both average speed and speed differential are major causes in traffic casualties.  The fact that the  average speed is a factor can be explained that 60 to 80 percent of vehicle collisions on Saskatchewan provincial highways are single vehicle collisions.  2.2.5  UK Experience Under the Managing Speeds of Traffic on European Roads (MASTER) Project,  Baruya of the Transport Research Laboratory developed an accident model for UK and European roads (Baruya 1998).  The data he used for his research were from The  Netherlands, Sweden, Portugal and the UK, which included speed, road geometry and accidents on 28 links from The Netherlands, 73 from Sweden, 39 from Portugal, and 63 from the UK. His model, called the "EURO model", suggested that accident frequency is a function of flow (Q), link length (L), speed (V), proportion of drivers exceeding the speed limit (P), number of junctions (NJ), speed limit (S), and road width (W). The equation obtained was: £P  _ 5 6f53 * Q * 074  * £ 0  8  4  7  * T / - 2 - 4 9 2 * p O . l 14 * ^ 0 . 0 3 8 ^ 7 - 0 . 0 5 6 ^ + 0 . 0 2 3 5  ^  where AF  =  Accident Frequency, Accidents per year  If all variables were held constant except the mean speed, then equation 2-5 can be reduced to the following equation:  9  Thomas Y.W. Kwan  LITERATURE REVIEWS (2-6)  ALn(AF) = ( ^-)Av ]  v where mean speed, km/hr  v  change in speed, km/hr  Av  For example, for every 1 km/hr reduction when the mean speed is say 60km/hr, the accident frequency will reduce by 2.56 percent. Thus, the EURO model indicates that both mean speed and the change in speed affect the accident frequency. 2.3  SPEED AND ACCIDENT SEVERITY Unlike speed and accident involvement, the relationship between speed and  accident severity is well understood by traffic safety professionals. Given that a collision has occurred, what is the likelihood of someone getting injured or killed? The answer is quite obvious that the faster a vehicle is moving before collision; the change in speed during collision is greater. The fundamental equation of kinetic energy of a moving object is E = Vi mv . This equation indicates that the effect of speed on accident severity 2  is not linear but increases non-linearly as speed increase. A lOkm/hr change in speed in a low speed range has a much less impact than a lOkm/hr change in speed in a high speed range.  This relationship of speed and accident severity can be described as the  consequence of a vehicle accident. Two empirical studies that focus on the relationship between speed and accident severity are presented here. 2.3.1  Solomon In his 1964 study on the relationship of speed and accident on rural highways,  Solomon also studied the relationship between the collision speed and accident severity.  10  Thomas Y.W. Kwan  LITERATURE REVIEWS  H e defined accident severity with two measures: injury rate and property damage cost. Injury rate was expressed as the number o f people injured per number o f crash-involved vehicles.  Property damage cost was given in property damage cost per crash involved  vehicle. Figure 2-4 and 2-5 show Solomon's finding.  Solomon's Injury vs. Speed Curve 160  1  1  1  1  1  1  1  0 -!  1  1  h-  1  1  1  1  0  10  -i  20  30  40  50  60  70  1  1 80  Travel Speed (MPH)  Figure 2-4 Person Injured per 100 Accident-Involved Vehicles (Solomon 1964). Figure 2-4 showed that at speeds o f around 72 mph, there were 100 injuries per 100 accident involved vehicles, which also meant that there would be at least one injury per car at speeds higher than 72 mph.  The next study also showed that an accident  occurring at speeds above 71 mph are more certain to result in a fatality or serious injury.  11  Thomas Y . W . K w a n  LITERATURE REVIEWS  Solomon's Property Damge vs. Speed Curve  10  20  30  40  50  60  70  80  Travel Speed (MPH)  Figure 2-5 Property Damage per Accident-Involved Vehicle vs. Travel Speed Curve (Solomon 1964).  2.3.2  Joksch Joksch studied the relationship between accident severity and collision speed  from 1975 to 1993. In 1975, he showed that, when compared to the risk o f an occupant fatality in a crash at 40 mph, the risk o f fatality was 2.5 times greater at 60 mph, 6 times greater at 70 mph, and approximately 20 times greater at 80 mph. In 1983, Joksch studied data from the National Crash Severity Study ( N C S S ) and found the fatality risk o f a car-car collision to be proportional to the fourth power o f Delta V (speed change during the collision). Figure 2-6 shows the fatality risk and Delta V curve.  12  Thomas Y . W . K w a n  \ LITERATURE REVIEWS  Fatality R i s k vs. Delta  V  1. 0. 0. 0.  S  0 .6  0.5 *  0  fe  ~ 0. 0. 0. 0. 10  20  30 Delta V  40  50  60  70  (mph)  F i g u r e 2-6 F a t a l i t y R i s k v s . D e l t a S p e e d C u r v e ( J o k s c h 1983).  Then in 1993, Joksch studied the data from the National Accident Sampling System (NASS), which contained accident data from 1980 to 1986 for passenger cars of model years 1980 and later in the US. In his 1983 study, Joksch simply ignored those accidents that didn't have an estimate for the collision speed. This time Joksch included all accidents with and without an estimate for the collision speed in his study and imputed the Delta V value for those cases missing the estimated collision speed. The fatality risk and speed curve yielded the following relationship: Fatality Risk  fAvY  (2-7)  v71y  where Av  Change in Speed During Collision, mph  13  Thomas Y.W. Kwan  LITERATURE REVIEWS  Equation 2-7 tells us that i f the change in speed during a collision is greater than 71 mph, the occupant in the car would certainly die. Let's assume that the change in speed is the speed just before collision, then this observation can be compared to Solomon's study.  A s mentioned in the Solomon study, at speeds higher than 72 mph  (116km/hr) there would be at least one injury per each accident involved vehicle. This observation supports Joksch's result. Later on, Equation 2-7 will be used as the equation representing the consequence o f a fatal collision in the risk based approach.  2.4  THEORY OF RISK  This definition o f risk was first formulated by Daniel Bernoulli in 1738 in his paper title "Specimen Theoriae Novae de Mensura Sortis (Exposition o f a N e w Theory on the Measurement Risk)" submitted to the Academy o f Sciences in St. Petersburg. Bernoulli's thesis was based on the fact that the calculations o f the expected value o f an event did not consider the consequences o f an event.  The traditional way o f computing  expected value is by "multiplying each possible gain by the number o f ways in which it can occur, and then dividing the sum o f these products by the total number o f cases." Bernoulli was the first to introduce the idea o f "Expected Utility." H i s argument was that "utility resulting from any small increase in wealth will be inversely proportionate to the quantity o f goods previously possessed." Bernoulli's work was revised in its modern form by N . C . Rasmussen in 1981. Rasmussen used what is called the "Probabilistic Risk Analysis ( P R A ) approach to evaluate the risk associated with various energy related projects.  The definition o f risk  given by Rasmussen was:  14  Thomas Y . W . K w a n  LITERATURE REVIEWS  „. , .Consequence event Consequence Risk( ) = Frequency { ) x Magnitude^ ) unit time unit time event To  demonstrate  equation  2-8, Rasmussen  used  (2-8)  a simple example using  automobile accidents as the event. (15xl0  6  a  c  c  i  d  e  n  t  s  year  l X  d  e  a  t  )=5 0 , 0 0 0 ^  h  300 accidents  (2-9)  year  Rasmussen also differentiated the term "hazard" and "risk." Hazard was a term used to describe the consequence o f an event that could happen. O n the other hand, risk was associated with the likelihood o f such consequences happening.  These two terms  had been used interchangeably. Navin (1999) adopted this definition o f risk and developed a fundamental relationship between traffic accidents and many attributes o f the road, vehicle, driver and speed enforcement. The equation was:  Risk = £ x | / + c[k(y* + dvp )f }x Z>[(l - /w)(l + ^X * v  +  d  v P  It  O  1  0  )  where E  =  Exposure, vehicle kilometres o f travel.  =  Posted speed limit (km/hr).  a,b,c,d,m,k  =  calibration factors.  n  =  result o f crash: i f death, n = 4; i f serious injury, n = 3;  v  p  if injury, n = 2. Navin's equation indicates that the probability o f an accident was a speed squared function and the consequence o f a fatal accident was the fourth power function o f  15  Thomas Y . W . K w a n  LITERATURE REVIEWS  collision speed.  Assuming the collision speed and the mean travelling speed are similar,  then the risk o f fatal collisions is a function o f speed raised to the sixth power.  2.5  CONCLUSION The  relationship between  accident  severity and  travelling  speed  is  well  understood by traffic safety professionals. However, the relationship between the chance o f getting into an accident and travelling speed is much more complicated. Also there has not been a consistent methodology to analyze and to develop an equation relating speed and traffic accident. Early research indicated that speed variance is the main cause of speed related accident.  However, the U-shaped curve o f speed variance and  involvement  rate proposed by Solomon  has  received mix reactions  from  other  researchers.  O n the other hand, average vehicle travelling speed is also considered an  important factor and should not to be neglected. The modern theory o f risk originated from the early work o f Bernoulli in the 1700s. Risk is best described as the product o f the exposure, the probability , and the consequence o f an event. energy related projects.  Rasmussen used this definition and evaluated the risk o f In terms o f a traffic safety study, Navin used the same risk  theory and showed that the probability o f a crash was a speed-squared function and the risk o f a fatal crash was a function o f speed raised to the power o f six.  16  Thomas Y . W . K w a n  DATA COLLECTION  CHAPTER 3 DATA COLLECTION 3.1  INTRODUCTION The data primarily needed for this research are traffic accidents and speed data.  As shown in the previous chapter, there are two ways to analyze the accident and speed data: analyzing the data on an individual case basis or analyzing the data on an aggregate basis.  Solomon's study examined nearly 100,000 traffic accident records on a case by  case basis, whereas L i u and P o p o f f s study looked at the overall traffic accident and speed data on a portion o f the provincial highways. This thesis follows L i u and Popoff s approach to analyze speed and accident data on an aggregate basis. Data from the province o f British Columbia, Canada and Bangkok, Thailand were collected during the summer o f 1999 to the summer o f 2000. The accident and speed data collected were the overall accident and speed data.  Section 3.2 describes the data  collection process in the province o f British Columbia and Section 3.3 focuses on the date collection process in a rapidly motorizing city in the Southeast Asia region, Bangkok, Thailand. Some o f the data collected were not used because the speed data were simply not available.  F o r example, an accident database o f all accidents that occurred on Hong  K o n g ' s ten Expressways was obtained from the Department o f Highways in H o n g Kong; however, no corresponding speed data were available, and therefore the accident data could not be analyzed. This was also the case with another accident database obtained from the Department o f Highways in Thailand.  See Appendix 3 - A for a sample o f the  H o n g K o n g Expressways and Bangkok Highways accident database.  17  Thomas Y . W . K w a n  DATA COLLECTION  3.2  DATA COLLECTION IN BRITISH COLUMBIA Vehicle collision data on 2-lane rural provincial highways from January 1987 to  December 1997 were collected from the British Columbia Ministry o f Transportation and Highways ( B C M o T H ) .  A sample o f the collision report provided by B C M o T H can be  found in Appendix 3-B. F o r each highway segment, the collision report contains the number o f property damage only, injury, and fatality related accidents, the Annual Average Daily Traffic ( A A D T ) , the highway segment length, and the accident rate. Accident rate is defined as the number o f collisions per million vehicle-kilometres. Accidents that occurred at highway intersections are not included in this study due in part to the difficulty in allocating the intersection traffic volume to the major and minor road. The only B C speed data available were inductive speed loop surveys conducted by the Insurance Corporation o f British Columbia ( I C B C ) , following the introduction o f photo radar in 1995. Speed loops were set up at various highways throughout B C . The speed loop collected vehicles' travelling speed for eight consecutive days in one month th  and the mean speed, 15 accordingly. study.  th  percentile and the 85  percentile speed were tabulated  A n y data with unusually high or low traffic volume were neglected in this  The annual mean travelling speed is assumed to be the average o f the available  average monthly travelling speed. A list o f the speed loop locations is given in Appendix 3-C.  The speed loop data from I C B C were manually matched up with the appropriate  accident data from the M o T H report using the available location description o f the speed loops.  The average vehicle travelling speeds were then assumed to be the same  throughout the whole segment o f the highway.  Figure 3-1 shows the map o f B C  provincial highways.  18  Thomas Y . W . K w a n  D A T A COLLECTION  Numbered Highways in British Columbia Northern British Columbia  3%-^  N  f  •A  Southern British CoJymfcia  • V  1  if  F&T"  SB  S£ Vancouver fsiaftB"  Figure 3-1 M a p of B C P r o v i n c i a l Highways.  There was an interesting observation regarding the relationship between the posted speed limit and the mean travelling speed. There seemed to be a good correlation between the posted speed limit and the mean travelling speed on B C provincial highways. Figure 3-2 shows the speed data from 1995 to 1999. Note that two imaginary points are inserted into the diagram. It is assumed that cars on average will not go less than 40 km/hr and no faster than 120km/hr. Thus no matter what the speed limit is, the lowest and the highest average travelling speed would be 40km/hr and 120km/hr respectively.  19  Thomas Y.W. Kwan  DATA COLLECTION  To check the validity o f the lower bound assumption, two spot speed studies were carried out at two different 30km/hr speed zones in Vancouver. The average vehicle travelling speeds were found to be 45 km/hr and 40 km/hr, which lies closely on the assumed speed Limit and average speed curve in Figure 3-2. The spot speed survey also showed the influence o f speed enforcement. There was no observable speed enforcement along the 45km/hr location, but there is considerable police enforcement along the 40km/hr section. There was no way to validate the upper bound assumption.  Posted Speed vs. Mean Speed on BC Rural Highways  30km/hr zone data  —i  0  10  1  1  1  1  1  1  1  1  20  30  40  50  60  70  80  90  1  1  1—  100 110 120 130 140  Posted Speed (km/hr)  Figure 3-2 Vehicle Travelling Speed vs. Posted Speed Limit in BC.  20  Thomas Y . W . K w a n  DATA  3.3  COLLECTION  DATA COLLECTION IN B A N G K O K The Kingdom o f Thailand, covering an area o f 514,000 square kilometres, lies in  the heart o f Southeast Asia, roughly equidistant between India and China. It shares borders with Myanmar to the west and north, Lao P . D . R . to the north and northeast, Cambodia to the east and Malaysia to the south (see Figure 3-3 for a map o f Thailand).  Figure 3-3 M a p of T h a i l a n d . Thailand has a population o f roughly 60 million people. Thailand's capital Bangkok is situated in the central part o f the country, on the Chao Phraya River near the Gulf o f Thailand. Greater metropolitan Bangkok extends for more than 32 kilometres (20 miles) in all directions. It includes much o f five neighbouring provinces (Nakhon Pathom, Nonthaburi, Pathum Thani, Samut Prakan, and Samut Songkhram) and covers an area o f 7,758 square kilometres (2,995 square miles).  21  In 1998, the population o f  Thomas Y . W . K w a n  DATA COLLECTION  Bangkok Metropolis was estimated at 5,647,799 within an area o f 1,568 k m . With the 2  surrounding provinces included, the population was 8,661,228. Bangkok has long been known as a traffic-chaotic city. This is evident from the low travelling speed during morning peak hour. The Japanese International Corporation Agency (JICA) conducted a study in 1989 to survey the morning rush hour traffic and found the average vehicle speed to be 8.1 km/hr on trunk roads and 11.4 km/hr on expressways.  Appendix 3-D shows some o f the speed data on Bangkok's roads.  The  main reason for the traffic jams is the imbalance o f the vehicle usage and road infrastructures.  The "road area ratio" within Bangkok is around 8%, far lower than  Tokyo at 13.6% or N e w Y o r k at 23.2%.  Also, the number o f registered vehicles in  Thailand has been growing at a high rate from 1989 to 1998.  In 1998, there were  18,860,512 vehicles registered in Thailand, which is a 290 % increase from 1989.  In  Bangkok alone, there were 4,016,594 vehicles registered in 1998. Figure 3-4 shows the plot o f the number o f registered vehicles in Thailand and Bangkok from 1989 to 1998.  22  Thomas Y . W . K w a n  DATA COLLECTION  Number of Registered Vehicles in Thailand  o o o 73  IS  > X!  B  1989  1990  1991  1992  1993  1994  1995  1996  1997  1998  I Thailand • Bangkok  Figure 3-4 Motorization Trends in Thailand and Bangkok. The one unwanted side effect o f increased motorization is traffic accidents. There were 73,725 reported road traffic accidents, leading to 12,234 deaths and 53,538 injuries in 1998 in Thailand. It is believed that the actual value is much higher due to the high level o f underreporting, especially in the rural areas. The associated cost o f these accidents is estimated at 1,378.67 million Baht (an equivalent o f $33 million U S ) . That is an increase o f 1800 % over the past 10 years, which was 76.6 million Baht in 1988. Figure 3-5 illustrates a plot o f the traffic accident trends from 1989 to 1998 in Thailand. Casualties included those who were killed, seriously and slightly injured. Appendix 3-E contains the detailed version o f traffic accident statistics in Thailand.  23  Thomas Y . W . K w a n  DATA COLLECTION  Traffic Accidents Trend in Thailand 120000  w CU  100000  «  80000  Z  60000  S  40000  3  20000  1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 I Number of Accidents H Number of Casualties  Figure 3-5 Traffic Accident Trends in Thailand. There are many organizations and agencies in Thailand that are in charge o f road transport issues in one-capacity or another.  In the city o f Bangkok, the Bangkok  Metropolitan Authority ( B M A ) is responsible for planning and providing transportation engineering on roads and bridges. The Department o f Highways is a national agency and they oversee  all highway operations  and maintenance  within Thailand.  Another  organization called The Expressway and Rapid Transit Authority o f Thailand ( E T A ) is responsible for the planning, construction, and operation o f the tolled expressways in the Bangkok Metropolis. A s shown in Figure 3-6, there are many government agencies that have a say in transportation issues.  24  Thomas Y . W . K w a n  D A T A COLLECTION  National Economic and So rial Development Board (NESDB) -National economic and social development planning, formulating and coordinating plans on the infrastructure, and development.  Office of the Commission for the Management of Road Traffic (OCMRT) - Formulating, transport-related plans, coordinating government organizations, assessing projects.  Metropolitan Rapid Transit Authority (MRTA) - The Bangkok subway system  Police Department (PD) - Traffic Management as part of nationwide Thai Police operations  Department of Town and Country Planning (DTCP) - Urban Planning  Public Works Department (PWD) - Regional roads and Chao Phraya River bridges in Bangkok's suburbs  Expressway and Rapid Transit Authority (ETA) expressways in Bangkok and other cities.  Urban  Department of Highways (DOH) - Thai National highways throughout the country, and provincial highways.  Ministry of Transportation  and Communication (MOTC)  Department of Land Transport (DLT) - Compulsory automobile testing, deriver licenses, truck terminals, and other land transport administration.  State Railway of Thailand (SRT) - Construction and operation of railways nationwide. Bangkok Mass Transit Authority (BMTA) services op eration in Bangkok  Public bus  Figure 3-6 Responsibilities of Thailand's Urban Transport Administrations.  25  Thomas Y.W. Kwan  DATA COLLECTION  Elevated tolled expressways in Bangkok are own and operated by E T A , which is a state enterprise under the Thailand Ministry o f Interior.  There are currently five  expressways operating in the city o f Bangkok: First Stage Expressway (FSE), Second Stage Expressway (SSE), Ramintra -  A t Narong Expressway ( R A E ) , Bang N a -  Chonburi Expressway, and Bang Pa In - Pak Kret Expressway. expressways are intercity expressways.  The latter two  The F S E has been in operation since 1981 and  remains the busiest expressway out o f the five. F S E is 27.1 km in length and is centrally located in the downtown area and near one o f the port facilities in Bangkok. The S S E was opened to the public in 1993 and has a total length o f 29.8 km. Ram-Intra Expressway is the latest addition to the expressway networks. It runs along the east side of Bangkok and has a very low traffic volume.  Table 3-1 lists the length and opening  date o f the expressway in operation. Figure 3-7 and Figure 3-8 show a map o f Bangkok Expressways and a picture o f the expressway network in Downtown Bangkok.  Table 3-1 B a n g k o k Expressways Characteristics. Expressway Names  Length (km)  Opening Date  First Stage Expressway  27.1  1981  Second Stage Expressway  29.8  1993  Ramintra - A t Narong  18.7  1996  Bang N a - Chonburi  55.0  2000  Bang P a In - Pak Kret  34.0  1999  26  Thomas Y . W . K w a n  DATA COLLECTION  Figure 3-7 Map of Expressway System in Bangkok.  27  Thomas Y.W. Kwan  DATA COLLECTION  Figure 3-8 Expressway Networks in Downtown Bangkok. A total o f 1,630 traffic accidents occurred on the F S E , S S E , and R A E in 1999. The number o f traffic accidents has fluctuated in recent years, but the accident rate has been on the decline since 1988. The accident rate on Bangkok Expressways in 1988 was 144.06 and it was 46.74 in 1999. E T A defined accident rate as the number o f accidents per 100 million vehicle-km. O f those 1,630 accidents, 43 % o f them were due to over speeding. Figure 3-9, 3-10, and 3-11 shows the accident trends, accident rate, and major causes o f traffic accidents on Bangkok Expressways.  28  Thomas Y . W . K w a n  D A T A COLLECTION  Traffic Accident Trends on Bangkok Expressways  1630  1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Fiscal Year Figure 3-9 Traffic Accident Trends on Bangkok Expressways.  Accident Rate Trends on Bangkok Expressways 160  dent  u a  140  IT  u w ee cu  <*- >  s 3^ p CU  P5  1  120 100 80  .126.00 98.32  K8J18_  .93.60 60.89  —  S  60  o a o  40  u  20  cu  144.06  58.21  i-H  0 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 Fiscal Year Figure 3-10 Accident Rate on Bangkok Expressways.  29  Thomas Y.W. Kwan  D A T A COLLECTION  Causes of Accidents on Bangkok Expressways in 1999 Malfunction 3%  Puncture 4% Lane Shifting 7%  Carelessness 30%  Over Speed 43%  Incapable 3%  Slow Traffic 1%  Figure 3-11 Causes of Traffic Accidents on Bangkok Expressways. The E T A office does not have a computerized traffic accident database. Every accident is recorded in an accident form, which is filled out by the E T A traffic accident rescue team.  They are responsible for attending accident scenes and cleaning up the  expressway. The accident form contains accurate information on the exact location of the accident on the expressway and this is very important because the accident data are going to be match up with the approximated speed data at that corresponding portion of the expressways. The accident form also indicates the major cause(s) of the accidents, which are divided into three main categories: human, weather, and vehicle.  Within each  category there are four to five sub-categories. Since all accidents are recorded on paper, a small accident database on spreadsheet was created for the year 1999 with the help of an English-Thai speaking interpreter in order to analyze the traffic accident data. All injury and fatality accident data for the FES and SSE were recorded in the database. A sample of the accident database can be found in Appendix 3-F.  30  Thomas Y.W. Kwan  DATA COLLECTION  In 1998, a total o f 128,802,278 vehicles used the F S E , 92,984,870 vehicles used the S S E , and 18,841,486 vehicles used the R A E .  However, accurate traffic volumes  along each portion o f the expressways are not readily available because there are no permanent traffic counters embedded on the expressways. Only entrance vehicle counts are collected continuously at the tollbooth for revenue calculation purpose; there are no exit counts. In order to determine the traffic volume along an expressway segment, E T A annually conducted a traffic count at each entrance and exit o f all three intra-city expressways for 3 consecutive days.  Assuming vehicles entering and exiting ratios are  similar throughout the year, the sectional traffic volumes are determined by multiplying the overall annual traffic volume by the corresponding section entering and exiting ratio. There are 13 sections on the F S E and 16 sections on the S S E ; Appendix 3 - G shows the sectional traffic volume for the F S E and S S E in each direction. During the same 3 days, E T A also conducted vehicle speed studies and classified each expressway segment into four different speed ranges.  The speed ranges are less  than 30km/hr, 33-55 km/hr, 55-80 km/hr, and 80-100 km/hr.  The complete sectional  speed data can also be found in Appendix 3-G.  3.4  CONCLUSION Traffic accident data are more difficult to collect in developing countries than in  developed countries due to financial resource constraints o f the responsible agencies. In one instance the author went to a police station in Bangkok and the only traffic accident data they maintained were the number o f accidents for each month.  The level of  accuracy o f the accident data suffers due to high level o f under-reporting.  31  Thomas Y . W . K w a n  D A T A COLLECTION Overall, there should be a greater emphasis on maintaining quality traffic accident data. One thing to note is that the E T A accident form is similar to the British Columbia M V I 0 4 accident form used by the Vancouver police department.  The potential to  develop an adequate traffic accident database for Bangkok expressways is a relatively straightforward task.  32  Thomas Y.W. Kwan  DATA ANALYSIS  C H A P T E R 4 A N E W RISK T H E O R Y  4.1  INTRODUCTION A new risk theory to study and quantify the relationship between speed and traffic  accident is presented in this chapter. This chapter is divided into 3 sections. Section 4.2 shows the basic idea o f the new risk theory. Section 4.3 describes the development o f the speed-collision probability relationship.  Then section 4.4 focuses on making use o f the  speed-crash probability and incorporating that into the speed-collision risk relationship.  4.2  THEORY The basic idea for the new theory is to be found in the definition o f risk. Risk is  defined as the product o f exposure, probability o f an event and consequences o f an event. This definition was first formulated by Bernoulli in 1738 and was revised in its modern form by Rasmussen in 1981.  The units o f risk are usually given in events per unit  exposure per year, for example collisions per 10 vehicles-km per year. 6  Exposure in the risk equation for road safety is usually specified in vehicle kilometres for highway segments or vehicles entering an intersection. Estimates o f these values come from either on-road estimates or transportation planning studies o f travel demand.  The consequence o f a vehicle collision is the chance that occupants o f the  vehicle are  injured  or killed.  Research  and observations  have  shown that  the  consequence o f death or serious injury in a motor vehicle crash is best estimated by the speed lost during collision raised to the fourth power. Exposure and the  consequence  o f a vehicle collision is well known and  documented, the only remaining variables that are not well tested in the risk equation is  33  Thomas Y . W . K w a n  D A T A ANALYSIS  the probability o f a vehicle collision.  Section 4.3 presents a new method in developing  an equation for speed and the crash probability. Combining all three variables yields an equation o f the relationship between the average vehicle travelling speed and the risk o f a certain type o f accident. Note that the author distinguishes between the risk o f a collision and the probability o f a collision.  4.3  THE SPEED-COLLISION PROBABILITY EQUATION To  determine the probability o f a collision as a function o f speed, two  assumptions need to be made. First, there is a speed that when travelled by all traffic is so low that the probability o f a crash is zero. That speed is set at zero km/hr. A t the other extreme a vehicle may be driven at a speed well beyond the handling limit at which it is certain to result in a collision.  Setting this upperbound is problematic but for the  purposes o f this analysis, it is assumed to be 300 km/hr. There has been some criticism of the 300km/hr limit. For the most part, the top speed o f most modern family sedans is about 225 km/hr and high performance vehicles are about 300 km/hr. A simple analysis is carried out later to show the speed o f 300km/hr is indeed the right choice.  These  assumptions give two points on the speed and collision probability plane (0,0) and (300 km/hr, 100 million collisions per 100 million veh-km). One other point is needed to construct a curve and this third point comes from the observed values o f vehicular speed and collision rate data on rural highways. L i u and P o p o f f s Saskatchewan speed and casualty rate data are used to demonstrate the new theory.  First the Saskatchewan casualty rate data must be converted to represent the  overall collision rate. A study by the Insurance Corporation o f British Columbia ( I C B C ) found that the percentage o f fatal and injury related accidents to the total number o f  34  Thomas Y . W . K w a n  DATA ANALYSIS  accident in a 90 to 100 km/hr speed zone is 36 % . Data from the National Highway Transportation Safety Agency gave 34 % ( N H T S A 1999). Table 4-1 shows the value o f the Saskatchewan casualty and collision rate data using the I C B C conversion factor. A l l three points are plotted in Figure 4-1 on the speed and collision probability plane. Table 4-1 Saskatchewan Rural Highway Speed and Collision Data. Speed (km/hr) 102.3 106.8 104.8 101.3 102.3 100.3 101.1 101.6 102.6  Casualty Rate (Casualties per 100 million veh-km) 70.23 79.95 73.29 46.67 48.17 38.44 33.46 33.51 30.38  0  50  100  150  Imputed Collision Rate (Collisions per 100 million veh-km) 195.08 222.08 203.58 129.64 133.81 106.78 92.94 93.08 84.39  200  250  300  Average Vehicle Operating Speed (v ), km/hr Q  Figure 4-1 Collision Probability vs. Speed Based on Liu and Popoff s Data.  35  Thomas Y . W . K w a n  D A T A ANALYSIS  The general relationship between the probability o f a collision and speed in Figure 4-1 has the approximate form:  /* = v /  (4-1)  where /*  =  Involvement Rate, collisions per 100 million veh-km, and  v  =  Average operating speed, km/hr, and  p  =  Controlling Exponent  o  To show the pronounced effect o f speed on involvement rate, another function is defined to relate the controlling exponent, p, with the operating speed. Rearranging for the controlling exponent:  MO Using published data from L i u & P o p o f f s work and the two extreme points and applying them in Equation 4-2, values o f the controlling exponents at different operating speeds are calculated and are shown below in Table 4-2. The data point are best fitted with a linear trendline, as shown in Figure 4-2, and the equation is:  p = ( 0 . 0 1 0 7 7 ) x7  0  (  36  4  .  3  )  Thomas Y . W . K w a n  DATA ANALYSIS  Table 4-2 Controlling Exponent at Different Speed. Speed (km/hr)  Involvement Rate (Collisions per 100 million veh-km)  Controlling Exponent, p  0  0  0  102.3  195.08  1.14  106.8  222.08  1.16  104.8  203.58  1.14  101.3  129.64  1.05  102.3  133.81  1.06  100.3  106.78  1.01  101.1  92.94  0.98  101.6  93.08  0.98  102.6  84.39  0.96  300  100000000  3.23  If the high extreme speed was set at 250 km/hr or 350 km/hr, the value o f the exponents changes only slightly (3.34 and 3.14 respectively). A linear best-fit curve does not fit well with these two speeds. The exponent value at a speed o f 0 km/hr is either greater than or less than zero.  This does not follow the no accident at 0 km/hr  assumption. O n the other hand, the power curve fits well with these new speeds. Figure 4-2 shows a comparison o f the exponent and speed curve for all three speed fluctuation.  37  Thomas Y . W . K w a n  D A T A ANALYSIS  Exponents vs. Speed - Sask Provincial Highways 4.00  T3MT  y = 0.01077x  y = 0.0025x  3.50  R = 0.9784 z  3.00 ce  |  2.50  |  2.00  0.8962  y = 0.0166X  & 1.50 1.00  R = 0.9729 z  0.50 0.00 200  300  400  Speed (km/hr) •Linear (300km/hr)  Power (250km/hr)  Power (350km/hr)  Figure 4-2 Comparison of Exponents vs. Speed Curves. As shown in Figure 4-2, the linear curve of 300km/hr is the best-fit curve among all three curves and the R-Squared value is also the highest. What Figure 4-2 suggests is that there is a one to one relationship between the average vehicle travelling speed and the involvement rate when the average travelling speed is around lOOkm/hr. This meant that a 10% increase in speed at lOOkm/hr would result in a 10% increase in involvement rate. If the travelling speed is below lOOkm/hr, speed does not contribute much to the occurrence of traffic accidents. Whereas if the travelling speed is above lOOkm/hr, the relationship between average vehicle speed and traffic accidents is exponential because the exponent of the speed and vehicle involvement equation exceeds one.  Now,  combining equation 4-1 and 4-3: r*  —(0.01077)v  0  (4-4)  38  Thomas Y.W. Kwan  D A T A ANALYSIS  The measure o f probability is collisions per 100 million vehicle kilometres; this is similar to the definition o f involvement rate used by Solomon. The curve o f involvement rate and speed is shown below in Figure 4-3.  Involvement Rate vs. Average Travelling Speed 1000  u tu  a.  800 600  3 S  "o  5  s o  400 200  e  50  60  70  80  90  100  110  120  130  140  150  Speed (km/hr) Figure 4-3 Involvement Rate vs. Average Travelling Speed (50 to 150 km/hr). A s shown in Figure 4-3, the involvement rate-speed curve is almost linear in the speed range less than 90km/hr.  Beyond 90km/hr the slope o f curve becomes steeper,  which is expected because the involvement-speed  curve exceeds  the one to  one  relationship. Figure 4-3 also indicates that i f the average driving speed is 100 km/hr on a provincial highway in Saskatchewan, the probability o f getting into a collision is 142.5 per 100 million veh-km or 0.000002.  For example, i f the road section is 5km with an  A A D T o f 3,000, the annual vehicle kilometre travelled is 5.475 million and there will be 8 collisions per year.  39  Thomas Y . W . K w a n  D A T A ANALYSIS  4.4  THE SPEED-COLLISION RISK EQUATION In Section 4.3, the speed-collision probability equation has been established. The  next step will be to use the equation to formulate the speed-collision risk equation. A s mentioned earlier, risk is the product o f the exposure, the probability o f an event, and the consequences o f an event.  The unit o f risk is events per unit exposure per year.  Exposure in the risk equation for road safety is usually given in vehicle-kilometers for highway segments or vehicles entering an intersection.  Probability o f an automobile  collision on rural highways is given in collision per 100 million vehicle-kilometers. The last variable, the consequence o f an automobile collision is usually represented as a percentage. Depending on what type o f a collision risk is desired, the consequence equation would be different.  The three main types o f collisions are property-damage-only (PDO),  injury, and fatality.  This research focuses on fatal and serious injury accidents.  Researches and observations have shown that the consequence o f death or serious injury in a motor vehicle crash can be best estimated by the speed lost during collision raised to the fourth power.  Nilsson o f Sweden (1990) found that the ratio o f the fatality rates  before and after a change in speed limits was found to be proportional to the fourth power of the ratio o f the corresponding median speeds. National Crash Severity Study ( N C S S ) ,  Joksch found, using data from the  that fatality risk in car-car collisions is  proportional to the fourth power o f the speed loss during the collision (AS).  The  approximate relationship o f Joksch's equation is:  40  Thomas Y . W . K w a n  DATA ANALYSIS  '  Death •  AS  ^  4  (4-5)  v l 14.24 j  Where AS  =  Change in speed during collision, km/hr  For simplicity, assume that v equals to A S , which implies that all speed is lost a  during the collision. The consequence equation approaches a value o f 1 at a speed o f 115 km/hr (71 mph) and this means that any speed beyond 115 km/hr would result in a death. Using Joksch's equation as the fatality consequence equation and the probability equation developed from section 4-3, then the risk o f a fatal crash can be determined by multiplying the probability and the consequence equations.  The risk o f fatal crash is as  follows:  Fatality Risk = E x  (0.01077)v  •V  0  V„ v  114.24  (4-6) y  Where Fatality Risk  =  Total deaths per year  E  =  Exposure, veh-km o f road traveled per year  =  Average travelling speed, in km/hr  v  0  41  Thomas Y . W . K w a n  DATA ANALYSIS  (Unit Fatality Risk vs. Average Travelling Speed  4.0E-06 i  3.0E-06 Vi  s  %  cs ta  2.0E-06  *s 1.0E-06  O.OE+00 50  60  70  80  90 100 110 120 130 140 Speed (km/hr) Figure 4-4 Unit Fatality Risk vs. Average Travelling Speed (50to 150km/hr). Figure 4-4 is a plot o f the unit fatality risk equation.  150  T o demonstrate the use o f  the fatality risk equation, consider the hypothetical example used in section 4-3. Assume a 5 k m section o f a rural highway with an A A D T o f 3,000 has an average vehicle speed of 100 km/hr.  The unit fatality risk at 100 km/hr is 8.37E-07 from Equation 4-6 and the  exposure is 5.475 millions veh-km per year.  The expected number o f death per year  would be 5; See Appendix 4 - A for the detailed calculations.  42  Thomas Y . W . K w a n  DATA ANALYSIS  4.5  CONCLUSION In many o f the previous studies about the relationship between speed and  collision, the terms "risk" and "probability" have been used interchangeably and this has often created confusion.  This chapter clearly defines the difference between the  probability o f a collision and the risk o f a collision. The probability o f a vehicle collision is a function o f speed raised to an exponent, where the exponent is also a function o f speed. The risk o f a collision, depending on which type o f collision, is the. product o f the exposure, the probability o f a collision, and the consequences o f the collision. On Saskatchewan rural highways, the average travelling speed is shown to be a collision factor at speeds above 90 km/hr. A t speeds lower than 90km/hr, the average travelling speed diminishes in importance. speed that accounts for accidents.  A t lower speeds it may be the variation o f  This conclusion partially supports the work by  Solomon and Lave that it is the speed variance, not the average speed, which causes accidents to occur on roads and highways.  43  Thomas Y . W . K w a n  A P P L I C A T I O N OF T H E N E W R I S K T H E O R Y  CHAPTER 5 APPLICATION OF THE NEW RISK THEORY 5.1  INTRODUCTION A s shown in Chapter 4, the speed-collision probability and speed-collision risk  equations can be used to assess the relationship between speed and traffic accidents on rural highways. The methodology used to develop these two equations is now applied to different types o f roads and highways given the average vehicle speed and accident data are available. In Section 5.2, speed and accident data from Solomon's study are used to develop a speed-probability equation for U S rural highways. development  Section 5.3 describes the  o f the speed-probability equation for urban expressways in Bangkok,  Thailand.  5.2  SOLOMON'S DATA Solomon's work in 1964 examined speed and collision data on 2-lane and 4-lane  rural highways consisting o f 35 sections in 11 states in the U S . H e plotted the average vehicle travelling speed against the accident data and obtained a "U-Shape" curve. For the daytime curve, the lowest accident involvement rate o f 85 accidents per 100 million veh-miles occurred at a speed o f 68mph. The accident involvement rate increases as the speed deviates, both positively and negatively, from 68mph. Converting the speed and the lowest accident involvement rate into metric units (HOkm/hr, 134.4 collisions per 100 million vehicle-km), the data point is used to develop a speed-collision probability equation.  Referring to section 4.2, two assumptions are  made about the low and high speed conditions. A t a speed o f zero km/hr, the accident rate is zero and at a speed o f 300km/hr, the accident rate is one. Figure 5-1 shows the  44  Thomas Y . W . K w a n  APPLICATION OF THE N E W RISK T H E O R Y exponent versus speed curves for the Solomon data. The speed of 300km/hr is used in this case in order to compare with Saskatchewan results. The other speed of 250km/hr and 350km/hr are shown in Figure 5-1 for comparison purposes.  Exponents vs. Speed - Solomon's Data 4.0  1.1269  y = 0.0013X 1.4167  3.5  y = 0.00522x  3.0 |  2.5  cu  § 2.0 a *  0.9538  y = 0.0118x  1 «  R  1.0  2  = l  0.5 0.0 100  •Power (300km/hr)  200 Speed (km/hr) Power (250km/hr)  300  »  »  w  400  Power (350km/hr)  Figure 5-1 Exponents vs. Speed For Solomon's Data. A power curve, instead of a linear curve, fits better with Solomon's data, as shown by the indicated equation of the curve on the graph. The equation obtained from the above exponent-speed curve is: p = (0.00522)v  -1.1269  (5-1)  o  The equation of the speed-collision probability curve is: — (0.00522)v I* =  -1.1269  v  o  (5-2)  a  45  Thomas Y.W. Kwan  A P P L I C A T I O N OF T H E N E W RISK T H E O R Y  Involvement Rate vs. Average Travelling Speed  Speed (km/hr) - ~ H - - Solomon  •  Sask  Figure 5-2 Comparison of Involvement Rate vs. Average Travelling Speed for US and Saskatchewan Rural Highways. A s shown in Figure 5-2, it appears that driving at a high speed on Saskatchewan provincial highways is more hazardous than on U S 2-lane or 4-lane rural highways. However, it is worth noticing that the accident and speed data from Solomon's study were from the 1950s, therefore it may not represent the current traffic and safety conditions. Today, the average speed data would have likely increased in most states in the U S and the involvement rate would have decreased due to better engineering, education, and technology such as ITS. The speed-collision risk equation can also be developed as well.  Combining  equation 5-2 and equation 4-5, the resulting fatality risk equation is:  46  Thomas Y . W . K w a n  APPLICATION OF T H E N E W RISK T H E O R Y  —1.1269  Fatality Risk = Ex  -(0.00522)v  0  (5-3)  114.24  Figure 5-3 shows the plot o f the unit fatality risk and average vehicle travelling speed curve for Solomon's Data.  The unit fatality risk curve for Saskatchewan is  included in Figure 5-3 for comparison purposes. T o demonstrate the use o f equation 5-3, the same hypothetical example in section 4.4 is used here again. A t an average speed o f lOOkm/hr, the fatality risk on U S rural 2 lane and 4 lane highways is 4.38E-07. The number o f fatal accidents is 3 for a highway segment that is 5 km long and has an A A D T of 3,000.  Unit Fatality Risk vs. Average Travelling Speed 4.0E-06  A.  3.0E-06  s Vi  £ es es fc  2.0E-06  + J  1.0E-06  0.0E+00  1  50  60  70  80  90  100  1  110  1  120  1  130  1  140  150  Speed (km/hr) Solomon  •  Sask  Figure 5-3 Unit Fatality Risk vs. Average Travelling Speed for Solomon's Data.  47  Thomas Y . W . K w a n  A P P L I C A T I O N OF T H E N E W RISK T H E O R Y  5.3  B A N G K O K EXPRESSWAYS Traffic accident and speed data in 1999 on Bangkok's First Stage Expressway  (FSE) and Second Stage Expressway (SSE) were collected from the E T A office. speed and accident data is shown in Table 5-1.  The  The first step to develop the speed-  collision probability equation is to examine the exponent and speed curve.  Again, the  three speeds 250km/hr, 300 km/hr, and 350 km/hr are compared with each other to see which speed choice is the best fit to the data. Figure 5-4 shows the exponent-speed curve and the linear curve for 250km/hr has the highest R-squared value among the three speed choices.  This is reasonable because in an urban area there would be more interactions  among vehicles, and it is more likely that a driver would be involved in an accident before reaching a speed o f 300km/hr.  Table 5-1 Traffic Accident and Speed on Bangkok Expressways. Average Travelling Speed  Involvement Rate  Location  (km/hr)  (Accidents per 100 million veh-km)  FSE-Northbound  73.85  87.5  FSE-Southbound  70.77  57.2  SSE-Northbound  77.78  77.7  SSE-Southbound  69.19  80.2  48  Thomas Y . W . K w a n  A P P L I C A T I O N OF T H E N E W RISK T H E O R Y  Exponents vs. Speed - Bangkok Expressway  4.00  y = 0.0289x  y = 0.0134x  3.50  R  2  = 0.997  ^  .  08259  R = 0.9919 2  3.00  1 s  2.50  | o  2.00  I  y = 0.0439x° R  2  7 2 8 6  = 0.9926  1 5 0  1.00 0.50 0.00  1  50  1  100  1  1  1  150  200  250  300  1  350  400  Speed (km/hr)  •Power (300km/hr)  Linear (250km/hr)  Power (350km/hr)  Figure 5-4 Exponents vs. Average Travelling Speed for Bangkok Expressways.  Equations  o f the exponent-speed  linear trendline  and the speed-collision  probability for Bangkok expressways are as follow:  /> = (0.0134K  (5-4)  -(0.0134K  (5-5)  Figure 5-5 shows the involvement rate and average travelling speed curve for both Bangkok expressways and Saskatchewan rural highways. It appears that the chance o f getting into an accident on Bangkok expressways is much higher than on Saskatchewan rural highways, as shown by the higher involvement rate and rate increase.  49  Thomas Y . W . K w a n  APPLICATION OF THE NEW RISK THEORY  Involvement Rate vs. Average Travelling Speed on Bangkok Expressways  a. w  S  8000  - —  6000  ~« .2 S 2  4000  S° § S e  2000 50  60  80  70  90  100  110  120  i  r  130  140  150  Speed (km/hr) Bangkok Expressway — • Figure 5-5 Involvement Expressways.  Rate vs. Average Travelling  Sask. Speed  on Bangkok  The consequence equation from Joskch is based on accident and speed data on US roads and highways.  Since the characteristics of Bangkok expressways and drivers'  attitudes differ greatly from US roads and drivers, Joskch's consequence equation may not be apply to Bangkok expressways.  But for the purpose of demonstration, the  consequence equation from Joskch is still used and the unit fatality equation is as follows: —(0.0134)v  Fatality Risk = E x v„  -  V  0  114.24  50  (5-6)  Thomas Y.W. Kwan  APPLICATION OF T H E N E W RISK T H E O R Y  Unit Fatality Risk vs. Average Travelling Speed on Bangkok Expressways 1.0E-04  M  8.0E-05  5 £> 6.0E-05 4.0E-05 "3 &  2.0E-05 0.0E+00 50  60  70  80  90 100 110 Speed (km/hr)  120  Figure 5-6 Unit Fatality Risk vs. Average Travelling Expressways.  130  140  150  Speed for Bangkok  Figure 5-6 shows the unit fatality risk curve for Bangkok Expressways. Using the previously mentioned hypothetical example to demonstrate the use o f the unit fatality risk equation, the results are shown below in Table 5-2.  Table 5-2 Comparisons of Results of Hypothetical Example. # o f accidents  # o f fatal accidents  Saskatchewan Rural Highways  8  5  U S Rural 2 lane and 4 lane highways  4  3  Bangkok Expressways  26  16  Location  51  Thomas Y . W . K w a n  APPLICATION OF T H E N E W RISK T H E O R Y  5.4  CONCLUSION This chapter used speed and accident data from the literature and also from a  mega city o f a developing country.  The results shown in Table 5-2 are for comparison  purpose only and the speed-collision risk equation is not meant for use as an accident prediction model. It does, however, serve as a tool to help establish what level o f fatality risk is acceptable or not. Are eighty-seven accidents tolerable in Bangkok? I f not, then measures should be taken to address the problem o f speeding. The speed-collision probability and speed-collision risk equation developed for U S rural highways and Bangkok expressways are based on very limited speed and accident data. purposes  only.  The use o f Joskch's consequence equation is also for demonstration Different types o f roads and highways would result in different  relationships between collision speed and accident severity. Therefore, more speed and accident data and a more appropriate consequence equation is needed to establish site specific collision probability and collision risk equations for the different jurisdictions.  52  Thomas Y . W . K w a n  ADDITIONAL RESEARCH  CHAPTER 6 ADDITIONAL RESEARCH 6.1  INTRODUCTION A traffic accident is usually the result o f many factors such as speed, road  geometry, weather, driver's inattention, and time o f day. This research has only studied the effect o f the average vehicle travelling speed on traffic accidents. suggests extensions to the current research.  This chapter  Section 6.2 describes how more quality data  can improve the validity o f the new speed-collision risk equation and Section 6.3 shows how  the same methodology may be used to develop a relationship between speed  variance and the probability o f a collision for future research.  6.2  MORE QUALITY DATA There are three main areas where more data and more quality data can help  improve this research.  First o f all, the assumption o f a collision probability o f one at a  speed o f 300km/hr needs further data to support its validity. One suggestion would be to use the accident data o f professional car racing. That is the only place where one can find accidents that occur at an average vehicle speed well over 200km/hr. Having this data point could help bridge the gap between the real data point from around lOOkm/hr to the assumption point at 300km/hr. The race car data point could also help depict the shape o f the speed-collision probability curve because the exponential shape o f the curve is largely dependent on the assumed 300km/hr data point.  53  Thomas Y . W . K w a n  ADDITIONAL R E S E A R C H The second area for improvement is the need for more speed data. No speed data was found for Bangkok highways and Hong Kong expressways. Even the speed data obtained for the Bangkok Expressways was from a 3-day survey and was given in different speed ranges. Thus, the accuracy of the speed data was questionable. Having the right speed data can help understanding the role that speed plays in traffic accidents. If speed was found to be a major cause of traffic accidents, government and city officials could wisely spend the money and effort into targeting the speeding problem.  The  amount of money saved from the safety benefit of fewer traffic accidents would far outweigh the money spent on collecting the speed data. The third improvement is to examine accident records individually. The accident data of B C provincial highways were data extracted from their accident database and were a summary of all accidents on B C provincial highways. Reviewing each accident record individually can help classify accidents into different categories.  The analysis in  this study assumes that all rural or provincial highways are the same and the analysis treats all the accident data in one group. Also, another piece of important information contained in many of the accident reports is the estimated collision speed and this ties into the next section.  6.3  SPEED VARIANCE-COLLISION PROBABILITY RELATIONSHIP Many studies have agreed that speed variance is a major contributing factor in  vehicle accidents. Speed variance is defined as the difference between the speed of the colliding vehicle(s) and the mean travelling speed of the rest of the vehicles on the road at the same time. Having an accident database in which the collision speed of each accident is available can determine the speed variance on the road when the accident occurred.  54  Thomas Y . W . Kwan  ADDITIONAL RESEARCH  K n o w i n g the speed variance and the accident involvement rate, a speed variancecollision probability equation can be developed using the methodology outlined in Chapter 4. A different set o f assumptions would be needed, such as what would be the limit o f positive and negative speed variance and their associated collision involvement rates.  These assumptions are largely dependent on the shape o f the speed variance-  collision rate curve, for examples Solomon's "U-shaped" curve, as shown in Figure 2-2, or M U R A C ' s linear relationship. To take a step further, the speed variance and average speed data can be analyzed together to form a three-dimensional collision probability plane as shown in Figure 6-1. Assuming Solomon's curve is the correct form o f the speed variance and collision involvement rate curve, it can be projected orthogonally to the average speed and involvement rate curve and thus creates an accident rate surface plane.  /  | Solomon's curve | I in space  A  Solomon's Curve on I-Av plane  | Average SpeedI Involvement Rate V Figure 6-1 Average Speed, Speed Variance, and Involvement Rate Plane.  55  Thomas Y . W . K w a n  ADDITIONAL RESEARCH 6.4  CONCLUSION  The greatest difficulty encountered in this study was the quantity and quality of data. Having more speed and accident data can confirm the proposed speed-probability equation. Due to the limited speed and accident data used in this thesis, little statistical testing was provided. As mentioned earlier, some jurisdictions do not collect any speed data and some do not even have an accident database. This really creates a huge technical problem for researchers who want to study the real problem associated with traffic safety.  The  responsible agencies should look into increasing the funding for collecting more traffic related data and maintaining well organized databases. Speed variance is viewed as a major cause of traffic accidents.  Applying the  proposed risk theory with speed variance data can help determine what conditions does speed variance affects traffic accidents, and also what conditions do both speed variance and mean travelling speed affects traffic accidents.  56  Thomas Y.W. Kwan  CONCLUSION  CHAPTER 7 CONCLUSION Previous studies have not provided a consistent theory to define the relationship between speed and traffic accident. A new risk theory to study and to quantify the relationship between the average vehicle travelling speed and traffic accident is presented in this study.  Risk, as defined by Rasmussen, is the product of the exposure, the  probability of an event, and the consequence of an event. The following are the main conclusions of this research: •  At the theoretical level, the probability of a crash is a function of speed raised to an exponent, in which the exponent itself is also a function of speed, for rural roads and other situations not involving intersections.  •  The equations of average travelling speed and collision probability are: -(0.01077)^  Saskatchewan rural highways: 7* = v  —1.1269  (0.00522)v  o  US rural highways: I*  ^o  Bangkok urban expressways:  r*  _  ~  — ( °  0  1  3  4  K  The equation of the average travelling speed and fatality risk on Saskatchewan rural highways is:  Fatality Risk = E x v_  (0.01077)v  0  ( v  Y  l 14.24 j  Average travelling speed becomes an important factor in traffic collision when it is above 90km/hr on Saskatchewan rural highways.  57  Thomas Y.W. Kwan  CONCLUSION  •  Similar results are obtained from Solomon's data with Saskatchewan data, while Bangkok expressways yield a higher involvement rate than the others.  •  There is a linear relationship between the average vehicle travelling speed and the posted speed limit on B C rural highways  •  More  speed  and  accident data  are needed  to  confirm  the  proposed  methodology statistically for developing the probability and risk equations.  The speed-collision probability equation can determine whether speeding is a contributing factor in a collision prone area.  Once speeding is identified as a problem,  then measures can be taken to correct the speeding problem, one o f the measures is setting the right speed limit.  This research has been able to show that to reduce the  number o f accidents on 2 lane rural highways, the average vehicle travelling speed must be kept below 90km/hr. Assuming the relationship between the average travelling speed and the posted speed limit holds, as from the observation on B C rural highways, reducing the posted speed limit will reduce the number o f vehicle accidents. Other measure such as more police enforcement and photo radar programs may reduce the average travelling speed as well. The effects o f these measures are still to be studied. Future research should be carried out on collecting speed and accident data for different types o f roads and highways in both rural and urban areas. B o t h the lowest and highest speed ends o f the speed-collision probability curve should be investigated. Also, analysis on speed variance, along with the average travelling speed, is recommended in order to better understand which variable contributes more to traffic accident at different speed ranges and on different types o f highways.  58  Thomas Y . W . K w a n  BIBLIOGRAPHY  BIBLIOGRAPHY Bernstein, P . L , Against The God, The Remarkable Story of Risk (New Y o r k . Wiley, 1996), 99-115. Baruya, A . ; "Speed-Accident Relationships on Different Kinds o f European Roads," Transportation Research Laboratory, U . K . September 1998. Department o f Land Transport, Ministry o f Transport and Communications Thailand, "Number o f vehicles Registered," (Brochure) 1998. Expressway and Rapid Transit Authority o f Thailand, "Annual Traffic Study," Thailand, 1998. Expressway and Rapid Transit Authority o f Thailand, "Statistical Report 1998,: Thailand, 1998. Fildes, B . N . , Rumbold, G . , and Leening, A . ; "Speed Behaviour and Drivers Attitude to Speeding," Report 16, Monash University, Accident Research Centre, Australia, 1991. Insurance Corporation o f British Columbia, Speed L o o p and Accident data. Japan International  Cooperation Agency, "The Second Country Study for Japan's  Official Development Assistance to the Kingdom of Thailand," M a r c h 1996. Joksch, H . C , "Velocity Change and Fatality Risk in a Crash," Accident Analysis and Prevention, Volume 25, 1993, pp 103-104. Joksch, H . C , " A n Empirical Relation Between Fatal Accident Involvement and Speed," Accident Analysis and Prevention, Volume 7, 1975, ppl29-132.  59  Thomas Y . W . K w a n  BIBLIOGRAPHY  Joksch, H G . , "Light-Weight Car Safety Analysis, Phase II, Part II: Occupant Fatality and Injury Risk in Relation to Car Weight," M o t o r Vehicle Manufactures Association o f the United States, Detroit, M i , June 1983. Kloeden, C . N . , et al; "Travelling Speed and the Risk o f Crash Involvement," Report N o . C R 172, Federal Office o f Road Safety, Canberra, Australia, November 1997. Liu,  G . , Popoff, A . ; "Provincial-Wide Travel Speed and Traffic  Safety Study in  Saskatchewan," Transportation Research Record 1595, T R B , Washington, D C . pp 813. Ministry o f Transportation and Highways o f British Columbia, B C rural highways accident report. 1996-1999. National Highway Traffic Safety Administration, "Traffic Safety Facts 1998," Chapter 5: States, U S D O T , Washington, D C , October 1999, pp 169. Navin,  F.,  "Model  for  Road  Safety  Planning,  Theory  and  Policy Example,"  Transportation Research Record 1695, T R B , Washington, D . C . , pp 49-54. Nilsson G , "Reduction in the speed limit from lOOkm/hr to 90 km/hr during summer 1989: effects on personal injury accidents, injured and speeds" Linkoping, Sweden: Swedish Road and Traffic Research Institute. Report N o . 358A, 1990. Office o f the Commission for the Management o f Land Traffic ( O C M L T ) o f Thailand, "Traffic  and  Transport  Information  -  Travel  Time/Delay," 10 March.  2000  <http://www.ocmlt.go.th/sjreng/tdmceng/13.html> (21 September, 2000). Office o f the National Police, Office o f the Prime Minister and Traffic Engineering Division, Department of Highways, 1998.  60  Thomas Y . W . K w a n  BIBLIOGRAPHY  Panwai, S., "Identification o f Hazardous Locations on Bangkok Expressways," Asian Institute o f Technology, Master Thesis, April 1998. Rasmussen, N . C . , "The Application o f Probabilistic Risk Assessment Techniques  to  Energy Technologies," Annual Review of Energy, Volume 6, 1981, pp 123-138. Solomon, D . ; "Accidents on M a i n Rural Highways Related to Speed, Drivers, and Vehicle." Bureau of Public Roads, U . S . Department o f Commerce, July 1964. Transportation Research Board, Special Repot 254 "Managing Speed, Review o f Current Practice for Setting and Enforcing Speed Limits," National Research  Council,  Washington D . C . , 1998, Appendix B , pp 221-276. Watanabe, H . , "Government Response to Urban Transport Problems in Asia," Wheel  Extended, N.97, 1996, pp 5-13.  61  Thomas Y . W . K w a n  APPENDICES  APPENDICES 3-A) Sample Accident Databases of Hong Kong's Expressway and Bangkok's Highways. 3-B) BC MoTH Collision Report. 3-C) Speed Loop Location in British Columbia Provincial Highways. 3-D) Average Travelling Speed in Bangkok. 3-E) Traffic Accident Statistics in Thailand. 3-F) ETA Accident Form & Database. 3- G) ETA's Traffic Speed, Volume, and Accident Data in 1999. 4- A) Sample Calculations of Speed-Collision Probability Equation.  62  Thomas Y.W. 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C N C N C N C N C N C N C N C N C N C N C N C N C N C N C N C N o c N C N C N o o o f N o c N o ^ H t N C N o o f N o o o c N o c N o o o  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  O O  o o o o o o o o o o o o o o o o o o o o o o o o o o O O  O C  O O  O  O  O  O O O O O O O C I O O O O O O  O  O  O  O  O  O  O  O O  O O  O O  O  O  O  O O  O  O  O  O  O  O  O  O O O O O O O O O O O O O O O O O O O O  O  O  O  O  O  O  O  O  O  O  O  o o o o o o o o o o o o o o o o o o o o o o o o o o  o o o o o o o o o o o o o o o o o o o o o o o o o o  H  C/3  o z  1  w  ui Uifc4 Ui *i Ui Ui wi o o oo O o o a a z z <: < m oac oa PQ OQ CQ  Ui Ui Wi Ui Ui Wi Wi ui ^ Wi Ui Wi Wio Uio o wi o o o o O O oz az az az o Z z o Z z o z Z z z z •«cq Z Z z <Qc CQ CQ CQ CQ CQ CQ OQ OQ CQ CQ CQ CQ CQ m CQ C  o o o o O o o O o O o o O O o o O o O q q q q q o o a CQ  Q O  z  » U U f i o o o o o o M m c o n o o n o o n ( < i « m o o o o < n o o o o o o » »  i  —  I  V  O  V  O  O  O  O  O  O  O  t  —  I  r — I t - H i — I r t O O O t — l O O O O O t — I t — I r - H  in in 'n in iri in in in in in in 'n i/i >n in in in in in <r, in in in *n in Q cs W  o p  oIQIQooooooooooooooooooooooo  o o o o o o o o o o o o o o o o o o o o o o o o o o  o  Appendix 3-B) B C M o T H Collision Report Samples Region/District 2/17 CENTRAL CARIBOO 2/17 CENTRAL CARIBOO 2/17 CENTRAL CARIBOO 1/ 6 LOWER MAINLAND 1/ 6 LOWER MAINLAND 1/ 6 LOWER MAINLAND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND 1/ 4 HOWE SOUND  Hwy 99 99 99 99 99 99 99 99 99 99 99 99 99  Fatality Rate* Region/District 0 2/17 CENTRAL CARIBOO 1.827 2/17 CENTRAL CARIBOO 02/17 CENTRAL CARIBOO 0 1/ 6 LOWER MAINLAND 0 . 079 1/ 6 LOWER MAINLAND 0 1/ 6 LOWER MAINLAND 0 1/ 4 HOWE SOUND 1.562 1/ 4 HOWE SOUND 0.547 1/ 4 HOWE SOUND 1.108 1/ 4 HOWE SOUND 0.122 1/ 4 HOWE SOUND 0 1/ 4 HOWE SOUND 0.063 1/ 4 HOWE SOUND  Seg. 907 907 907 2910 2910 2915 2920 2920 2920 2930 2930 2933 2933  Length Start - End 0.1 0.0 09030907 74.6 0.1-74.6 74.7 0907NULL 0.1 0.0 29102915 0.1 29.2 0.1-29.2 29.1 11.8- 40.8 0.1 0.0 NULL2920 31.9 0.1-31.9 9.1 33.1-42.1 4.7- 52.7 48.1 61.5-88.7 27.3 0.0 29302933 0.1 0.1-91.5 91.5  FAT 0 5 0 0 2 0 0 20 2 16 1 0 1  INI 3 63 0 1 40 22 15 401 57 382 137 0 25  •Accident Rate is in accident per million vehicle-km **Fatality Rate is in fatality per 100 million vehicle-km  71  PDO 5 110 0 7 80 55 25 511 59 644 167 3 54  Class RC RC RC RF RF RF RC RC RC RC RC RC RC TOT 8 178 0 8 122 77 40 932 118 1042 305 3 80  ADT 917 892 892 19726 21077 18376 9767 9767 9767 7304 7304 5760 4215  Accident Rate* 21.236 0.65 0 0.987 0.048 0.035 9.969 0.728 0.323 0.721 0.372 1.267 0.05  Weighted RoadAcc.Rate FatAccRate 3.344 0 0.091 0.303 0 0 0.132 0 0.006 0.01 0.004 0 1.62 0 0.106 0.232 0.045 0.079 0.107 0.15 0.054 0.023 0.139 0 0.007 0.008  o  I/i  N  v s r ^ o a e r - o^ s v t - o x o o o o o o i n f j i - i o T t T t f S i - i r s  N  o c\ O N f~ 9 \ h- r»H  O  w  O  O  ^z ^z ^z  <rtrt-  C ^ O r t O r t r t X J r t l r t O O t N r N O r N r N O O O f N r t r N O c N r N  IT)  o  Z  j £ j r t C l r t C O ^ r t < » > ^ r t r t l « l * i r t V ) l / ? r t  rt rt t~  I— rt _ CN rt  ON ON  ON ON  >. 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"o  U  XJ Vi  •c co  g  #  Vi  a  o T5 os u o  -a  n rt"  o o  -J  •a CU CU  CJ  a  C/3 40  ect  -3 c  X>  Cd  ^  -  CO  J fl  CU  S3  a.  o  U  -J  3  « « « 3 £ Z  u o  o o o o O  Ul  CN VO  rt rt ^ rt CN C ^ VO  00  VO Ov  Tl  O O O O VO VO 00 00 m t rn CN CN CN rt VD v o v o v o  O Ov tS —I v o  O Ov (*1 CN v o  o o >-/>  o  o  o  O r t O O O O r t O O O rt O m c i c o o v c N O v o v m m I t • * 00 Ifl i n vo h ^ Cl f ) C l 00 CN CN 00 rt rtCNWlOVCNOVOVCNOVt^ CN CN CN v o v o v o m v o v O ' n < o v o m « l v o m m v o v O ' n v D  *  ON J rn  rs  ON NO  co  VI  VI  T t  ro  O  O  NO  ON  O  T t  x  o  O  ro o ro  O  ro  rs  oo vi  o  w O WD  fl  5  00 rs  w  O  Vl NO V)  vi  T t  o  NT  r-'  VI  o  ro  ON  o NO  o  o rr~' v>  o o o  s?  r»i  00 oq vi  NO  r-'  o T t  ro  VI  vi  SN  §1  00 ro  vi  S? NO  SN  ON  sr  N?  V)  o ©  N? O Tt  o"  00  c O  ON  T t  2?  N?  Nr o ro  00  N»  N*  N?  CM  00  V)  ON  ON  oq ro'  Nt  ON  T t  V)  vi  00  ro  rs  00  T t  00 rs  T t  ro'  rs vi  NO  NO  T t  00 r-'  NO  00  rs  c-  rs rs  rs o  ON  NO  rs  ro oo"  Tt  VI  V)  ro'  00*  NO  00  ON  ©'  NO  VO  oo'  Tt  rs rs  93  03 .fl •d  F^  5  w H  rs NO  rs rN  NO  IN  CU  00  NO  ON  ON  rs'  ON  90  t y  C  C/3  cu  u  ON VI  VN  WD fl  VI ON NO  ro  So  ro'  00 ro vi  •FN  2 1  >  ee FN  H  <B  CU  WD C3 FN CU  >  •9 3 at| t f  PH  3  I 3 PH  I  Pi  8  3 3 Pi  rt  PH  cu  •a  p  o  -rt H  O  3  PH  2  PH  rt  "I rt  3 Pi  IS  1  I OH  a  c  PH  £  a  3 oi  3 Pi  I G in •rH  u  H  ca  1/13 ca  •FN  fl CU  SN PH  <  2  S 5 rs  ro  Tt  VI  NO  W  oo  m rs  in in ro  T t  H  o  APPENDIX 3-E) Traffic Accident Statistics in Thailand Whold Kingdom of Thailand Number of Injuries Number of Deaths 9026 3005 8812 2908 8289 2700 8706 1908 8589 2104 13504 2015 13050 6963 18252 5765 19458 6319 20702 8184 25330 9496 43541 15176 50718 16727 50044 14405 48711 13836 52538 12234  Year 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998  Number of Accident 17864 18445 18420 23959 24132 35289 42532 40481 43966 61329 84892 102610 94362 88556 82336 73725  Year 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998  Highways of Department of Highways Number of Injuries Number of Accident* Number of Deaths 5286 1661 2875 3473 1063 2061 5681 1629 3178 4859 1466 2614 4569 1564 2872 5563 2115 3173 6893 2674 4573 7477 3011 5453 7837 5617 2882 13488 12568 5886 16544 6799 17060 19849 7732 20871 20449 7064 19482 19502 4769 16708 1849 4097 16160 13281 2891 13902  * Traffic Accident - A n accident occurred on national highways resulting in injury or death and damaged property.  75  Cost (Million Baht) N/A N/A N/A N/A N/A 76.6 275 259.8 344.1 607.8 1408.2 1408.2 1631.12 1561.71 1571.79 1378.67  APPENDIX 3-F) ETA Accident Database Date When Month Time Km + Location Direction Symbol Location ID Private Car Pickup 6-Wheel Truck 10 wheel truck Truck and Trailer Vehicles Involved MiniBus Transit Bus Van Motorcycle Taxi > 10 wheel truck Minor Injury Accident Severity Seriuos Injury Fatality Normal Rain Weather Condition Storm Fog Dry Wet & Slippery Surface Condition Flooding bumpy Straight Curve Road Characteristics On-ramp Off-ramp Alcohol Sleeping Driver's Causes Drug Disease Other Brake Engine Vehicle's Casues Flat Tire Short Circuit Other Slow Speeding Casues Changing Lanes Other  8 June 14:20 3 200 A 1  28 June 14:22 2 500 A 1  21 July 21:29 4 0 A 2  1  1  4 1  10 October 14:13 4 500 A 2  11 September 2:06 4 500 A 2  12 April 4:32 6 600 A 3 4  1 1  1  1 1  1 1 1  1 1  1 1  2  2  1 1  1  1  1  1  1  1  1  1  1  1  1  1  1 1  Careless  Careless  1  1  76  1  1  Careless 1  Careless  1  1  Appendix 3-G) ETA's Traffic Speed, Volume, and Accident Data in 1999 First Stage Expressway Location Distance Speed  Daily  From  To  ID  (km)  Port Interchange Rama 4 Sukhumvit Phetchaburi  Rama 4 Sukhumvit Phetchaburi D i n Deang  A4 A3 A2 Al  0.99 2.21 0.75 2.35  68 68 44 80  84686 82806 92511 84207  17 14 4 7  55.553 20.959 15.795 9.691  A9 A8 A7 A6 A5  2.50 1.55 2.35 1.35 1.05  90 90 68 80 90  69237 92617 96424 106400 110867  21 4 19 7 6  33.239 7.634 22.973 13.351 14.121  A13 A12 All A10  2.67 4.49 1.42 1.35  68 44 80 90  44488 66920 52614 67636  17 25 11 38  39.210 22.795 40.337 114.019  BI B2 B3 B4  2.35 0.75 2.27 0.94  90 44 68 30  70291 81860 74295 76768  5 3 20 6  8.293 13.387 32.490 22.780  B5  1.25 1.35 1.95 1.55 2.50  44  B6 B7 B8 B9  90 90 90 80  97950 98790 92055 91085 75223  22 18 11 5 9  49.228 36.977 16.789 9.703 13.112  BIO Bll B12 B13  1.55 2.00 3.63 3.70  68 68 90 68  72590 63811 80498 42328  19 1 12 3  46.265 2.147 11.251 5.248  Port Interchange - Din Deang, Northbound  (km/hr) Vol in 1999 Casualty "Casualty Rate  Bangna - Port Interchange Bangna Sukhumvit 62 A r d Narong Interchange A r d Narong Port 1  Sukhumvit 62 A r d Narong Interchange A r d Narong Port 1 Port Interchange  Dao Khanong - Port Interchange Dao Khanong Suksawat Rama 3 Along River  Suksawat Rama 3 Along River Port Interchange  Din Deang - Port Interchange, Southbound D i n Deang Phetchaburi Sukhumvit Rama 4  Phetchaburi Sukhumvit Rama 4 Port Interchange  Port Interchange - Bangna, SouthEast Port Interchange Port 2 A r d Narong A r d Narong Interchange Sukhumvit 62  Port 2 A r d Narong A r d Narong Interchange Sukhumvit 62 Bangna  Port Interchange - Dao Khanong Port Interchange Along River Sathupradith 2 Suksawat  Along River Sathupradith 2 Suksawat Dao Khanong  a. Casualty Rate = (# of Casualty * 100 million Veh) / ( A A D T * Road Length * 365 days) Casualty is given i n casualty per 100 million vehicle-km  77  Appendix 3-G) ETA's Traffic Speed, Volume, and Accident Data in 1999 Second Stage Expressway From  To  Daily Location Distance Speed (km/hr) Vol in 1999 Casualty Casualty Ra (km) ID  Cheang Wattana - Asoke Cheang Wattana Ngam Wong Warn Prachachuon Ratchadapisek Bang Sue Paholyothin Toll Prapa 2 Phayathai Interchange Paholyothin 1 Makkasan Interchange Asoke 2  Ngam Wong Warn Prachachuon Ratchadapisek Bang Sue Paholyothin Toll Prapa 2 Phayathai Interchange Paholyothin 1 Makkasan Interchange Asoke 2 Asoke 1  17911 46985 46985 68141 71572 80768 83719 58922 56922 39363 28091  12 3 12 8 10 10 2 N/A 6 2 1  36.711 14.457 38.874 13.805 23.629 19.722 9.218 N/A 26.253 12.655 24.383  44 90 68 68 80 68 90 68 90 90 90  27509 34890 58814 58399 74189 69415 65399 60075 44144 44144 24747  N/A 1 N/A 10 6 2 7 1 2 9 14  N/A 7.139 N/A 104.254 14.674 8.580 18.102 1.957 6.896 46.163 30.998  1.90 2.50 1.12 1.22 2.96  80 90 44 68 80  63318 53915 49742 33130 34260  25 16 9 5 17  56.933 32.522 44.260 34.004 45.865  2.85 2.18 1.72 1.42 0.48 1.90  80 90 80 68 80 68  43313 39224 53467 51976 45707 54313  21 15 7 5 N/A 7  46.608 48.060 20.854 18.600 N/A 18.585  B16 B15 B14 B13 B12 Bll BIO B9 B8 B7 B6  5.00 1.21 1.80 2.33 1.62 1.72 0.71 1.70 1.10 1.10 0.40  68 55 80 80 80 80 44 80 68 80  A7 A8 A9 A10 All A12 A13 A14 A15 A16 A17  0.40 1.10 2.10 0.45 1.51 0.92 1.62 2.33 1.80 1.21 5.00  30  Asoke - Cheang Wattana Asoke 2 Makkasan Interchange Paholyothin 1 Phayathai Interchange Paholyothin 1 Phayathai Interchange Prapa 2 • Paholyothin Toll Prapa 2 Bang Sue Paholyothin Toll Ratchadapisek Bang Sue Prachachuon Ratchadapisek Ngam Wong Warn Prachachuon Cheang Wattana Ngam Wong Warn Asoke 1 Asoke 2 Makkasan Interchange  Phayathai Interchange - Bang Klilo Interchange Phayathai Interchange Yommarath Sawong Bridge Surawong Sathon  Yommarath Sawong Bridge Surawong Sathon Bang Khlo Interchange  B5 B4 B3 B2 BI  Bang Khlo Interchange - Phayathai Interchange Bang Khlo Interchange Chan Surawong Hua Lampong Urupong Yommarath  Chan Surawong Hua Lampong Urupong Yommarath Phayathai Interchange  Al A2 A3 A4 A5 A6  78  Appendix 4-A) Sample Calculations of Speed-Collision Probability Equation Exponents 1.14 1.16 1.14 1.05 1.06 1.01 0.98 0.98 0.96 3.23 3.34 3.14  Involvement Rate Casualty Rate Speed 195.08 70.23 102.3 Sask 222.08 79.95 106.8 Sask 203.58 73.29 104.8 Sask 129.64 46.67 101.3 Sask 133.81 48.17 102.3 Sask 106.78 38.44 100.3 Sask 92.94 33.46 Sask 101.1 93.08 33.51 101.6 Sask 84.39 30.38 102.6 Sask 100000000 300.0 Assumption 100000000 Assumption 250.0 100000000 Assumption 350.0 Involvement Rate is given in # of collisions per 100 million veh-km  Exponents vs. Speed - Sask Provincial Highways  0.50 0.00  =  J 0  1  1  1  50  100  150  1  1  200  250  1  . 300  1  350  400  Speed (km/hr) ^ — L i n e a r (300km/hr) ^ — P o w e r (250km/hr) ^ — P o w e r (350km/hr)  The three trendlines above all have a high R-Square value and the 300km/hr Linear curve has the highest among all three. Therefore, 300km/hr is chosen to be the speed where is the probability of collision is 1. The equation of the linear trendline is:  p = 0.01077 V  0  The equation of the involvement \*=V  P 0  R = 0.9899 2  _  0.01077 v  0  79  Appendix 4-A) Sample Calculations of Speed-Collision Probability Equation Speed (km/hr) 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300  Consequence 0.000 0.000 0.001 0.005 0.015 0.037 0.076 0.141 0.240 0.385 0.587 0.860 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000  Involvement Rate 0.000 1.281 1.907 3.001 4.900 8.220 14.094 24.605 43.622 78.388 142.561 262.082 486.557 911.448 1721.598 3276.992 6282.602 12126.317 23554.358 46027.087 90452.091 178715.977 354924.762 708330.631 1420267.070 2860575.886 5786398.893 11753377.624 23968991.385 49069051.912 100827447.747  Exponents 0.000 0.108 0.215 0.323 0.431 0.539 0.646 0.754 0.862 0.969 1.077 1.185 1.292 1.400 1.508 1.616 1.723 1.831 1.939 2.046 2.154 2.262 2.369 2.477 2.585 2.693 2.800 2.908 3.016 3.123 3.231  Fatality Risk 0.0E+00 7.5E-13 1.8E-11 1.4E-10 7.4E-10 3.0E-09 1.1E-08 3.5E-08 1.0E-07 3.0E-07 8.4E-07 2.3E-06 4.9E-06 9.1E-06 1.7E-05 3.3E-05 6.3E-05 1.2E-04 2.4E-04 4.6E-04 9.0E-04 1.8E-03 3.5E-03 7.1E-03 1.4E-02 2.9E-02 5.8E-02 1.2E-01 2.4E-01 4.9E-01 1.0E+00  Sample Calculations of the Hypothetical Example AtlOOkm/hr  p= I* = Risk= AADT = Section Length = Annual Vehicle km travelled = Expected # of Collisions  :  1.077 142.561 8.37E-07 3000 5.000 5475000  collisions per 100 million veh-km  km  Veh-km travelled multiply by I* 5475000 * 142.561 / lOOmillion 8 accdients  Expected # of Fatal Collisions = Veh-km travelled * Risk = 5475000 * 8.37E-07 5 accdients  80  

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