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Influence of vertical alignment on perception of horizontal curvature Bidulka, Shaun David 2001

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INFLUENCE OF VERTICAL ALIGNMENT ON PERCEPTION OF HORIZONTAL CURVATURE by SHAUN DAVID BIDULKA B.A.Sc, The University of British Columbia, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Civil Engineering)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April 2001 © Shaun David Bidulka, 2001  UBC Special Collections - Thesis Authorisation Form  In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s o r h e r r e p r e s e n t a t i v e s . I t i s understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n .  Department o f GtiJt(  Ch^\Y\'5.e.r \y\^  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver,- Canada  Page 1 of 1  11 University of British Columbia Abstract INFLUENCE OF VERTICAL ALIGNMENT ON PERCEPTION OF HORIZONTAL CURVATURE by Shaun David Bidulka Since most of the driver's required information is obtained visually, the importance of the driver receiving precise visual cues from the road environment cannot be overstated. If the visual cues are confusing or in any way cause the driver to incorrectly assess the approaching road environment, the crash risk of the driver may increase. Of particular concern are the perceptual problems induced by superimposing horizontal and vertical curves. To investigate the effect of overlapping vertical alignment on the perceived horizontal curvature, dynamic and static computer generated threedimensional presentations of the driver's view of a road were created. Phase I of the experiment collected qualitative data to test the hypothesis that overlapping crest curves made horizontal curvature appear sharper and overlapping sag curves made horizontal curvature appear less sharp. Phase II of the experiment quantified the perceived radius Rp. The statistical analysis of the Phase II data showed that horizontal curvature appeared consistently sharper when it was overlapped with a crest curve and consistently flatter when it was overlapped with a sag curve at a level of significance a = 5%. Overall this "optical illusion" effect was more prevalent when sag curves were overlapping horizontal curves. Several regression equations that predict driver perception of horizontal curvature were also developed. For sag vertical curves, the actual radius Ract, the turning direction, and the vertical curve parameter A affected the perceived radius Rp. However, for crest curves, the only geometric parameter found to be a significant predictor of Rp was the actual horizontal curve radius R a . Ct  iii  TABLE OF CONTENTS Abstract Table o f Contents List o f Figures List o f Tables..: Acknowledgments 1.0 Introduction 1.1 Background 1.2 Problem Definition 1.3 Thesis Objectives 1.4 Thesis Structure  ii iii iv vi viii •1 1 2 3 4  ;  2.0 Literature Review 2.1 Background 2.1.1 The Human Factor. 2.1.2 The Design Driver 2.1.3 Managing Driver Variability 2.1.4 Design Consistency 2.1.5 Driver Workload 2.1.6 H i g h w a y Esthetics 2.1.7 Sight Distance 2.2 Driver Perception 2.3 Perception o f Horizontal Curves 3.0 Experimental Design... 3.1 Background 3.2 Highway Design Parameters 3.3 M o d e l Creation 3.4 Presentation & Data Collection Design 3.4.1 Phase 1 Design 3.4.2 Phase II Design  5 5 5 6 7 7 9 10 14 16 22  :  •.  30 30 31 36 40 42 45  4.0 Experimental Results 4.1 Phase I Results 4.2 Phase II Results  49 49 76  5.0 Data Analysis & Discussions 5.1 Phase I Analysis 5.2 Phase II Analysis 5.2.1 Hypothesis Testing - R a w Data 5.2.2 Hypothesis Testing - M o d i f i e d Data 5.2.3 A N O V A Analysis 5.2.4 Regression Analysis 5.3 Conclusions  87 87 87 88 88 92 94 98  References Appendix A : Experimental Data Details Appendix B : A N O V A Analysis Details Appendix C : Regression Analysis Details  102 107 134 146  iv  LIST OF FIGURES Figure 1.1. 3 D V i e w s of Superimposed Vertical and Horizontal Curves  4  Figure 2.1. Example of Poor and G o o d Alignment Solutions  11  Figure 2.2. Affect of Incorrect and Correct Leveling Fault on R o a d Guidance  11  Figure 2.3. Alignment Design Cases to be A v o i d e d .  12  Figure 2.4. L a c k of 3 D A l i g n m e n t Coordination causes " F l u t t e r i n g " of the R o a d due to too many Vertical Faults  13  Figure 2.5. Poor Adjustment of Vertical Elements causes Hidden D i p in the Road  13  Figure 2.6. Affect of M i l d e r Inclines on V i s u a l Guidance  14  Figure 2.7. Improved Optical Guidance with Pavement Markings  18  Figure 2.8. Horizontal Alignment Curving out of Sight  23  Figure 2.9. Components o f Required P V S D  25  Figure 2.10.Participant's Curve Perceptions  29  Figure 3.1. Superelevation Development with Tangent Runout Options  34  Figure 3.2. Horizontal Curve Symbols..-  .  Figure 3.3. Screenshot o f Hwysurfl.exe Input Prompts  35 36  Figure 3.4. Screenshot of Final A u t o C A D D r a w i n g  37  Figure 3.5. Screenshot of Phase I Presentation  43  Figure 3.6. Phase I Questionnaire & Data Collection Sheet  44  Figure 3.7. Screenshot of Phase II Presentation  47  Figure 4.1. Effect of Vertical Alignment on Perceived Horizontal Curve Radius - Phase 1  54  Figure 4.2. Effect of R on Perceived Horiz.Curve Radius (expected response) - Phase 1  55  Figure 4.3. Effect of R on Perceived Horiz.Curve Radius (Rp = R ^ ) - Phase 1  56  Figure 4.4. Effect o f R on Perceived H o r i z . C u r v e Radius ( R opposite to expected) - Phase I p  57  Figure 4.5. Effect of A on Perceived Horiz.Curve Radius (expected response) - Phase 1  58  Figure 4.6. Effect of A on Perceived Horiz.Curve Radius (Rp = R ^ - Phase 1  59  Figure 4.7. Effect of A on Perceived H o r i z . C u r v e Radius (Rp opposite to expected) - Phase 1  60  Figure 4.8. Effect of K on Perceived Horiz.Curve Radius (expected response) - Phase I....... 61 Figure 4.9. Effect o f K on Perceived Horiz.Curve Radius (Rp = R ^ ) - Phase 1  62  Figure 4.10. Effect of K on Perceived H o r i z . C u r v e Radius ( R opposite to expected) - Phase 1  63  p  V  Figure 4.11. Effect o f e on Perceived Horiz.Curve Radius (expected response) - Phase 1  64  Figure 4.12. Effect o f e on Perceived Horiz.Curve Radius (Rp = Ract) - Phase 1  65  Figure 4.13. Effect o f e on Perceived H o r i z . C u r v e Radius (Rp opposite to expected) - Phase 1  66  Figure 4.14. Effect o f T u r n i n g Direction on Perceived H o r i z . C u r v e Radius (expected response) - Phase I  67  Figure 4.15. Effect o f T u r n i n g Direction on Perceived H o r i z . C u r v e Radius (Rp=Rac,)-Phase!  :  :  68  Figure 4.16. Effect o f T u r n i n g Direction on Perceived H o r i z . C u r v e Radius (Rp opposite to expected) - Phase 1  69  Figure 4.17. Effect o f Sight Distance on Perceived H o r i z . C u r v e Radius (expected response) - Phase 1  1  70  Figure 4.18. Effect o f Sight Distance on Perceived H o r i z . C u r v e Radius (Rp=R )-PhaseI a a  71  Figure 4.19. Effect o f Sight Distance on Perceived H o r i z . C u r v e Radius (Rp opposite to expected) - Phase 1  72  Figure 4.20. Effect o f Background on Perceived H o r i z . C u r v e Radius (expected response) - Phase 1..  73  Figure 4.21. Effect o f Background on Perceived Horiz.Curve Radius (Rp = R ^ ) - Phase I.... 74 Figure 4.22. Effect o f Background on Perceived H o r i z . C u r v e Radius (Rp opposite to expected) - Phase 1  75  Figure 4.23. Effect of Vertical Alignment on Perceived Horizontal Curve Radius - Phase II. 79 Figure 4.24. Effect o f Horizontal Curve Radius on Curve Perception - Phase II  80  Figure 4.25. Effect o f Vertical Curve Parameter A on Curve Perception - Phase II  81  Figure 4.26. Effect of K on Curve Perception - Phase II  82  Figure 4.27. Effect o f Turning Direction on Curve Perception - Phase II  83  Figure 4.28. Effect o f e on Curve Perception - Phase II  84  Figure 4.29. Effect o f Sight Distance on Curve Perception - Phase II  85  Figure 4.30. Effect o f Background on C u r v e Perception - Phase II  86  Figure 5.1. Regression M o d e l Predictions o f Rp vs. M e a n Rp o f Experimental Data vs. actual R  97  VI  LIST OF TABLES Table 2.1. Number of Illusions Experienced Related to Horizontal Alignment  ....20  Table 2.2. Number o f Other Types of Illusions  20  Table 2.3. Number of the Illusions Experienced Related to Vertical Alignment  21  Table 2.4. Inferred Causes o f Visual Illusions (Daytime)  21  Table 2.5. Preliminary Design Values of Required P V S D  25  Table 2.6. Road Design Parameters  :  :  28  Table 2.7. One-Tailed t-Test of Hypothesis  29  Table 3.1. Test-curve Road Design Parameters  38  Table 3.2. Reference-curve Road Design Parameters  39  Table 3.3. Phase I Setup  46  Table 3.4. Phase II Setup  48  Table 4.1. Summation of Responses to R o a d Animation (Dynamic) Presentations - Phase 1. 53 Table 4.2. Summation of Responses to R o a d Image (Static) Presentations - Phase 1  53  Table 4.3. Summation of Responses to Road Image (Static) Presentations - Phase II  78  Table 5.1. Test of Hypothesis on the Mean V a l u e of Perceived Radius  90  Table 5.2. Test of Hypothesis on the Adjusted M e a n V a l u e of Perceived Radius  91  Table 5.3. A N O V A Analysis Data Setup  93  Table 5.4. A N O V A Analysis: Effect of Overlapping Vertical Alignment on Rp  93  Table 5.5. Variables used in Regression M o d e l Development Trials  96  Table A . 1. Sample Characteristics - Phase 1  108  Table A . 2 . Experimental Data: Animated Crest Combinations - Phase 1  110  Table A . 3 . Experimental Data: Animated Sag Combinations - Phase I  112  Table A . 4 . Experimental Data: Image Crest Combinations - Phase 1  114  Table A . 5 . Experimental Data: Image Sag Combinations - Phase 1  116  Table A . 6 . Experimental Data: Crest Combinations Summary - Phase 1  118  Table A . 7 . Experimental Data: Sag Combinations Summary - Phase 1  119  Table A . 8. Sample Characteristics - Phase II  120  Table A . 9 . Experimental Data: Image Crest Combinations - Phase II  122  Table A . 10. Experimental Data: Image Sag Combinations - Phase II  124  Table A . 11. Experimental Data: Crest Combinations Summary - Phase II  126  Table A . 1 2 . Experimental Data: Sag Combinations Summary - Phase II  127  Vll  Table A . 13. M o d i f i e d Data: Image Crest Combinations - Phase II  128  Table A . 14. M o d i f i e d Data: Image Sag Combinations - Phase II  130  Table A . 15. M o d i f i e d Data: Crest Combinations Summary - Phase II  ...132  Table A . 16. M o d i f i e d Data: Sag Combinations Summary - Phase II  133  Table B . l . A N O V A setup Summary  135  Table B.2. A N O V A : Effect of R  136  Table B.3. A N O V A : Effect of A  137  Table B.4. A N O V A : Effect of K  138  Table B.5. A N O V A : Effect of e  139  Table B.6. A N O V A : Effect of Sight Distance  140  Table B.7. A N O V A : Effect o f Background Image  141  Table B.8. A N O V A : Effect of Turning Direction, R=300m  142  Table B.9. A N O V A : Effect o f Turning Direction, R=500m  143  Table B.10. A N O V A : Effect of Turning Direction, R=700m  144  Table B . l l . A N O V A : Effect of Overlapping Vertical Curve  145  Table C l . Summary of Regression Variables  147  Table C . 2 . Regression Analysis Trials Summary - Combined Curve Equations  148  Table C . 3 . Regression Analysis Trials Summary - Sag Curve Equations  148  Table C.4. Regression Analysis Trials Summary - Crest Curve Equations  149  Table C . 5 . S P S S Regression Results for M o d e l ( M l )  150  Table C.6. S P S S Regression Results for M o d e l ( M 2 )  152  Table C.7. S P S S Regression Results for M o d e l ( M 3 )  154  Table C.8. S P S S Regression Results for M o d e l ( M 4 )  155  VU1  ACKNOWLEDGMENTS  The financial support by the Insurance Corporation of British Columbia (ICBC) is gratefully acknowledged. The author also wishes to express sincere appreciation to Dr. Tarek Sayed, Dr. Yasser Hassan, and Dr. Frank Navin, for their assistance in the preparation of this manuscript.  To Dori, whose continued support made this endeavour possible.  1  1.0 INTRODUCTION  1.1 Background  This thesis endeavors to provide a model for predicting how drivers perceive horizontal curvature based on the presence of specific highway design parameters.  Ultimately, this model (or models) could be used as  another means of improving highway design consistency and safety by minimizing the occurrence of inaccurate curve perception. Highway design initially seems straightforward. In theory you simply provide a means of getting from point A to point B. However, as one delves deeper into the intricacies of highway design, it becomes clear that highway design is in fact quite a complex process, often involving a compromise between various goals. The complexity doesn't lie so much with the technical challenges, but more so with the socio-economic impacts of the final product. While escalating construction costs or poor public support for a project may cause a political backlash, it is the highway's safety performance that can have the greatest ongoing socio-economic impact. With an estimated 500,000 people killed and more than 10 million people injured annually in automobile crashes worldwide (Gibreel 1999), the resulting socio-economic costs are in the hundreds of billions of dollars (Gibreel 1999, OECD 1999).  Considerable research has been conducted into the factors contributing to automobile crashes.  Studies by, Sabey and Staughton (1975), and Treat  (1980) concluded that road crashes could be attributed to deficiencies in one of three components of the road system (or various combinations thereof). These components are: the driver, the vehicle, and the road environment. Of these the driver is the most influential component, contributing to over 90% of all  2  road crashes. Although thesefindingssuggest that efforts should be directed at reducing the contribution of driver error to road crashes, in practice, most of the effort has been directed at vehicle and road improvements. This focus is primarily due to the fact that these two components can be readily defined and corrected with countermeasures, while the variability of human behavior is significantly more difficult to manage.  Nonetheless, it is essential for safety  professionals to understand and consider human factors when designing a highway (Kanellaidis 1999). 1.2 Problem Definition The driving task involves an interaction between the driver, the vehicle, and the road. (movement),  The driver receives information through the kinesthetic vestibular  (equilibrium), auditory (hearing)  and, most  importantly, visual senses (Wright et al. 1998). In fact, 90% of the driver's required information is obtained visually (Alexander and Lunenfeld 1986). Therefore, one cannot overstate how important it is to ensure that the visual cues the driver receives from the spatial view of the road environment are clearly understood. If the visual cues the driver receives are confusing or misleading, the driver may incorrectly assess the approaching road environment, increasing the crash risk of the driver. While the visual cues are a function of a roads esthetics and/or alignment coordination, the interpretation of these visual cues are functions of the driver's driving experience, physiology, and psychological characteristics. Since driver error contributes to over 90% of vehicle crashes, it is important to understand.how drivers perceive visual cues, particularly how drivers perceive horizontal curves. Thirty percent of all rural accidents occur at curves (Stewart and Chudworth 1990) while crash rates on curves are 1.5 to 4 times those of similar tangents (Zegeer et all992) suggesting that understanding driver curve perception  3 could significantly reduce crash rates on highways resulting in substantial social-economic benefits. However, even if the road alignment is precise, there may still be situations that exist where the road alignment/features will cause the driver to experience Optical illusions, precipitating an inaccurate perception of the degree of horizontal curvature (or other feature).  Such inaccurate  perceptions could be detrimental to road safety, especially if the driver perceives a horizontal curve to be less sharp than it is in reality. One such situation where optical illusions may occur is when horizontal curves are combined with a vertical curve (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994). 1.3 Thesis Objectives  Smith and Lamm (1994) hypothesized that the perception of horizontal curvature would appear to be less sharp when overlapped with a sag vertical 1  curve, and more sharp when overlapped with a crest curve (Figure 1.1). If this theory is valid, higher operating speeds, and maybe higher subsequent crash occurrence, would occur in situations where the horizontal curvature appears less sharp than with horizontal curves without an overlapping sag curve. In contrast, speed choice and subsequent crash risk should be lower when horizontal curves are overlapped with a crest curve (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Smith and Lamm 1994). The purpose of this thesis is to investigate the hypothesis that horizontal curves overlapped with vertical curves may cause a violation of driver expectancy with respect to the perception of horizontal curvature, potentially increasing the crash risk of the driver (Hassan and Easa Visual 2000,  1  A vertical curve and horizontal curve coincide.  Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994). The following are key focal points: •  Investigate the validity of the Smith and Lamm's hypothesis.  •  Identify critical highway design parameters that contribute to this phenomenon.  •  Identify relationships between driver perceptions of horizontal curvature and highway design parameters contributing to this phenomenon.  a.) Horizontal C u r v e , b.) Horizontal Curve with superimposed crest vertical curve, c.) Horizontal C u r v e with superimposed sag vertical curve (Note: same horizontal radius for all views)  Figure 1. 1. 3D views of superimposed vertical and horizontal curves  1.4 Thesis Structure Chapter One provides an overview of the thesis and its structure followed by a literature review presented in Chapter Two. Chapter Three explains the experimental design process and data collection techniques. Chapter Four presents the results of the experiment while Chapter Five covers the data analysis and discussions.  5  2.0 LITERATURE REVIEW  Section 2.1 presents an overview of some of the fundamental issues concerning highway design and safety, which, among other things, requires an understanding of how driver variability influences highway design. Section 2.2 discusses the issue of driver perception and finally, section 2.3 reviews recent research closely related to the work of this thesis, namely driver perception of horizontal curves.  2.1 Background  2.1.1 The Human Factor As mentioned earlier, human error contributes to over 90% of all recorded automobile crashes (Sabey and Staughton 1975, Treat 1980). Therefore, understanding the human factors related to highway design is essential. Because human beings vary in just about every characteristic, unless something is specifically designed for an individual, it may impose some level of handicap upon the user. Fortunately, humans are highly adaptable and can accommodate design deficiencies.  Indeed the application of human factors  principles to groups of people would be impossible unless individuals were adaptable; without this capacity, "graceful degradation" of performance would not be possible.  Moreover, everything would have to be designed for the  individual.  Mutabazi et al. (1998) classified human characteristics as either physiological or psychological. During their literature review, they found that most of the highway and traffic engineering studies focused on physiological rather than the psychological aspects, likely due to the role these former  6  aspects play in roadway design and traffic control devices (i.e. driver reaction time, tolerable acceleration and deceleration rates, etc.). They found only one study that attempted to address the psychological aspects of human factors.  2.1.2 The Design Driver In the case of highway design, "success of a highway facility is reflected in the extent to which it satisfies the needs of its users" (Kanellaidis et al. 1997). The road user, or driver, represents a population who are not only diverse culturally and socially,  but also exhibit  unique physiological and  psychological characteristics per individual. As the population of drivers increase, so does the diversity in driver behavior. Current geometric highway design practice looks at drivers as a whole population and doesn't specifically account for the abilities of each driver. Instead, characteristics of a "design driver" have been established which are used for detenruning key geometric design elements of a highway based on the design-speed concept. Parameters found to be directly related to driver behavior mainly include speed, friction demand, and perception-reaction  time (Dimitropoulos and Kanellaidis 1995),  thus values for these three parameters have been specified for the design driver, which, it is assumed, represent the majority of the driving population. The difficulty of dealing with driver variability is the extent to which the assumed design values are 'representative' of actual driving behavior, particularly when it comes to driver perception. "What is information to one road user, might not be information to another or what is information to one road user at a certain moment might not be information to that same road user at another moment. It is the perceived situation not the physical reality that determines behavior" (Rumar 1985).  7  2.1.3 Managing Driver Variability  Driver variability can be managed in one of two ways. It can be limited to a predetermined threshold or it can be accounted for in highway design (Dimitropoulos and Kanellaidis 1995).  The first method involves the  determination of "optimal" driver performance values.  Once established,  various measures can be implemented to achieve the desired driver behavior. These measures include public safety campaigns, enforcement, driver education and licensing. The more rigorous the performance values, the more restrictive the access to driving, giving rise to the debate of whether driving is a right or a privilege.  The other method accepts that driving behavior will  sometimes deviate from the optimal or desirable values.  The goal is to  muumize the consequences of this deviation by providing passive and active safety measures such as seatbelts, air bags, crash barriers, rumble strips, etc. The term "forgiving highways" can be used to describe infrastructure designed to accommodate driver variability (i.e. non-design drivers).  2.1.4 Design Consistency  While the establishment of road safety standards has greatly improved urfrastructure performance, strict adherence to design standards doesn't guarantee a highway will operate safely. Some of the crash occurrence can be attributed to a lack of geometric design consistency.  Geometric design  consistency may be defined as the degree to which highway systems coordinate successive geometric elements to rninimize the frequency and extent of violations of driver expectancy so most drivers can safely operate at their desired speed along the highway (Gibreel 1999, Nicholson 1998, AlMasaeid et al. 1994). The belief is, that consistent geometric road designs will exhibit smoother (more stable) vehicle operations with less crash occurrence.  8  Design inconsistencies may arise due to the evolutionary changes in design guidelines, arbitrary decisions regarding the termination of highway design projects leaving inadequate transitions between old and newer road sections, and the use of above-irunimum design values (Kanellaidis 1997). Rural roads are particularly vulnerable to design inconsistencies primarily due to their historic development. These roads often originated as trails or wagon roads that have evolved over the decades to accornmodate increased mobility needs rather than being originally designed for a consistent speed. Subsequently, the demands placed on rural roads by current drivers may exceed the roads' capabilities.  These inconsistencies between a driver's  demands or expectations, and the road's characteristics, are believed to be a major contributor to the high crash risk on rural roads (Wright et al. 1998). Vehicle speed changes are a visible and easily measurable indicator of inconsistency in alignment design (Nicholson 1998) and thus are the most common and simplest criteria to evaluate design consistency (Gibreel 1999). Two kinds of speed variations have been closely linked to road safety. They are: (1) drivers varying their operating speeds to adjust to road features encountered, such as intersections, accesses and curves in the alignment. The greater and morefrequentthe speed variations, the higher the probability of collision; and (2) drivers traveling substantially slower or faster than the mean speed have a higher risk of collision (Dimitropoulos and Kanellaidis 1995). Therefore, a designer can enhance road safety by producing a design that encourages operating speed uniformity (Geometric  1999).  A review of  applicable research (Lamm et al. 1997, Lamm and Heger 1997) found that the most important parameter in the explaining variability in operating speed and crash rates was the degree of curve. Safety experts have recognized that abrupt changes in horizontal alignment create abrupt changes in operating  9  speeds that lead to automobile crashes (Lamm et al. 1997, Lamm and Heger 1997).  2.1.5 Driver Workload Vehicle speed changes are manifested in response to the many stimuli received and processed by the driver during the driving task. The senses used by drivers include: visual, kinesthetic, vestibular (equilibrium), and auditory (Wright et al. 1998). However, 90% of the driver's required information is obtained by vision (Alexander and Lunenfeld 1986). These visual cues are a function of the road esthetics, which are related to alignment coordination, which determine the available sight distance, which affects driver decision times. For example, as drivers approach a curve in the road, they must be able to see a sufficient distance in advance of their vehicle in order to judge whether or not the speed they are traveling is adequate to negotiate the approaching curve safely and comfortably.  The driver's past experiences  with curves, as well as the visual information received, will play an important role in deterrnining how the horizontal curvature is perceived.. The kinesthetic and vestibular senses provide important feedback (to the driver) concerning the centripetal force acting on the vehicle and the driver's body when negotiating the curve. This feedback information, combined with continued visual and possible auditory cues (i.e. skidding tires), will confirm whether or not the driver made the correct judgment about the curve sharpness. The mental processing of this information has been labeled as driver workload. Kanellaidis (1997) described driver workload as the "basic link between highway design and driver behavior" and defined workload as the "time rate at which a given amount of driving tasks have to be performed". While all drivers experience some level of driver workload, if they are surprised by  10  events (expectancy not met), they may not have adequate decision time (mental workload), to perform correct evasive maneuvers to avoid some hazardous condition or to physically stop the vehicle. Abrupt increases in driver workload are known to increase collision potential (Geometric 1999) and may be attributed to geometric design inconsistencies. Wooldridge et al. (Comparison 2000) found that the effects of curve radius on visual demand were similar regardless of whether the tests were in a driving simulator, on a test track, or on a public road. However, there were differences in the baseline demand level between contexts, which indicate that only relative levels of workload can be determined and not absolute levels.  2.1.6 Highway Esthetics Highway esthetics relate not only to how well the highway appears to blend into the surroundings, but also to the evoked driver emotions related to comfort or safety.  The importance of esthetics is not superficial. An  esthetically pleasing highway design can promote safer and more efficient mobility (Lipar 1997, Smith and Lamm 1994), perhaps due to the improved coordination of the horizontal and vertical alignments. Figures 2.1 through 2.6 illustrate good and poor highway design techniques with respect to esthetics. These figures emphasize the importance of visualizing the road from the driver's perspective early in the planning stages to ensure wellbalanced road sections are constructed that eliminate unsafe feelings and driver discomfort (Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994).  11  (Above) (Below)  Short Sag on Long H o r i z o n t a l Curve Long Sag on Long H o r i z o n t a l Curve  Broken-Back V e r t i c a l  Curve  Figure 2.1. Example of Poor and Good Alignment Solutions (Smith and Lamm 1994).  Incorrect fault - the direction i n w h i c h the road continues is unclear. Correct fault - the direction i n w h i c h the road continues is more apparent.  Figure 2.2. Affect of Incorrect and Correct Leveling Fault on Road Guidance (Lipar 1997).  HL  ML  VL  *  Optical Break, Caused by Hori rontol Tangent.  Optical Break. Caused by Horizontal Curve.  ML  OpHcat Break in Crest Vertical Curve  -A-  Diving id Tangent and Curve  Ml  Jumping  HL  yrrtTT HL  Fluttering in Tangent ond Curve  Figure 2.3. Alignment Design Cases to be Avoided (Smith and Lamm 1994).  VL  13  /  •  j  Figure 2.4. Lack of 3D Alignment Coordination causes "Fluttering" of the Road due to too many Vertical Faults (Lipar 1997).  Figure 2.5. Poor Adjustment of Vertical Elements causes a Hidden Dip in the Road (Lipar 1997).  14  Figure 2.6. Affect of Milder Inclines on Visual Guidance (Lipar 1997).  Lipar (1997) suggests that the images on the right {Figure 2.6) are more esthetically pleasing and provide better guidance cues for the driver.  The  tangential sight distance is also increased, as the mclines get flatter.  2.1.7 Sight Distance  Sight distance requirements are a function of vehicle type, the speed by which they are operating, and the highway alignment. Drivers need to see the roadway an appropriate distance in advance of their vehicle for safe vehicle operation. For example, if an object is obstructing the larie in the vehicle's path, the driver needs to see that object, decide what to do, and then have sufficient time to react. Furthermore, there must be sufficient (road) distance to physically stop the vehicle once the driver has initiated braking. The more time the driver has to "process" mcoming stimuli (decision time), the greater  15  the probability that they will make the correct decision and corresponding action. Therefore, as jpart of the design process, adequate driver sight distance is determined for each geometric element based on the design speed. The faster the design speed, the greater the required sight distance. Horizontal and vertical alignments may also pose additional constraints to the driver's view of the roadway. For example, sight lines are affected by the lateral clearance on the inside of horizontal curves and may be obstructed by the roadway surface itself in the case of vertical curves.  When street lighting is not present,  nighttime driving vision is generally limited to the range of the vehicles' headlights.  Therefore, the headlight sight distance (HLSD) must also be  checked to ensure that the road geometry and surrounding topography isn't a limiting factor.  A special case of sight distance called preview sight distance (PVSD), has been suggested by Gattis and Duncan (1995). They described PVSD as the distance traveled "while the driver perceives and reacts to upcoming roadway guidance cues ... Inadequate PVSD arises when the available viewing distance of the roadway is less than the driver needs to react and make vehicle guidance adjustments" (Gattis and Duncan 1995). If vehicle-operating speeds exceed the highway's design speed, which is quite common on many rural roads, inadequate PVSD may occur. Several studies (Gattis and Duncan 1995, Schnell and Zwahlen 1999) have tried to quantify PVSD in terms of preview times (PVT). A literature review by Gattis and Duncan (1995) found that PVT times ranged from 2 to 9 seconds, while the results of their PVT measurements on three winding highway sections and one urban street indicated a required minimum preview time of around 1.3 to 1.7 seconds. Although, Gattis and Duncan's (1995) results could not be generalized for highway design because only one driver was tested, based on previous  16  research and their own experience, Gattis and Duncan (1995) suggested preview times rangingfrom2.5 to 4 sec or more. On the other hand, Schnell and Zwahlen (1999) and Zwahlen and Schnell (Driver 1999), suggested a pavement marking preview time of 3.65 sec. In summary, highways must be designed to provide a safe means of mobility for users who exhibit a diverse range of physiological and psychological characteristics. Much like general product design, highways are designed to accommodate the majority of users using the concept of the "design driver".  The characteristics of the design driver, used in conjunction  with the design speed characteristics of the highway, ensure that sufficient sight distance is available to the driver to avoid obstacles and maneuver vehicles safely through the highway's geometric elements at the anticipated vehicle speed. Vehicle speed changes, a common measurement of design consistency, are a manifestation of the driver's response to the visual and other sensory information they receive from the road environment. These speed changes are an indication of how the driver perceives the road geometric elements. 2.2 Driver Perception Since over 90% of automobile crashes involve driver error (Sabey and Staughton 1975, and Treat 1980) understanding how drivers perceive their surrounding environment is important to improve road safety. According to Murch (1973) "The constant interaction with the environment and the associated mental process of interpreting the impact and import of external events characterizes the process known as perception".  17  If perception is considered dependent upon the stimuli received and the total experiences of the individual, than each individual's perception of stimuli will be unique. Since each individual has a unique experience the problem arises of how to measure perception if it is personal and subjective. To resolve this problem four different approaches have been used (Murch 1973). The first method, called thephenomenological approach, recognizes the subjective nature of perception and requires the individual to relate their personal perceptions of an event as the method of assessment. The disadvantage of this approach lies in the lack of control over the accuracy of the subject's recollection of events.  Furthermore, even when similar perceptions for  different individuals are recorded, it doesn't guarantee that the subjects had the same perceptual experience. The second scheme, called the behavior ist's functional approach, emphasizes that even though perception is subjective, there is a commonality between individual responses. With this approach only the common aspects of perception can be observed and recorded, not the unique aspects. The third method combines the phenomenological and the functional approaches by measuring both the individual's observed response, and recording the individual's declared perception, which are then compared for inconsistencies.  A final solution summarized by Murch (1973) requires  the use of "highly trained observers ... trained to attend to important aspects of a stimulus and to communicate their perceptions ... in unambiguous terms." From a transportation point of view, the use of highway speed profiles to analyze the highway performance seems to fit better into the behaviorist's functional approach. Drivers may use any number of different visual cues to maintain their vehicle position on the road including: the surrounding topography, tree lines, utility poles, fencing, buildings, and the road surface or ditches. Perhaps the most common visual cue is that of pavement markings. The more distinct the  18  pavement markings, the more obvious the direction of the road is to the driver (Figure 2.7).  The addition of edge lines can also induce "a more favorable  lateral position on rural roads without having negative effects on subjective appraisal, driving performance or mental workload (Steyvers and DeWaard 2000)."  Figure 2.7. Improved Optical Guidance with Pavement Markings (Smith and Lamm 1994).  Many studies (Schnell and Zwahlen 1999, Zwahlen and Schnell Visibility 1999, Zwahlen and Schnell Visibility 1995, Steyvers and DeWaard 2000, Lu and Barter 1998) have investigated the various properties of pavement markings to determine the optimal design for use to maximize visibility for the driver. Parameters investigated include pavement lane marking width, color, retroreflectivity, durability and cost.  While one of the goals of transportation engineers is to design highways that provide drivers with clear and concise visual guidance cues, there is no way to ensure that drivers will perceive those visual cues accurately. There may exist situations that cause the driver to experience some sort of optical illusion. For instance, to insure drivers slow down sufficiently at roundabouts or exit ramps, lines can be painted across the road that get closer together  19  nearer the roundabout or exit road.  These lines give the driver a vivid  impression of speed resulting in a faster braking rate then would have occurred if the lines were not present (Bruce and Green 1985). While the painted lines are an example of a desired optical illusion, research by Mori et al. (1995) showed that drivers can experience optical illusions while driving that were not intentionally planned. The question raised is whether these unintentional optical illusions contribute to the crash occurrence on highways. Mori, et al. (1995) conducted surveys to determine the occurrence and causes of optical illusions experienced along a 50 km long expressway section in the vicinity of Osaka in 1992. They conducted two experiments; For the first experiment, 150 highway patrol personnel were given questionnaires that asked if they had experienced particular optical illusions along a specified section of the freeway. Sixty-one of the 150 highway patrol personnel responded to the questionnaire, identifying 57 different locations along the freeway where optical illusions were experienced. The second experiment involved test drives in which the participants were asked various questions about their perception of the road alignment they were driving on. The responses were recorded and compared to the actual alignment characteristics and any discrepancies between perception and reality were identified. The results of their research are summarized in Tables 2.1 to 2.4. While Mori et al. (1995) failed to confirm the relationship between the optical illusions and accident data, they did nonetheless, confirm that visual illusions do occur.  Table 2.1. Number of the Illusions Experienced Related to Horizontal Alignment (Mori et al. 1995).  Daytime  Nighttime  Gentle Curve —• Sharp Curve  7  S  Sharp Curve —*• Gentle Curve  13  4  20  12  Type of  Visual Illusions  Total  Note: "A - * B" means that" Although I thought it was A, it was actually B."  Table 2.2. Number of Other Types of Illusions (Mori et al. 1995).  Type of Visual Illusion  Daytime  Nigh time  Roadway Ahead Seemed Disappeared  2  3  Running Car Seemed Stopping  2  4  Car in Opposite Direction Seemed Oncoming  0  3  2  10  Total  21  Table 2.3. Number of the Illusions Experienced Related to Vertical Alignment (Mori et al. 1995). Daytime  Nighttime  Flat or Downgrade —» Upgrade  15  11  Flat or Upgrade —* Downgrade  7  9  Gentle Downgrade —* Steep Downgrade  0  1  Downgrade —* Steep Downgrade  3  2  Steep Downgrade —• Gentle Downgrade  1  2  Gentle Upgrade —• Steep Upgrade  1  I  Upgrade —* Steep Upgrade  1  5  Steep Upgrade Gentle Upgrade  1  2  Type of Visual Illusions  Total 30 Note: "A -+ B" means that" Although 1 thought it was A, it was actually B."  33  Table 2.4. Inferred Causes of Visual Illusions (Daytime) (Mori et al. 1995) Type of Illusions Factors of Vertical Alignments  Related to Vertical Alignments •After Long Successive Slopes • Before or After Crests or Sags • Around Points Gradient Changes • In Tunnels  Factors of Horizontal •Relatively Gentle Alignments Alignments  Visual •Noise Barriers Environment Other, Factors  Gentle Curve - * Sharp Curve  Sharp Curve —• Gentle Curve  •Relatively Steep Downgrade  • Downgrade  •Reversed Point of S-shaped Curve • Before Circular Curve in Compound Curve • Length of Clothoid Curve <300m • Length of Circular Curve <200m  • Reversed Point of S-shaped Curve • Before Circular Curve in Compound Curve • Length of Clothoid Curve <300m • Length of Circular Curve <300m  • Left Curve and Noise Barriers  • Left Curve and Noise Barriers  • Strong Effects by •Heavy Traffic • •Strong Effects by Alignments Behind Alignments Ahead  • Strong Effects by Alignments Ahead  22  2.3 Perception of Horizontal Curves  Perception of horizontal curves is particularly important because crash occurrence on curves is relatively high compared to tangent sections. A study by Persaud (OECD 1999) compared datafromCanada and the United States and found that the average crash rate for horizontal curves is approximately three times that of tangent sections, and the average single vehicle run-off the road crash rate for curves on rural roads was about four times that of tangents. Choueiri et al. (1994) found that the sharper the curve, the higher the number of run-off the road incidents, where the degree of curve was the most successful parameter in explaining the variability in crash rates. In general, isolated or thefirstin a series of curves following long tangents are the most dangerous (OECD 1999).  Several countermeasures have been implemented to improve curve perception, including physical improvement of the available sight distance, installation of lighting and/or curve delineation markers and signage. Zwahlen and Park (1995) studied curve radius perception accuracy as a function of the number of delineation devices and concluded that four equally spaced chevrons within a total visualfieldof eleven degrees provided adequate curve radius estimation cues for urifamiliar drivers approaching a curve at night. Zwahlen and Schnell (Knowledge 1995) developed computer software to determine the placement of curve delineation devices in order to eliminate the subjectivity of placement. Their hypothesis was that an adequate number of equally spaced delineation devices along a curve will provide an unfamiliar driver with the additional curvature information needed to choose the correct curve speed, thus resulting in fewer run-off the road crashes. Toru Hagiwara et al. (2001) performed afieldstudy of a driver's curve detection performance in the daytime and at night. Their results indicated that in the daytime, drivers  23  obtain directional information about the curve primarily from the road scene but at night, lighting midway through the curve had a greater effect on curve detection performance. The high crash experience on curves may also infer that sight distance is lacking. Gattis and Duncan (1995) briefly discussed the applications of the PVSD concept to sharp horizontal curves, where the PVSD was based on the extent of the driver's cone of vision needed to focus on the lane markings defining their own lane. The ability to perceive the markings clearly, was limited by the foveal vision range and scanning range of 29 and § degrees respectively.  As illustrated in Figure 2.8, the PVSD extends to the point  where the centerline (for two-lane highway) will fall outside the visual cone's right edge for any radius, less than R (Gattis and Duncan 1995).  lane edge  Figure 2.8. Horizontal Alignment Curving Out of Sight (Gattis and Duncan 1995).  24  Hassan and Easa (1998) suggested that stopping sight distance (SSD) and PVSD could be used to determine alignment coordination using threedimensional analysis.  Their primary concern was determining the proper  location of horizontal curves (in relation to the vertical curve) so that drivers may perceive horizontal curvature adequately.  For safety reasons, they  suggested that horizontal curves shouldn't start within locations along the road that were identified to have inadequate SSD or PVSD, and as such, these locations were labeled as Red Zones. In an attempt to quantify PVSD, Hassan and Easa (Modeling 2000) developed aframeworkfor calculating PVSD for horizontal curves. They defined PVSD as the "sight distance required to see and perceive a horizontal curve ahead and react properly to it."  Similar to  SSD, the PVSD calculation involved the summation of the distance traveled during the perception-reaction (PR) time and the distance traveled while decelerating. This combined distance, labeled the Si distance, was specified to he completely on the tangent if no spiral was present. If a spiral curve was present, then the Si distance could extend along the spiral but not extend into the horizontal curve. Unlike SSD, PVSD has an extra distance component labeled the S2 distance. The S2 distance was the distance the driver needs to see along the horizontal curve to perceive and estimate the horizontal curvature rate. Figure 2.9 illustrates the Si and S2 components of PVSD for vertical and horizontal alignments as defined by Hassan and Easa (Modeling 2000) while preliminary design values for PVSD in terms of the S] and S2 distances are shown in Table 2.5.  25  PVSD origin  (b) Horizontal AlignmenL  Figure 2.9. Components of Required PVSD: PVSD on Tangent Si and PVSD on Curve S (Hassan and Easa Modeling 2000). 2  Table 2.5. Preliminary Design Values of Required PVSD (Hassan and Easa Modeling 2000). REQUIRED PVSD (m)" Spiraled Curve R (m)  (D  400 600 800 1.000 1.200 1.400 1,600 1,800 2,000  Simple Curve  s, (2)  131 no 99 93 88 85 83 81 80  S,  (3) 50 62 70 76 80 83 83 83 81  A = 100 m  A = 200 m  s,  s, (5) 57  s, (66 6)  s* (93' 7)  63 70' 76" 80" 83" 83" 83" 81"  66 66 66 66 66 66 66 66  88 86 84 83 83" 83" 83" 81"  (4) 107 94 87 83 80 78 77 76 75  'Values are rounded to next integer. "Minimum value. 'Maximum value.  A = 300 m  s,  (8) 66 66 66 66 66 66 66 66 66  Si  0)  119' 119' 117 109 103 98 92 86 81"  26  Hassan and Easa (Modeling 2000) concluded that the "horizontal curve radius and configuration were found to have significant effect on the required PVSD on curve and the corresponding deflection angle. Generally, the value of the required PVSD on curve increases as the curve radius increases or when the spiral curve is used.  The turning direction was found to have an  insignificant effect on the results" (Hassan and Easa Modeling 2000).  While it is acknowledged that the optical leading of a road is important in general, there have been specific concerns about how driver perception of horizontal curvature can be influenced by the superimposition of vertical curves (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994). German engineers recognized very early that there were perceptual problems induced by superimposing horizontal and vertical curves (Smith and Lamm 1994).  Smith and Lamm (1994)  hypothesized that the perception of horizontal curvature would be less sharp when overlapped with a sag vertical curve and sharper when overlapped with a crest curve. In those situations where the curvature appears less sharp, higher operating speeds (and higher crash risks) might be expected than with horizontal curves without any overlapping of sag curves. In contrast, because horizontal curvature may appear sharper than it is in reality when overlapped with a crest curve, speed choice and subsequent crash risk should be lower (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Smith and Lamm 1994). To test this hypothesis, Smith and Lamm (1994) summarized the results of an earlier study (Lamm 1982) that analyzed a typical road section with an average crash rate of 3.6 crashes per million-vehicle-kilometers (mvk) over the entire length of the observed state route. At the site with the combined  27  horizontal curve and sag vertical curve, the crash rate was 8.3 crashes per mvk while at the crest curve site the crash rate was 1.4 crashes per mvk. Excessive speed was identified as the single most frequent cause of crashes at the sag vertical curve site. These results supported the hypothesis that overlapping sag vertical curves may create a potential hazard by making the horizontal curvature appear flatter than it really is. An alternate way to verify this hypothesis is to investigate driver perceptions rather than analyze crash statistics. Hassan and Easa (Visual 2000) used computer animation to simulate the driver's perspective of the road. Fourteen computer animations, simulating the driver's perspective of the road were created {Table 2.6). A randomly selected sample of 67 drivers, aged 16 to 61, viewed a test-curve animation and then three reference-curve animations with the same turning direction. The test-curves had a horizontal radius of 600m and were overlapped with a vertical curve. The referencecurves did not have an overlapping vertical curve and had horizontal curve radii of 500, 600, and 700m respectively. The participants were asked to state which of the reference-curves had a horizontal curve most similar to that of the test-curve. Thus, the perceived radius, R , was determined for a given radius, p  R. It should be noted that each participant did not view all eight of the testcurves and therefore the actual sample sizes for each respective test-curve ranged from 12 to 17 drivers (see Table 2.7). The subjects also provided information related to their driving history, age, gender, residence and visual acuity. Table 2.6 summarizes the ariimation design parameters used, while Table 2.7 and Figure 2.10 summarize the results of Hassan and Easa's experiment.  28  Table 2.6. Road Design Parameters (Hassan and Easa Visual 2000).  ConTnWnliliiiriitcrs Road Section Length = 2 km Vertical Curve Length = 340 m Shoulder Width = 2.5m Superelevation Rate = 6% Camera offsetfromCenterline =  Lane Width = 3.7 m Camera Spee 100 kph Camera Heig 1.05 m 1.50 m  A(%)  Horizontal Radius  Turning Direction  4 8 4 8  600 600 600 600  Right & Left Right & Left Right & Left Right & Left  Vertical Curve  A(%)  Horizontal Radius  Turning Direction  none none none  0 0 0  500 600 700  Right & Left Right & Left Right & Left  Animation No.  Vertical Curve  1 &2 3 &4 5 &6 7&8  Crest Crest Sag Sag  Animation No.  9& 10 11 & 12 13 & 14  The results of their study indicate support for the hypothesis that horizontal curves combined with crest curves appear sharper than reality, and overlapping sag curves cause horizontal curves to appear less sharp than reality. In addition, they found that the perceived radius of the horizontal curve didn't depend on turning direction or the algebraic difference of the vertical grades. However, as can be seenfromTable 2.7, the sample size is small and the standard deviations are high.  Therefore, Hassan and Easa  recommended increasing the sample sizes, studying more curve parameters, and the use of finer increments in the horizontal curve radii of the reference curves.  29 Table 2.7. One-Tailed t-Test of Hypothesis (Hassan and Easa Visual 2000). Vertical Curve  A (%) 4  a' (%, One-  Turning Direction  Sample Size  Mean  (m)  Standard Deviation  t*  Tailed) *  Right  17  552.9  80.0  -2.426  1.350  Left  14  564.3  74.5  -1.794  4.800  Right  17  558.8  93.9  -1.807  4.500 4.100  Left  13  553.8  87.7  -1.897  Right  17  647.1  87.4  2.219  2.050  Left  12  666.7  77.9  2.966  0.650  Right  14  664.3  63.3  3.798  0.100  85.5 14 650.0 Left 8 Sag" " Calculated value of the /-statistic. Level of significance for accepting the null hypothesis H„. ' H : R,, < R (600 m). Ho: R,, > R (600 m).  2.188  2.350  Crest *  8 4  6  {)  (a) Horizontal Curves Combined with Crest Vertical Curves.  (b) Horizontal Curves Combined with Sag Vertical Curves.  Figure 2.10. Participant's Curve Perceptions (Hassan and Easa Visual 2000).  30  3.0 E X P E R I M E N T A L D E S I G N  3.1 Background  As mentioned earlier, the main objective of this thesis is to investigate the validity of Smith and Lamm's hypothesis that horizontal curves overlapped with vertical curves may cause a violation of driver expectancy with respect to the perception of horizontal curvature, potentially increasing the crash risk of the driver (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994).  Secondly, this work endeavors to  develop an empirical model that will predict driver perception of horizontal curvature, based on the presence of specific highway design parameters. Of particular interest is the effect overlapping vertical curves may have on a driver's perception of horizontal curvature.  The framework for the  experimental design is relatively similar to the work of Hassan and Easa (Visual 2000).  However, more curve parameters, finer increments in the  radius of the reference curves, and larger sample sizes were used. In addition a significant increase in the quality of the animations and pictures was made to improve the realism of the road view. Three-Dimensional computer generated road models were created to enable control over the perspective view of the road, thus neutralizing all factors but those to be studied. Although the experimental design evolved over time, the process has been categorized into the following three main areas: (1) Choice of highway design parameters; (2) 3D model creation; and (3) Presentation and data collection design.  31  3.2 Highway Design Parameters  The first issue to resolve was the choice of road characteristics and design parameters to study. Initially, all possible factors that could potentially effect a driver's perception of horizontal curvature were considered. These included: • • • • • • • • • • • • • • • • • • • •  Tangential grades The central angle A The application of transition curves Single vs. multiple transitional curves Length of transition curves Equal vs. unequal spirals (i.e. approach spiral is differentfromthe departing spiral) Simple vs. compound horizontal curves Length of horizontal curve Radius of horizontal curve The superelevation rate The application of vertical curves Sag vs. crest vertical curves Symmetrical vs. asymmetrical vertical curves (i.e. gl = g2 vs. gl g2) Length of vertical curve Start of vertical curve in relation to horizontal curve Highway cross-section configuration (i.e. lane widths, shoulder widths, etc.) Horizontal curve turning direction (left or right) Sight distance (inside of curve) Design speed Night driving (no street lights)  Although not explicitly highway design parameters, the following factors nonetheless may also effect curve perception: • Surrounding topography / structures / vegetation • Visibility (i.e. night vs. day) • Weather Due to time constraints, it wasn't practical to study all of the factors identified above. Therefore, some sort offilteringprocess was required to reduce the list to a manageable, yet meaningfiil, set of parameters to study.  32  After discussion with several geometric design experts, it was decided to select the following: • • • • •  Symmetrical tangential grades (gl = g2) Simple horizontal curves (no spirals) Symmetrical vertical curves Mid-point of vertical curve = mid-point of horizontal curve 2-laned road (x-sectional characteristics based on the road classification and design speed)  In addition to the above design characteristics, the final list of parameters to be studied were as follows: • • • • • • • •  Effect of sag vs. crest curves Effect of horizontal curve radius R Effect of A Effect of K (K = L / A ) Effect of turning direction Effect of e Effect of sight distance Effect of background V  (300 - 700m) (2 - 8%) (25 - 125) (4 - 8%)  Other factors such as the influence of driving at night or the effect of different weather conditions were dropped from consideration due to the difficulties in modeling the parameters in a meaningful way. Considering that this research was conducted in British Columbia, it was also prudent that the factors studied were relevant to the design parameters used by the Ministry of Transportation and Highways (MoTH), although these design values are not much differentfromthe Canadian Standards. MoTH is the authority for all roads in unorganized territory and over specific routes within organized territory. All new roadwork under MoTH's jurisdiction must comply with the standards outlined in their Highway Engineering Design Manual {Highway 1994). Hence, to reflect the practice of road design in B.C., the manual's values were used where appropriate. While Hassan and Easa based the road cross-sectional elements on a design  33  speed of 110 km/h, a 90 km/h design speed was deemed more appropriate for B.C., where the majority of the highway network consists of rural 2-laned roads with posted speed limits of 80 - 90 km/h. Specifically, the crosssectional elements were based on MoTH's Rural Undivided Collector (RUC) road classification (> 450 DHV) which has a 90 km/h design speed. Although MoTH's design manual specifies minimum and maximum values for the highway design parameters according to the road classification and design speed, it was necessary to study the various design parameters with values above or below MoTH guidelines to establish the existence of any relationship between driver perception of curvature and the respective highway design parameters. Where appropriate, comparisons/discussions on the adequacy of MoTH guidelines with respect to the issues investigated in this research will be discussed in Chapter 5. For a 90 km/hr design speed, and the RUC road classification, the MoTH standards specify the following design parameters (Highway 1994): • A minimum horizontal curve radius = 340 m when e^ -6% • A minimum horizontal curve radius = 300 m when e^ = 8 % • A minimum spiral curve length = 80 m when e = 6 % • A minimum spiral curve length = 90 m when e = 8 % • Minimum crest curve K (for 0.150m object) = 90 when L > SSD • Minimum sag curve K (for headlight control) = 40 when L > SSD • Maximum grades of 5 % (rolling topography) and 7 % (mountainous topography) • • • •  Vehicle lane width = 3.6m Shoulder width = 1.5m Normal X-fall = 0.02 m/m Fill slope = 4 to 1  For two-lane roads, the tangent runout length is 20 to 30 m and is normally calculated by multiplying the number of lanes by 15 (Figure 3.1). For  34  example, a 2-lane road would have a tangent runout equal to 30m (15*2 lanes). Since the designed road sections are not constrained by physical topography, either the central angle " A " or the horizontal curve length " L " H  must be assumed to construct the animations {Figure 3.2). If the curve length is assumed constant, then the central angle A will vary. If the central angle A is assumed constant, then the curve length will vary. In practice, the horizontal curve length is usually calculated based on the known central angle, however, to simplify the data entry process, L was assumed constant. H  SC or CS Full Superelevation  TS or SC Normal Runout 1:400 (15*# of lanes]  Full Superelevation development over the Spiral Length  Reverse Crown  Normal Crown by either method Only the station changes  -Tangent Runout at same rate as superelevation through Spiral  Figure 330.J MoTH Supplement to Highway Engineering Design Manual Technical Bulletin DS98004 October 28, 1998 pg 5 of 5  Figure 3.1. Superelevation Development with Tangent Runout Options {Highway 1994).  35 STANDARD Pl  Point of intersection o( the mam tangents  TS  Tangent to Spiral: common point ot tangent and spiral - beginning of Spiral  SC  Spiral to Curve: common pomt of spiral ana circular curve - beginning of Circular curve  CS  Curve to Spiral: common point o( circular curve ana spiral - end ot circular curve  ST.  Spiral to Tangent: common point ot spral and tangent - end ol spiral  SCS  Mid-pcant ot a curve wrucri is transitional  Ihroughout  R  Radius of the circular curve  r  Radius ol a curve at any length on the spiral Length ol spiral between T S and S C Length between any two points on the spiral Tangent distance Pi. to T S . or S T . . apex distance External distance from P.I. to centre o( circular curve portion or to S.C.S. ot a curve transitional throughout  C U R V E WITH TRANSITION B O T H E N D S Figure ( a )  CIRCULAR Figure  CURVE (b)  Arc  Length ol circular curve from S C to C S intersection angle between the tangents ol the entire curve  Ac  Intersection angle between tangents at the S C . ana at the C S or the central angle ot a circular curve  ©s  Spiral Angle: The intersection angle between the tangent ot the complete curve ena the tangent at the S.C.  9  Intersection angle between tangent ot complete curve and tangent at any other point on the spiral  0s  Deflection angle from tangent at T S to S C  0  Deflection angle from tangent at any point on spiral to any other point on spiral  L.T.  Long tangent distance ol spiral only  ST.  Short tangent distance ol spral only  LC  Long chord of the spral curve: distance Irom T S . to S.C.  P  Offset distance Irom the tangent ol P C ol crcuiar curve produced  k  Distance from T S . to point on tangent ooposite the P.C. of the circular curve produced  X.Y  Coordinates ol S.C. from T S .  x.y  Coordinates ot any other point on spral Irom the TS.  Tc  Tangent distance P l to B C or E C  B.C.  Beginning ol Curve  E.C.  End ol curve  Arc  Length o l curve Irom B C to E C  Ac  Intersection angle between the tangents  EC  External distance Irom P i to centre ol c u r v e ;  Figure 340.B M o T H Highway Engineering Design Manual, August 1995, pg 340-3  Figure 3.2. Horizontal Curve Symbols (Highway 1994).  Crcuiar Curve only  36 3.3 Model Creation  The creation of the 3D Road models andfinalanimations involved the use of several computer software programs. Scriptfilesfor the element net of the road surface, side-slopes, delineation, and camera paths (drivers eye) were created (Figure 3.3). These scriptfileswere then subsequently imported into AutoCAD where the element nets were drawn and placed on the appropriate AutoCAD drawing layers (Figure 3.4). The completed AutoCAD drawing files were then imported into 3D Studio MAX for the final stages of the creation process.  The model backgrounds, lighting, element textures and  colors, camera movement, and environmental conditions, as well as the animation (AVI) and image (JPEG) renderings, were produced using 3D StudioMAX.  ; H MftftWfl  S u r f a c e of Combined 3-D Alignment; O c t o b e r 1'tfS V a s s e r Hassan yhassanPgale.lakeheadu.ca e ,i o b nane :? 0B1 r ximum element l e n g t h : ? 5 d t h o f D e l i n e a t i o n : ? .1 i g h t of edges ahoue t h e road s u r f a c e : ? .003  Figure 3.3. Screenshot ofHwysurfl.exe Input Prompts (Hassan et al. Automation 1997).  37  yiew jnsHl Format look Draw Dfneoaonfcioiryfianut  •IESJU]  LzlUMJ  a U l r l * M e | r f | "I"-! * l ^|ft»M  1^"—^d: •6i.4iay.aooai.-35.aM  osiwMODEL  TILE  '•  - •  Figure 3.4. Screenshot of Final AutoCAD Drawing Pavement delineation widths of 100mm were used in accordance with MoTH's Pavement Marking Manual (Pavement 1994). The driver's view of the road was simulated by positioning a camera 1.45m to the right of the centerline and 1.05m above the surface of the road (Zwahlen and Schnell Driver 1999, Highway 1994). Each road section created was 1000m in length (two 400m tangents connected by a 200m long horizontal curve). For the animations, the camera (driver's eye) was required to travel along the road at 90 km/hr (design speed). Therefore, with an animation playback speed of 15 frames-per-second (fps), and a road length of 1000m, a total of 600 animation keyframes were necessary to simulate driving along the road at 90 km/hr. A total of 40 test-curves and 70 reference/comparison-curves were created for  38  this experiment. Where the test-curves were roads that had horizontal curves overlapped with a vertical curve, and the reference/comparison curves were roads that had horizontal curves with no overlapping vertical curve. Tables 3.1 & 3.2 summarize the design parameters for each road section created.  Table 3.1. Test-Curve Road Design Parameters Test Curves - SAG  Test Curves - CREST Vertical Animation Curve File A% K% Length Number Base Case and Effect of R 400 4 100 001 1  Horiz. Curve Radius  Horiz. Curve Length  e  300  200  6  Horiz. Curve Radius  Horiz. Curve Length  e  Base Case and Effect of R 200 4 50 022 200 4 50 023  300  200  6  400  200  6  50  200  500  200  6  Animation File Number  A%  K%  Vertical Curve Length  002  4  100  400  400  200  6  003  4  100  400  500  200  6  024  4  004  4  100  400  600  200  6  025  4  50  200  600  200  6  005  4  100  400  700  200  6  026  4  50  200  700  200  6  Effect of A  Effect of A 2  006  6  007  100 100  200 600  500 500  200  6  027  2  50  100  500  200  6  200  6  028  6  50  300  500  200  6  029  8  50  400  500  200  6  25  100  500  200  6  75  300  500  200  6  125  500  500  200  6 6  8  100  800  500  200  6  009  4  50  200  500  200  6  030  010  4  75  300  500  200  6  031  4 4  011  4  125  500  500  200  6  032  4  008  Effect of K  Effect of K  Effect o f L e f t T u r n 4 012 100 4  013  4  014  100 100  Effect of Left T u r n 400 400 400  300 500 700  200  6  4  50 50  200 200  300 500  200  6  033 034  4  200 200  200  6  6  035  4  50  200  700  200  6  4  50  200  500  200  4  4  50  200  500  200  8  Effect of e  Effect of e 4  015  4  016  100 100  400 400  500 500  200 200  4 8  018  2  4 4  100 100  400  500  200  6  038  1  400  500  200  6  039  2  200  6  019 020 1  2  4  4 4  100  040  3  6  041  4  100  4  50  200  500  200  6  4  50  200  500  200  6  Effect of B a c k g r o u n d  Effect of Background 3  037  E f f e c t o f Sight D i s t a n c e  Effect o f Sight D i s t a n c e 017*  036  400 400  500 500  200  4 second P V S D (100m) - standard fog added 12 second P V S D (300m) - standard fog added  4  50  200  500  200  6  4  50  200  500  200  6  Photo Sky ( K C S - S K Y 3 ) 4  Computer Generated Sky  39  Table 3.2. Reference-Curve Road Design Parameters  Reference Curves File No.  File No.  R  R  File No.  R n  R.  [Right Turn 043 044 045 046 047 048 049 050 051 052 053 054 055 055b  200 250 300 350 400 450 500 550 600 650 700 750 800 900  200 200 200 200 200 200 200 200 200 200 200 200 200 200  6 6  056  200  200  6  079a  300  200  6  4 second PVSD (100m)  057  250  200  6  079  400  200  6  12 second P V S D (300m)  080  450  200  6  Photo Sky ( K C S - S K Y 3 )  500 550 600 700 300 400 450 500 550 600 650  200 200 200 200 200 200 200 200 200 200 200  6  Computer Sky  6  6 6 6  6 6 6 6 6  6 6 6  |Left Turn  058  300  200  059 060 061 062 063 064 065 066 067 068 068b  350 400 450 500 550 600 650 700 750 800 900  200 200 200 200 200 200 200 200 200 200 200  6 6  6 6 6  6 6 6  6 6 6 6  RI  Effect of e 300 200 069a 400 200 069 450 200 070 500 200 071 200 072 550 200 073 600 200 073b 700 300 200 074a 400 200 074 450 200 075 500 200 076 200 077 550 200 600 078 200 700 078b Effect of Sight Distance  081 082 083 083b 084a 084 085 « 086 c 087 55 088 088b  4 4 4 4 4 4 4  H  L  Effect of Background 089a 300 200 400 200 089 450 200 « 090 500 200 091 200 8 092 550 200 093 600 200 093b 700 094a 300 200 094 400 200 Z 095 450 200 096 500 200 55 097 550 200 098 600 200 98b 700 200  I  6 6 6 6 6 6 6  1  6 6  6 6 6 6  6 6 6 6  40  3.4 Presentation & Data Collection Design  One of the biggest challenges was designing the experiment's presentation format. Determining the animation and image resolutions, animation lengths, element colors and textures, output formats, etc., was quite difficult and for the most part, the process was that of trial and error. While the goal was to make the models look as real as possible, the more complex the model is, with respect to lighting, textures, etc., the longer it would take to create a final road animation.  Several test animations were created before the final textures,  background, colors, and other environmental effects were chosen. Another critical design aspect was how the animations would be presented to the participants and how and what type of data would be collected. The initial thought was to present the animations similar to Hassan and Easa's experiment, where one test-curve animation  (Ra t C  =  600m) was viewed,  followed by the three different reference-curve animations (Rp = 500m, 600m, and 700m). However, because this thesis involved the study of more design parameters with larger ranges, instead of three reference-curves, at least five reference-curves would have had to be viewed to maintain the same format as Hassan and Easa's experiment. It was felt that five reference-curves were too many, and after much consideration, it was decided to split the experiment into two phases. Phase I would focus on validating the hypothesis that horizontal curves overlapped with crest curves appear sharper, and that horizontal curves overlapped with sag curves appear less sharp than if the horizontal curve was not overlapped with a vertical curve. It was expected that the results of Phase I would justify the use of only three reference-curves for Phase II. Phase II would be used to record the perceived horizontal radii similar to Hassan and Easa's experiment, with the exception that the reference-curves would depend on whether the test-curve was overlapped with a crest or sag vertical curve.  41  Reference-curves for test-curves overlapped with a crest vertical curve would have horizontal curve radii equal to or less than (sharper) the test-curve, while the reference-curves for test-curves overlapped with a sag vertical curve would have horizontal curve radii equal to or greater than (less sharp) the test-curve. Thus, if the hypothesis in Phase I is accepted, then most of the driver population would perceive horizontal curves overlapped with a crest curve as equal to, or sharper than, that same horizontal curve without an overlapping crest curve, and conversely, that horizontal curves overlapped with sag curves would be perceived as equal to, or not as sharp as a horizontal curve without the presence of an overlapping sag curve. Microsoft FrontPage 2000 was used to create a web based presentation format (although not published online). It was also decided to investigate if participant perception would be different if they viewed static or dynamic presentations. The advantage of being able to use still images is two-fold: they are faster to create, and hard copies of the images can be created, enabling easier dissemination of the material to participants (i.e. a computer is not required to perform the experiment).  Zakowska (1999) investigated the validity of available presentation techniques for their usefulness in testing and evaluating the spatial road view. The laboratory presentation techniques were either static (2D) or dynamic (3D) methods of road perception, depending on the scope and objective of the study. A literature review by Zakowska (1999) found that static stimuli were used to evaluate curve direction, deflection, and curvature, and that 2D simulation in such research was acceptable.  For dynamic road view  presentations, video or computer-generated views were used. Zakowska (1999) found that drivers could discriminate different levels of curvature and curve angle better when such assessments were based on moving road views,  42  rather than when based on still pictures. In general, he felt that the choice of the visualization technique should depend on the particular design problem but recommended the use of computer-generated images when possible.  3.4.1 Phase I Design  The purpose of Phase I was to investigate the validity of the hypothesis that horizontal curve perception is effected by overlapping vertical curves. The setup for Phase I was simple. Participants would view two road animations/images per page (Figure 3.5). Both roads would have the same horizontal curve radii but one road would have an overlapping vertical curve (test-curve). The participants were asked if one of the roads appeared to have a sharper curve than the other, or if the road curves appeared to have the same horizontal radii.  Although a standardized randomization routine was not  used, the test-curve presentation order was initially randomized to maximize the contrast between subsequent road views.  Therefore each participant  viewed the same non-sequential sequence of road animations/images. The responses were then manually recorded on the questionnaire/response form shown in Figure 3.6. In addition, other personal characteristics such as gender, age, driving experience, etc. were also collected.  43  44  PHASE I - HUMAN PERCEPTION OF HORIZONTAL CURVATURE PURPOSE:  To determine how-various roaddesjgnparameters may effect the perception ofhcirizontal curvature. • Male • Female  PERSONAL: Gender:  • 16 to 2:5 yrs  Age:  D 26 to 40 • 41 to 60  • 61 and over  Residence (city): DRIVER:  Do you wear glasses or contact lenses for driving?  • Yes • No  Have you completed any driver educational courses?  • Yes  • No  How manyyears of driving experience do youhave? • Everyday • More than once per week • About once per week • About once per month • About once per year O Never • Less than 1 hour • 1 to 2 hours  How often do you drive on highways?  What duration is your average highway trip?  •  2to3hours  • D • •  3 to 4 hours 4to 6 hours 6 to 12 hours over 12 hours  OBSERVED RESULTS: Record whether the Cornparison Curve(C.C) appears More Sharp, Less sharp, or the Same as the Test Curve I M A G E  A N I M A T I O N S C C . C C . is  C C .  is  s cc.  is  is  u  L  s  001  M  L  s  022  M  L  s  023  M  L  s  002  M  L  S :  023  M  L  8  s  024  M  L  s  003  M  L  s  024  M  L  S  L  s  028  M  L  8  004  M  L  s  02-3  M  L  s  M  L  s  020  M  L  S  005  M  L  s  020  M  L  s  DOS  M  L  ~~s  027  M  L  s  000  M  L  8  027  M  L  8  007  M  L  s  028  M  L  s  007  M  L  s  026  M  L  s  OOS  M  L  s  02S  M  L  8  003  M  L  s  020  M  L  s  000  M  L  s  030  M  L  S~j  009  U  L  8  030  M  L  8  010  M  L  s  031  W  L  8  |  010  M  L  8  031  M  L  s  011  M  L  8  032  M  L  8  jj  011  M  L  S  032  M  L  s  012 013  M M  L  033 034  M M  L  S  L L  8  8  033 034  L  8  M M  M  L  012 013  8  L  s s  M  L  s  014  M  L  s  03S  M  L  s  014  M  L  s  035  M  L  s  01S  M  L  s  038  M  L  S  01S  M  L  S  038  M  L  s  010  M  L  s  037  M  L  s  010  M  L  8  037  M  L  017 '  M  L  s  038  M  L  8  017  M  L  S  038  M  L  s  018  M  L  s  039  M  L  S  018  M  L  8  030  M  L  s  010  M  L  s  040  M  U  010  M  L  8  040  M~ L  s  020  M  L  s  041  M  L  020  M  L  8  041  M  L  8  001  M  L  s  022  002  M  L  s  003  M  L  004  M  006  |  i  -  i  s  [  Figure 3.6. Phase I Questionnaire & Data Collection Sheet.  45  Both the still images and ariimations had a resolution of 600x300 pixels. The still images represented the view from a vehicle 100m in advance of the horizontal curve (BC), which equates to a preview time of 4 seconds for a vehicle traveling at 90km/hr. The only exception was for files 017 & 038 (and their corresponding reference curves) that limited the driver's sight distance to only 100m. The imagesfromthesefilesrepresented a vehicle 25m in advance of the horizontal curve (BC).  The animations started at a vehicle  position 150m before the BC and ended at the BC.  Initially, full-length  animations were created at a resolution of 800x400, however, feedback from the control group indicated that it was too difficult for the participants to remember their impressions of test-curve horizontal curvature after viewing the three reference-curves. They suggested that curve comparisons would be easier if the animations were on the same page and were shorter. Since the issue under investigation was a driver's perception of an approaching horizontal curve, the animations were shortened to show just the approach to the curve. It was argued that drivers made their speed choice based on their curve perception prior to actually reaching the curve. Once the curve was reached, their decision (good or bad) had already been made.  Table 3.3  summarizes the test-curve reference-curve combinations used in the Phase I setup, while the results of Phase I are presented in Chapter 4. 3.4.2 Phase II Design  The purpose of Phase II was to collect data that would enable the development of a model to predict how drivers perceive horizontal curvature based on the presence of specific highway design parameters (i.e. overlapping vertical curves). The presentation setup for Phase II involved showing one test-curve and three reference-curves (Figure 3.7).  46 Table 3.3. Phase I Setup.  Bl  REF. CURVE No.  TEST  IT' 061 002  SI i*iCJ|R\JL  022 02"  mil  045 047 049 051  005 006  053 049  n'f  mr  049  OOS  049 049 049  II  049 058 062  n  003  009  010 011  012 on 014  REF. C U R V E No.  UN  02 ^  045 047 049 051 053  027  . 049 049  w  049 049 049  OV) 031 033 031  i -  049 058 062  n  OIK  076 081 086  066 071 076  038 039  081 086  ul"  091  040  096  IPWo4itiig£  091 096  066 071  01 ^ 016 017  - ' i020H^  036  N O T E : see Tables 3.1 & 3.2 for curve details  Images Frame N o . 180 ( 100m before P C )  600 x 300 resolution .  ( except Image #17 + #38 where frame #225 was u s e d )  Animations  600 x 300 resolution  Frame N o . 150 to 240 ( w h e r e frame # 150 is 150m before P C & frame # 240 is at the P C )  One of the reference-curves had horizontal radii equal to that of the test-curve. The other two reference-curves had horizontal curve radii, either less than (crest) or greater than (sag) the test-curve horizontal curve radius, depending on whether the test-curve was overlapped with a crest or sag vertical curve.  47 This assumption was justified by the results of Phase I and further confirmed by the results of Phase II.  Four animations/images were required to be  presented on each web page. To do this, the animation/image resolution had to be reduced to 400x200 from 600x300 pixels. Table 3.4 summarizes the test-curve reference-curve combinations for the Phase II setup.  Figure 3.7. Screenshot of Phase II Presentation.  48  Table 3.4. Phase II Setup REF. II M | G u K v e * N ^ Curve No. 045 044 001 043 047 045 002 043 049 003 047 045 051 004 . 049 047 053 00-< 051 049 049 (H 047 045 049 007 047 045 049 047 045 049 Ml 1 047 045 049 047 010 045 II  III  IS  REF. TIM *Curve°No.i C u r v e N o . 049 047 H 1 045 058 057 012 056 062 060 i'l • 058 066 014 064 062 071 069 on 69a 076 <>l< 074 74a 081 017 079 79a 086 018 084 84a 091 089 89a 096 094 020 94a  MSI ( HIM  No  022  023  02^ 026  028  030 03|  REF. Curve No. 045 047 049 047 049 051 049 051 053 051 053 055 053 055 55b 049 051 053 049 051 053 049 051 053 049 051 053 049 051 053  II s | ( IIIW  No  0 '2  II  03 4 0 3-> 0 (  REF. Curve No. 049 051 053 058 060 062 062 064 068 066 068 68b 071 073 73b 076 078 78b 081 083 83b 086 088 88b 091 093 93b 096 098 98b  400 x 200 resolution Animations 400 x 200 resolution Images Frame N o . 150 to 240 Frame N o . 180 ( 100m before P C ) frame N o . 150 is 150m before P C frame N o . 225 used for Image #17 + #38 frame N o . 240 is at the P C  Each participant was asked to choose one of the three roads on the right (Figure 3.7) that had a horizontal curve most similar to that of the test-curve road on the left.  The participants identified their choice by simply stating  "Top", "Middle", or "Bottom" with reference to the position of the road on the right that had the most similar horizontal radius to the test-curve on the left. Thus the perceived radius R was recorded for a known horizontal curve p  radius R.  The responses were once again manually recorded on a  questionnaire/ response form similar to Phase I. The results of Phase II are presented in Chapter 4, while Chapter 5 describes the data analysis.  49  4.0 E X P E R I M E N T A L R E S U L T S  4.1 Phase I Results  As previously stated, Phase I investigated the hypothesis that horizontal curves appear sharper when overlapped with a crest curve and appear less sharp when overlapped with a sag curve compared to a horizontal curve without an overlapping vertical curve. The participants viewed both a testcurve and a reference-curve.  Each pair of roads viewed had the same  horizontal curve radii, but the test-curve had an overlapping vertical curve. The participants were asked if the reference-curve appeared less sharp, sharper, or about the same as the horizontal curve shown in the test-curve. Thus the responses provided a qualitative means of assessing the validity of the hypothesis. Each participant, ranging in age from 16 yrs to 61+ yrs, viewed the same non-sequential sequence of road animations/images. A total of 80 responses were collected per participant , 40 for the animations and 40 for the 2  images.  A total of 81 people viewed the ariimation presentations and 91  people viewed the static image presentations. The parameters investigated, in addition to the effect of overlapping vertical curves on the perception of horizontal curvature, included: • • • •  2  Effect of Horizontal Radius Effect of K (K = L/A) Effect of Turning Direction Effect of Background  10 participants viewed only the static presentation  • • • •  Effect of A (|gl - g2|) Effect of e Effect of Sight Distance Dynamic vs. Static Presentation  50  Tables 4.1 and 4.2 summarize the experimental results for Phase I. File numbers 001 - 020 have overlapping crest curves while file numbers 022 041 have overlapping sag curves. If the hypothesis is valid, the frequency of responses of R  and Rp >  = Ract  for  R  p  p  > Ract  < Ract  for files 001-  Ract responses.  020  should be considerably larger than Rp  For files 022  - 041,  the frequency of responses  should be considerably larger than the  R  p  < Ract  and R  p  = Ract  responses. Figures 4.1 through 4.22 are the graphical representations of Tables 4.1 and 4.2 that focus on the respective parameter being investigated. Although the frequency was lower than expected, 76% of the respondents perceived horizontal curvature inaccurately when an overlapping vertical curve was present.  Effect of Overlapping Vertical Curve (Figure 4.1.) The results suggest that an overlapping vertical curve causes an erroneous perception of horizontal curvature. A key factor is the available sight distance, which explains why this "optical illusion" is more prevalent for overlapping sag curves than for overlapping crest curves. This applies to all parameters except for K, where the two parameters interact opposite to each other: as K increases the vertical alignment becomes flatter and the sight distance increases.  The experimental data identified that approximately 50% of the  sample population thought curves and approximately  R  p  < Ract  60%  when crest curves overlap a horizontal  of the sample population thought  Rp > Ra t C  when sag curves overlap a horizontal curve. More insight into the effect of vertical curves on perception is provided in the following sections.  51  Effect of R (Figures 4.2 - 4.4)  The results suggest that as the horizontal curve radius increases, the effect of an overlapping vertical curve on the perception of horizontal curvature becomes more pronounced and therefore more drivers will perceive the horizontal curve incorrectly.  Effect of A (Figures 4.5 - 4.7)  The results suggest that as the algebraic sum of the tangents increase, the effect of an overlapping vertical curve on the perception of horizontal curvature becomes more pronounced and therefore more drivers will perceive the horizontal curve incorrectly.  Effect of K (Figures 4.8 - 4.10)  The results suggest that as K decreases, the effect of an overlapping vertical curve on the perception of horizontal curvature becomes more pronounced and therefore more drivers will perceive the horizontal curve incorrectly.  Effect of Turning Direction (Figures 4.11 - 4.13)  The results suggest that turning direction doesn't seem to have an effect on the horizontal curve perception when an overlapping vertical curve is present.  Effect of e (Figures 4.14 - 4.16)  The results suggest that the maximum superelevation rate doesn't seem to have an effect on the horizontal curve perception when an overlapping vertical curve is present.  52  Effect of Sight Distance (Figures 4.17 - 4.19)  The results suggest that a sufficient amount of sight distance is necessary (somewhere between 100m and 300m) for this phenomenon to exist. As a driver's sight distance increases beyond 100m, the effect of an overlapping vertical curve on the perception of horizontal curvature becomes more pronounced and therefore more drivers will perceive the horizontal curve incorrectly.  The results also indicated that sag vertical curves were more  sensitive to the effects of sight distance than crest curves.  Effect of the Background Image (Figures 4.20 - 4.22)  The results do suggest that the background image can effect curve perception. What was surprising is that the trend observed for the crest curves was opposite the trend observed for the sag curves.  53  Table 4.1. Summation of Responses to Road Animation (Dynamic) Presentations - Phase I ANIMATIONS Sample Size  82  82  82  81  81  81  82  81  81  82  81  81  82  81  81  81  81  81  81  81  File No.  001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020  Rp < Ract  0.44 0.41 0.60 0.59 0.60 0.42 0.54 0.68 0.68 0.56 0.48 0.46 0.52 0.59 0.48 0.52 0.09 0.42 0.46 0.44 0.29 0.38 0.21 0.25 0.25 0.42 0.18 0.16 0.16 0.16 0.32 0.36 0.24 0.26 0.31 0.27 0.80 0.38 0.30 0.33 0.27 0.21 0.20 0.16 0.15 0.16 0.28 0.16 0.16 0.28 0.20 0.19 0.23 0.15 0.21 0.21 0.11 0.20 0.25 0.22  Rp  =  Ract  Rp  >  Ract  Sample Size File No. Rp  <  Ract  Rp  =  Ract  Rp  >  Ract  82  82  82  82  82  81  81  81  81  81  81  82  81  81  81  81  81  81  81  81  022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041  0.16 0.15 0.09 0.17 0.11 0.15 0.11 0.09 0.14 0.10 0.11 0.20 0.14 0.17 0.20 0.12 0.16 0.27 0.16 0.19 0.32 0.18 0.26 0.18 0.17 0.37 0.11 0.10 0.12 0.26 0.30 0.38 0.28 0.20 0.12 0.20 0.73 0.28 0.14 0.07 0.52 0.67 0.66 0.65 0.72 0.48 0.78 0.81 0.74 0.64 0.59 0.43 0.58 0.63 0.68 0.68 0.11 0.44 0.70 0.74  Table 4.2. Summation of Responses to Road Image (Static) Presentations - Phase I IMAGES - Sample Size  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  File No.  001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020  Rp ^ R a c t  0:41 0.36 0.52 0.46 0:59 0.35 0.44 0.52 0.48 0.48 0.43 0.40 0.55 0.53 0.48 0.46 0.09 0.34 0.41 0.41 0.24 0.33 0.19 0.27 0:12 0.52 0.19 0.12 0.20 0.25 0.43 0.31 0,14 0.26 0.22 0.21 0.86 0.25 0.30 0.29 0.35 0.31 0.30 0.26 0.29 0.13 0.37 0.36 0.32 0.26 0.14 0.30 0.31 0.21 0.30 0.33 0.05 0.41 0.30 0.31  Rp  =  Ract  Rp^Ract  Sample Size File No. Rp  K  Ract  Rp  =  Ract  Rp  >  Ract  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041  0.15 0.11 0.13 0.12 0.090.07 0.10 0.13 0.13 0.08 0.10 0.13 0.18 0.15 0.09 0.09 0.07 0.22 0.21 0.20 0.32 0.31 0.32 0.18 0.11 0.46 0.22 0.19 0.23 0.31 0.35 0.36 0.16 0.16 0.22 0.31 0.89 0.36 0.19 0.12 0.53 0.58 0.55 0.70 0.80 0.470.68 0.68 0.64 0.62 0.55 0.51 0.66 0.68 0.69 0.60 0.04 0.42 0.60 0.68  54  Rp < R  Rp = R  Rp > R  Perceived Curvature Rp (a) crest combinations (excluding files 017 & 018 responses).  Rp < R  Rp = R  Rp > R  Perceived Curvature Rp (b) sag combinations (excluding files 038 & 039 responses).  Figure 4.1. Effect of Vertical Alignment on Perceived Horizontal Curve Radius - Phase I.  55  R p < Rai  80%  O  60%  o  O o  40% -  «  O Rp, Animations o Rp, Images  20% 0% 200  300  400  500  600  700  800  Horizontal Curve Radius R (m) (a) crest combinations (files 001-005).  R p > R  a  o O  80% H  O  60%  o  O o  40%  0 Rp, Animations o Rp, Images  20% 0% 200  300  400  500  600  700  800  Horizontal Curve Radius R (m) (b) sag combinations (files 022 - 026).  Figure 4.2. Effect of R on Perceived Horiz.Curve Radius (expected response) - Phase I.  O Rp, Animations o Rp, Images  O o  o o  o o  200  300  400  500  600  700  800  Horizontal Curve Radius R (m) (a) crest combinations (files 001-005).  O Rp, Animations  -  o Rp, Images  0  O  o O 0  O o  1 200  300  400  500  600  i  700  800  Horizontal Curve Radius R (m) (b) sag combinations (files 022 - 026).  Figure 4.3. Effect of R on Perceived Horiz.Curve Radius (R = R ^ - Phase I. p  57  Rp R-act >  200  300  400  500  600  700  800  Horizontal Curve Radius R (m) (a) crest combinations (files 001-005).  Rp Ract <  80% O Rp, Animations u  60% -  o Rp, Images  c  40% —  20%  O  o  O o  500  600  0% 200  300  400  700  800  Horizontal Curve Radius R (m) (b) sag combinations (files 022 - 026).  Figure 4.4. Effect of R on Perceived Horiz.Curve Radius (R opposite to expected) - Phase I. p  58 Rp Ract <  80% i  O o  60% 0>  O o  U_  O Rp, Animations  20%  o Rp, Images  0% 4  6  10  A(%)  (a) crest combinations (files 006, 003,007, 008).  >  60%  a  I  Ract  O o  o  o  o  40%  O Rp, Animations  u,  o Rp, Images  20% 0% 4  6  10  A(%) (b) sag combinations (files 027, 024, 028, 029).  Figure 4.5. Effect of A on Perceived HorizXurve Radius (expected response) - Phase I.  59  80% 60% -  3 3" OJ  O Rp, Animations  o  c  40% -  o R p , Images  O  — —  20% 0% 4  0  10  (a) crest combinations (files 006, 003, 007, 008).  80%  60%  O Rp, Animations o Rp, Images  o  40%  O  20% H  o O  o O  0%  —i—  0  4  6  8  10  A(%) (b) sag combinations (files 027, 024, 028, 029).  Figure 4.6. Effect of A on Perceived Horiz.Curve Radius (R = R ^ - Phase I. p  6(1  Rp Ract >  rs  60%  zz u  ar  (a) crest combinations (files 006, 003, 007, 008).  Rp Ract <  80%  60%  O Rp, Animations o Rp, Images  cr u  40%  20%  4 o  o  O  O 0% 0  2  4  6  8  10  A(%) (b) sag combinations (files 027, 024, 028, 029).  Figure 4.7. Effect of A on Perceived Horiz.Curve Radius (R opposite to expected) - Phase I. p  61  Rp Ract <  80%  O o  60%  O o  40%  O Rp, Animations  20%  o Rp, Images 0% 25  50  75  100  125  150  K (a) crest combinations (files 009, 010, 003, 011).  Rp> Ract  80% 60%  -I  40% O Rp, Animations o Rp, Images  20% 0% 25  50  75  100  125  150  K  (b) sag combinations (files 030, 024, 031, 032).  Figure 4.8. Effect of K on Perceived Horiz.Curve Radius (expected response) - Phase I.  62  80%  >» o c 35  O Rp, Animations o Rp, Images  60%  o  40%  O  o  20%  d  O  0%  i  —•— •• i  25  50  75  125  100  150  K  (a) crest combinations (files 009, 010, 003, 011).  25  50  75  125  100  150  K  (b) sag combinations (files 030, 024, 031, 032).  Figure 4.9. Effect of K on Perceived Horiz.Curve Radius (R = R ^ - Phase I. p  63  Rp Ract >  80% -  a  ORp, Animations o Rp, Images  60% -  B  3  s CT  40% O  20%  O  o  o  0% 0  25  75  50  125  100  150  K (a) crest combinations (files 009, 010, 003, 011).  Rp Ract <  O Rp, Animations  -  o Rp, Images  c S  40% -  s-  20%  0 0%  $  1  1  1  1  !  25  50  75  100  125  150  K  (b) sag combinations (files 030, 024,031, 032).  Figure 4.10. Effect of K on Perceived Horiz-Curve Radius (R opposite to expected) - Phase I. p  64  Rp Ract <  80% O  60%  •  c  B Er  o  40%  o o O Rp, Animations o Rp, Images  20% 0% 6  10  e(%) (a) crest combinations (files 003, 015, 016).  Rp Ract >  80% o d 3  s  60%  o  o  o  o  40% O Rp, Animations  20%  o Rp, Images -  0% 4  6  10  e(%) (b) sag combinations (files 024, 036, 037).  Figure 4.11. Effect of e on Perceived Horiz.Curve Radius (expected response) - Phase I.  65  80%  4.  O Rp, Animations  60%  o Rp, Images 40% 20%  4  O o  O o  0 %  6  10  e(%)  (a) crest combinations (files 003, 015, 016).  80% .  O Rp, Animations  60%  o Rp, Images  u  s r  4 0 %  tr.  o 2 0 %  -\  O 10  0 %  e(7b (b) sag combinations (files 024, 036, 037).  Figure 4.12. Effect of e on Perceived Horiz.Curve Radius (R = R ^ - Phase I. p  66  Rp Ract >  cOJ 3  e(%)  (a) crest combinations (files 003, 015, 016).  Rp < Ract  80%  I  3 —  60%  O Rp, Animations o Rp, Images  40% 20% 0%  O o  o O  T~ 10  4  e(% (b) sag combinations (files 024, 036, 037).  Figure 4.13. Effect of e on Perceived Horiz.Curve Radius (R opposite to expected) - Phase I . p  Rp act <  R  80% 60% H 6  f  40% 20% i  o  O Rp, Animations RT  o • Rp, Animations L T  o Rp, Images RT  A Rp, Images LT  0% 100  300  700  500  Horizontal Curve Radius R (m)  (a) crest combinations (files 001, 012, 003, 013, 005, 014).  Rp Ract >  o  80% 60%  •  *  8  •  40% 20%  O Rp, Animations RT  • Rp, Animations LT  o Rp, Images RT  A Rp, Images L T  0% 200  300  400  500  600  700  800  Horizontal Curve Radius R (m)  (b) sag combinations (files 022, 033, 024, 034, 026, 035).  Figure 4.14. Effect of Turning Direction on Perceived Horiz.Curve Radius (expected response) - Phase I.  80% 60%  O Rp, Animations RT  • Rp, Animations L T  o Rp, Images RT  A Rp, Image LT  40% -  4  o  20% -  o 0% 100  300  500  700  Horizontal Curve Radius R (m)  (a) crest combinations (files 001, 012, 003, 013, 005, 014).  100  300  500  700  Horizontal Curve Radius R (m)  (b) sag combinations (files 022, 033, 024, 034, 026, 035).  Figure 4.15. Effect of Turning Direction on Perceived Horiz.Curve Radius (R = R ^ - Phase I. p  Rp act >  100  R  300  500  700  Horizontal Curve Radius R (m)  (a) crest combinations (files 001, 012, 003, 013, 005, 014).  Rp Ract <  80% 60%  O Rp, Animations RT  • Rp, Animations L T  o Rp, Images RT  A Rp, Images L T  40% 20% i 0% 300  100  500  s  o  700  Horizontal Curve Radius R (m) (b) sag combinations (files 022, 033, 024, 034, 026, 035).  Figure 4.16. Effect of Turning Direction on Perceived Horiz.Curve Radius (R opposite to expected) - Phase I. p  Rp Ract <  100% 80% 4  O Rp, Animations o Rp, Images  60%  O o  40% 20% 0% 0  200  400  600  800  1000  Sight Distance (m)  (a) crest combinations (files 003, 017, 018).  Rp Ract >  100% 80%  o  60%  o  40% O Rp, Animations 20% 0%  o Rp, Images  o o  200  400  600  800  1000  Sight Distance (m)  (b) sag combinations (files 024, 038, 039).  Figure 4.17. Effect of Sight Distance on Perceived Horiz.Curve Radius (expected response) - Phase I.  100% 80% O Rp, Animations  60% 40%  o Rp, Images  4  O o  20% 0% 0  200  400  1000  800  600  Sight Distance (m)  (a) crest combinations (files 003, 017, 018).  100% o  80%  O 60%  O Rp, Animations o Rp, Images  -  40%  o  o  O  O  20% 0%  1  1  1  200  1 400  1  1 600  1  1 800  1  1 1000  Sight Distance (m) (b) sag combinations (files 024, 038, 039).  Figure 4.18. Effect of Sight Distance on Perceived Horiz.Curve Radius (R = R )- Phase I. p  act  Rp Ract >  100% 80% O R p , Animations 60%  o Rp, Images  40%  o  O  o  20%  200  400  800  600  1000  Sight Distance (m)  (a) crest combinations (files 003, 017, 018).  Rp Ract <  100% 80% O Rp, Animations 60%  o Rp, Images  40% 20%  m 200  400  600  800  1000  Sight Distance (m) (b) sag combinations (files 024, 038, 039).  F i g u r e 4.19. Effect o f Sight Distance o n Perceived H o r i z . C u r v e R a d i u s (R  p  o p p o s i t e to e x p e c t e d ) - P h a s e I.  Rp Ract >  -I  80%  O Rp, Animations 60%  o Rp, Images  40%  o  A  20%  o  o  O  O  Mnt  Sky  O  0% Sky#2  Background Image  (a) crest combinations (files 003, 019, 020).  Rp * Ract 1  80%  O  60%  o  O  O  o  o  40%  ORp,  Animations  o Rp, Images  20% 0% Mnt  Sky  Sky #2  Background Image  (b) sag combinations (files 024, 040, 041).  Figure 4.20. Effect of Background on Perceived Horiz.Curve Radius (expected response) - Phase I.  O Rp, Animations o Rp, Images  O o  O o  Sky #2  Sky  Mnt  Background Image  (a) crest combinations (files 003, 019, 020).  80% 60%  O Rp, Animations o Rp, Images  40% 20% 0%  o O o O i  i  i  Mnt  o O i  Sky  Sky #2  Background Image  (b) sag combinations (files 024, 040, 041).  Figure 4.21. Effect of Background on Perceived HorizXurve Radius (R = Rac*)-PhaseI. p  Rp act <  R  80%  O Rp, Animations o Rp, Images  60% 40% 20% 0% Mnt  Sky #2  Sky Background Image  (a) crest combinations (files 003, 019, 020).  Rp Ract <  80% 60%  O Rp, Animations o Rp, Images  40% o  20% -j o  O  Mnt  Sky  O 0%  Sky #2  Background Image (b) sag combinations (files 024, 040, 041).  Figure 4.22. Effect of Background on Perceived Horiz.Curve Radius (R opposite to expected) - Phase I. p  76  4.2 Phase II Results  Phase II of the experiment endeavored not only to substantiate the findings of Phase I, but to develop a prediction model of a driver's perception of horizontal curvature based on the presence of specific highway design parameters. Each participant compared three reference-curves to one testcurve for each of the forty presentations (see Chapter 3 Section 3.4). Similar to Phase I, each participant viewed the same non-sequential sequence of road images for a total of 40 responses per participant. A total of 90 people aged 16yrs to 61+ yrs were sampled. The parameters investigated were the same as in Phase I with the exception that only static presentations were used. Table 4.3 summarizes the experimental results for Phase II.  Once again, if the  hypothesis is valid, the responsefrequencyof  for files 001- 020  should be considerably less than the sum of R  p  R  = Ract  p  < Ra t C  and R  p  Forfiles022 through 041, thefrequencyof responses for R considerably less than the cumulative  R  p  > Ract  and R  p  »  « p  Ract = Ra Ract  Ct  responses. should be  responses.  Figures 4.23 through 4.30 are the graphical representations of Table 4.3 that focus on the respective parameter being investigated. Effect of Overlapping Vertical Curve (Figure 4.23)  The results show that overlapping crest curves cause the perceived horizontal radius to be less than the actual curve radius and overlapping sag curves cause the perceived horizontal radius to be greater than the actual curve.  Effect of R (Figure 4.24)  The results suggest that a horizontal curve radius of 500m appears to be a critical value for curve perception. In addition there appears to be opposite trends for overlapping crest and sag vertical curve. When crest curves are  77  overlapping horizontal curves, more drivers experience the "optical illusion" as R decreases from 500m to 300m, whereas there is a minimal effect as R increasesfrom500m to 700m.  When sag curves are overlapping the "optical  illusion increases as R increases from 300m to 500m but there is little change in the responsefrequencyas R increasesfrom500m to 700m.  Effect of A (Figure 4.25)  The results suggest that A is not an important factor in curve perception.  Effect of K (Figure 4.26)  The results suggest that K is not an important factor in curve perception.  Effect of Turning Direction (Figure 4.27)  The results suggest that turning direction seems to have an effect on the horizontal curve perception when an overlapping vertical curve is present, but only for specific horizontal radii and/or the type of overlapping vertical curve.  Effect of e (Figure 4.28)  The results suggest that e is not an important factor in curve perception.  Effect of Sight Distance (Figure 4.29)  The results suggest that sight distance can influence curve perception, particularly when overlapping sag curves are present. Effect of the Background Image (Figure 4.30)  The results suggest that the background image is an issue when sag curves are present but not when crest curves are present.  78  T a b l e 4.3. S u m m a t i o n o f R e s p o n s e s t o R o a d I m a g e ( S t a t i c ) P r e s e n t a t i o n s - P h a s e I I  IMAGES Files 001 - 020 have an overlapping crest curve and files 022 - 041 have an overlapping sag curve. Sample Size File No. A% K Lv R 1*  e Sight Distance Rp  Ract, "T"  =  R p R a c t , "M" <  Rp  |  <  Ract, "B"  K  Sample Size File No. A% K Ly R LH  e Sight Distance Rp  =  Rp  >  Rp  >  Ract, "T" Ract, "M" :  >  Ract, "B"  90 001 4 100 400 300 200 6  90 002 4 100 400 400 200 6  90 003 4 100 400 500 200 6  90 004 4 100 400 600 200 6  90 005 4 100 400 700 200 6  90 006 2 100 200 500 200 6  90 007 6 100 600 500 200 6  90 008 8 100 800 500 200 6  90 009 4 50 200 500 200 6  90 010 4 75 300 500 200 6  90 011 4 125 500 500 200 6  90 012 4 100 400 300 200 6  90 013 4 100 400 500 200 6  90 014 4 100 400 700 200 6  90 015 4 100 400 500 200 4  90 016 4 100 400 500 200 8  1000* 1000' 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000*  90 017 4 100 400 500 200 6  90 018 4 100 400 500 200 6  100  300  90 019 4 100 400 500 200 6  90 020 4 100 400 500 200 6  1000* 1000*  0.36 0.38 0.54 0.53 0.48 0.52 0.52 0.48 0.54 0.53 0.41 0.37 0.41 0.56 0.54 0.51 0.63 0.56 0.50 0.60 0.32 0.32 0.20 0.20 0.24 0.22 0.27 0.21 0.16 0.22 0.29 0.22 0.18 0.17 0.23 0.20 0.22 0.19 0.21 0.23 0.32 0.30 0.26 0.27 0.28 0.26 0.21 0.31 0.30 0.24 0.30 0.41 0.41 0.28 0.22 0.29 0.14 0.26 0.29 0.17 * sight distance was restricted only by the surface of the road and ground ( > 300m but < 1000m ). 90 90 037 038 4 4 50 50 200 200 500 500 200 200 8 6 1000 100 0.39 0.31 0.21 0.21 0.20 0.22 0.17 0.18 0.16 0.17 0.17 0.40 0.38 0.36 0.30 0.37J.57 0.31 0.27 0.23 0.29 0.27 0.38 0.24 0.32 0.32 0.28 0.32 0.32 0.31 0.22 0.21 0.19 0.21 0.30 0.42 0.56 0.50 0.53 0.40 0.59 0.50 0.52 0.56 0.51 0.28 0.31 0.42 0.49 0.44 0.22  90 022 4 50 200 300 200 6 1000  90 023 4 50 200 400 200 6 1000  90 024 4 50 200 500 200 6 1000  90 025 4 50 200 600 200 6 1000  90 026 4 50 200 700 200 6 1000  90 027 2 50 100 500 200 6 1000  90 028 6 50 300 500 200 6 1000  90 029 8 50 400 500 200 6 1000  90 030 4 25 100 500 200 6 1000  90 031 4 75 300 500 200 6 1000  90 032 4 125 500 500 200 6 1000  90 033 4 50 200 300 200 6 1000  90 034 4 50 200 500 200 6 1000  90 035 4 50 200 700 200 6 1000  90 036 4 50 200 500 200 4 1000  90 039 4 50 200 500 200 6 300 0.43  90 040 4 50 200 500 200 6 1000 0.32  90 041 4 50 200 500 200 6 1000 0.42  0.33 §J3 <U8 0.23 0.44 0.30  79  in 3  -5 id  =2  | 3  u o  N  g  9  11  13  File Number (a) crest combinations.  9  11  13  15  17  File Number (b) sag combinations.  Figure 4.23. Effect of Vertical Alignment on Perceived Horizontal Curve Radius - Phase II.  80  1.0 l%ofT's  0.8  S o  |D%(M + B)  0.6  2 0.4 0.2 0.0  111 300  400  500  600  700  Horizontal Curve Radius (m) (a) crest combinations (files 001 - 005)  • %ofT's • %(M + B)  300  400  500  600  700  Horizontal Curve Radius (m) (b) sag combinations (files 022 - 026)  Figure 4.24. Effect of Horizontal Curve Radius on Curve Perception - Phase II.  81  1.0 B%ofT's 0.8  • % ( M + B)  a o.6 m =)  5T 0.4 -\ 0.2 0.0  2  8  A(%) (a) crest combinations (files 006, 003, 007, 008)  • %ofT's 1.0  • % ( M + B)  0.8  I  0.6 4  a* S  0.4 0.2 4 0.0  4  6  8  A(%) (b) sag combinations (files 027, 024, 028, 029)  Figure 4.25. Effect of Vertical Curve Parameter A on Curve Perception - Phase II.  1.0 l%ofT's  0.8  1  |D%(M + B)  0.6  _______  m  |i  or ^ 0.4 0.2 1  0.0 50  75  125  100 K  (a) crest combinations (files 009, 010, 003, 011)  • %ofT's 1.0  • %(M + B)  0.8  1  0.6  6 0.4 P H  0.2 0.0 25  75  50  125  K  (b) sag combinations (files 030, 024, 031, 032)  Figure 4.26. Effect of K on Curve Perception - Phase II.  83  1.0 • %ofT's 0.8  I 3  t  fe  • %(M + B)  0.6 0.4 0.2 0.0  300 LT  300  500 LT  500  700 LT  700  Horizontal Curve Radius (m) & Turning Direction (a) crest combinations (files 001, 012, 003, 013, 005, 014)  • %ofT's • %(M + B)  300 LT  300  500 LT  500  700 LT  700  Horizontal Curve Radius (m) & Turning Direction (b) sag combinations (files 022, 033, 024, 034, 026, 035)  Figure 4.27. Effect of Turning Direction on Curve Perception - Phase II.  84  1.0  • %ofT's  0.8  • % ( M + B)  0.6  3 a*  e 0.4 0.2 0.0 4  6 e (%)  (a) crest combinations (files 015, 003, 016)  H%ofT's 1.0  • % ( M + B)  0.8 A  S 0.6 m  cr 2 0.4 0.2 0.0 4 e (%)  (b) sag combinations (files 036, 024, 037)  Figure 4.28. Effect of e on Curve Perception - Phase II.  85  1.0 l%ofT's  0.8  • %(M + B)  g 0.6  8 0.4 tin  0.2 0.0  100  300  1000  Sight Distance Restriction (m) (a) crest combinations (files 003, 017, 018)  • %ofT's • %(M + B)  100  300  1000  Sight Distance Restriction (m) (b) sag combinations (files 024, 038, 039)  Figure 4.29. Effect of Sight Distance on Curve Perception - Phase II.  1.0 • %ofT's  0.8  • %(M + B)  1 0.6 -I cr 2 0.4 0.2 0.0  Mnt  Sky#l  Sky#2  Background Picture (a) crest combinations (files 003, 019, 020)  r/oofT's | d % ( M + B)  Mnt  Sky#l  Sky#2  Background Picture (b) sag combinations (files 024, 040, 041)  Figure 4.30. Effect of Background on Curve Perception - Phase II.  87  5.0 D A T A A N A L Y S I S & DISCUSSIONS  5.1 Phase I Analysis  A detailed statistical analysis on the Phase I results was not performed, primarily due to the qualitative nature of the data collected. However the results did reveal that horizontal curves overlapped with vertical curves do affect curve perception of horizontal curvature, in that overlapping crest curves make horizontal curvature appear sharper and overlapping sag curves make curves appear less sharp. In general, this phenomenon was revealed to be more evident with the overlapping of sag curves. It is interesting to note that the static presentation results were quite comparable to the dynamic presentations.  On average, with an overlapping crest curve, 76% of the  sample perceived the horizontal radius as less than or equal to the actual horizontal curve radius, while 86% perceived the horizontal radius as less than or equal to the actual horizontal curve radius when an overlapping sag curve was present. Based on these results, it was decided that the proposed Phase II presentation setup, previously discussed in Chapter 3 section 3.4, could be justified.  5.2 Phase II Analysis  A detailed statistical analysis was performed on the collected Phase II data using SPSS, and has been detailed in the following four sections. Section 5.2.1 tests the significance of the difference between the perceived horizontal radius R and actual horizontal curve R. Section 5.2.2 provides calculations p  similar to section 5.2.1 but for the adjusted R . Section 5.2.3 tests the p  significance of the design parameters under investigation, and section 5.2.4 details the results of the linear regression analysis trials.  88  5.2.1 Hypothesis Testing - Raw Data  Although Transportation Engineers typically use 85 percentile values th  rather than mean values to evaluate situations, using 85 percentile values th  weren't appropriate this experiment because for each question (road presentation) there was only 1 of 3 possible responses. Using the data from file No. 1 as an example, the participant responses were either R = 200m, R p  p  = 250m or R = 300m. The perceived horizontal radius R = 200m represents p  p  the 0 - 30 percentile, Rp = 250m represents the 40 - 60 percentile, and Rp th  th  th  = 300m represents the 70 - 100 percentile. Therefore, it was deemed th  th  appropriate to use the mean perceived radius R . As depicted in Figure 4.23, p  the mean value of perceived radius R was consistently smaller than the actual p  horizontal radius Ract when a horizontal curve was overlapped with a crest curve, and R was consistently larger than the actual horizontal radius when a p  horizontal curve was overlapped with a sag curve. the difference between R and p  Ra , Ct  To test the significance of  SPSS was used to perform a one-sample t-  test on the collected data with the null hypothesis, Ho:  R  p  = Ra t. C  Considering  each test-curve as a separate sample, Table 5.1 shows that the null hypothesis is rejected for all cases using a level of significance of a = 5%. Therefore the difference between the actual horizontal curve radius Ract, and the perceived horizontal curve radius R , is statistically p  significant.  5.2.2 Hypothesis Testing - Modified Data  The setup for Phase II was based on assumptionsfromthe results of Phase I. These assumptions were that most of the driver population would perceive horizontal curves overlapped with a crest curve as equal to, or sharper than, a  89  similar horizontal curve without an overlapping crest curve, and conversely, that horizontal curves overlapped with sag curves would be perceived as equal to,  or not as sharp as a horizontal curve without an overlapping sag curve.  However, the results of Phase I indicated that on average, 19% of the sample population perceived the horizontal radius opposite to this assumption. Therefore, a proportion of the "T" responses (Rp =  Ract)  in Phase II are not true  "T" responses but include some proportion of responses that are opposite to what was assumed or expected.  Therefore, if the results of Phase I are  assumed to reflect the characteristics of the driver population, then the proportion of drivers who perceived the radius opposite to what is expected should be the same as was identified in Phase I. The impact of making this consideration is such that the average Rp will increase when an overlapping crest curve is present and will decrease when an overlapping sag curve is present. The question is whether or not this will affect the significance of the difference between  Ra  Ct  and R as determined in section p  5.2.1  above. Once  again, SPSS was used to perform a one-sample t-test on the adjusted data with the null hypothesis, Ho:  R ' = Ract p  • Considering each test-curve as a separate  sample, Table 5.2 shows that the null hypothesis is still rejected for all cases using a level of significance of a = 5%. Therefore the difference between the actual horizontal curve radius Ra t, and the adjusted perceived horizontal curve C  radius R p ' , is still statistically significant.  90  Table 5.1. Test of Hypothesis on the Mean Value of Perceived Radius Standard Vertical  File  Parameter  Sample  Curve  No.  Tested  Size  0)  (2) 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041  (3) R R R R R A = 2% A = 6% A = 8% K = 50 K = 75 K - 125  (4) 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90  Crest  Sag  LEFT TURN LEFT TURN LEFT TURN e = 4% e = 8% SIGHT = 100m SIGHT = 300m BACKGROUND BACKGROUND  R R R R R A = 2% A = 6% A = 8% K = 25 K = 75 K = 125 LEFT TURN LEFT TURN LEFT TURN e = 4% e = 8% SIGHT = 100m SIGHT = 300m BACKGROUND BACKGROUND  Ract (5) 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500  Mean  Deviation  RP  RP  ta  a'(%)  (6) 252 308 429 527 620 427 431 417 424 429 411 248 400 628 432 422 449 430 421 443 391 511 634 729 833 618 642 632 637 639 634 388 593 807 619 608 566 580 612 588  (7) 41 82 85 86 85 85 80 88 89 84 84 44 91 87 82 87 74 85 87 77 83 85 81 80 79 77 76 76 74 76 75 82 83 88 87 90 82 80 87 85  (8) -11.0862 -10.6153 -7.9252 -8.1034 -8.9220 -8.2298 -8.1457 -9.0113 -8.0466 -8.0510 -10.0318 -11.1868 -10.4040 -7.8353 -7.8538 -8.4692 -6.5692 -7.7766 -8.6264 -7.0263 10.4159 12.3449 15.7559 15.3479 15.9463 14.4579 17.6591 16.4650 17.4914 17.3400 16.9621 10.1713 10.6430 11.4430 12.9234 11.3321 7.5542 9.5338 12.2108 9.8465  (9) 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0:00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%  Calculated value o f the t -statistic. b  L e v e l o f significance for accepting the n u l l hypothesis H „ : Rp = R ^ .  b  91  Table 5.2. Test of Hypothesis on the Adjusted Mean Value of Perceived Radius Adjusted Standard Mean  Deviation  Ract  Rp*  RP'  ta  a'(%)  (4) 90  (5) 300  (6) 261  (7) 55  (8) -6.7121  (9) 0.00%  R  90  400  323  105  -6.9277  0.00%  R  90  500  459  117  -3.3340  0.12%  004  R  90  600  551  113  -4.0893  0.01%  005  R A = 2%  90  700  646  115  -4.4796  0.00%  90  500  439  100  -5.7849  0.00% 0.44%  Vertical  File  Parameter  Sample  Curve  No.  Tested  Size  0)  (2) 001  (3) R  002 003  006  Crest  007  A = 6%  90  500  464  115  -2.9217 .  008  A = 8%  90  500  448  K = 50  90  500  456  123 122  -4.0307 -3.4592  0.01%  009 010  K = 75  90  500  459  116  -3.3618  0.11%  011  K - 125  90  500  424  103  -6.9516  0.00%  012  LEFT TURN  90  300  256  56  -7.5547  0.00%  013  LEFT TURN  90  500  424  123  -5.8281  0.00%  014  LEFT TURN  90  700  650  112  -4.2190  0.01%  015  e = 4%  90  500  459  111  -3.5115  0.07%  ,016  e = 8%  90  500  449  117  -4.1332  0.01%  017  SIGHT = 100m  90  500  454  81  -5.3388  0.00%  500  457  114  -3.5993  0.05% 0.00%  018  SIGHT = 300m  90  019  BACKGROUND  90  500  446  115  020  BACKGROUND  90  500  471  105  -2.6053  1.08%  022  R  90  300  380  100  17.5303  0.00%  023  R  90  400  498  107  23.4230  0.00%  024  R  90  500  629  93  20.9084  0.00%  025  R  90  600  719  99  22.4130  0.00%  026  R  90  700  826  95  -9.5188  0.00%  A = 2%  90  500  613  86  14.0443  0.00%  636  92  12.7237  0.00% 0.00%  028  A = 6%  90  500  029  A = 8%  90  500  624  93  13.8177  030  K = 25  90  500  630  89  14.7751  0.00%  031  K = 75  90  500  634  86  14.4423  0.00%  032  K = 125  90  500  630  85  -11.8310  0.00%  033  LEFT TURN  90  300  376  100  24.9162  0.00%  034  LEFT TURN  90  500  578  106  24.2981  0.00%  LEFT TURN  90  700  790  113  -8.1821  0.00% 0.00%  035 036  e = 4%  90  500  606  110  8.5287  e = 8%  90  500  597  108  6.1356  0.00%  038 .  SIGHT = 100m  90  500  559  91  5.5422  0.00%  039  SIGHT = 300m  90  500  561  105  8.0160  0.00%  040  BACKGROUND  90  500  596  113  4.7915  0.00%  041  BACKGROUND  90  500  560  119  9.8465  0.00%  037  Calculated value o f the t -statistic. b  0.08%  -4.4796  027  Sag  b  L e v e l o f significance for accepting the n u l l hypothesis H,,: Rp = R^,.  92  5.2.3 ANOVA Analysis Microsoft EXCEL 2000 was used to perform a single factor ANOVA analysis on the data. To test the significance of the test-curve parameters under investigation, 19 different ANOVA analyses were conducted, the setup of which is summarized in Table 5.3 and detailed in Appendix B. The null hypothesis of R = Ra was tested at a level of significance of a = 5%. For p  Cti  example, if the value of K doesn't have a significant effect on the perception of horizontal curvature, than the mean values of R (n = 90) forfiles9, 10, 3, p  & 11 should be the same and the F statistic of the ANOVA analysis will be less than the critical F value. However, if F > F crit., than the null hypothesis is rejected, indicating that the variation in the means was not random, and the parameter is significant. The results of the analysis were as follows: •  The horizontal radius was significant for both crest and sag curves.  •  The turning direction was significant for crest curves when R = 500m and significant for sag curves when R = 500m and 700m.  •  For sag curves, sight distance and the background image were significant.  •  The type of vertical curve (crest vs. sag) overlapping a horizontal curve, significantly affects the perceived horizontal radius (Table 5.4).  93  T a b l e 5.3.  Overlapping  Crest  A N O V A  Analysis Data  Curve  Setup  Overlapping Sag  Curve  Effect of R, compare Rp of files 1, 2, 3, 4, 5  Effect of R, compare Rp of files 22, 23, 24, 25, 26  Effect of A, compare Rp of files 6, 3, 7, 8  Effect of A, compare Rp offiles27, 24, 28, 29  Effect of K, compare Rp of files 9, 10, 3, 11  Effect of K, compare Rp offiles30, 24, 31, 32  Effect of LT Turn, compare Rp of files 12, 1  Effect of LT Turn, compare Rp offiles33, 22  Effect of LT Turn, compare Rp of files 13,3  Effect of LT Turn, compare Rp of files 34, 24  Effect of LT Turn, compare Rp of files 14, 5  Effect of LT Turn, compare Rp offiles35, 26  Effect of e, compare Rp of files 15, 3, 16  Effect of e, compare Rp of files 36, 24, 37  Effect of Sight, compare Rp of files 3, 17, 18  Effect of Sight, compare Rp offiles24, 38, 39  Effect of Back, compare Rp of files 3,19, 20  Effect of Back, compare Rp of files 24, 40, 41  Effect of Vertical, compare Rp of files 1 - 20 to files 22-41  T a b l e 5.4.  A N O V A  Analysis: Effect of Overlapping Vertical Alignment on  ANOVA: Single Factor Groups Column 1 (files 001 - 020) Column 2 (files 022 - 041)  Count 1800 1800  Sum Average 769250 427.36 1103500 613.06  Variance 14861.01 17467.03  MS 1 31034184 3598 16164.02  F 1919.95  Column 1 has overlapping crest curves. Column 2 has overlapping sag curves.  ANO\ \ Source of Variation SS Between Groups 31034184 Within Groups 58158160 Total  89192344  df  3599  P-value 0  F crit 3.84  Rp.  94  5.2.4 Regression Analysis SPSS was used to develop several stepwise linear regression models from the data collected in Phase II of the experiment. The goal was to develop a usable model(s) that could be used by highway designers to predict drivers' perception of horizontal curve radius (Rp) based upon the presence of measurable geometric highway design parameters (Table 5.5). Three general types of equations were initially proposed in one of the two forms shown by equations (5.1) and (5.2). However, since the ANOVA analysis revealed that the presence of vertical curves are quite significant (Table 5.4), it was decided to focus on developing separate equations for crest and sag curves rather than develop combined equation models. By focusing on models exclusive to crest and sag curves, the relationship between the geometric variables and R should p  be captured better. Equation Forms: y = aixi + a x + a x + a x + c  (5.1)  y = x, * EXP(a x + a x + a x + c)  (5.2)  2  2  3  3  n  n  al  2  2  3  3  n  n  The results of the regression analysis show that models in the form of equation (5.1) have a higher adjusted r value than when in the form of 2  equation (5.2). However, the advantage of equations in the form of (5.2) is that the perceived radius R will equal zero when the actual radius is equal to p  zero (R = 0 when R = 0). This is not the case for equations in the form (5.1) p  where the perceived radius will have a value not equal to zero when the actual radius is equal to zero (Rp * 0 when R = 0). Therefore, if equations in the form of (5.1) are used, appropriate boundary conditions must be set (i.e., some minimum value for R).  95  During the regression analysis trials, it was also found that when a variable was removed from consideration, the model results were significantly better if the files associated with that variable were removed as well. The four best regression models developed (a = 1 0 % ) , in terms of the number of significant geometric variables, are Usted below along with the respective coefficient tstatistic denoted t_.  The details of each regression model are presented in  Appendix C.  Sag Curve Equations: R  = 1.078 X i + 3.737X + 26.094X6 + 42.088,  p  2  f, = 53.391,  f = 2.047, 2  r, = 51.929,  t = 1.909, 2  t = 4.446, 6  t = 3.727, 6  r = .744 2  (Ml)  t.constant = 3.140  736  (M2)  747  (M3)  722  (M4)  tconstant = 7.289 t  Crest Curve Equations: R  p  = 0.956 Xi - 50.778, = -3.724  R  p  - Xi  1.113 *  0.4118,  /i = 34.161,  ^constant  = -4.407  Where X] = R, X = A, and X = turning direction. 2  6  96  Table 5.5. Variables used in Regression Model Development Trials. Dependent Variable:  w  XI  =  Horizontal curve radius, R (m)  X2  =  Vertical curve parameter A (%)  X3  =  Vertical curve parameter K  X4  =  Superelevation rate e (%)  X5  =  0, overlapping sag curve 1, overlapping crest curve  X6  =  0, left-turn 1, right-turn  X7  0, 1000m sight distance = - 1, 300m sight distance 2,100m sight distance  X8  1, mountain background (base case) = • 2, sky photo background 3, sky computer generated  X9  =  • 0, male 1, female  Xll  =  r 0, doesn't wear corrective lenses [ 1, wears corrective lenses  X12  =  <B  idependent VariabI  Y = Perceived horizontal curve radius, Rp (m)  r 1, 16-25 yrs old  Driving experience (yrs).  XlO  = .  X13  =  2, 26 - 40 yrs old 3, 41 - 60 yrs old .4, 61+yrs old r 0, No driving school education [ 1, Driving school education  Several conclusions can be drawnfroman examination of models (Ml) through (M4). For all models, the perceived horizontal radius R is always p  greater than the actual horizontal radius  present and  Rp  is always less than  Ract  Ract  when an overlapping sag curve is  when an overlapping crest curve is  present. For sag vertical curves, the perceived radius Rp increases as the algebraic sum of the grade (A) increases and if the horizontal curve curves to the right. The superelevation rate e, driver experience, and driving education were never significant in any of the sag curve model trials, while for crest curves, A, K, e, turning direction, background, and driving education were never significant. The only geometric parameter found significant in the crest curve models (M3) and (M4) was the actual horizontal curve radius Ract-  Of  course, the most significant geometric predictor implied by all the models is the presence of a vertical curve. Figure 5.1 illustrates that the regression models (Ml) to (M4) compare quite well to the experimental data.  97  200 -I—i 0  1  1  1  2  3  1 1 1  1—i  1—i  4  7  9  5  6  8  1 1 1 1 1 1  1—i  1  1—i  10 11 12 13 14 15 16 17 18 19 20 21  File Number (a) crest c o m b i n a t i o n s  (b) s a g c o m b i n a t i o n s  Figure 5.1. Regression Model Predictions of Rp vs. Mean Rp of Experimental Data vs. actual R  98  5.3 Conclusions and Recommendations The purpose of this thesis was to investigate the hypothesis that horizontal curves overlapped with vertical curves may cause a violation of driver expectancy with respect to the perception of horizontal curvature, potentially increasing the crash risk of the driver (Hassan and Easa Visual 2000, Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994). Based on the experimental data collected, and the subsequent statistical analysis, the following conclusions may be drawn: 1. The perceived radius of a horizontal curve is affected by the overlapping vertical alignment.  Specifically, the average perceived  radius is less than the actual horizontal radius when overlapped by a crest curve and greater than the actual horizontal radius when overlapped by a sag curve. These results agree with the findings of Hassan and Easa (Visual 2000) and demonstrate the validity of Smith and Lamm's (1994) hypothesis. 2. The perceived radius, for the four regression models presented, were dependent upon the actual horizontal radius, presence and type of vertical curve, turning direction (sag only), and the algebraic sum of the tangential grades (sag only).  Highway designers could use these  equations as an additional tool in the assessment of geometric design consistency. For sag curves the following models can be used:  Sag curve models: Rp = 1.078 R + 3.737A + 26.094T + 42.088, r = .744  (Ml)  R  (M2)  2  D  = R<>-898*  e  (0.0064A+0.0401T + 0.782),  f  2 _  y^ft  99  Where T = 0 for a turning direction to the left and T = 1 for a turning direction to the right, A = (|gi - g |) and R = curve radius in meters. For 2  the model (Ml) it is necessary to specify a minimum value for R because the equation is not valid when R equals zero. For crest curves the following models can be used: Crest curve models: R = 0.956 R - 50.778, R  p  = 0.4118 R  1  1  1  3  r = .747  (M3)  r = .722  (M4)  2  p  2  ,  3. Under conditions of limited sight distance (< 100m) overlapping vertical alignment doesn't appear to affect horizontal curvature perception. Somewhere between 100m and 300m, the optical illusion becomes pronounced. Sight distance appears to be more of a factor with sag vertical curves than crest vertical curves. 4. In all situations, the ijifluence on curve perception was more pronounced for sag curves than crest curves. From a safety perspective, this is more of a concern, since drivers will perceive the horizontal curve as less sharp (Rp  > Ract)  than it really is which may  cause them to negotiate the curve with a higher speed. 5. The background image seems to play a role in effecting driver perception, particularly with sag vertical curves. However, more research is required to determine the specific relationship, if indeed one can be quantified.  100  There are many different parameters and/or possible variations of the presentation techniques used in this study. Therefore, future research should expand upon the work described herein and address some of the following issues: a. Will the location of the static image effect perception results? b. How sensitive are the experimental results to the question posed to the sample population? c. Does image resolution or color affect the response? d. Does the presence of spiral curves affect perception? e. How does the inclusion of objects (trees, power poles, signs, vehicles, etc.) affect curve perception? f.  Will asymmetrical tangential grades be a significant predictor?  g. What is the effect of staggered overlapping vertical curves? h. Do the x-sectional road elements affect response? i.  How does different vehicle heights affect response?  j.  Influence of sound, vibration and lack of participant personal injury risk?  k. How does topography affect curve perception? 7. The presentation of the road curves in this study was not specifically randomized between samples. Rather, the same random order was presented to all the subjects. Future experiments should use some randomization routine (randomized block design) to reduce possible errors due to learning curves. 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"Driver-Headlamp Dimensions, Driver Characteristics, and Vehicle and Environmental Factors in Retroreflective Target Visibility Calculations", Transportation Research Record 1692, Transportation Research Board, Washington, D.C, pp. 107-118. Zwahlen, H.T., and Schnell, T. (1999). "Visibility of Road Markings as a Function of Age, Retroreflectivity Under Low-Beam and High-Beam Illumination at Night", Transportation Research Record 1692, Transportation Research Board, Washington, D.C, pp. 152-163.  APPENDIX A : E X P E R I M E N T A L D A T A D E T A I L S  108  Table A . l . Sample Characteristics - Phase I "TT  Sample No.  Population Type  Xiii 'u  O  <  18  G  F  G  M  :1 ~Kx~  1  G  F  2  E  M  B  VANCOUVER  E  M  B  VANCOUVER  Y  9  N  B  B  F  G  F  B  BURNABY  TM  16  Y  D  D  40 41  G  4  G  M  B B  5  G  M  B  BURNABY  Y  20  N  C  C  42  G  F  B  VANCOUVER  Y  9  Y  D  A  fi  E  M  B  VANCOUVER  N  14  Y  D  A  G  F  D  N O R T H VAN.  Y  45  N  D  A  G  M  B  VANCOUVER  Y  15  N  B  A  43 44  G  F  B  N O R T H VAN.  N  13  N  C  8  G  F  B  VANCOUVER  Y  17  N  D  B  45  G  M  D  N O R T H VAN.  Y  43  N  B  A" A  9  E  M  A  •N.  7  N  E  C  16  G  M  B  N O R T H VAN.  •N  13  N  B  A  D  A A  =  L.  41  S  S u  o  '41 it  E  M  C  11  E  M  A  12  E  M  P  E  14 Is  il rs  '7 it  a VANCOUVER  Wear (.kisses  Population Type  '•G  *B  10  "  1) ft. X '  td  tt s  ser  D  B  Y  8  N  A  A  39  Y  M  A  VANCOUVER  -E • T  F  A  F  A  N O R T H VAN.  Ifi  E  M  e  N  17  E  F  B  VANCOUVER  18  E  F  A  VANCOUVER  19 '20  E  F  G  n u  B  TM  B  A  51  T  M  D  VICTORIA  Y  52  G  D  VANCOUVER  N  C  53  G  C  N O R T H VAN.  Y  50 "IM 24 TM  C  B  M M  A  A  C  A  54  G  .F  B  VANCOUVER  C  A  G  F  B  NORTH V A N  D  A  55 Sfi  G  F  B  C  A  57  G  M  C  Y  A  N  14  N  Y  i;5  Y  VANCOUVER  Y  20  VANCOUVER  Y  -N Y  9  TM  E  A  10  N  B  A  VANCOUVER  16  Y  C  A  VANCOUVER  Y  Y  C  A  TM  E  G  F  C  VANCOUVER  Y  G  F  B  VICTORIA  N  0.5  Y  C  A  G  M  B  VICTORIA  N  10  N  A  A  61  G  F  B  VANCOUVER  Y  10  Y  e  B  B  62  G  M  A  VANCOUVER  B  B  63  G  F  C  VANCOUVER  N  38  N  D  B  D  A  64  G  F  B  VANCOUVER  Y  13  Y  E  B  A  65  E  F  A  VANCOUVER  Y  6  Y  B  B  D  A  66  G  F  B  VANCOUVER  Y  8  Y  D  B  N  D  A  67  G  F  B  N  N  B  B  N  B  A  68  G  M  B  N  TM  C  A  N  N  D  A  B  A  8  N  D  VANCOUVER  Y  7  Y  A  VANCOUVER  N  9  Y  C  A  VANCOUVER  Y  6  N  M  B  VANCOUVER  . N  10  M  B  BURNABY  Y  M  B  VANCOUVER  N N  Y "NT Y  43 40  N  VANCOUVER  A  15  25  B  A  C  N  A  F  B  Y  N O R T H VAN.  A  G  Y  15  B  C  Y  13  Y  F  A  VANCOUVER  N  VANCOUVER  G  Y  B  VANCOUVER  B  C  Y  M  A  D  7  G  B  Y  6  28 29  N  Y  Y  T  14  15  N  26  N  16  50  T  N  VANCOUVER  Y  B  2^  12  B  N  C  F  N  91 fa B  A  VANCOUVER  Y  T  B  a VANCOUVER  VANCOUVER  5  B  s  IE  B  Y  B  ii  !E *c .»er»  B  49  F  B  F  48  D  M  u  M  A  D  E  B>  ^.  G  B  N  G  _B  61  c  G  Y  9  23 24  a  ,41  at  W"  Y  7  22  en  <• S5  B  »T5  , SB-  5.  s  ,  12  G  VANCOUVER  V  it  41.  N  47  A  B  a  5  VANCOUVER  A  F  o •o  4), cn >  B  C  15  it  M  N  G  G  B.  , fl  Y  N  27  U)  fa-  VANCOUVER  21  Ui ' TV,  p* Y  B  B  s  '.©-  ai i  17  M  "ST  =  IE  Y  E  CS U  '3  'Z  VANCOUVER  3  * B  <-o •>  Engineer  Sample No.  B*  T = Transportation  Duration on llw\s  E = Engineer u  Duration on ll\v>s  G = General Public  E  G  B  ^8 s9  A  60  D  A  Y  D  14  Y  17  Y  10  Y  C  N  0  30  G  F  B  N  31  T  M  B  Y  15  *2  G  F  D  VANCOUVER  N  50  Y  D  C  69  G  M  B  V,  G  M  D  VANCOUVER  Y  50  N  D  A  70  G  M  B  G  M  B  VANCOUVER  Y  12  Y  C  A  71  G  F  A  TM  N  D  A  5  N  B  B  72  G  F  B  Y  N  C  A  i S  T  F  A  COQUITLAM  Y  36  G  M  B  VANCOUVER  Y  18  N  D  A  73  G  M  B  N  N  B  A  37  G  F  B  VANCOUVER  N  19  Y  D  A  74  G  F  B  N  TM  C  A  109  77  en  < C  n  •cc  p  to B  A  83  M  B  N  N  A A  84  F M  C B  m  u  B  CS  it  F  B  M  A  PORT MOODY  N  oc _s  Y  B" S  <u  8  N  C A  85  •s*  4f yi*  it  •3  z  4>  en  C  A.  B  SURREY  Y  20  N  A  B A  B  NAN1AMO  Y  21  N  B  A  VANCOUVER  N  12  N  E  C  VANCOUVER  Y  4  Y  VANCOUVER  •N  30  N  B  B  VANCOUVER  Y  47  Y  C  B  VANCOUVER  Y  7  Y  B  A  86  F  VANCOUVER  Y  D  87  M  G  F  B  VANCOUVER  Y  Y Y  D  80  20 14  D  C  88  F  C  89 «0  M F  B D  91  M  D  C  A  L.  Y  B  N  s  It.  Y  A  10  Q *  12  F  Y  S  5 * 41  '>.  24  M  VANCOUVER  .«-. CJ  Y  T  B  E O  Y  G  M  et,  -X'-  RICHMOND  79  82  03 U S t3  VANCOUVER  78  81  it ^ „ = o it « «. it ^ it  B  Duration on Hww  =  "O  r  e  a.-, a . ~e o>v JS >  Driving Expericnci  G T  'it -  a  O M  u  C«  X  Population Type  G  7ft  £• Y  Sample No.  Population Type  75  )5»  if 41  e  9  </>  '  u <u '•I <u  Duration on Hvt>s  Sample No.  Table A . l . Cont.  110  Table A.2. Experimental Data: Animated Crest Combinations - Phase I S =  > R'  M =  O v e r l a p p i n g  'V  Crest  L = " Rp < R "  =R"  - Animation Files  C u r v e  Hi '•m  ssfs II  iSH mm 1 2 3  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  S  S  L  L  M  L  L  L  L  L  S  L  L  S  S  L  S  S  L  S  L  L  L  L  L  S  L  S  L  L  L  S  L  L  L  L  S  L  L  L  L  L  S  L  L  L L  L  L  L  L  L  L  L  S  S  L  L  L  L  L  L  L  L  L  S L  L  L  S  L  L  L  L  M  s  L  L  L  L  L  M  L  M-  M  L  L  L  S  L M  S  L  L  4  S  L  L  L  L  L  L  L  5  L  L  L  S  L  S  L  L  M  S L  M  L  M  L  L  L  L  M  M  M  7  M  L L  S  L  L  S  S  S  M  S  S  S  S  L  L  L  8  L  S  L  L  M  S  M  L  L  M  L  L  M  M  S  L  S  M  M  M  9 10  M M  M  M  M  M  M  M  M  M  M  S  M  M  L  M  M  L  L  M  S M  M  L  L M  M  L  M M  M  M  M  L  M  L M  M  11  S  S  S  M  L  S  M  S  S  M  S  S  S  S  S  M  S L  L  M  M  12  M  S  S  L  L  S  . M  L  L  L  L  L  L  L  13  L  M  M  L  s  L  M  M  L  S  L  L  M  M  S M  L  L  s  L  S  s  L  M  S  L  M  M  M  L  L  M  M  S  M  M  M  S  S  L  L  M  L  S  S  L  L  S  M  S  L  M  S  M  S  M  L  L  S  S L  S  L  S  L  L  L  L  L  L  L  L  L  S  L  L  L  L  L  S  S  S  S  S  S  S  M  S  L  6  14  S  S  M  L  15  S  S  M  M  16  M  S  L  L  L  L  L  S  L  L  17  L  L  L  L  L  L  L  L  L  L  18  S  L  S  L  L  S  S  S  L  L  S  s L  M  19  L  M  S  L  L  M  L  M  L  S  L  L  M  L  L  L  20  L  S  L  S  S  M  L  L  L  L  S  S  M  L  S  S  s  M  L  S  21  S  L  L  L  L  L  L  L  L  L  S  L  S  L  S  L  S  22  L  S  S  S  L  L  L  S  S  L  L  s  L  s  L  S L  S  L  s  S  L  23  M  M  M  M  M  S  M  M  M  M  L  M  M  M  M  M  M  L  24  S  S  L  L  S  M  S  M  L  M  L  S  S  M  S  L  S  L  L  M  S  S  L  S  S  M  L  S  M  M  s s s s  S  M  L  s s  S  M  M  M  M  M  L  M  S  S  M  S  L  L  S  L  25  L  L  S  S  S  S  S  S  L  S  M  L  26  M  M  M  L  S  L  M  L  M  L  L  27  M  M  M  M  M  s s  M  M  M  M  M  M  M  M  S  M  28  M  M  M  M  S  M  M  M  M  M  M  M  M  M  M  M  L  L  L  L  S  L  M  L  M  L  S  S  S  L  L  M  L  M  S  L  L  L  L  L  L  L  L  s  M  29 30 31 32  L L  S L  L  L L  L L  L  L  L  L L  L  33  L  L  L  L  L  L  L  L  L  L  L  L  L  L  34  L  L  L  L  L  L  L  L  L  L  L  L  L  S  35  S  M  S  S  S  S  L  S  L  M  L  S  S  L  S  S  36  L  L  L  L  L  M  L  L  L  S  L  L  L  L  L  L  37  L  L  L  S  L  S  L  L  L  L  L  S  M  M  S  L  L  L  S  L  L  L  L  L  L  L  L  L  L  L  M  L  L  L  L  L  L  L  M  M  S  S  M  M  L  M  L  M  38 39  S L  S L  L L  L  L  40  M  S  L  M  L  L  S  L  M  S  L  41  L  S  L  S  M  L  M  L  L  L  M  42  M  M  M  M  L  S  M  L  L  M  L  M  L  L  L  s .s s s  s s s s  s  L  s  S  M  L  L  L  S  M  M  L  S  L  L  L  M  L  S  M  M  M  M  S  M  L  L  L  M  M  M  S  M  Ill Table A.2. Cont. 43  L  L  L  L  L  S  L  L  L  L  L  L  L  L  L  L  L  L  L  L  44  M  S  M  S  S  M  S  L  S  S  S  M  S  S  S  S  S  S  S  S  L  M  S  L  M  S  S .  L  L  M  S  L  L  L  M  M  S  S  S  S  L  L  L  L  L  L  L  L  L  L  L  M  L  L  L  L  M  L  M  L  s  L  L  s s s  L  s  L  L  L  L M  L S  s  L S  L  M  L L L  L S  L  L M M  L  M  S  S  M  S  S  S  45 46  M  L  L  L  L  47  L  L  L  L  L  L S  L M  L S  L L  L  L  S S L  S M  L  L  L  L  L  L  L S L  M  S  S  M  M  M  M  S  S  L  L  S  s  s  S  S  S  S  S  S  M  S  S  S  M  S  S  L  S  L S  L S  L  L S L  S  48 49  L M  S ivi  L M  50  M  L  52  L  s  53  S  54  S  s s  55  M  L  :  s  51  S  S  M  S  M  M  s  M  s  s  M  L  S  M  L  L  L  L  L  L  L  L  L  L  L  L  L  S  S  L  L  s  S  M  L  M  L  M  M  L  L  M  L  M  S  S  M  M  M  s  M  M  M  S  s  s  56  S  s  57  M  M  M  M  M  M  M  M  M  M  M  M  M  L  S  58  M  S  M  L  S  S  S  S  S  M  M  M  S  L  M  S  M  S  S  S  S  s  L  L  S  S L  L  L  L  L  S S  S  S  S L  L  S L  S L  M  M  S  L  S  M  M  S  s  M  L  s  S  S  L  s s s s s s  L  L  L  S  S  S M  59 60  S L  61  S  62  S  S-  s s s  L  S  S L  L  L  L  L  L  S  M  L  M  S  M  L  S  s  L  L  L L  M  S  S  L  S  L  S  S  L  L  L  S  M  S  S  S  S  M  M  M  L  M  M  M  M  M  M  M  M  L  L  L  S  S  L  L  L  S  L  L  L  L  S  S L  L  L  L  L  L  S  L  L  L  L  S  S  S  L .  S  L  S  L  S  L  S  L  L  L  L  L  L  L  L  64  M  S  S  S  S  S  L  M  L  65  L  M  M  M  M  M  M  L  66  M  S  L  S  L  S  M  L  67  L  s  L  L  L  S  L  L  L  68  S  L  L  L  L  L  L  L  L  L  L  S  L  70  L  L  L  L  L  L  L  S  L  S  L  71  S  S  L  L  L  L  S  L  S  L  S  L  s  72  L  S  S  S  L  S  L  L  L  L  L  L  S  S  L  S  L  L  L  L  S  L L  63  69  S  L  L  S  S  s  S  L  M  M  S  L  S  L L  L  M  s  M  L  S  s  L  .S  L  s  S  L  S  s s  S  L  S  L'  73  L  L  L  L  S  L  L  L  S  L  L  L  L  S  L  S  S  L  74  L  L  L  L  S  L  L  S  L  S  L  M  S  S  L  L  L  L  S  L  S  L  L  L  L  L  L  L  L  L  L  S  L  L  L  L  L  L  S  L  L  S  L  L  L  L  M  L  L  L  M  s  L  L  L  L  M  s s  L  M  L  L  L  L  L  L  L  L  S  L  L  S  S  s s s s s s s s  S  S  S  S  L  S  S  L  L  L  S  L  L  L  S  S  L  M  L  L  L  75 76  S  L  L  L  L  L  77  L  M  S  L  L  M  78 79  L M  M M L  L M L  S S.  s  L L S  M L S  L S M  L L • L  L L S  S S  S S  L S  L M  S S  S  S  80  L  81  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  82  S  L  L  L  L  L  S  L  L  L  S  L  L  L  L  L  S  S  L  L  L  S  L  L  L  L  L  S  L  S  S  L  s  L  L  L  L  L  L  L  L  L  M  L  L  L  L  L  83  L  L  84 85 86 87 88 89 90 91  112  Table A.3. Experimental Data: Animated Sag Combinations - Phase I M = "Rp>R"  S = "Rp = R "  O v e r l a p p i n g  L = "Rp<R"  S a g C u r v e - Animation Files  Hi HI  Pi  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  1  S  L  M  M  S  L  M  S  S  M  S  M  S  M  S  S  S  M  M  S  2  M  M  S  S  M  S  M  M  M  M  M  S  S  M  M  M  S  M  M  M  3 4  M  M  M  M  M  M  M  M  S  M  M  S  S  M  M  L  S  M  S  M  S  M  S  S L  M  M  M L  L  M  S M  M  M  M  M  M  M  M  M  M  M  M  S  M  M  M  M  M  M  M  M  M  M  M  L  M L  5 6  L M L  M M  M  M  M  S  M  M  M  S  M  L  M  M  M  S  L  L  L  L  M  L  L  L  L  L  L  L  M  M  L  M  S  M  M  8  S  9  •L M  M  M  M  M  M  M  M M M  M  M  7  M  M  M  M S  S  L  L  M  L  M  M  S  L  L  M  • M  S  L  L  L  L  L  L  L  L  S  L  L  L  M  M  M  M  S  M  M  M  M  M  M  M  M  L  M  M  M  S  11  S  S  M  S  S  S  M  L  M  M  S  M  M  M  M  M  S L  M  M  S M  S  M  M M  M  M  M M  S  12  M M  s s  M  M  L  M  M  13  L  S  S  S  L  S  L  L  L  L  M  L  M  L  M  L  L  L  S  M M  14  M  S  M  M  M  S  M  M  M  M  M  L  M  M  M  L  M  M  L  M  M  M  S  M  M  M  M  M  L  M  S  S  S  S  M  L  M  S M  M  M  M  M  L  S  s  M  M  M  M  L  L  L  M  M  M  L  L  L  L  M  S  M  S  L  L  M  L  M  M  L  M  M  S  M  M  M  10  15  S  M  S  16  M  S  M  S  M  M  M  M  17  M  L  M  L  M  L  M  M  19  M  M  M  S  M  M  M  M  M  M  L  M  S  S M  20  L  M  M  M  M  M  M  M,  M  S  M  S  M  M  M  S  21  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  S  M  M  M  22  -M  M  S  M  M  M  M  S  M  M  S  M  M  M  M  S  M  M  M  M  M  L  M  S  L  M  L  L  M  M  L  M  L  M  S  M  L  M  M  M  M  M  S  L  M  L  M  M  S  M  M  M  S  M  S  S  S  S  S  M  M  L  L  M  S  S  L  M  18  23 24 25  S  L M S  S  L L M  S  M M  S  L M  M  M S  S  M M  M  M  M  M  M  M  S  S  M  L  • M  26  M  M  S  L  S  M  S  L  S  M  M  S  S  L  27  L  L  • M  S  M  L  M  L  L  L  L  L  M  M  L  L  S  L  L  L  28  M  L  M  M  M  S  L  M  M  L  L  L  M  L  L  S  S  M  L  M  S  S  S  S  S  M  M  M  M  S  M  M  S  S  S  S  S  M  M  S  M  M  M  S  M  M  M  M  S  M  M  S  M  M  S  M  M  M  M  M  L  M  M  M  M  M  M  M  M  M  M  M  M  M  29 30 31  M  M  S  34  M  M  M  M  M  S  M  M  M  S  M  M  M  M  M  35  S  M  S  L  L  M  M  M  S  S  S  S  S  M  M  L  s s s s  36  M  M  M  M  M  M  M  M  M  M  L  S  L  M  M  M  M  L  M  L  37  S  S  S  L  M  L  S  M  M  M  M  S  M  S  M  M  M  M  M  38  M  M  M  M  M  M  M  M  M  M  M  M  M  M  L  M  s s  S  M  M  L  L  L  L  L  L  L  M  M  L  L  L  L  L  L  L  M  M  S  M  M  S  M  S  M  M  L  M  M  L  M  M  M  M  M  L  L  M  L  32 33  39 40  S M  L M  M M  L M  M M  L M  M M  L M  M M  L L  M  L  M  L  M  M  L  41  M  M  M  M  M  M  M  M  M  M  M  M  M  M  42  L  M  L  M  M  M  M  M  M  M  M  M  M  M  .  113  Table A.3. Cont. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91  S  S s s  M M  S S S S  M S L M M S M  S  S L M M L M  S  M M M M M M M  S M... M M L S M M M S M M M M M M S M L L L M L M  M  S S  M M M M  M  M M S M  L M M. M  M M M M L S L M M M M M M M M M M M M  M S M M M M  S  M. M M S L  S S L S L  M M M M M M M  L M M M M M M M M  S S S S  L M M M  M S L M M M  M L M M  S  M M M M S M L M M M S M. M M M M M S M  M  M  M  M  S  S M  S  M M M M  S  M  M S  M  S  M S M  M  S M  M M M M  M M M M M M M M  M M M M M M  M M S M M  M  M  L  L  M  S  M  S S  M  S  S  M  S S S  M M  M  M  S  M S S  S S  M M M M M M L M  M  M  L  S  M M M M L M  S S S S S S S S S S M S S M M M s S S s S M M M M M M S M S M M M L L M L M M M S S S S  S S  M M M M M M  S  M S M M M S  M S M  M M M M M  S  M  L S  M  s  M  M M L M L M M M M M M M S M M M M M M M S M M M M  M  M  s  L S L  S  M  S  M M M M M M M M M M  S S S  M M  S  S  M M M M  M M M M  M  M  L  L  S S S S S S S S s 'M M M S S M L L S S M S M M S  L  S  M M M M M S M M M  S  M M M M M M M M M  M  L S M M M M M M S M M M M M M M  L M M M  S  M M M M  M M M M M L M M M M M S M M M M  M  M  S  L M M S M M  S  M S  s M M M M  L  S  M L M S M  S  M M M S M  L M M M  S  M M M M S M S M M  L S M M L S L  M M  M  M  M M  S S  M  M M M M M M S M  M  M  S  s  M S M M L M M M M  L  L  S  M M S  L L M M L S M M M M M M M M M M M M M M M M  M  M  S  M M M M M M M M  S  M M  S S S S S L S M M M S L S M M S S S M M M  M L M M M M L M  L  S S  L M L  s  S  L S  M M M M M  L  L  s S s  M S  M L M M M M  S  M  M  S S S S M M s . SS M M s s M M S s s M M M s L M M S s S S S M s L S S M s L M M L M L S M M M M  M S L L L  M M M M M M M M M  M  S S S S S  S S  L M M M M  S S S S S S  M  M  S S S  S S S S M S M S M S S S  M  M L L  L  M M  M M L M M M  S  M M M  M L M L M M M M M M M M M M M L M M  M  M  S  M M M M M M M M M  S S S S M  M M  L M L  S S S S  M  114 Table A.4. Experimental Data: Image Crest Combinations - Phase I S =  M = "Rp > R " Overlapping  10 11  M M  L M  S  M S M  L  S  L  L  L  L  L  L  L  L  M  L  L  L  L M  L  L  L  L  L  L  M  L  M  M  M  S  M M  S  M  M  M  M  M  M  s  M  M  M  M  M  M  s  M  M  M  M  M  M  M  M  S  L  L  L  L  L  L  L  L  L  L  L  S  S  S  L  L  L  L  L  M  L  S  M  S  S  M  S  M  S  S  s  L  M  M  S  L  L  M  M  L  L  L  M  L  L  L  L  M  L  L  L  9  S  L  L  S  S  L  L  L  M  L  L  L  L  M  L  M  L  L  S  L  L  L  L  L  8  M  L  L  L  L  S L  L M  M  L  L  L  L  L  M  M  S  L  L  L  S  M  S  L  L  S  L  L  M  L  L  L  L  M  L  15  1  7  20  14  2  6  19  13  6  L  18  12  5  L  17  11  4  S  16  10  3  L  - Image Files  9  2  5  Curve  8  1  L  Crest  L = " Rp<R"  =R"  7  isS&SS  3 4  'V  L M L M  S M S S S  M M L  s  M  M M L M  M M M M  M  M  S  L S  M  M L  M  M  L  M  L  M  L S  M M  12  L  S  S  S  S  s  S  L  S  S  S  S  L  L  S  L  13  M  M  L  M  . M  M  M  M  M  M  M  M  L  M  L  M  14  L  L  L  L  M  S  L  L  L  L  L  L  L  L  M  L  S  S  S  S  S  L  M  M  S  S  S  L  M  M  L  L  L  L  L  L  M  L  L  L  S  L  L  L  L  L  L  L  S  L L  M  M  M  S  M  M  M  S  S  L  s s s s  L  L  S  S  S L  15  S  M  16  L  M  L  L  L  17  S  M  L  S  L  18 19  M M  S L  S L  S L  M L  S L  M S  M S  S  M  M  L  L  L  S  L  L  L  S  L  L  L  L  L  L  L  M  M  M  L  L  L  L  L  L  L  L  M  S  L  S  S  M  L  M  M  L  L  M  S  M  M  M  M  M  20  M  S  M  M  L  S  S  M  S  L  21  L  L  L  L  L  L  L  L  L  L  22  L  L  L  L  L  L  L  L  L  L  23  M  S  L  S  M  S  L  S  L  M  L  S  L  s  L  L  L  L  S  L  S M  24. 25 26  L M M  S L M  L L  L L  L L  s s  M M  M  M  M  S  S  M  s  M  L  M  M  S  M  M  s  M  27  M  M  M  M  M  28  M  M  M  M  M  29  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  30  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  L  31  M  S  S  S  L  L  L  M  L  M  L  L  M  S  L  M  L  L  L  L  L  L  S  L  L  M  L  S  L  L  L  L  L  L  L  L  M  L  L  L  L  L  L  L  L  L  L  L  M  M  M  L  L  L  32 33 34  L M L  L L L  L L  L L  L L  L  L  L  L  s  s s s  M  S  S  M  M  M  s s  M  L  L  M  S  S  L  L  L  L  L  L  L  s s  M  S  S  S  S  S  s s s  L  L  L  L  L  L  S  L  L  s  L  L  M  s s s s s s s  L  L  S  S  S  S-  L  M  S  S  S  M  M  M  M  L  L  L  L  L  L  s  s  L  S  L  s s  S  L  L  L  L  L  L  L  S  L  s s  M  M  M  S  S  S  35  S  S  S  S  M  S  M  M  M  L  M  L  M  36  M  L  L  M  L  M  L  L  L  S  L  L  L  37  M  L  M  L  M  M  L  M  L  S  S  M  M  S  M  M  M  S  S  M  M  M  M  S  M  M  M  S  M  S  M  L  M  M  S  M  L  L  L  L  L  L  M  L  M  s  S  s  M  L  L  L  L  L  L  M  M  L  L  L  S  M  M  L  S  S  S  L  L  M  L  S  M  S  S  M  M  M  L  S  S  S  S  M  S  S  M  M  S  S  M  M  M  L  M  M  M  M  M  M  38 39 40 41 42  M S S L  S S M  M M L  S S M  L M  L . L  M  M  M  115  Table A.4. Cont. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91  L S S M  M L S M S S S S M M M M L L M L M S M M L S L L S L L L S S M S M L L L L L L L S L L S M  S S M S M L S M S M M S s M M S L L L S M L M M S L S L S S L L L L M L M L L L S ' S L S s s L M M  L S M M M S S M S M S S S M M M L L M M M L M M L L L L L M L L L L S L M L L L L L L -S S  L S M S M S L M L M M M S M M M L L M S M L M M L L L L  L S L L L L L L S L L S S L S s s L s L M L . L L L  L M M S L L M S S M M M S S M M L L L M M L M M L S L L L L S L L L L L  s L L L L L L S L L L M L  S S S S M S L L M M S S L S S S S S S S M S L S s L L S L S L L L L M S M S L L L S S L S L M S M  L M L S M L  M S M M M M S M M M L S L M M M M M L L S L L S S s L L M L S S L L L L L M S L M M M  S S M M M S L L S M M S L M M M L L M L M S M M S L L S L L L S L L L L M L L L L L L L L L M M M  L M S S M L S L L M M M L M M M L L L M M M M L L L S L L S S L L S M L S M L S L S L S L L L L M  L S S s M S L L S s M M L M M M L L M S M M M M S L L S L L L S L L L L S L L L S S  s L S L L L M  L S L S M S S S L M S S S S S M L L M S M S M S L L S L S S L L L L L L S S L L L S S L S L L M M  L S L M M S S M S S M S S S M M L S S  s M S  s M L S L S S L L S S S M L S M L L L L L L L L L L M  L S L S M L L L L M S S L M M M L L M M M L M M S L L S L M L S L L L L S M L L L L L M S L M ,M M  L S L M  M L L S L S M S S M S M L L M S M M M L L S L L S L S L L L L L S s L S L S L S S L L L L  L S S s M L M L S S s s L S M M L L M M M L M L S M L S L L L S L L L L S M L L L S L M S L S M M  L S L S M S S L L M M S L M M M L S M S M S M M L L S L S M S L L L M L S L L L L L S L S L S M M  S S S S s s s s s s s s  s s s s s s s s s s s s s s s s  s s s s s  s L s  s L M  s s s L s s s L S L  L M M S L L S S S S S M S M M S L M M M M M S M L L M L S s s L S L M L S M L L L S L S L L M M M  L M L S M M L L S M S S L S M M L L M S M M M M S M L S L L L S S S M L S L L L L L S S L L M M M  L S S M M L L L S S s s L S M M L L L M M M M M L L S L S M S L L M L L S S L L L S S s L L M M M  116  Table A.5. Experimental Data: Image Sag Combinations - Phase I M = "RP > R "  O v e r 1 a p p i ng  L = " Rp < R "  =R "  S =  Sag Curve  - Image Files  ? \  1 2 3 4  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  M  M  L  M  M  S  M  M  M  M  M  M  M  M  M  M  S  M  M  M  M  M  M  S  S  M  M  L  M  M  S  M  M  M  S  L  M  M  M  M  M  M  M  M  M  M  M  S  M  M  M  M  M  M  M  S  M  M  S  M  S M  L  L  s s s  M  S  M  s  M  M  M  L  L  S  S  s  L  L  L  S  S  L  L  M L S  M M  M M  M S  M  M  L  S  M  M  M  M M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  S M  M  M  s  6  M  M  M  ' M  M M  M  M  7  M  M  S  S  M  S  S  S  M  M  M  S  S  L  S  S  5  8  L  L  L  M  L  S  M  M  L  M  M  L  L  L  L  M  9  L  L  L  L  L  L  L  L  L  L  L  S  L  L  L  L  10  M  M  S  M  M  M  M  M  S  S  S  M  M  S  M  S  S  S  S  S  11  M  L  L  L  M  M  M  S  M  M  S  S  M  L  S  S  S  M  L  12.  M  S  M  M  M  M  M  S M  M  M  M  S  M  M  M  M  M  M  L  S  L  L  S  S M  S  L  L  L  M  S  S  s  M  M  L  L  L  M  M  ' M  M  M  M  S  M  M  M  S  M  M  M  M  S  S  L  M  L  S  s s s s s s s s s s s s s s s s s s s s s s s  S  L  M  M  L  M  S  S  M  M  S  L  M  S  L  M  M  M M  13  L  S  L  14  M  M  S  M  M  S  M  M  M  15  M  M  S  M  M  S  M  M  L  16  L  L  M  L  M  S  M  L  S  S  M  M M  M  L  M  17  S  M  S  M  M  S  M  M  M  M  S  M  L  L  M  M  18  M  M  M  M  M  M  M  M  M  M  S  M  M  S  M  S  L  M  M  L  S  s  L  M  M  L  S  M  M  M  M  M  19  S  S  S  L  S  S  S  S  S  S M  20  S  S  S  M  M  S  M  M  S  S  21  M  M  M  M  M  M  M  M  M  22  M  M  M  M  M  M  M  M  M  S  M  M  M  M  M  M  S  M  M  M  s s  M  M  L  M  M  M  M  M  M  M  M  M  M  S  L  L  L  M  23  M  M  M  M  24  M  M  M  M  M  M  M  M  M  M  M  25  L  L  L  L  L  S  S  S  L  L  S  26  M  M  M  S  L  M  S  M  S  S  S  M  L  S  S  M  27  L  L  S  M  M  L  L  L  S  L  L  L  L  L  M  L  28  L  L  .L  L  M  L  L  L  M  M  S  L  L  L  M  L  29  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  M  S  M  S  M  M  L  S  M  S  M  M  M  M  S  M  M  M  M  M M  30 31 32  M S M  S M  M M  S M  S M  M  M  M  33  S  M  S  M  M  M  M  M  S  M  M  M  S  M  M  34  M  M  M  M  M  S  M  M  M  M  S  S  M  M  M  M  35  M  M  S  S  M  S  M  M  M  S  S  M  L  M  M  M  M  M  M  M  M  M  M  ' M  M  s-  36  M  M  M  M  S M  S  S  M  L  S  S  S  L  S  M  S  L  M  S  M  M  M  S  S  M  L  M  S  S  L  L  L  L  M  L  L  M  M  S  M  M  37  S  38  S  S  S  M  M  S  M  39  L  L  M  L  M  M  L  40  M  M  M  M  M  M  M  M  L  L  S  • S  M  41  M  M  L  S  M  M  M  M  M  M  M  M  M  M  M  M  42  L  M  S  L  M  M  S  M  M  M .  M  S  L  M  M  M  S  M  M  L  L  M  M  M  S  L  S M  S  S  L  L  L  L  M  L  M  M  M  M  M  M  S  M  M  L  M  M  S  M  M  S  M  M  s s s  S  M  M  M  L  L  L  M  M  L  M  L  L  s s s  L  M  M  L  M  M  L  M  L  117  Table A.5. Cont. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91  S S M S S  M L S S M S S  S L S S M S  M S  L M M M M S M M M M M M M S S M L S  M M M S S M S M M S M  M S M S M S S  S S L S M  s s s s  M M M S L  M S M M M S L M M L S S M L M S S M M M S  S M M M L M M M M M M M M S M S S M M M M M M M M M S S M M M M S M M M S M S S S M S S S S S M M M M M S M M S  M S M S M L M M M M L S S M M L S M M M S M M M M S M S M M M M M M M S M M M M M M M ,M M M M M M M M M M M S M M M S M M M M S M M M M M M M S M S M M S S M M M M M M M M M M S M M M M M M M L M  S S M S M S S S L M S  M S M S M M L M L S S  S  S  S M M  M M M S S M M M L M M M M  S  S M S  s  L  S  M M M M M S M M M M M M S  L M S M M S  S M S S M M S  M  M  M M M S  s s  M M L M S M M S M S M M S M M M M  M S  M S M M L M M L S S M M M S  M S  M M L M M L S M M S M M M M M M S M S M M M M M S M M M L L M  M M S S S M S S M M S M M S M S S s S L S S M s M s S M s M M M L M L M M S M M M M M M S S S M L L S M S M S M M L M M S M M M M S M S M M M M M S S M s M M M M M M M M M M M M S L S M M M M S M M S M M M M M M M M S S S M' S S s M s M M M S M M M M L M M M M L M M M  S M M S M M M M M L S M M  M S M S L M M M L S S S M L M M S  S M S L M S  M M S M S M M M S  M S M M S  s  M M S S  S S s  M L L M  M M M S  M M S M L M S  M S M S M S s  M L M  M L M S M M M M  S  S  M M M M L M M M S M M S M S M S M M M M L S M M M S M M S M M M M  M M M M L M M M M  s  M  M M M M S M S M L M M M M M M S M S  s  M M M M  M M M M M M L S M S  s s s s  M S M M M M M M M S  M S M S M M M M M L S  S M S M S S S  s  M L M M L M s s M M S M M M M M S M S M M M M M M M S M M M S S M M M S M M M M M M M M S S S M M M L S L M M  S S MS L S S  M  s  M  s s s s s s s s s  M S S S M S M M S M M M S L S S M S M M L M  s s  L M L S s M s S M L S M s M s M s L s S s' L s M s M s S s M s L s S s M s L s M s M  L  s  s  L  s s s s s s s s  L  M S M S M M M M L L S M M L M L M M S S L M M M S M M M M M M M M M M M S  S M M M M M L S M M L M  M M M S S M M M L L M M M M M L M M M M L M M M M M M M M M S M M M S M M S M M M  S M S S M M L M  118  Table A.6. Experimental Data: Crest Combinations Summary - Phase I  O v e r 1 a p pi n g Test-Curve N o . |  1  2  3  4  5  6  36  34  49  48  49  34  7  Crest  Curves 17  18 | 19 | 2 0  42  7  34  37  36  22  65  31  24  27  15  16  48  39 25  8  9  10  11  12  13  14  55  55  46  39  37  43  IfiJJlL  \niniations Total # o f " L "  L = " Rp < R "  S = •Rp == R "  >R"  M =  44  Total # o f " S "  24  31  17  20  20  34  15  13  13  13  26  29  20  21  Total # o f " M "  22  17  16  13  12  13  23  13  13  23  16  15  19  12  17  17  9  16  20  18  Sample Size  82  82  82  81  81  81  82  81  81  82  81  81  82  81  81  81  81  81  81  81  % o f L's %ofS's % o f M's Images Total # o f " L "  44% 4 1 % 60% 59% 60% 4 2 % 54% 68% 68% 56% 48% 46% 52% 59%48% 52% 9% 42% 46% 4 4 % 2 9 % 3 8 % 2 1 % 2 5 % 2 5 % 4 2 % 1 8 % 1 6 % 1 6 % 16% 3 2 % 3 6 % 2 4 % 2 6 % 3 1 % 2 7 % 8 0 % 3 8 % 3 0 % 3 3 % 2 7 % 2 1 % 2 0 % 1 6 % 1 5 % 16% 2 8 % 1 6 % 16% 2 8 % 2 0 % 1 9 % 2 3 % 1 5 % 2 1 % 2 1 % 1 1 % 2 0 % 2 5 % 2 2 % '+ * 37  33  47  42  54  32  40  47  44  44  39  36  mi50s! 48  44  42  8  31  37  37  19  78  23  27  26  Total # o f " S "  22  30  17  25  11  47  17  11  .18  23  39  28  13  24  20  Total # o f " M "  32  28  27  24  26  12  34  33  29  24  13  27  28  19  27  30  5  37  27  28  Sample Size  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  91  Average  4 1 % 36% 52% 46% 59% 35% 44% 52% 48% 48% 4 3 % 40% 55% 53% 48% 46% 9% 34% 4 1 % 4 1 % 2 4 % 3 3 % 1 9 % 2 7 % 1 2 % 5 2 % 1 9 % 1 2 % 2 0 % 2 5 % 4 3 % 3 1 % 14% 2 6 % 2 2 % 2 1 % 8 6 % 2 5 % 3 0 % 2 9 % 3 5 % 3 1 % 3 0 % 2 6 % 2 9 % 1 3 % 3 7 % 3 6 % 3 2 % 2 6 % 14% 3 0 % 3 1 % 2 1 % 3 0 % 3 3 % 5 % 4 1 % 3 0 % 3 1 % ||jI|P§ff|f|g IBjjt  % o f L's  42% 39% 56% 53% 60% 39% 49% 60% 58% 52% 46% 43% 54% 56% 48% 49% 9 % 38% 4 3 % 4 3 %  %ofS's  2 7 % 3 5 % 2 0 % 2 6 % 18% 4 7 % 18% 14% 18% 2 1 % 3 7 % 3 3 % 19% 2 6 % 2 6 % 2 4 % 8 3 % 3 2 % 3 0 % 3 1 %  % of M's  3 1 % 2 6 % 2 5 % 2 1 % 2 2 % 15% 3 3 % 2 6 % 2 4 % 2 7 % 17% 2 4 % 2 7 % 18% 2 5 % 2 7 % 8% 3 0 % 2 7 % 2 6 %  % o f L's %ofS's % o f M's  119  Table A.7. Experimental Data: Sag Combinations Summary - Phase I M  >R"  S = 'Rp =  24  25  26  27  Total # o f " S "  29  30  31  32  33  34  35  jjBil  ISlffiimatibiis Total # o f " L "  28  L = " Rp < R "  S a g Curves  O v e r l a p p i n g Test-Curve N o . 1 22 1 23  R"  13 26  12  7 21  15  14 15  9 14  12 30  9 9  36  37  38  39 J 40 | 41  >  7 8  11 10  8 21  9 24  16 31  11 23  16  10  13  22  13  16  10  16  59  23  11  6  36  57  60  81  81  81  Total # o f " M "  43  55  54  53  59  39  63  66  60  52  48  35  47  51  55  55  9  Sample Size  82  82  82  82  82  81  81  81  81  81  81  82  81  81  81  81  81  % o f L's %ofS's %ofM's Images Total # o f " L " Total # o f " S " T o t a l * of " M " Sample Size % o f L's %ofS's % of M ' s •\\cragc  15  14  16% 1 5 % 9 % 17% 1 1 % 15% 1 1 % 9 % 14% 10% 1 1 % 2 0 % 14% 17% 2 0 % 12% 16% 2 7 % 16% 19% 3 2 % 18% 2 6 % 18% 17% 3 7 % 1 1 % 10% 1 2 % 2 6 % 3 0 % 3 8 % 2 8 % 2 0 % 1 2 % 2 0 % 7 3 % 2 8 % 14% 7 % 52% 67% 66% 65% 72% 4 8 % 78% 8 1 % 74% 64% 59% 43% 58% 63% 68% 68% 11% 44% 70% 74%  s 14 29 48 91  i  10 28 53 91  USUI 12 29 50 91  11 16 64 91  8 10 73 91  6 42 43 91  9 20 62 91  12 17 62 91  12 21 58 91  7• 28 56 91  9 32 50 91  12 33 46 91  16 15 60 91  14 15 62 91  8 20 63 91  18  8  6  20  19  28  81  33  17  11  38  55  62  55 91  4 91  91  91  91  15% 1 1 % 1 3 % 12% 9 % 7 % 10% 1 3 % 1 3 % 8 % 10% 1 3 % 18% 1 5 % 9 % 9 % 7 % 2 2 % 2 1 % 2 0 % 3 2 % 3 1 % 3 2 % 18% 1 1 % 4 6 % 2 2 % 19% 2 3 % 3 1 % 3 5 % 3 6 % 16% 16% 2 2 % 3 1 % 8 9 % 3 6 % 19% 12% 53% 58% 55% 70% 80% 47% 68% 68% 64% 62% 55% 51% 66% 68% 69% 60% 4 % 4 2 % 60% 68%  Spit  % o f L's  16% 1 3 % 1 1 % 1 5 % 1 0 % 1 1 % 1 1 % 1 1 % 1 3 % 9 % 1 1 % 1 6 % 1 6 % 1 6 % 1 4 % 1 1 % 1 1 % 2 5 % 1 8 % 19%!  %ofS's  3 2 % 2 5 % 2 9 % 1 8 % 14% 4 2 % 1 7 % 1 4 % 1 8 % 2 8 % 3 2 % 3 7 % 2 2 % 1 8 % 1 7 % 2 5 % 8 1 % 3 2 % 1 6 % 1 0 %  % of M's  53% 63% 60% 67% 76% 48% 73% 75% 69% 63% 57% 47% 62% 66% 69% 64% 8% 4 3 % 65% 7 1 %  Table A.8. Sample Characteristics - Phase II E = Engineer  s J? \  Population Type  mi 11  ** 1 "c. | 1  G  F  si  B  2  G  M  B  3 4  G  F M  B B  M  5  B  tf*  a NORTH VAN.  N  13  A  38  T  F  A  VANCOUVER  Y  39  T  M  A  PORT M O O D Y  N  7  N  A A  A  B  40  M  VANCOUVER  N  8  N  D  VANCOUVER  Y  8  Y  C  C B  N  7  Y  C  A  m* w  mt  N  c A  mt  fi Pi tea*  • tf»  ex  _t id  IS  c mt  >  mi  s  mt *  T = Transportation Engineer  >  Population Type  G = General Public  x ry  it  illliiliii^llililiiii  a mt  mt  mi  m*  mt  tf*  it  mi  *s  «*  7  ..mm-.  Y  A  WILLIAMS L A K E  Y  15  N  VANCOUVER  N  15  Y  VANCOUVER  Y  9  N  B  B  41  E E  M  B B  VANCOUVER  Y  N  C  A  42  E  F  A  VANCOUVER  NAN1AMO  Y  N  B  A  43 44  E E  F  A  VANCOUVER  Y  1  Y  C  A  F  A  NORTH V A N .  N  7  Y  A  A  45  E  M  A  SURREY  N  4  N  A  B  46  E  F  B  RICHMOND  Y  6  Y  A  A B  21  6  F  7  M  8  F  C  VANCOUVER  Y  24  Y  M  B  VANCOUVER  Y  4  Y  B  B  9  E  10 11  G  F  D  VANCOUVER  N  30  N  B  B  47  T  M  A  VANCOUVER  Y  8  Y  C  G  M  D  VANCOUVER  Y  47  Y  C  B  48  E  M  B  VANCOUVER  N  11  Y  E  E  A  VANCOUVER  N  2  Y  C  A  49  E  F  A  COQUITLAM  Y  4  N  A  A  12  T  M  13  T  M  50  E  F  A  VANCOUVER  Y  6  N  C  B  51  G  F  B  VANCOUVER  Y  17  N  E  D  52  G  M  B  VANCOUVER  N  12  Y  C  A  12  Y  A  14  T  M  15  T  M  B  B  17  E  M  B  BURNABY  Y  15  Y  B  B  53 54  G  M  B  VANCOUVER  Y  15  N  D B  18  T  M  B  VANCOUVER  Y  9  Y  A  B  55  E  M  B  VANCOUVER  Y  3  N  C  B  19  E  M  A  VANCOUVER  Y  7  N  B  A  56  G  F  A  VANCOUVER  Y  2  N  C  A  20  E  M  B  VANCOUVER  N  2  Y  D  C  57  E  M  B  VANCOUVER  N  10  Y  C  A  E  M  B  NORTH VAN.  Y  7  Y  A  A  58  E  F  A  VANCOUVER  Y  8  N  C  A  VANCOUVER  Y  18  Y  C  A  59  E  M  A  VANCOUVER  N  6.5  N  B  B  60  E  M  B  VANCOUVER  N  20  N  E  C  61  E  M  C  VANCOUVER  N  29  Y  A  B  Y  5  N  E  E  16  21 22  E  T  M  M  B  C  23  G  M  C  24  G  M  D  VANCOUVER  N  11  Y  B  B  ARMSTRONG  N  37  N  A  A  VANCOUVER  N  43  Y  A  A  G  F  B  VANCOUVER  Y  M  B  PEMBERTON  Y  5  Y  C  A  62  E  M  A  VANCOUVER  G  F  C  ARMSTRONG  N  20  N  A  A  63  E  M  A  VANCOUVER  Y  A  A  M  C  VERNON  Y  38  N  C  D  64  E  M  C  RICHMOND  N N  7  G  23  Y  B  A  G  F  B  KELOWNA  N  21  Y  D  A  65  G  F  C  VANCOUVER  N  15  N  E  C  29  E  M  A  OTTAWA  Y  9  Y  D  B  66  E  M  B  NORTH VAN.  Y  18  Y  D  A  30  E  M  B  VANCOUVER  N  10  N  B  A  67  E  F  B  BURNABY  Y  10  N  A  A  B  VANCOUVER  Y  20  N  C  C  N  14  N  A  A  42  N  B  A A  25  G  26 27 28  VANCOUVER  Y  6  N  C  A  68  G  M  A  VANCOUVER  Y  5  Y  B  B  69  G  F  B  DELTA  B  VANCOUVER  Y  14  Y  E  B  70  G  M  D  NORTH VAN.  Y  M  A  VANCOUVER  Y  4  Y  B  A  71  E  M  A  VANCOUVER  Y  6  Y  C  M  B  VANCOUVER  Y  11  Y  B  A  72  E  M  B  VANCOUVER  Y  17  N  A  B  G  F  A  VANCOUVER  9  Y  D  A  73  G  F  B  VANCOUVER  Y  9  Y  D  A  T  M  C  BURNABY  N Y  28  Y  B  B  74  G  M  B  VANCOUVER  Y  10  Y  B  A  31  T  F  A  32  T  F  33  G  F  34  E  35  G  36 37  121  Table A.8. Cont lot  B i  a  y Cl  *t  H B w  1 s  B.  o  i-  1 miX  o  mi IMP mv SC f**l %af s ^BMI  X  M  • s g  ii  CU  *  B  a  H  r  «  0£  4*  t  ,-Sl  iVjM  CL  *  Q  £,  ICS*  N  10  Y  C  A  83  G  F  B  VANCOUVER  Y  12  Y  c  A  84  G  F  VANCOUVER  N  0  N  F  VANCOUVER  Y  13  Y  D  B  VANCOUVER  N  8  N  D  B  ALDERGROVE  N  9.5  N  A  B  s  er»  o  S Sir teal  4* SC  a  o  76 77  E E E  M  A  VANCOUVER  Y  6  Y  E  B  M  A  VANCOUVER  N  7  Y  D  A  85  G  M  A B  78  G  M  C  VANCOUVER  Y  31  N  B  A  86  G  F  A  79  G  M  C  VANCOUVER  80  G  F  B  VANCOUVER  81 82  T G  M M  B B  VANCOUVER VANCOUVER  zr  ii  "> b  75  VANCOUVER  w  '> 'E IQl  k  Cu  c  s $  B  r l i  F  *r  «*  y.  Y  8  Y  D  B  88  E E  N Y  11 12  N N  D B  D A  89 90  G G  N  17  Y  C  A  87  M  A  M  A  COQUTTLAM  M F  C C  VANCOUVER VANCOUVER  i*  Y  7  N  B  A  Y Y  38 35  Y Y  D D  G  122  Table A.9. Experimental Data: Image Crest Combinations - Phase II O v e r l a p p i n g  C r e s t  C u r v e  z  i 1 fes. 1 300  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  400  500  500  600  500  300  300  400  500  400  300  500  700  400  500  500  300  400  300  2  300  200  300  500  600  500  500  500  500  500  400  200  400  600  500  500  300  500  500  500  3 4  250  300  600  500  500  400  300  300  500  300  300  300  600  500, 400  500  500  500  500  250  200  400 300  600  600  500  400  300  400  400  500  200  300  700  400  300  400  400  500  500  .5  250  200  300  500  500  300  500  300  300  300  400  250  300  500  300  300  500  500  400  500  6  200  200  500  400  500  300  500  400  500  500  300  200  300  700  400  300  300  500  400  500  7  300  400  500  600  600  500  500  300  400  500  500  250  500  500  500  500  500  500  500  400  8  200  300  500  600  700  500  500  400  500  500  500  300  300  700  400  300  300  500  500  500  400  300  300  500  500  300  500  500  500  400  300  250  300  600  400  400  500  500  500  500  400  300  9  200  300  500  600  700  500  500  500  500  400  10  200  200  300  400  500  300  500  300  300  300  700  500  300  400  200  300 400  700  500  400  300  500  300  300 500  200  500  700  500  500  400  500  400  300  200  500  400  500  400  500  200  700  300  500  500  300 500  300  300  400 500  500 400  500  500  500  500  500  300  500  700  500  500  300  500  500  500  300  500  500  500  500  700  500  500  300  500  500  400  300  ,500 . 500  300  300 200  500  700  500  500  300  500  500  500 500  500  300  500  300  500  300  300  500  300  300  500  400  500  400  500  500  300  500  700  500  300  500  500  500  500  400  400  400  500  200  500  400 400  500  500  400  400  300  400  500  500  300  500  700  500  700  500  300  300  500  300  300  400  400  300  500  500  700  500  600  700  300  600  500  600  500  500  400  300  400  500  500  500  500  500  300  600  700  500  300  300  400  400  600  300  300  400  500  600  600  300  400  500  600  17- 250  400  500  18  300  200  19  200  300  11  250  200  400  12 13  300  300  300  400  14  250  15 16  20  300  200  500  600  700  500  500  400  500  400  300  250  300  700  500  300  300  500  300  300  200  300  700  400  300  400  300  300  300  400  400  300  300  500  200  300  500  500  500  500  500  400  300  400  400  500  500  500  250  300  700  300  400  500  300  300  500  400  400  400  300  500  400  200  400  700  300  500  300  500  400  300  600  500  400  300  300  300  300  250  400  500  500  300  500  400  500  500  500  400  300  500  400  400  300  300  600  500  500  400  400  500  400  300  300  500  500  500  300  200  300  500  300  300  400  300  300  300  500  500  400  500  300  200  300  400  700  300  22  200  200  300  400  500  500  23  300  300  500  500  700  300  24  200  200  500  400  700  400  25  300  200  400  400  700  26  200  200  500  600  27  250  400  500  400  700  28  200  400  300  600  500  400  500  300  500  200  500  700  500  500  500  500  300  500  250  400  700  400  300  300  300  400  300  300  300  500 • 4 0 0  300  300  700  300  300  500  500  300  500  500  300  500  300  300  300  500  500  500  400  500  300  300  400  500  500  500  300  300  500  600  500  500  500  500  500  500  500  500  400  300  300  300  250  300  500  300  500  500  300  300  400  500  500  400  500  400  500  250  400  700  400  300  400  300  300  300  300  500  300  300  400  500  500  500  500  600  700  500  400  400  500  500  400  300  300  400  700  500  300  200  300  400  700  300  500  250  300  300  500  500  400  34  200  300  300  400  700  35  200  300  500  400  700  200  300  400  30  250  400  31  200  200  32  200  33  300  300  21  29  400  500  36  200  200  300  400  500  300  300  400  300  300  300  200  300  500  300  37  250  400  500  600  700  500  300  500  300  400  500  300  500  700  500  500  38  250  200  300  600  500  400  300  300  500  400  300  200  300  700  300  400  500  500  300  400  39  200  200  500  400  600  500  300  500  500  400  300  200  300  700  300  300  300  400  300  500  40  250  400  500  600  600  400  500  400  300  400  400  300  500  700  500  500  500  400  500  500  41  200  400  400  400  500  500  400  300  500  300  500  200  300  300  400  400  42  250  400  500  600  500  500  500  500  500  500  500  300  300 . 500 400 300 500 600 500 " 5 0 0  500  300  400  400  123 Table A.9. Cont. 43  300  300  400  600  700  500  500  500  500  400  500  200  300  600  400  500  500  500  400  500  300  500  44  300  300  400  400  600  300  500  500  500  500  500  250  300  700  500  400  400  500  45  250  400  400  600  700  500  500  500  500  500  500  300  500  700  500  300  500  500  500  500  46  200  300  300  400  700  300  400  400  300  500  500  200  400  500  500  400  500  300  300  300  47 48 49  300  400  500  600  700  500  400  500  300  500  400  300  500  600  500  300  500  500  300  500  200  200  500  600  500  400  300  400  400  500  300  250  400  700  300  400  500  500  400  500  200  400  500  400  700  300  500  500  300  500  400  300  500  500  500  500  400  400  300  500  300  500  500  600  400  500  500  500  400  400  300  400  700  500  400  500  500  400  500  400  400  400  500  400  250  500  700  300  400  500  500  500  500  500  500  250  300  600  500  500  500  300  500  500  500  300  400  500  500  500  500  500  500  500  500 400  50 51 52 53 54  300 300 250 250 250  300 400 300 400  500 500 300 500  400 400 400 600  500 700 500 700  500 300 300 500  400 500 500  500 500 300  500 500 500  400 500  400 500  200 300  400 500  700  500  500  55  300  400  500  500  700  400  500  500  500  400  400  200  500  700  500  500  500  500  500  56  300  300  400  500  600  400  500  500  400  300  500  300  500  700  500  400  500  500  400  400  57  250  400  500  600  600  500  400  500  500  500  300  300  500  600  500  500  500  500  400  500  58  300  200  500  600  700  300  400  300  400  300  300  250  300  700  500  300  400  300  500  500  59  200  300  500  600  600  500  500  500  300  500  500  300  500  700  500  500  500  500  500  400  60  250  400  500  400  700  500  300  300  500  500  500  300  300  700  500  300  400  300  300  500  61  300  300  500  500  700  400  500  300  500  400  500  250  400  500  400  400  500  500  400  500  500  500  500  400  500  500  200  300  500  300  500  500  500  500  500  500  400  200  500  500  300  500  400  400  500  500  700  500  500  400  500  500  500  400  300  400  62 63 64  200 300 250  200 200 400  500 300 500  600 600 600  600 700 700  300 500  500 500  500 500  300 300  500  300  250  500  65  300  300  400  500  600  400  400  400  500  400  400  250  400  600  400  300  400  66  250  400  500  600  700  400  500  500  500  500  500  200  500  700  500  500  500  500  500  500  67  200  300  500  600  600  300  500  500  500  500  300  200  300  500  500  500  500  300  300  300  68  250  200  300  600  500  400  300  400  500  500  400  200  400  700  300  500  500  500  500  300  69  250  400  500  600  700  300  300  500  300  300  300  250  500  500  500  500  400  300  300  500  70  200  400  500  400  500  500  500  300  300  300  400  200  300  700  400  500  400  400  300  400  71  200  400  500  600  600  500  500  300  500  500  400  200  500  500  400  500  500  500  400  500  500  500  500  400  500  250  500  500  500  500  500  500  500  500  300  300  700  300  400  500  300  300  300  300  500  500  500  500 300  72 73 74  250 200 300  300 200 400  500  400 500  500  500  400  500  500  500  400  200  500  700  400  500  500  500  300  400  300  400  500  500  300  500  700  500  500  500  300  500  400  300  400  500  500  300  200  300  700  300  400  300  400  500  500  500  500  300  300  300  300  300  700  500  500  500  400  500  500  500  300  200  500  700  300  500  500  300  400  300  600  500  500  300  500  500  500  500  500  400  500  700  400  500  300  600  500  500 500  300 300  500 500  500 600  700 500 700  500 400  400 500  500 300  500 500  300  200  500  500  500  500  500  500  500  500  500  300  300  500  700  400  300  500  500  500  500  300  700  400  500  500  500  500  500  300  500  700  500  500  500  500  500  500  500  300  400  600  400  400  400  400  500  400  400  200  400  600  400  500  400  500  500  500  700  500  400  400  300  300  400  500  400  300  500  300  400  400  500  200  500  700  500  500  300  200  500  500  400  500  300  300  500  500  500  400  300  500  500  500  500  500  500  300  300  300  300  200  300  600  700  500  500  300  500  83  250  200  400  500  700  300  500  500  84  250  400  500  500  600  300  300  500  85  300  400  500  600  700  500  400  400  500  600  700  500  250  500 500  82  86  500 500  600  600  500 600  600  400  300 300  600  300  300 200  500  78  300 500  400  200  500  500  300  300  300  500  400  400  400  400  400  500  500  300  300  500  300 500  250  81  500  300 300  77  300  600  500  500  700  76  80  500  500  700  600  300  250  300  400  300  75  79  400  87  200  300  500  500  600  400  400  500  88  200  400  400  600  500  500  400  500  89  300  300  500  600  500  500  300  500  300  400  400  250  500  90  200  400  400  600  600  400  500  300  300  300. 400  300  500  124  Table A.10. Experimental Data: Image Sag Combinations - Phase II O v e r l a p p i n g  S a g C u r v e  Y.  i>  e. E a  mm 22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  600  500  600  500  1  500  600  800  900  700  700  500  700  700  700  400  600  800  700  2  300  600  700 600  700  800  800  600  600  700  600  600  600  300  500  700  700  500  700  500  700  500  3  300  600  500  700  800  500  700  700  700  700  600  300  700  900  500  500  500  500  700  600  4  300  400  600  600  800  500  700  500  700  700  500  300  600  800  500  500  700  500  500  500  5  300  500  700  800  900  500  700  600  500  500  600  300  600  900  600  700  500  600  700  500  6  500  600  700  600  900  500  600  600  500  700  600  300  500  800  600  500  500  600  700  500  7  300  600  700  700  900  600  600  500  500  700  600  500  600  900  600  500  500  600  600  700  8  400  600  500  800  900  700  700  700  700  700  700  400  600  900  600  500  700  700  700  700  9  300  600  700  700  900  600  600  600  600  600  600  400  500  700  600  500  600  500  500  500  700  900  700  600  700  600  700  700  400  500  900  500  700  500  500  500  500  700  700  500  500  700  700  600  600  700  500  700  500  700  600  500  700  600  10 11  500 300  600 500  600 600  800  900  700  700  700  12  400  400  700 .600  800  700  700  700  600  700  600  500  700  700  700  13  300  700  800  800  700  700  700  600  700  700  500  700  900  700  700  600  700  700  700  14  300  600 400  700  600  700  500  500  500  500  500  500  800 800  500  500  700  600  500  500  15  400  500  600  800  900  700  700  700  700  600  500 700  300  500 700  500  700  500  700  500  16  300  600  700  800  800  700  700  700  700  600  600  300  700  800  500  700  700  600  700  600 500  17  400  500  700  700  700  600  600  700  600  600  600  300  500  700  500  500  500  500  500  600  18  300  500  500  600  900  700  700  700  600  700  600  500  600  700  600  500  700  700  500  600  19  400  500  600  800  900  500  700  500  700  500  700  500  500  700  500  600  500  600  500  700  400  500  700  800  900  700  700  600  700  700  600  300  500  900  700  500  500  500  500  600  800  700  500  700  700  600  700  600  400  500  800  500  500  500  600  600  600  500  400  600  700  500  500  700  500  500  600  700  600  500  600  500  600 600  20 21 22 23  300 400 500  500 400 600  600 500 700  700 800  700 900  30  300  500  600  800  900  700  700  700  600 700  700  500  600  600  500  700  700  500  500  500  600  700  700  500  900  700  500  500  600  700  700  700  700  700  600  700  500  500  700  500  300  700  600  700  700  600  800  600  700  700  600  500  300  500  700  500  700  700  500  600  900  700  800  700  500  600  700  600  900  700  700  400  600  700  600  500  700  700  700  700  500  700  800  700  700  600  500  500  900  500  700  400  700  500 600  600  700  27  700  300  500  800  700  400  500  700  600  700  700  600  600  500  400  700  700  300  500  700  500  500  500  600  700  800  700  600  500  700  700  700  600  700  700  600  500  600  700  500  500  500  900  600  600  500  500  500  500  700  400  600  700  700  700  500  500  500  500  700  500  700  700  700  600  500  700  700  700  300  600  700  700  600  500  500  500  500  700  700  700  500  600  600  800  900  700  600  700  700  700  700  400  700  32  300  600  600  800  900  500  700  500  700  600  600  500  33  400  600  700  700  900  600  700  600  700  500  500  300  34  400  400  500  800  900  600  600  600  700 . 700  600  35  300  400  700  600  700  600  500  500  700  500  600  700  600  600  31  36 37  400 300  38  400  600 400  700 500  700 600  700 700  500 500  700  700  500  900 700  700  400  500  600 600  700  300  26  500  400 500  25  500  500 700  900  300  600 700  800  29  600  600  700  500  700  700  600  700  600  600  700  500  700  400  500  500  700  600  24  28  600  500  500  600  600  800  800  600  600  500  500  600  600  500  500  900  500  600  500  39  500  500  500  700  800  600  600  700  700  700  600  300  600  700  500  700  500  600  500  500  40  500  600  700  800  700  700  700  700  700  700  700  700  700  500  600  800  700  700  500  700  700  900  500  500  500 700  600  400  300 300  900  500  700 700  700  41  700 700  700  500  500  42  300  500  700  700  800  500  600  600  700  600  600  400  500  800  700  500  600  500  700  700  125  Table A.10. Cont. 43 44  500 500  600 600  700 700  800 700  900 900  700 600  700 700  700 700  600 700  700 700  700 700  500  700  900  500  700  500  500  700  700  400  500  900  700  700  600  700  600  700  700  700  700  45  300  500  700  700  900  700  600  600  600  700  600  500  500  900  700  700  700  46  400  400  500  600  700  700  600  600  600  500  700  500  500  700  500  700  500  500  600  600  47  500  400  700  700  900  700  600  700  600  700  600  300  600  800  700  700  500  600  600  600  48 49  400  500  600  600  900  600  700  700  700  700  600  300  700  900  700  600  500  600  600  600  400  600  700  800  700  700  700  600  600  600  700  300  600  900  700  700  600  600  500  700  50  300  500  700  700  900  700  700  600  700  700  700  400  600  700  700  500  500  500  500  500  600  700  800  900  600  700  700  700  700  700  300  500  900  700  500  500  500  700  500  900  700  700  700  700  600  700  400  700  700  700  700  500  500  700  700  700  500  700  400  500  800  600  600  600  600  600  500  300  500  900  600  700  700  600  700  700  700  600  600  700  700  700  700  500  500  500  600  500  51 52 53 54 55 56  300 500 300 500 500 500  500 500 400 400 500  700 700 500 700 500  600 700 800 700 600  900 900 900 900  700 600 700 700  600 700 700 700  600 600 600 600  700 500 700  600 600 700  700 700 700  500 400  600 700  800  700  57  400  600  700  800  900  600  600  700  700  600  600  400  700  900  600  700  700  500  600  600  58  500  400  700  700  700  600  700  700  700  600  500  500  700  700  500  600  500  600  500  600  59  300  400  700  800  800  500  500  600  600  600  600  300  500  800  500  500  700  500  600  600  60  300  600  700  700  900  500  700  600  700  500  700  400  600  900  600  600  700  500  600  500  61  400  400  600  800  800  500  500  600  500  700  500  300  500  900  500  700  500  500  700  600  62  400  500  600  700  800  700  500  600  700  700  700  400  600  900  600  700  700  700  700  600  700  800  500  700- 700  700  700  700  400  500  800  700  600  600  600  700  500  700  600  500  700  700  400  700  800  500  700  500  600  700  700  700  700  700  500  700  900  700  700  500  700  700  700  700  900  500  700  500  500  700  500  700  600  700  600  600 600  63 64 65 66 67  300 500 500 300 300  600 600 600 600 500  500 600 700 700 700  800 800 800 800  700 900 900 800  700 700 600  700 700 700 700  700 700 700  500 700  500 700  700 700  300 400  700  700  700  68  400  400  500  800  900  700  500  500  500  700  700  300  600  900  600  500  500  500  700  69  400  400  700  800  700  600  500  700  700  600  600  400  500  900  700  700  500  600  700  500  70  400  400  500  600  800  600  500  500  700  700  500  300  600  900  700  500  600  600  700  500  71  500  400  500  700  700  600  600  700  700  700  600  300  600  800  700  700  600  500  600  700  800  800  600  600  600  600  700  700  400  500  700  500  500  500  600  600  500  700  600  500  300  500  700  700  600  600  500  600  500  900  700  700  500  500  500  700  900  700  700  600  500  700  700 500  72 73  400 300  400 600  700 600  800  800  700  700  700  74  300  500  700  600  800  500  500  600  700  600  600  500  600  75  300  600  700  800  900  700  700  600  700  700  500  500  500  79 80 81 82  400  400  600  600  500  600  600  900  700  500  600  500  500  700  500  700  600  500  500  600  500  500  500  500  600 500  700  700  700  700  700  500  600  600  600  600  600  600  700  600  500  600  600  700  400  700 700  900 700 700  500 600  500 600  700 600  600  300  700  700  700  700  600  500  700  400  600  800  700  700  500  500  500  500  600  500  300  500  800  700  500  500  500  500  500  600  600  700  700  400  700  900  700  700  500  700  700  600  600  700  700  600  500  500  600  900  600  600  500  500  600  500  700  600  700  700  700  300  500  900  700  700  600  500  600  600  700  600  500  500  300  700  700  700  500  700  500  700  500  500  700  700  700  700  500  600  600  500  600  700  800  900  600  500  500  500  600  800  900  600  500  500  86  500  600  700  800  900  700  700  87  400  500  700  600  900  600  800  600  800  900 900  600 700  400  600  300  800  600  500  400  800  600  700  500  85  700  700  900 "700  84  600  500  800  600  400  500  500  600  90  700  500  300  700  700  700  500  500  700  600  400  700  700  700  900  300  700  500  700  800  89  700  600  700  500  700  700  500  700  400  600  700  700  600  300  500  700  900  500  900  83  88  700  500  800  800  600  700  500  500  600  700  400  600  500  700  700  400  600  700  300  600  600  700  700  500  400  500 600  500  400  500  800 700  500  500 500  700  700  300  78  500  700  700  77  500  600  700  500  700  800  600  76  700  700  700 . 700  700  700  700  126  Table A . l l . Experimental Data: Crest Combinations Summary - Phase II  Overlapping 300  400  500  600  700  500  500  500  Crest 500  500  Curves 500  300  500  700  5  Ki  500  500  500  500  500  500  500  500  500  600  700  500  500  500  500  500  500  300  500  700  500  400  500  400  400  400  300  300  200  300  600 500  400 300  400 300  400  300  400 300  250  300  400 300  400  300  600 500  400  400  300  400 300  400 300  400 300  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  Total Sample Size 90 32 Total» o f T"  90 34  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  49  48  43  47  47  43  48  37  33  37  50  49  46  57  50  45  90 54  29  29  18  18  22  20  24  19  49 14  20  26  20  16  15  21  18  20  17  19  21  37  25  20  26  13  23  26  15  R : p  "T" = 300  400  " M " = 250 "B" = 200  300 200  Test-Curve No.  Total # of "M" Total# of "B" %ofT's % of M's % of B's % (M + B) Ran  Ave.  R p  STDEV VAR  29  27  23  24  25  23  19  28  36% 38% 54% 53% 48% 52% 52% 48% 32% 32% 20% 20% 24% 22% 27% 21% 32% 30% 26% 27% 28% 26% 21% 31% 64% 62% 46% 47% 52% 48% 48% 52%  27  22  27  37  54% 53% 41% 37% 41% 56% 54% 51% 63% 56% 50% 60% 16% 22% 29% 22% 18% 17% 23% 20% 22% 19% 21% 23% 30% 24% 30% 41% 41% 28% 22% 29% 14% 26% 29% 17% 46% 47% 59% 63% 59% 44% 46% 49% 37% 44% 50% 40%  300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  252  308  429  527  620  427  431  417  424  429  411  248  400  628  432  422  449  430  421  443  84 84 89 88 80 85 85 82 85 86 41 1711 6793 7246 7371 7236 7146 6437 7697 7935 7021 7066  87 77 85 74 1961 8315 7647 6703 7591 5448 7292 7527 5854 44  91  87  82  87  127  Table A.12. Experimental Data: Sag Combinations Summary - Phase II  Sag C u r v e s  Overlapping 300 Ract R : "T" = 300 p  81 a o Q.  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  600  600  "M" = 400 "B" = 500  500  600  700  800  600  600  600  600  600  600  400  600  800  600  600  600  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  Total Sample Size 90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  Total # of "T"  35  28  19  19  18  20  15  14  15  34  32  27  33  29  38  24  21  26  24  34  22  29  25  29  28  20  19  17  51 19  39  28  15 29  36  Total # of "M"  16 29  30  21  25  Total* of "B"  27  38  50  45  48  36  53  45  47  50  46  25  28  38  44  40  20  21  40  27  %ofT's Ul  500  400  600  Test-Curve No.  CO  500  400  % of NTs % of B's  17% 40% 38% 36% 30% 37% 57% 43% 32% 42% 31% 27% 23% 29% 27% 38% 24% 32% 32% 28% 32% 32% 31% 22% 21% 19% 21% 33% 23% 28% 30% 42% 56% 50% 53% 40% 59% 50% 52% 56% 51% 28% 31% 42% 49% 44% 22% 23% 44% 30% 61% 69% 79% 79% 80% 78% 83% 82% 84% 83% 83% 60% 62% 64% 70% 63% 43% 57% 68% 58% 39% 31% 21% 21% 20% 22%  17%  18%  16%  17%  CO  % ( M + B)  or  R ,  300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  Ave. Rp  391  511  634  729  833  618  642  632  637  639  634  388  593  807  619  608  566  580  612  588  STDEV VAR  80 87 85 87 90 82 82 83 88 74 75 76 76 76 81 79 77 85 80 83 6886 7291 6553 6347 6292 5973 5838 5804 5494 5774 5654 6703 6921 7820 7617 8141 6778 6337 7602 7152  tl)  ac  Table A.13. Modified Data: Image Crest Combinations - Phase II  Sample No.  O v e r l a p p i n g  1  2  3  4  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  300  300  300  300  300  200  300  500  300  300  300  300  300  300  300  300  300  200  300  500  300  300  300  300  300 300  300 300  300  500  300  300  300  300  300  300  300  300  300  300  300  300  300  300  1  200  200  300  400  500  2  200  200  300  400  500  300  200  200  300  400  200  300 300  300  300  200  300  500  300  300 300  300  300  200  300  500  300  500  300  300  300  300  300  300  200  300  500  300  300  300  300  300  300  300  300  300  300  300  300  200  300  500  300  300  300  300  300  300  300  400  500  300  300  300  300  300  200  300  500  300  300  300  300  300  400  500  300  300  300  300  300  200  300  500  300  300  300  300  300 300  300  200  300 300  200  200  300  400  500  300  300  300  300  300  300  200  300  500  300  300  300  300  300  300  200  200  300  400 400  500  300  300  •300  300  300  300  200  300  500  300  300  300  300  500  300  300  300  300  300  300  200  300  500  300 ' 300 300 300  300  300  300  300  300  300  300  300  200  300  500  300  300  300  300 300  300  300  300  300  200  300  500  300  300  400  300  300  300  300  500  300  300  400  300  300  300  300  300  400  300  8  200  200  9  200  10  15  300  500  300  200  14  300  400  200  200  7  13  300  400  200  6  200 200 200 200  200 200 200 200  300 300 300 300  400 400 400  500 500 500  300 300 300  300  300  300  400  500  300  300  300  200  5  12  300  500  400  200  11  500  300 300  300 300  200 200  4  C u r v e  5  300  3  C r e s t  300 300  300 300  300 300  300  300  200  300  16  200  200  300  400  500  300  300  300  300  300  300  200  .300  500  300  300  400  17  200  200  300  400  500  300  300  300  300  300  300  200  300  500  300  300  400  300  300  400  18  200  200  300  400  500  300  300  300  300  300  300  200  300  300  400  300  300  400  200  200  300  400  500  300  300  300  300  300  300  200  300 300  500  19  500  300  300  400  300  300  400  20  200  200  300  400  500  300  400  300  300  300  300  200  300  500  300  300  400  300  300  400  21  200  200  300  400  500  300  400  300  300  300  300  200  300  500  400  300  400  300  300  400  300  400  500  300  400  300  300  300  300  200  300  500  400  300  400  300  300  400  400  300  300  400  300  200  300  500  400  300  400  300  300  400  300  400  300  200  300  500  400  300  400  400  300  400  300  500  400  300  400  400  300  400  300  400  400  300  400 400  22 23 24 25 26  200 200 200 200 200  200 200 200 200 200  300 400 400 400  400 400 500 500  500 500 500 600  300 400 400 400  400 400 400  400  400  400  400  300  400  400  400  200  300  600  400  400  400  400  400  400  400  400  400  400  400  200  300  600  400  400  400  400  400  400  400  400  400  400  400  200  300  600  400  400  400  400  400  400  400  400  400  200  300  600  400  400  400  400  400  400  300  600  .400  400  400  400  400  400  400  400  200  300  400  500  600  400  400  500  600  400  32  250 250  300 300  400 400  500 500  600 600  400 400 400  400 400  28  600  600 600  400  500  300 300  400  400  200 200  600  300  300  200  300  500  250  400  300  400  400  .30 31  300  400  300  200 300  300  300  300  200 200  300  400  27 29  300  400 400  400 400  400  400  400  200  33  250  300  400  500  600  400  400  400  400  400  400  200  .300  600  400  400  400  400  34  250  300  400  500  600  400  400  400  400  400  400  200  300  600  400  400  500  400  400  400  35  250  300  400  500  600  400  400  400  400  400  400  200  300  600  400  400  500  400  400  400  300  400  500  600  400  400  400  400  400  400  200  300  600  400  400  500  400  400  400  500  600  400  400  400  400  400  400  200  300  600  400  400  500  400  400  500  400  400  400  400  400  250  400  600  400  400  500  400  400  500  400  250  400  600  400  400  500  400  400  500  400  400  500  400  400  500 500 500  36 37 38 39 40  250 250 250 250 250  300 300 300 300  400 400 400 400  500 500 500  600 600 600  400 400 400  41  250  300  400  500  600  400  42  250  300  500  500  600  400  400 400  400 400  400 ' 400 400 400  400 400  400 400  400  250  400  600  400  400  400 ' 250  400  .700  400  400  500  500  400  500  400  400  400  700  500  400  500  500  400  250  129  Table A.13. Cont. 43 44  250 250  300 300  500 500  600 600  600 600  400 500  400 500  400 400  500 500  500 500  400 400  250  400  700  500  400  500  500  400  500  250  400  700  500  400  500  500  400  500  400  500  45  250  300  500  600  600  500  500  400  500  500  400  250  400  700  500  500  500  500  46  250  300  500  600  600  500  500  400  500  500  400  250  400  700  500  500  500  500  500  500  47  250  300  500  600  600  500  500  400  500  500  400  250  400  700  500  500  500  500  500  500  48  250  300  500  600  700  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  49  250  300  500  600  700  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  50  250  300  500  600  700  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  300  500  600  700  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  500  400  250  400  700  500  500  500  500  500  500  700  500  500  500  500  500  500  700  500  500  500  500  500  500  500  500  500  500  500  500  500  500  51 52 53 54 55 56  250 250 250 250 250 250  300 300 300 300 300  500 500 500 500 500  600 600 600 600 600  700 700 700 700 700  500 500 500 500  500 500 500 500  500 500 500 500  500 500 500 500  500 500 500  500 500 500  250 250 250  500 500 500  700  57  250  400  500  600  700  500  500  500  500  500  500  250  500  700  500  500  500  500  58  250  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  59  300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  60  300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  61  300  400  500  600  700  500  600  500  500  500  500  300  500  700  500  500  500  500  500  500  62  300  400  500  600  700  500  600  500  500  500  500  300  500  700  500  500  500  500  500  500  500  600  600  600  500  500  300  500  700  500  500  500  500  500  500  600  500  300  500  700  500  500  500  500  500  500  500  700  500  500  500  500  500  500  500  500  500  500  600 600  63 64 65 66  300 300 300 300  400 400 400 400  500 600 600 600  600 600 600 600  700 700 700 700  500 500 500  600 600 600  600 600 600  600 600 600  600 600  500 500  300 300  700  600  600  500  600  300  500  700  600  600  500  600  500  600  300  600  700  600  600  500  600  600  600  500  300  600  700  600  600  500  600  600  600  600  500  300  600  800  600  600  500  600  600  600  600  600  500  300  600  800  600  600  500  600  600  600  600  600  500  300  600  800  600  600  500  600  600  600  600  800  600  600  500  600  600  600  600  600  400  600  600  700  500  600  600  600  600  500  300  68  300  400  600  600  800  500  600  600  600  600  500  69  300  400  600  700  800  500  600  600  600  600  500  70  300  400  600  700  800  500  600  600  600  600  71  300  400  600  700  800  500  600  600  600  700  800  500  600  600  600  600  73 74  300 350  400 400 400  600 600 600  700 700  800 800  500 500  600  600  500  500  300  300  700  500  67  72  500  600  600  500  300  75  350  400  600  700  800  500  600  600  600  600  500  300  600  800  600  600  500  600  76  350  400  600  700  800  500  600  600  600  600  500  300  600  800  600  600  500  600  600  600  77  350  500  600  700  800  500  600  600  600  600  500  350 . 600  800  600  600  500  600  600  600  78  350  500  600  700  800  500  600  600  600  600  500  350  600  800  600  600  500  600  600  600  700  800  500  600  600  600  600  600  350  600  800  600  600  500  600  600  600  600  600  600  600  600  350  600  800  600  600  500  600  600  600  600  350  600  800  600  600  500  600  600  600  600  600  600  79 80 81  350 350 350  500 500 500  600 600 600  700 700  800 800  600 600  600  600  600  600  82  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  500  83  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  500  600  600  600  84  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  500  600  600  600  85  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  500  600  600  600  86  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  600  600  600  600  600  700  800  600  600  600  600  600  600  350  600  800  600  600  600  600  600  600  600  600  600  600  600  350  600  800  600  600.  600  600  600  600  600  800  600  600  600  600  600  600  600  600  600  600  600  600  87 88 89 90  350 350 350 350  500 500 500 500  600 600 600  700 700 700  800 800 800  600 600 600  600 600  600 600  600 600  600 600  600 600  350 350  600  800  Table A.14. Modified Data: Image Sag Combinations - Phase II O v e r 1 a p p in g S a g  C u r v e  o Z  ii  "EL £ 22 1 2 3  500 500 500  23 600 600 600  24 700 700 700  25 800 800 800  26 900 900 900  27 700 700 700  28  29  30  700  700  700  700  700  700  700  700  700  31  32  33  34  35  36  37  38  39  40  41  700 700  700  500  700  900  700  700  700  700  700  700  500  700  900  700  700 700  700  700  700  700  900  700  700  700  700  700  700  700  700  700  700  500  700  4  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  5  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  6  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  7  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  8  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  9  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  900  700  700  700  700  700  700  700  700  700  700  700  700  700  700  10 11 12 13 14 15  500 500 500 500 500 500  600 600 600 600 600 600  700 700 700 700 700  800 800 800 800 800  900 900 900 900 900  700 700 700 700  700 700 700 700  700 700 700  700 700 700  700 700  700 700  500 500  700  900  16 17  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  18  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  19  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  20  500  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  700  800  900  700  700  700  700  700  700  500  700  900  700  700  600  700  700  700  .700  700  700  700  700  500  700  900  700  700  600  600  700  700  700  500  700  900  700  700  600  600  700  700  500  700  900  700  700  600  600  700  700  700  700  600  600  700  700 700  21 22 23 24 25  500 500 500 500 500  600 600 600 600 600  700 700 700 700  800 800 800 800  900 900 900 900  700 700 700 700  700 700 700  700 700 700  700 700 700  700 700 700  700 700  500  700  900  26  500  600  700  800  900  700  700  700  700  700  700  400  700  900  700  700  600  600  700  27  500  600  700  800  900  700  700  700  700  700  700  400  700  900  700  700  600  600  700  700  600  700  800  900  700  700  700  700  700  700  400  700  900  700  700  600  600  700  600  700  700  700  700  700  700  400  600  900  700  700  600  600  700  600  700  700  400  600  900 . 700  700  600  600  700  600  600  900  700  600  600  700  600  600  700  600  28 29 30 31  400 400 400 400  600 600 600  700 700 700  800 800 800  900 900 900  700 700  700 700  700 700  700 700  700  700  400  700  32  400  600  700  800  900  700  700  700  700  700  700  400  600  900  700  700  600  33  400  600  700  800  900  700  700  700  700  700  700  400  600  900  700  700  600  600  700  600  34  400  600  700  800  900  700  700  700  700  700  700  400  600  900  700  700  600  600  700  600  400  600  700  800  900  700  700  700  700  700  700  400  600  900  700  700  600  600  700  600  700  800  900  700  700  700  700  700  700  400  600  900  700  700  600  600  700  600  600  700  700  700  700  700  400  600  900  700  700  600  600  700  600  700  700  700  400  600  900  700  700  600  600  700  600  800  700  700  600  600  700  600  700  500  600  700  600 600 600  35 36 37 38 39 40  400 400 400 400 400  600 600 600 500 500  700 700 700 700  800 800 800 800  900 900 900 900  600 600 600  700 700 700  700 700 700  700 700  700 700  700 700  400 400  600 600  800  700  41  400  500  700  800  900  600  700  700  700  700  700  400  600  800  700  600  500  600  600  42  400  500  700  800  900  600  700  700  700  700  700  400  600  800  700  600  500  600  600  131  Table A . H . Cont. 43 44 45  400 . 500 400 400  500 500  700 700 700  800 800 800  900 900 900  600 600 600  700 700 700  700 700 700  700 700 700  700 700 700  700  400  600  800  700  600  500  600  600  600  700  400  600  800  700  600  500  600  600  600  800  600  600  500  600  600  600  600  600  600  700  400  600  46  400  500  700  700  900  600  700  600  700  700  700  400  600  800  600  600  500  47  400  500  700  700  900  600  700  600  700  700  600  400  600  800  600  600  500  600  600  600  48 49  400 400  500  700  600  700  600  600  700  600  400  600  800  600  600  500  600  600  600  700  700 700  900  500  800  600  700  600  600  700  600  400  600  800  600  600  500  600  600  600  50  400  500  700  700  800  600  700  600  600  700  600  400  600  800  600  600  500  600  600  600  500  600  700  800  600  700  600  600  600  600  400  600  800  600  600  500  600  600  600  800  600  700  600  600  600  600  400  600  800  600  600  500  500  600  600  700  600  600  600  600  400  600  800  600  600  500  500  600  500  600  600  400  600  800  600  600  500  500  600  500  600  800  600  600  500  500  600  500  800  600  600  500  500  600  500  600  500  51 52 53 54 55 56  400 400 400 400 400 300  500 500 500 500 500  600 600 600 600 600  700 700 700 700 700  800 800 800 800  600 600 600 600  600 600 600  600 600 600  600 600 600  600 600  600 600  300 300  600  57  300  500  600  700  800  600  600  600  600  600  600  300  500  800  600  600  500  500  58  300  500  600  700  800  600  600  600  600  600  600  300  500  800  600  500  500  500  600  500  59  300  500  600  700  800  600  600  600  600  600  600  300  500  700  600  500  500  500  600  500  60  300  500  600  700  800  600  600  600  600  600  600  300  500  700  600  500  500  500  600  500  61  300  500  600  700  800  600  600  600  600  600  600  300  500  700  600  500  500  500  600  500  300  500  600  700  800  600  600  600  600  600  600  300  500  700  600  500  500  500  500  500  700  800  600  600  600  600  600  600  300  500  700  600  500  500  500  500  500  600  600  600  600  600  600  300  500  700  500  500  500  500  500  500  600  600  300  500  700  500  500  500  500  500  500  700  500  500  500  500  500  400  700  500  500  500  500  500  400 400  62 63 64 65  300 300 300  400 400 400  600 600 600  700 700  800 800  600  600  600  600  66  300  400  600  700  800  600  600  600  600  600  600  300  500  67  300  400  600  700  800  600  600  600  600  600  600  300  500  68  300  400  600  700  800  600  600  600  600  600  600  300  500  700  500  500  500  500  500  69  300  400  600  700  800  600  600  600  600  600  600  300  500  700  500  500  500  500  500  400  70  300  400  600  700  800  600  600  600  600  600  600  300  500  700  500  500  500  500  500  400  71  300  400  600  700  800  500  600  600  600  600  600  300  500  700  500  500  500  500  500  400  500  600  800  500  600  600  600  600  600  300  500  700  500  500  500  500  500  400  600  600  600  600  600  300  500  700  500  500  500  500  500  400  600  600  300  500  700  500  500  500  400  500  400  700  500  500  500  400  500  400  400  400  72 73 74 75  300 300 300 300  400 400 400 400  500 500 500  600 600 600  700 700 700  500 500 500  600 600  600 500  600 600  600  600  300  500  76  300  400  500  600  700  500  500  500  600  500  500  300  500  600  500  500  500  400  77  300  400  500  600  700  500  500  500  500  500  500  300  400  600  500  500  500  400  400  400  78  300  400  500  600  700  500  500  500  500  500  500  300  400  600  500  500  500  400  400  400  600  700  500  500  500  500  500  500  300  400  600  400  500  500  400  400  400  500  500  500  500  500  200  400  600  400  500  500  400  400  400  500  500  200  400  600  400  400  500  400  400  400  400  600  400  400  500  400  400  400  500  400  400  400  79 80 81 82  300 300 200 200  300 300 300 300  500 500 500 500  600 600 500  700 700 700  500 500 500  600  400  400  400  500  500  500  200  400  600  400  400  500  400  400  400  400  400  500  500  200  400  600  400  400  400  400  400  400  400  400  400  500  500  200  400  600  400  400  400  400  400  400  400  400  400  400  400  400  200  400  600  400  400  400  400  400  400  400  400  400  400  400  400  200  400  600  400  400  400  400  400  400  400  400  400  200  400  600  400  400  400  400  400  400  200  400  600  400  400  400  400  400  400  500  500  500  400  600  500  600 600  84  200  300  500  500  600  85  200  300  500  500  600  86  200  300  400  500  400  500  89 90  200 200  300 300  400 400  500 500 500  600 600  200  400  500  400  500  200  700  300  500  500  500  200  500  500  500  88  500 500  300  300  500 500  200  200  500  500  500  83  87  500  400 400  400 400  400 400  400  400  400  132  Table A.15. Modified Data: Crest Combinations Summary - Phase II C, = A s s u m e d response (and value) i f subjects were given this option. Based on Phase I percentage o f responses opposite to what was expected.  O v e r 1 a p pi n g C r e s t Ract  Curves  300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  350  500  600  700  800  600  600  600  600  600  600  350  600  800  600  600  600  600  600  600  "T" = 300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  "M" = 250  300  400  400 300  600 500  300  300  400 300  400  300  400 300  400  200  400 300  400  300  400 300  400  300  400 300  250  300  400 300  400  200  600 500  400  "B" = 200  500 400  2  3  4  5  6  7  8  9  10  It  12  13  14  15  16  17  18  19  20  Total Sample Size 90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  90  17  14  27  22  23  11  30  28  28  27  12  14  22  20  24  24  5  24  22  25  30  25  22  52  26  23  29  19  21  26  15 28%  Test-Curve No.  #of^  1  # of True "T" 15 Total # of "M" Total # of "B" (0  o (A c  29 29  20 29  27  19% 16%  %of^ % of True T's  17% 22%  22  26  20  36  17  23  24  25  23  24 19  30%  24%  26%  12%  33%  18  24%  18  29%  22  22%  20  40%  19%  15  21  21  od  22%  30%  24%  46%  47%  52%  300  500  600  700  500  500  500  500  646  439  464  448  456  100  115  123  122  116  11022  13684  12864  13295  10044  13328  52%  15107  46%  29%  17%  46%  49% 37% 44%  50%  40%  14856  28%  500  500  300  500  700  500  500  500  500  500  500  459  424  256  424  650  459  449  454  457  446  471  103  56  123  13459  Results from Phase I  Average % o f sample with " L " resp.  10632  3115  15126  1 12 12640  111  117  81  114  115  105  12336  13763  6553  13045  13295  11066  = 42 %  where: " L " resp.  s  Rp < R  Average % o f sample with " S " resp.  = 27 %  "S"resp.  =  Rp = R  Average % o f sample with " M " resp.  =31%  "M"resp.  s  Rp>R  where: " T " resp.  =  R =R  N o . o f " T " responses by sample  = 32  % o f sample with " T " responses  = 36 %  £ = M / ( S + M ) = 3 1 % / (27% + 3 1 % ) = " T " = S / (S+M) = 2 7 % / (27% + 31%) =  54.7 % 46.3 %  The no. o f assumed C, responses by sample N o . o f assumed  23%  44%  using Test-curve file 001  True  21%  59% 63% 59%  47%  Sample Calculation:  Results from Phase I I :  20% 22% 19% 29% 14% 26%  29% 22% 18% 30% 41% 41%  16%  31%  3021  23% 22%  23%  17% 21%  VAR  32%  17%  30% 23%  21%  1 13 115  26%  31%  27%  117  24%  31%  26%  105  6% 27%  24% 58% 29%  37  22%  55  27%  28%  37  28%  STDEV  27%  33%  27  24%  551  22%  22  27%  459  13% 16% 24% 28% 21% 17%  27  20%  323  23  15  26%  261  13  16  20%  Adj. Ave. Rp  26  20  32% 30% 64% 62% 400  20  26  32% 32%  48%  18  25  21 20  17  20  % of B's  48%  15  14  % of M's %(M + B)  19  19 28  10  o a:  25  True  T responses by sample  300  V  (proportion o f " T " resp. that are actually R p > R ) (proportion of " T " resp. that actually are R p = R ) = 32 * 53.7 % = 1 7 = 32 * 46.3 %  = 15 (instead of 32 )  133 Table A.16. Modified Data: Sag Combinations Summary - Phase II C, = A s s u m e d response (and value) i f subjects were given this option. Based on Phase I percentage o f responses opposite to what was expected.  Sag C u r v e s  Overlapping 300  400  500  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  t> 200 »X" = 300  300  400  500  600  400  400  400  400  400  400  200  400  600  400  400  400  400  400  400  600  700  500  500  500  500  500  500  300  500  700  500  500  500  500  500  500  600  400  600  800  600  600  600  600  600  600  Ract R: P  "M" = 400 "B" = 500  500  600  700  800  600  600  600  600  600  700  800  900  700  700  700  700  700  700  500  700  900  700  700  700  700  700  700  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  90  90  90 25  Total Sample Size  90  90  #of£  10  12  5  9  16  14  10  # of True "T"  m  P °  o vt c  o cc  500  600  Test-Curve No.  Ifl  400  25  90  90  90  90  11  14  15  12  10  6  17  15  25  20  17  15  23  45  22  14  13  29  28  20  19  17  19  30  21  25  46  25  28  38  44  40  20  21  40  27  12%  11%  17%  28%  7  6  4  4  9  9  8  11  11  29  25  29  50  4 16  90  90  6  7 11  90  90  90  90  90  90  90  90  90  Total # of "M"  28  24  21  26  24  34  22  29  Total* of "B"  27  38  50  45  48  36  53  45  47  6%  10%  8%  4%  7%  8%  7%  4%  4%  16%  17%  13%  16%  11%  12%  18%  10%  10%  9%  12%  12% 28% 22%  19%  17% 26%  32%  28%  32% 32%  31%  22%  21%  19% 21% 33%  23%  28%  52%  56%  51% 28%  31%  42%  49%  44% 22% 23%  44%  30%  83% 60% 62%  64%  70%  63% 43% 57%  68%  58%  %of£ % o f True Ts  11% 13% 28%  18%  % of M's  31% 27%  23%  29%  27%  38%  24%  32%  % of B's  30% 42% 61% 69%  56%  50%  53%  40%  59%  50%  % (M + B)  300  500  500  500  500  500  300  500  700  500  500  500  500  500  500  636  624  630  634  630  376  578  790  606  597  559  561  596  560  92  93  89  86  85  100  106  1 13 110  108  91  105  113  119  11186  12820  11562  8291  10943  12789  14112  400  500  600  700  719  826  99  95  86  498  STDEV  100  107  93  9933  500 613  80%  380  VAR  82%  79%  Adj. Ave. Rp  11456  8594  9864  9115  83%  14%  83%  78%  79%  629  84%  7% 19%  50% 24% 16%  7461  8385  8609  7966  7452  7292  9958  11991  APPENDIX B: ANOVA ANALYSIS DETAILS  135  Table B . l . A N O V A Setup Summary Overlapping Crest Curve  Overlapping Sag Curve  Effect of R, compare Rp of files 1, 2, 3, 4, 5  Effect of R, compare Rp offiles22, 23, 24, 25, 26  Effect of A, compare Rp offiles6, 3, 7, 8  Effect of A, compare Rp offiles27, 24, 28, 29  Effect of K, compare Rp offiles9, 10, 3, 11  Effect of K, compare Rp offiles30, 24, 31, 32  Effect of LT Turn, compare Rp offiles12, 1  Effect of LT Turn, compare Rp offiles33, 22  Effect of LT Turn, compare Rp offiles13, 3  Effect of LT Turn, compare Rp offiles34, 24  Effect of LT Turn, compare Rp offiles14, 5  Effect of LT Turn, compare Rp offiles35, 26  Effect of e, compare Rp of files 15, 3, 16  Effect of e, compare Rp offiles36, 24, 37  Effect of Sight, compare Rp offiles3, 17, 18  Effect of Sight, compare Rp offiles24, 38, 39  Effect of Back, compare Rp offiles3, 19, 20  Effect of Back, compare Rp offiles24, 40, 41  Effect of Vertical, compare Rp offiles1 - 20 tofiles22-41  136  Table B.2. A N O V A : Effect of R. (a) Crest Combinations  sii\i\um Average  Sum  Count  Groups  Variance  C o l u m n 1 (file 001)  90  22650  251.6667  1710.6742  C o l u m n 2 (file 002)  90  27700  90  38600  307.7778 428.8889  6792.7591  C o l u m n 3 (file 003) C o l u m n 4 (file 004) C o l u m n 5 (file 005)  90 90  47400  526.6667  55800  620  7370.7865 7235.9551  7245.9426  overlapping crest curves  A N O V A : Single Factoi Source of Variation Between Groups W i t h i n Groups  SS  MS  4f  P-value  4 2073188.889 341.4779408 4.0308E-134 445 6071.223471  8292755.556 2701694.444 10994450  Total  F  F cm 2.391985277  449  (b) Sag Combinations SUMYlAin  Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 022)  90  35200  391.1111  6886.3920  C o l u m n 2 (file 023)  90  46000  511.1111  7290.8864  C o l u m n 3 (file 024)  90  57100  634.4444  6553.0587  90  65600  90  75000  728.8889 833.3333  6347.0662 6292.1348  .  C o l u m n 4 (file 025) C o l u m n 5 (file 026)  overlapping sag curves  A N O V A : Single Factor Source of Variation  SS  Between Groups  10964088.89  W i t h i n Groups  2969888.889  Total  .13933977.78  MS  df  F  4 2741022.222 410.7072468 445 6673.907615 449  P-value  F cm  7.4762E-148  2.391985277  137  Table B.3. A N O V A : Effect of A . (a) Crest Combinations SUMM \R> Average  Sum  Count  Groups  Variance .  C o l u m n 1 (file 006)  90  38400  426.6667  7146.0674  C o l u m n 2 (file 003)  90  38600  428.8889  7245.9426  C o l u m n 3 (file 007)  90  38800  431.1111  6436.9538  C o l u m n 4 (file 008)  90  37500  416.6667  7696.6292  i overlapping crest curves  A N O V A : Single Factor SS  Source of Variation Between Groups W i t h i n Groups  3 3657.407407 356 7131.398252  2549750  Total  MS  df  10972.22222 2538777.778  F  P-value  F crit  0.51285979 0.673661786 2.629988671  359  (b) Sag Combinations SI M M A i n Groups  Sum  Count  Average  Variance  C o l u m n 1 (file 027)  90  55600  617.7778  5972.5343  C o l u m n 2 (file 024)  90  57100  634.4444  6553.0587  C o l u m n 3 (file 028)  90  57800  642.2222  5837.7029  C o l u m n 4 (file 029)  90  56900  632.2222  5803.9950  overlapping sag curves^  A N O V A : Single Factor Source of Variation  SS  Between Groups  28111.11111  W i t h i n Groups  2150888.889  Total  2179000  MS  df 3  9370.37037  356 6041.822722 359  F  P-value  F cm  1.550917795 0.201060846 2.629988671  138  Table B.4. A N O V A : Effect of K .  (a) Crest Combinations SUMM \RV 90  C o l u m n 1 (file 009)  Variance  38200  Average A2AAAAA  7021.2235  Sum  Count  Groups  7935.0811  C o l u m n 2 (file 010) .  90  38600  428.8889  C o l u m n 3 (file 003)  90  38600  428.8889  7245.9426  C o l u m n 4 (file 011)  90  37000  411.1111  7066.1673  ANON  overlapping crcsl curves  \  ss  Source of Variation Between Groups W i t h i n Groups  MS  df  P-value  Fcrit  • 3 6370.37037 0.870613661 0.456446522 2.629988671 7317.10362 356  19111.11111 2604888.889  -359  . .2624000  Total  F  (b) Sag Combinations sii.vivnm Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 030)  90  57300  636.6667  5494.3820  C o l u m n 2 (file 024)  90  57100  634.4444  6553.0587  C o l u m n 3 (file 031)  90  57500  638.8889  5774.0325  C o l u m n 4 (file 032)  90  57100  634.4444  5654.1823  overlapping sag curves.  ANOVA Source of Variation  SS  MS  df  F  P-value  F cm  3 407.4074074 0.069417854 0.976208089 2.629988671  Between Groups  1222.222222  W i t h i n Groups  2089333.333  356 5868.913858  Total  2090555.556  359  139  Table B.5. A N O V A : Effect of e. (a) Crest Combinations SUMMARi Sum  Count  Groups  Average 432.2222  Variance 6702.8714  C o l u m n 1 (file 015)  90  38900  C o l u m n 2 (file 003)  90  38600  428.8889  7245.9426  C o l u m n 3 (file 016)  90  38000  422.2222  7590.5119  overlapping crest curves *  ANOVA SS  Source of Variation Between Groups  MS  df  F crit  267 7179.775281  1917000  269  1921666.667  Total  P-value  2 2333.333333 0.324986959 0.722822182 3.029597906  4666.666667  W i t h i n Groups  F  (b) Sag Combinations SI'MM \ R \ Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 036)  90  55700  618.8889  7616.7291  C o l u m n 2 (file 024)  90  57100  634.4444  6553.0587  C o l u m n 3 (file 037)  90  54700  607.7778  8141.0737  overlapping sag curveV  A NOV \ Source of Variation Between Groups W i t h i n Groups Total  SS 32296.2963 1985666.667 .2017962.963  MS  df  F  P-value  F cm  2 16148.14815 2.171339041 0.116034223 3.029597906 267 7436.953808 269  140  Table B.6. A N O V A : Effect of Sight Distance.  (a) Crest Combinations SUMMARi Average  Sum  Count  Groups  Variance  428.8889  7245.9426  C o l u m n 1 (file 003)  90  38600  C o l u m n 2 (file 017)  90  40400  448.8889  5448.1898  C o l u m n 3 (file 018)  90  38700  430.0000  7292.1348  overlapping,crest curves  ANOVA SS  Source oJ Variation  MS  df  Between Groups  22140.14014  W i t h i n Groups  1778777.778  2 11370.37037 267 6662.089055  Total  1801518.519  269  F \.106121466  P-value  F crit  0.183432274 3.029597906  (b) Sag Combinations SUMMARY Groups  -  Average  Sum  Count  Variance  C o l u m n 1 (file 024)  90  57100  634.4444  6553.0587  C o l u m n 2 (file 038)  90  50900  565.5556  6777.7778  C o l u m n 3 (file 039)  90  52200  580.0000  6337.0787  WON  o\erlapping sag curves  \  Source of Variation  SS  MS  df  Between Groups  237555.5556  2 118777.7778  W i t h i n Groups  1750444.444  261 6555.971702  Total  1988000  269  F  P-value  F crit  18.11749397 4.18519E-08 3.029597906  141  Table B.7. A N O V A : Effect of Background Image. (a) Crest Combinations SUMMARY  I!  Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 003)  90  38600  428.8889  7245.9426  C o l u m n 2 (file 019)  90  37900  421.1111  7526.8414  C o l u m n 3 (file 020)  90  39900  443.3333  5853.9326  \ V > \  m e r l a p p i n g . c r e s t curves  \ SS  Source of Variation  MS  df  Between Groups  22888.88889  W i t h i n Groups  1835777.778  2 11444.44444 267 6875.572201  Total  1858666.667  269  F  P-value  1.664507929 0.191241806  F crit 3.029597906  (b) Sag Combinations SUMMAKN Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 024)  90  57100  634.4444  6553.0587  C o l u m n 2 (file 040)  90  55100  612.2222  7601.7478  C o l u m n 3 (file 041)  90  52900  587.7778  7152.3096  o \ e i lapping sag curves  ANO\ \ Source of Variation  SS  MS  df  F  2 49037.03704 6.904318275  Between Groups  98074.07407  W i t h i n Groups  1896333.333  267 7102.372035  Total  1994407.407  269  P-value  F cm  0.001192496  3.029597906  142  Table B.8. A N O V A : Effect of Turning Direction, R = 300m.  (a) Crest Combinations si M M \ n Sum  Count  Groups C o l u m n 1 (file 012)  90  22300  C o l u m n 2 (file 001)  90  22650  Average 247.7778  Variance 1961.2984  251.6667  1710.6742  overlapping crest curves  A.NON \  ss  Source of Variation Between Groups  680.5555556  W i t h i n Groups  326805.5556  Total  .327486.1111  F  MS  df  1 680.5555556 0.370675733  P-value 0.543412375  F crit 3.894228939  178 1835.986267  .  179  (b) Sag Combinations Sl'MMAKN Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 033)  90  34900  387.7778  6702.8714  C o l u m n 2 (file 022)  90  35200  391.1111  6886.3920  ANON  overlapping sag curves.  \  Source of Variation  SS  1  W i t h i n Groups  1209444.444  178  Total  .1209944.444  179  Between Groups  F  MS  df 500  500 0.073587506 6794.63171  P-value  F cm  0.786497584  3.894228939  143  Table B.9. A N O V A : Effect of Turning Direction, R = 500m. (a) Crest Combinations SUMMARY  C o l u m n 2 (file 003)  Variance  Average  Sum  Count  Groups C o l u m n 1 (file 013)  90  36000  400.0000  8314.6067  90  38600  428.8889  7245.9426  ANON \ Source of Variation  df  SS  MS  Between Groups  37555.55556  W i t h i n Groups  1384888.889  178  - 1422444.444  179  Total  F  1 37555.55556 4.827021823  P-value 0.029308478  F crit 3.894228939  7780.274657  (b) Sag Combinations SUMMAR\ Variance  Average  Sum  Count  Groups C o l u m n 1 (file 034)  90  53400  593.3333  6921.3483  C o l u m n 2 (file 024)  90  57100  634.4444  6553.0587  ~  j.  Source of Variation Between Groups  :  *  *~  SS 76055.55556  df  MS 1 76055.55556  W i t h i n Groups  1199222.222  178 6737.203496  Total  .1275277.778  179  *  I I I I II [ M I U H I M  F  — -  P-value  11.28889095 0.000953979  F crit 3.894228939  144  Table B.10. A N O V A : Effect of Turning Direction, R = 700m. (a) Crest Combinations SUMMARY C o l u m n 1 (file 014) C o l u m n 2 (file 005)  Variance  Average  Sum  Count  Groups  90  56500  627.7778  7646.6916  90  55800  620.0000  7235.9551  ...  NNON \ SS  Source of Variation  MS  df  F  P-value  F crit  Between Groups  2722.222222  W i t h i n Groups  1324555.556  1 2722.222222 0.365825015 0.546059089 3.894228939 178 7441.323346  Total  1327277.778  179  (b) Sag Combinations SUMMAKN Groups  Average  Sum  Count  Variance  C o l u m n 1 (file 035)  90  72600  806.6667  7820.2247  C o l u m n 2 (file 026)  90  75000  833.3333  6292.1348  ANON \ Source of Variation Between Groups  SS 32000  W i t h i n Groups  1256000  Total  1288000  P-value F 32000 4.535031847 0.034582149 3.894228939  MS  df 1  178 7056.179775 179  145  Table B . l l . A N O V A : Effect of Overlapping Vertical Curve.  SUMMAR\  Groups  Count  Average  Sum  C o l u m n 1 (files 001 - 0 2 0 )  1800  769250  427.3611  C o l u m n 2 (files 022 - 0 4 1 )  1800  1103500  613.0556  Variance 14861.0146 17467.0342  C o l u m n 1 has overlapping crest curves. C o l u m n 2 has overlapping sag curves.  WON  \  Source of Variation  SS  df  MS 1 31034184.03  Between Groups  31034184.03  W i t h i n Groups  58158159.72  3598  Total  .89192343.75  3599  16164.02438  F 1919.954047  P-value  F crit 0  3.8440362  APPENDIX C: REGRESSION ANALYSIS DETAILS  147  Table C l . Summary of Regression Variables Dependent Variable:  Y = Perceived horizontal curve radius, R p (m)  XI  =  Horizontal curve radius, R (m)  X2  =  V e r t i c a l curve parameter A (%)  X3  =  Vertical curve parameter K  X4  =  Superelevation rate e (%)  X5  =  X6  =  0, overlapping sag curve 1, overlapping crest curve  Vi  i  X7  =  >  Independs  c  nt  X9  =  1, 300m sight distance  1, right-turn 1, mountain background (base case)  0, 1000m sight distance . 03  0, left-turn  X8  =  2, sky photo background  2, 100m sight distance  3, sky computer generated  0, male  1, 16 - 25 yrs o l d  1, female  XlO  =  2, 26 - 40 yrs o l d 3,41 - 6 0 yrs o l d  Xll  X12  =  =  0, doesn't wear corrective lenses  4, 61+ yrs o l d  1, wears corrective lenses  D r i v i n g experience (yrs)  X13  =  0, N o driving school education 1, D r i v i n g school education  148  Table C.2. Regression Analysis Trials Summary - Combined Curve Equations Test-Curve Files  5  SPSS scti  *£ f-  SO ON  s • •  2 7 1 20 14 38 19 13 42 37 52 50 41 51 49 32 26 31 25  ~-  T T  y y y  • • •  y  •  • • •  Tf  • •  y  OS  y y y  • • • • • •  y  • •  V V  • • • • • •  • • • • •  •  •  • •  • • •  y  V  •  y y  •  • • • • •  • • •  y • y  •  • • •  VN  r-  ON  ro ro ro ro T T T t O ro s o 00 ro • • ro • ro•  •  y  y  y  •  •  y  <N  •  • y y V  s/  y  V  <N  VN  <N  • • • • • •  y  —  T T  •  •  SD  T T  63 «" £3  !s  00  T  93 «- 33  1 1 1 1 4 4 10 4 4 13 10 14 14 13 14 14 7 7 7 7  o  Z  Variables  Sag Combinations  Crest Combinations  —  • • • y • y •  •  y  •  • • •  y y y y y  T Tf s/  • • • • •  • • •  Adjusted  Tt  X  >•  7  •Tt  J  • •  • •  •  •  •  • • •  v-  •  • • • •  —  • • •  y  •  y y  • • • •  •  • •  • •  • • • • • • •  • •  • •  of Included in Stepwise Regression Analysis  V0  X  • • • • • •  y  X  X  X  Os  X  X  •  •  •  •  •  y y  y  • •  •  y  •  • • • • • • • •  •  •  • •  • • y  •  • • •  •  y s  •  • •  • • • • •  y_  • • • • •  • •  •  y_  •  •  y_  • • • •  •  X  X  ro X  R  2  0.703  •  • • • •  so  (S  •  •  0.705 0.723 0.726 0.737  •  •  y  • •  • • •  • • •  ' y  •  y  • •  • •  y  •  •  •  •  y  •  y  y  •  •  fS  m  X  X  •  /  0.739  V  0.754 0.758 0.760 0.772 0.774 0.777 0.779 0.784 0.798 0.799 0.806 0.808 0.827 0.829  y  •  _. Significant Predictor  Table C.3. Regression Analysis Trials Summary - Sag Curve Equations Test-Curve Files  3 3 3 3 12 12 12 12 6 6 6 6 15 15 9 9 9 9  !s  "C H 11 12 5 6 47 48 45 46 23 24 17 18 54 53 36 30 35 29  </-,  00  T  t SO  —  T o  Tt  T (N  SD  OO  t  T  sr,  r-  Model | M 2 , Model ( M l )  o rl  T  sD rs<  TJ  T T  *  >  00  O Tt  —i  m  T T  Of  m  33 -»  o Z  Variables  Sag Combinations CN VN r~ os Os m m 30 ->  SPSS  -  Crest Combinations  SD r*N  f*N  • • •  • • • • • y  y  y  y  • • y • y • y •  y  y  y  y  y  y  y  y  •  y  y  y  y  y  y  y  y  y  y  y  y  v  *  •  y  y  y  y  y  y  y  y  y  y  y  y  y  y  y  •  •  • •  y  y  y y y y  • • • • • •  • • • y • y • y  Adjusted X y  • •  y  •  • •  z r\ y_ —1  •  y  • y y  y  y_  •  y  y  y  y  y_  •  •  y  y  y  • •  •  y  • •  y  y  y  •j  •  y  y_  y_  /  •  • •  y_  • •  /  y  y  y  y  y  y  y  y  • • •  y  y  •  X  • • •  y  y  X  • •  ~y[  y y  y  •  X  X  y  y  X  SO  y  y_  y  00  VN  S  • • y  y  m <* M X  • • • • • • •  y  y_  •  w•  —  •  /  ON  X  X  •/  y  • •  y y  y y y  y  • •  y  •  y  y_  y_  • • • • • •  y  •  • •  y  y  y  •  •  y  R  2  0.604 0.610 0.626 0.631 0.643 0.646 0.655 0.656 0.666 0.669 0.676 0.679 0.735 0.744 0.774 0.782 0.793 0.799  149  Table C.4. Regression Analysis Trials Summary - Crest Curve Equations Test-Curve Files  5 3  t  SPSS  IX  oo oo  2 2 2 2 5 5 5 5 11 11 11 11 8 8  ci Z IS T !• H 10 • 4 • 9 • 3 22 .16 21 • 15 V 44 • 40 43 • 39 • 34 28 V 33 • 27  c  t  • • • V  • •  I  • • • • • • •  t  • • • • • V  • V  T m  o  so cN  T t  f  f  t  CN rN  C-  O rn  CO  CN  V  • • • • • •  Variables  Sag Combinations o irj o fN Cl m en m  Crest Combinations  • • •  • • • •  1  rs  t  r«~i  o  t  f  SO  00  m  m  • • • •  Adjusted  —  *  > z  —i  ./  >  LNX  —  X  •  /  • •  • • •  •  • •  £ •  • •  • • • • • • •  • • • • • •  v~> X X X  /  Included in Stepwise Regression Analysis  • •  X  X  X  •  •  •  •  £ •  •  •  V  Model (M3)  o X  • • £ • •  Model (M4)  • • £ Significant Predictor  rN  vo 00 X  • • • •  • •  —  £ £  £ £  £  • £ •  £  •  £ £  •  •  £  X  •  •  £ • £  •  •  •  •  •  • £  V  •  •  •  •  R  2  0.539 0.548 0.550 0.559 0.590 0.597 0.604 0.612 0.658 0.663 0.677 0.682 0.722 0.729 0.747 0.754  150 Table C.5. SPSS Regression Results for Model ( M l ) \ ar'iablesT- ntiied Variables  Model  Method  Entered  Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101).  1  R  2  turning direction Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). A  3 a. Depe ndent V a r i a b l e : Perceived Radius  KH89BI^^ Adjusted R  Model l  a  2  b  3  C  2  82.2887  b. Predictors: (Constant), R , turning direction  0.8624  0.7437  0.7432  81.3801  c. Predictors: (Constant), R, turning direction,  0.8630  0.7448  0.7441  81.2490  ^, * W / '  ^ ANOVA l  A  i  d  18818000  1  Mean „ Square 18818000  6690172  988  6771  Total  25508172  989  Regression  18971542  2  9485771  6536630  987  6623  25508172 18999199  989 3  6333066  6508973  986  6601  25508172  989  Sum o f Squares  Residual  Residual Total Regression  3°  a. Predictors: (Constant), R  0.7375  Residual Total  df  n  Regression  b  Estimate  0.7377  Model  l  o f the  Square 0.8589  ' -  a  Std. E r r o r  R  R Square  .  F  Sig.  2779.0294  0.0000  1432.3063  0.0000  959.3531  0.0000  a. Predictors: (Constant), R b. Predictors: (Constant), R , turning direction c. Predictors: (Constant), R , turning direction, A d. Dependent Variable: Perceived Radius  1  151  Table C.5. SPSS Regression Results for Model ( M l ) Cont. (  Model  2  Unstandardized  Standardized  Coefficients Std. Error B  Coefficients Beta  (Constant)  77.374  10.552  R (Constant)  1.078 57.037  0.020 11.257  0.859  t  Sig. 7.333  0.000  52.717  0.000  5.067  0.000  1.078  0.020  0.859  53.305  0.000  turning direction  27.963  5.807  0.078  4.815  0.000  (Constant)  42.088  13.404  3.140  0.002  1.078  0.020  0.859  53.391  0.000  26.094  5.870  0.072  4.446  0.000  3.737  1.826  0.033  2.047  0.041  R  3  oefficicnts'1  R  turning direction A  a. Dependent V a r i a b l e : Perceived Radius  1 SSS^SSffles^ Collinearity Model  1* 2  b  A  turning direction A  Beta i n 0.045 0.078 0.033  t  Sig.  Statistics Tolerance 1.000  2.746  0.006  0.087  4.815  0.000  0.151  1.000  0.065  0.976  2.047  a. Predictors i n the M o d e l : (Constant), R b. Predictors i n the M o d e l : (Constant), R, turning direction c. Dependent V a r i a b l e : Perceived Radius  Partial Correlation  0.041  152 Table C.6. SPSS Regression Results for Model (M2)  \ .iii.ihles 1 ntcrcd Model  Variables  !  Method  Entered  Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101).  1  LN R  2  turning direction Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). Stepwise (Criteria: Prbbability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). A  3  a. Depe ndent V a r i a b l e : N a t u r a l l o g o f Perceived Radius  : V . ^ « ^ r V ^ f j ^ M o d e l Summan Adjusted R  Model l  a  2  b  0.8549 0.8575  3C  0.8580  R Square  0.7308  l  2  b  3°  Std. Error  R  o f the  Square  Estimate  0.7306  0.1499  0.7353  0.7347  0.1488  0.7362  0.7354  0.1486  a. Predictors: (Constant), L N R b. Predictors: (Constant), L N R, turningdirection c. Predictors: (Constant), L N R, turningdirection, A  Regression  60.3134  1  Mean „ Square 60.3134 0.0225  Model  a  1  Sum o f Squares  df  M  Residual  22.2146  988  Total  82.5280  989  Regression  60.6792  2  30.3396  Residual  21.8488  987  0.0221  Total  82.5280  989  Regression  60.7597  3  20.2532  Residual  21.7683  986  0.0221  Total  82.5280  989  a. Predictors: (Constant), L N R b. Predictors: (Constant), L N R , turning direction c. Predictors: (Constant), L N R , turning direction, A d. Dependent V a r i a b l e : Natural l o g o f Perceived Radius  I  F  Sig.  2682.4548  0.0000  1370.5654  0.0000  917.3733  0.0000  Table C.6. SPSS Regression Results for Model (M2) Cont. ^^^^^^^^^^^^^^^^^^^^^^^ejenis^^^^^^^^^^^^^g Unstandardized Model B  2  (Constant)  0.8118  0.1077  LN R  0.9021  0.0174  (Constant) LN R  0.8027  0.1069  0.8985  0.0173  0.0432  0.0106  turning direction  3  Coefficients Std. Error  (Constant)  0.7820  LN R  0.8977  turning direction  0.0401  A  0.0064  Standardized Coefficients Beta  Sig. 7.5383  0.0000  51.7924  0.0000  7.5111  0.0000  0.8514  51.9188  0.0000  0.0667  4.0651  0.0001  7.2893  0.0000  0.8507  51.9290  0.0000  0.0618  3.7274  0.0002  0.0316  1.9091  0.0565  0.8549  0.1073 0.0173 0.0107 0.0033  t  a. Dependent Variable: Natural log o f Perceived Radius  |l^^^^^^^^clJ^^^rifiles • ,  Collinearity Model  l  a  2  b  A  turning direction A  Beta i n  t  Sig.  Partial Correlation  Statistics Tolerance  0.0411  2.4977  0.0127  0.0793  0.9990  0.0667  4.0651  0.0001  0.1283  0.9973  0.0316  1.9091  0.0565  0.0607  0.9753  a. Predictors i n the M o d e l : (Constant), L N R b. Predictors i n the M o d e l : (Constant), L N R, turning direction c. Dependent V a r i a b l e : N a t u r a l l o g o f Perceived Radius  154  Table C.7. SPSS Regression Results for Model (M3) V ariables Entered Model  Variables Entered  1  Method  Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). R 1 a. Depe ndent Variable: Perceived Radius  M o d i l Sum m a n Model  R  R Square  Adjusted R Square  l  0.8646  0.7474  0.7469  a  Std. E r r o r  78.7269  of the Estimate  A NOV V Model  l  a  Mean Square  df  Sum of Squares 8217778 2776672 10994450  Regression Residual Total  a. Predictors: (Constant), R h  1  8217778  448 449  6198  F 1325.8909  Sig. 0.0000  a. Predictors: (Constant), R b. Dependent Variable: Perceived Radius  CoeifficKnts  !  Unstandardized Model B  Coefficients Std. E r r o r  13.6359 -50.7778 (Constant) 0.0262 0.9556 R a. Dependent Variable: Perceived Radius  Standardized Coefficients Beta  .  0.8646  t -3.7238 36.4128  Sig. 0.0002 0.0000  155  Table C.8. SPSS Regression Results for Model (M4) \ ariables Entered  1  Model  Variables Entered  Method  Stepwise (Criteria: Probability-of-F-to-enter <= .100, Probability-of-F-to-remove >= .101). LN R ndent Variable: Natural l o g o f Perceived Radius a. Depe 1  M S I Mimmar> Adjusted  Std. E r r o r  Model  R  R Square  R Square  o f the Estimate  l  0.8501  0.7226  0.7220  0.2079  a  Model  l  a  Regression Residual Total  Mean Square  df  Sum o f Squares 50.4429 19.3649 69.8077  a. Predictors: (Constant), L N R  1.0000 448.0000 449.0000  50.4429  F 1166.9788  Sig. 0.0000  0.0432  a. Predictors: (Constant), L N R b. Dependent V a r i a b l e : Natural L o g o f Perceived Radius  Unstandardized Model  Coefficients Std. E r r o r B  Standardized Coefficients Beta  0.2013 -0.8871 (Constant) 0.0326 1.1133 LN R a. Dependent V a r i a b l e : Natural l o g o f Perceived Radius .  0.8501  t -4.4065 34.1611  Sig. 0.0000 0.0000  

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