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 Page 1 of 1 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the Univ e r s i t y of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of thi s thesis for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or pu b l i c a t i o n of th i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of GtiJt( Ch^ \Y\'5.e.r \y\^ The U n i v e r s i t y of B r i t i s h Columbia Vancouver,- Canada 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 three-dimensional 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 Ra C t . iii TABLE OF CONTENTS Abstract i i Table of Contents i i i List of Figures iv List of Tables.. : v i Acknowledgments v i i i 1.0 Introduction • 1 1.1 Background 1 1.2 Problem Definition 2 1.3 Thesis Objectives ; 3 1.4 Thesis Structure 4 2.0 Literature Review 5 2.1 Background 5 2.1.1 The Human Factor. 5 2.1.2 The Design Driver : 6 2.1.3 Managing Driver Variabil i ty 7 2.1.4 Design Consistency 7 2.1.5 Driver Workload 9 2.1.6 Highway Esthetics 10 2.1.7 Sight Distance 14 2.2 Driver Perception 16 2.3 Perception o f Horizontal Curves 22 3.0 Experimental Design.. . 30 3.1 Background 30 3.2 Highway Design Parameters 31 3.3 Mode l Creation 36 3.4 Presentation & Data Collection Design •. 40 3.4.1 Phase 1 Design 42 3.4.2 Phase II Design 45 4.0 Experimental Results 49 4.1 Phase I Results 49 4.2 Phase II Results 76 5.0 Data Analysis & Discussions 87 5.1 Phase I Analysis 87 5.2 Phase II Analysis 87 5.2.1 Hypothesis Testing - Raw Data 88 5.2.2 Hypothesis Testing - Modi f ied Data 88 5.2.3 A N O V A Analysis 92 5.2.4 Regression Analysis 94 5.3 Conclusions 98 References 102 Appendix A : Experimental Data Details 107 Appendix B: A N O V A Analysis Details 134 Appendix C : Regression Analysis Details 146 iv LIST OF FIGURES Figure 1.1. 3 D Views of Superimposed Vertical and Horizontal Curves 4 Figure 2.1. Example of Poor and Good Alignment Solutions 11 Figure 2.2. Affect of Incorrect and Correct Level ing Fault on Road Guidance 11 Figure 2.3. Al ignment Design Cases to be Avo ided . 12 Figure 2.4. Lack of 3 D Al ignment Coordinat ion causes "F lu t ter ing" of the Road due to too many Vertical Faults 13 Figure 2.5. Poor Adjustment of Vertical Elements causes Hidden D ip in the Road 13 Figure 2.6. Affect of Mi lder Inclines on Visual Guidance 14 Figure 2.7. Improved Optical Guidance with Pavement Markings 18 Figure 2.8. Horizontal Al ignment 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..- . 35 Figure 3.3. Screenshot o f Hwysurfl.exe Input Prompts 36 Figure 3.4. Screenshot of Final A u t o C A D Drawing 37 Figure 3.5. Screenshot of Phase I Presentation 43 Figure 3.6. Phase I Questionnaire & Data Collect ion Sheet 44 Figure 3.7. Screenshot of Phase II Presentation 47 Figure 4.1. Effect of Vertical Al ignment 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 Hor iz .Curve Radius (R p opposite to expected) - Phase I 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 Hor iz .Curve 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 Hor iz .Curve Radius (R p opposite to expected) - Phase 1 63 V Figure 4.11. Effect of e on Perceived Horiz.Curve Radius (expected response) - Phase 1 64 Figure 4.12. Effect of e on Perceived Horiz.Curve Radius (Rp = Ract) - Phase 1 65 Figure 4.13. Effect of e on Perceived Hor iz .Curve Radius (Rp opposite to expected) - Phase 1 66 Figure 4.14. Effect of Turn ing Direct ion on Perceived Hor iz .Curve Radius (expected response) - Phase I 67 Figure 4.15. Effect of Turn ing Direct ion on Perceived Hor iz .Curve Radius (Rp=Rac,)-Phase! : : 68 Figure 4.16. Effect of Turn ing Direct ion on Perceived Hor iz .Curve Radius (Rp opposite to expected) - Phase 1 69 Figure 4.17. Effect of Sight Distance on Perceived Hor iz .Curve Radius (expected response) - Phase 1 1 70 Figure 4.18. Effect of Sight Distance on Perceived Hor iz .Curve Radius ( R p = R a a ) - P h a s e I 71 Figure 4.19. Effect of Sight Distance on Perceived Hor iz .Curve Radius (Rp opposite to expected) - Phase 1 72 Figure 4.20. Effect of Background on Perceived Hor iz .Curve Radius (expected response) - Phase 1.. 73 Figure 4.21. Effect of Background on Perceived Horiz.Curve Radius (Rp = R ^ ) - Phase I.... 74 Figure 4.22. Effect of Background on Perceived Hor iz .Curve Radius (Rp opposite to expected) - Phase 1 75 Figure 4.23. Effect of Vert ical Al ignment on Perceived Horizontal Curve Radius - Phase II. 79 Figure 4.24. Effect of 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 of Turning Direction on Curve Perception - Phase II 83 Figure 4.28. Effect of 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 Curve Perception - Phase II 86 Figure 5.1. Regression Mode l Predictions of 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 Al ignment . . . .20 Table 2.2. Number o f Other Types of Illusions 20 Table 2.3. Number of the Illusions Experienced Related to Vertical Al ignment 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 Road Animation (Dynamic) Presentations - Phase 1. 53 Table 4.2. Summation of Responses to Road 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 Value of Perceived Radius 90 Table 5.2. Test of Hypothesis on the Adjusted Mean Value 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 Al ignment on Rp 93 Table 5.5. Variables used in Regression Model 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.12. Experimental Data: Sag Combinations Summary - Phase II 127 V l l Table A . 13. Modi f ied Data: Image Crest Combinations - Phase II 128 Table A . 14. Modi f ied Data: Image Sag Combinations - Phase II 130 Table A . 15. Modi f ied Data: Crest Combinations Summary - Phase II . . .132 Table A . 16. Modi f ied 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. SPSS Regression Results for Model ( M l ) 150 Table C.6. SPSS Regression Results for Mode l (M2) 152 Table C.7. S P S S Regression Results for Mode l (M3) 154 Table C.8. S P S S Regression Results for Mode l (M4) 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 these findings suggest 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. The driver receives information through the kinesthetic (movement), 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 overlapped1 with a sag vertical 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 Curve, b.) Horizontal Curve with superimposed crest vertical curve, c.) Horizontal Curve with superimposed sag vertical curve (Note: same horizontal radius for al l 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, Al-Masaeid 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 more frequent the 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 well-balanced road sections are constructed that eliminate unsafe feelings and driver discomfort (Taiganidis and Kanellaidis 1999, Lipar 1997, Smith and Lamm 1994). 11 (Above) Short Sag on Long H o r i z o n t a l Curve (Below) Long Sag on Long Horizontal 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 in which the road continues is unclear. Correct fault - the direction in which the road continues is more apparent. Figure 2.2. Affect of Incorrect and Correct Leveling Fault on Road Guidance (Lipar 1997). HL * VL ML Optical Break, Caused by Hori rontol Optical Break. Caused by Horizontal Tangent. Curve. HL M L OpHcat Break in Crest Vertical Curve -A-Diving id Tangent and Curve Ml yrrtTT Jumping HL Fluttering in Tangent ond Curve V L Figure 2.3. Alignment Design Cases to be Avoided (Smith and Lamm 1994). 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 ranging from 2.5 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". 1 7 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). T y p e o f Visual Illusions D a y t i m e Nighttime Gentle Curve —• Sharp Curve 7 S Sharp Curve —*• Gentle Curve 13 4 T o t a l 20 12 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 Total 2 10 21 Table 2.3. Number of the Illusions Experienced Related to Vertical Alignment (Mori et al. 1995). Type of Visual Illusions 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 Total 30 33 Note: "A -+ B" means that" Although 1 thought it was A, it was actually B." Table 2.4. Inferred Causes of Visual Illusions (Daytime) (Mori et al. 1995) Type of Illusions Related to Vertical Alignments Gentle Curve -* Sharp Curve Sharp Curve —• Gentle Curve Factors of Vertical Alignments •After Long Successive Slopes • Before or After Crests or Sags • Around Points Gradient Changes • In Tunnels •Relatively Steep Down-grade • Downgrade Factors of Horizontal Alignments •Relatively Gentle Alignments •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 Visual Environment •Noise Barriers • Left Curve and Noise Barriers • Left Curve and Noise Barriers Other, Factors •Heavy Traffic • •Strong Effects by Alignments Behind • Strong Effects by 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 data from Canada 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 the first in 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 visual field of 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 a field study 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). 2 4 Hassan and Easa (1998) suggested that stopping sight distance (SSD) and PVSD could be used to determine alignment coordination using three-dimensional 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 a framework for 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 S2 (Hassan and Easa Modeling 2000). Table 2.5. Preliminary Design Values of Required PVSD (Hassan and Easa Modeling 2000). REQUIRED PVSD (m)" Spiraled Curve R Simple Curve A = 100 m A = 200 m A = 300 m (m) s, S, s, s, s, s* s, Si (D (2) (3) (4) (5) (6) (7) (8) 0) 400 131 50 107 57 66 93' 66 119' 600 no 62 94 63 66 88 66 119' 800 99 70 87 70' 66 86 66 117 1.000 93 76 83 76" 66 84 66 109 1.200 88 80 80 80" 66 83 66 103 1.400 85 83 78 83" 66 83" 66 98 1,600 83 83 77 83" 66 83" 66 92 1,800 81 83 76 83" 66 83" 66 86 2,000 80 81 75 81" 66 81" 66 81" 'Values are rounded to next integer. "Minimum value. 'Maximum value. 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 reference-curves 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, Rp, was determined for a given radius, R. It should be noted that each participant did not view all eight of the test-curves 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 Lane Width = 3.7 m Vertical Curve Length = 340 m Camera Spee 100 kph Shoulder Width = 2.5m Camera Heig 1.05 m Superelevation Rate = 6% Camera offset from Centerline = 1.50 m Animation Vertical Horizontal Turning No. Curve A(%) Radius Direction 1 &2 Crest 4 600 Right & Left 3 &4 Crest 8 600 Right & Left 5 &6 Sag 4 600 Right & Left 7&8 Sag 8 600 Right & Left Animation Vertical Horizontal Turning No. Curve A(%) Radius Direction 9& 10 none 0 500 Right & Left 11 & 12 none 0 600 Right & Left 13 & 14 none 0 700 Right & Left 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 seen from Table 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 Turning Sample Mean Standard a' (%, One-Curve A (%) Direction Size (m) Deviation t* Tailed) * Right 17 552.9 80.0 -2.426 1.350 4 Left 14 564.3 74.5 -1.794 4.800 Right 17 558.8 93.9 -1.807 4.500 Crest * 8 Left 13 553.8 87.7 -1.897 4.100 Right 17 647.1 87.4 2.219 2.050 4 Left 12 666.7 77.9 2.966 0.650 Right 14 664.3 63.3 3.798 0.100 Sag" 8 Left 14 650.0 85.5 2.188 2.350 " Calculated value of the /-statistic. 6 Level of significance for accepting the null hypothesis H„. ' H{): R,, < R (600 m). Ho: R,, > R (600 m). (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 DESIGN 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 different from the 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 of filtering process 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 V / A ) • Effect of turning direction • Effect of e • Effect of sight distance • Effect of background 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 different from the 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 (300 - 700m) (2 - 8%) (25 - 125) (4 - 8%) 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 cross-sectional 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 H was assumed constant. TS or SC Normal Runout 1:400 (15*# of lanes] SC or CS Full Superelevation 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 C U R V E WITH TRANSITION B O T H E N D S Figure ( a ) CIRCULAR C U R V E Figure (b) T S S C C S S T . STANDARD P l Point of intersection o( the mam tangents Tangent to Spiral: common point ot tangent and spiral - beginning of Spiral Spiral to Curve: common pomt of spiral ana circular curve - beginning of Circular curve Curve to Spiral: common point o( circular curve ana spiral - end ot circular curve Spiral to Tangent: common point ot spral and tangent - end ol spiral S C S 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 ST. . apex distance External distance from P.I. to centre o( circular curve portion or to S.C.S. ot a curve transitional throughout 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 S T . Short tangent distance ol spral only L C 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 T S . Tc Tangent distance P l to B C or E C B.C. Beginning ol Curve E.C. End ol curve Arc Length ol curve Irom B C to E C Ac Intersection angle between the tangents EC External distance Irom P i to centre ol curve; Crcuiar Curve only Figure 340.B MoTH Highway Engineering Design Manual, August 1995, pg 340-3 Figure 3.2. Horizontal Curve Symbols (Highway 1994). 36 3.3 Model Creation The creation of the 3D Road models and final animations involved the use of several computer software programs. Script files for the element net of the road surface, side-slopes, delineation, and camera paths (drivers eye) were created (Figure 3.3). These script files were 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 Surface of Combined 3-D Alignment; October 1'tfS Vasser Hassan yhassanPgale.lakeheadu.ca e ,i o b nane :? 0B1 r ximum element length:? 5 dth of Delineation:? .1 ight of edges ahoue the road surface:? .003 Figure 3.3. Screenshot ofHwysurfl.exe Input Prompts (Hassan et al. Automation 1997). 37 •IESJU] yiew jnsHl Format look Draw Dfneoaon fcioiry fianut a U l r l *Me | r f | "I"-! * l ^|ft»M LzlUMJ 1^"—^d: •6i.4iay.aooai.-35.aM o s i w M O D E L T I L E '• - • 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 - CREST Test Curves - SAG Animation Vertical Horiz. Horiz. Animation Vertical Horiz. Horiz. File A% K% Curve Curve Curve e File A% K% Curve Curve Curve e Number Length Radius Length Number Length Radius Length Base Case and Ef fect of R Base Case and Ef fect of R 001 4 100 400 300 200 6 022 4 50 200 300 200 6 002 4 100 400 400 200 6 023 4 50 200 400 200 6 1 003 4 100 400 500 200 6 024 4 50 200 500 200 6 004 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 Ef fec t of A Ef fect of A 006 2 100 200 500 200 6 027 2 50 100 500 200 6 007 6 100 600 500 200 6 028 6 50 300 500 200 6 008 8 100 800 500 200 6 029 8 50 400 500 200 6 Effect of K Ef fec t of K 009 4 50 200 500 200 6 030 4 25 100 500 200 6 010 4 75 300 500 200 6 031 4 75 300 500 200 6 011 4 125 500 500 200 6 032 4 125 500 500 200 6 Effect of Le f t T u r n Ef fect of Le f t T u r n 012 4 100 400 300 200 6 033 4 50 200 300 200 6 013 4 100 400 500 200 6 034 4 50 200 500 200 6 014 4 100 400 700 200 6 035 4 50 200 700 200 6 Ef fect of e Ef fec t of e 015 4 100 400 500 200 4 036 4 50 200 500 200 4 016 4 100 400 500 200 8 037 4 50 200 500 200 8 Effect of Sight Distance Ef fect of Sight Dis tance 017* 4 100 400 500 200 6 0381 4 50 200 500 200 6 0182 4 100 400 500 200 6 0392 4 50 200 500 200 6 Ef fect of B a c k g r o u n d Ef fect of B a c k g r o u n d 019 3 4 100 400 500 200 6 0403 4 50 200 500 200 6 0204 4 100 400 500 200 6 0414 4 50 200 500 200 6 1 4 second PVSD (100m) - standard fog added Photo Sky ( KCS-SKY3 ) 2 12 second PVSD (300m) - standard fog added 4 Computer Generated Sky 39 Table 3.2. Reference-Curve Road Design Parameters Reference Curves File No. R n R . File No. RI File No. R H R L Effect of Background 089a 300 200 [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 6 6 6 6 6 6 6 6 6 6 6 6 Effect of e 069a 069 070 071 072 073 073b 300 400 450 500 550 600 700 200 200 200 200 200 200 200 4 4 4 4 4 4 4 089 « 090 I 091 8 092 093 093b 400 450 500 550 600 700 200 200 200 200 200 200 6 6 6 6 6 6 6 074a 074 075 076 077 078 078b 300 400 450 500 550 600 700 200 200 200 200 200 200 200 094a 094 Z 095 1 096 55 097 098 98b 300 400 450 500 550 600 700 200 200 200 200 200 200 200 |Left Turn 056 057 058 059 060 061 062 063 064 065 066 067 068 068b Effect of Sight Distance 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 6 6 6 6 6 6 6 6 6 6 6 6 « c 55 079a 300 200 6 079 400 200 6 080 450 200 6 081 500 200 6 082 550 200 6 083 600 200 6 083b 700 200 6 084a 300 200 6 084 400 200 6 085 450 200 6 086 500 200 6 087 550 200 6 088 600 200 6 088b 650 200 6 4 second PVSD (100m) 12 second PVSD (300m) Photo Sky ( K C S - S K Y 3 ) Computer Sky 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 (RaCt = 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 • 16 to 2:5 yrs D 26 to 40 Residence (city): PERSONAL: Gender: A g e : • 41 to 60 • 61 and over DRIVER: Do you wear glasses or contact lenses for driving? Have you completed any driver educational courses? How manyyears of driving experience do youhave? How often do you drive on highways? What duration is your average highway trip? • Yes • No • Yes • No • 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 • 2 t o 3 h o u r s • 3 to 4 hours D 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 A N I M A T I O N S I M A G E s C C . i s C C . i s C C . i s c c . i s 001 M L s 022 u L s 001 M L s 022 M L s 002 M L s 023 M L s 002 M L S : 023 M L 8 003 M L s 024 M L s 003 M L s 024 M L S 004 M L s 028 M L 8 004 M L s 02-3 M L s 006 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 M L s i 033 M L S 012 M L 8 033 M L 8 013 M L s 034 M L 8 013 M L 8 034 M L s 014 M L s 03S M L s 014 M L s 035 M L s 01S M L s - i 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 s 020 M L 8 041 M L 8 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 images from these files represented 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). Table 3.3. Phase I Setup. 46 TEST REF. B l SI REF. CURVE No. i*iCJ|R\JL CURVE No. IT' 061 045 022 045 002 047 02" 047 003 049 UN 049 mil 051 02 ^ 051 005 053 n'f 053 006 049 027 . 049 mr 049 049 OOS 049 II w 049 009 049 OV) 049 010 049 031 049 011 049 n 049 012 058 033 058 o n 062 031 062 014 066 i - 066 01 ^ 071 036 071 016 076 n 076 017 081 038 081 OIK 086 039 086 ul" 091 040 091 - ' i020H^ 096 IPWo4itiig£ 096 N O T E : see Tables 3.1 & 3.2 for curve details Images 600 x 300 resolution Frame N o . 180 ( 100m before P C ) . ( except Image #17 + #38 where frame #225 was used) Animations 600 x 300 resolution Frame No . 150 to 240 (where 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 II M R E F . T I M R E F . MSI R E F . II s | R E F . | G u K v e * N ^ Curve No. *Curve°No.i Curve No. ( H I M No Curve No. ( IIIW No Curve No. 045 049 045 049 001 044 H 1 047 022 047 0 '2 051 043 045 049 053 047 058 047 058 002 045 012 057 023 049 I I 060 043 056 051 062 049 062 049 062 003 047 i'l • 060 051 03 4 064 045 058 053 068 051 066 051 066 004 . 049 014 064 02^ 053 0 3-> 068 047 062 055 68b 053 071 053 071 00-< 051 on 069 026 055 0 ( 073 049 69a 55b 73b 049 076 049 076 (H II 047 <>l< 074 051 078 045 74a 053 78b 049 081 049 081 007 047 017 079 028 051 083 045 79a 053 83b 049 086 049 086 I I I I S 047 018 084 051 088 045 84a 053 88b 049 091 049 091 Ml 1 047 089 030 051 093 045 89a 053 93b 049 096 049 096 010 047 020 094 03| 051 098 045 94a 053 98b Images 400 x 200 resolution Animations 400 x 200 resolution Frame No. 180 ( 100m before P C ) Frame No. 150 to 240 frame No. 225 used for Image #17 + #38 frame No. 150 is 150m before P C frame No. 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 p was recorded for a known horizontal curve 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 RESULTS 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 test-curve 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 participant2, 40 for the animations and 40 for the 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: • Effect of Horizontal Radius • Effect of A (|gl - g2|) • Effect of K (K = L/A) • Effect of e • Effect of Turning Direction • Effect of Sight Distance • Effect of Background • Dynamic vs. Static Presentation 2 10 participants viewed only the 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 p < Ract for files 001- 020 should be considerably larger than Rp = Ract and Rp > Ract responses. For files 022 - 041, the frequency of responses for R p > Ract 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 R p < Ract when crest curves overlap a horizontal curves and approximately 60% of the sample population thought Rp > RaCt 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 A N I M A T I O N S 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 Rp = Ract 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 Rp > Ract 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 Sample Size 82 82 82 82 82 81 81 81 81 81 81 82 81 81 81 81 81 81 81 81 File No. 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 Rp < Ract 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 Rp = Ract 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 Rp > Ract 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 I M A G E S - 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 ^ Ract 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 Rp = Ract 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 Rp^Ract 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 Sample Size 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 File No. 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 Rp K Ract 0.15 0.11 0.13 0.12 0.09 0.07 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 Rp = Ract 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 Rp > Ract 0.53 0.58 0.55 0.70 0.80 0.47 0.68 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 < R a i 80% 60% 40% -20% -0% O o O « o O Rp, Animations o Rp, Images 200 300 400 500 600 Horizontal Curve Radius R (m) 700 800 (a) crest combinations (files 001-005). R p > R a 80% H 60% 40% 20% 0% O o O o o O 0 Rp, Animations o Rp, Images 200 300 400 500 600 Horizontal Curve Radius R (m) 700 800 (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 Horizontal Curve Radius R (m) 700 800 (a) crest combinations (files 001-005). -O Rp, Animations o Rp, Images 0 O o O 0 O o 1 i 200 300 400 500 600 700 800 Horizontal Curve Radius R (m) (b) sag combinations (files 022 - 026). Figure 4.3. Effect of R on Perceived Horiz.Curve Radius (Rp = R ^ - Phase I. 57 Rp > R-act 200 300 400 500 600 Horizontal Curve Radius R (m) 700 800 (a) crest combinations (files 001-005). Rp < Ract u c — 80% 60% -40% -20% 0% O Rp, Animations o Rp, Images o O O o 200 300 400 500 600 Horizontal Curve Radius R (m) 700 800 (b) sag combinations (files 022 - 026). Figure 4.4. Effect of R on Perceived Horiz.Curve Radius (Rp opposite to expected) - Phase I. 58 Rp < Ract 0 > U_ 80% i 60% 20% 0% O o O o O Rp, Animations o Rp, Images 4 6 A(%) 10 (a) crest combinations (files 006, 003,007, 008). > Ract 60% a I 40% u , 20% 0% O o o o o O Rp, Animations o Rp, Images 4 6 A(%) 10 (b) sag combinations (files 027, 024, 028, 029). Figure 4.5. Effect of A on Perceived HorizXurve Radius (expected response) - Phase I. c OJ 3 3" — — 80% 60% -40% -20% -0% 0 o O 4 O Rp, Animations o Rp, Images 59 10 (a) crest combinations (files 006, 003, 007, 008). 80% 60% 40% 20% H 0% 0 o O O Rp, Animations o Rp, Images o O o O 4 6 A(%) — i — 8 10 (b) sag combinations (files 027, 024, 028, 029). Figure 4.6. Effect of A on Perceived Horiz.Curve Radius (Rp = R ^ - Phase I. 6(1 Rp > Ract rs zz u ar 60% (a) crest combinations (files 006, 003, 007, 008). cr u 80% 60% 40% 20% 4 0% Rp < Ract 0 O Rp, Animations o Rp, Images o O o O 2 4 6 8 A(%) (b) sag combinations (files 027, 024, 028, 029). 10 Figure 4.7. Effect of A on Perceived Horiz.Curve Radius (R p opposite to expected) - Phase I. 61 Rp < Ract 80% 60% 40% 20% 0% 25 O o O o O Rp, Animations o Rp, Images 50 75 K 100 (a) crest combinations (files 009, 010, 003, 011). 125 150 80% 60% -I 40% 20% 0% 25 Rp> Ract 50 O Rp, Animations o Rp, Images 75 K 100 125 150 (b) sag combinations (files 030, 024, 031, 032). Figure 4.8. Effect of K on Perceived Horiz.Curve Radius (expected response) - Phase I. 62 >» o c 35 80% 60% 40% 20% 0% o d O O Rp, Animations o Rp, Images o O —•— •• i i 25 50 75 K 100 125 150 (a) crest combinations (files 009, 010, 003, 011). 25 50 75 K 100 125 150 (b) sag combinations (files 030, 024, 031, 032). Figure 4.9. Effect of K on Perceived Horiz.Curve Radius (Rp = R ^ - Phase I. 63 a B 3 CT s 80% -60% -40% 20% 0% 0 25 Rp > Ract O o 50 75 K ORp, Animations o Rp, Images O o 100 125 (a) crest combinations (files 009, 010, 003, 011). 150 c S s-40% 20% 0% 25 Rp < Ract -O Rp, Animations o Rp, Images -1 0 $ 1 1 1 ! 50 75 K 100 125 150 (b) sag combinations (files 030, 024,031, 032). Figure 4.10. Effect of K on Perceived Horiz-Curve Radius (Rp opposite to expected) - Phase I. 64 Rp < Ract O c B Er o 80% 60% 40% 20% 0% • o o O Rp, Animations o Rp, Images 6 e(%) 10 (a) crest combinations (files 003, 015, 016). Rp > Ract o d 3 80% 60% 40% 20% 0% s o o o o -O Rp, Animations o Rp, Images 4 6 e(%) 10 (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. 60% 40% 20% 4 O o O Rp, Animations o Rp, Images O o 0 % 6 e(%) 1 0 (a) crest combinations (files 003, 015, 016). 80% . 60% u s r 4 0 % tr. 2 0 % - \ 0 % o O O Rp, Animations o Rp, Images 10 e(7b (b) sag combinations (files 024, 036, 037). Figure 4.12. Effect of e on Perceived Horiz.Curve Radius (Rp = R ^ - Phase I. 66 Rp > Ract c OJ 3 e(%) (a) crest combinations (files 003, 015, 016). Rp < Ract I 3 — 80% 60% 40% 20% 0% O o T~ 4 o O O Rp, Animations o Rp, Images 10 e(% (b) sag combinations (files 024, 036, 037). Figure 4.13. Effect of e on Perceived Horiz.Curve Radius (Rp opposite to expected) - Phase I . Rp < Ract 80% 60% H 40% 20% i 0% f 6 o o O Rp, Animations RT • Rp, Animations LT o Rp, Images RT A Rp, Images LT 100 300 500 Horizontal Curve Radius R (m) 700 (a) crest combinations (files 001, 012, 003, 013, 005, 014). Rp > Ract 80% 60% 40% 20% 0% o • * 8 • O Rp, Animations RT • Rp, Animations LT o Rp, Images RT A Rp, Images LT 200 300 400 500 600 Horizontal Curve Radius R (m) 700 800 (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% 40% -20% -0% O Rp, Animations RT • Rp, Animations LT o Rp, Images RT A Rp, Image LT o 4 o 100 300 500 Horizontal Curve Radius R (m) 700 (a) crest combinations (files 001, 012, 003, 013, 005, 014). 100 300 500 Horizontal Curve Radius R (m) 700 (b) sag combinations (files 022, 033, 024, 034, 026, 035). Figure 4.15. Effect of Turning Direction on Perceived Horiz.Curve Radius (Rp = R ^ - Phase I. Rp > Ract 100 300 500 Horizontal Curve Radius R (m) 700 (a) crest combinations (files 001, 012, 003, 013, 005, 014). Rp < Ract 80% 60% 40% 20% 0% O Rp, Animations RT • Rp, Animations LT o Rp, Images RT A Rp, Images LT i s o 100 300 500 Horizontal Curve Radius R (m) 700 (b) sag combinations (files 022, 033, 024, 034, 026, 035). Figure 4.16. Effect of Turning Direction on Perceived Horiz.Curve Radius (Rp opposite to expected) - Phase I . Rp < Ract 100% 80% 4 60% 40% 20% 0% O o O Rp, Animations o Rp, Images 0 200 400 600 800 Sight Distance (m) (a) crest combinations (files 003, 017, 018). 1000 Rp > Ract 100% 80% 60% 40% 20% 0% o o O Rp, Animations o Rp, Images o o 200 400 600 800 Sight Distance (m) 1000 (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% 60% 40% 4 20% 0% O Rp, Animations o Rp, Images O o 0 200 400 600 Sight Distance (m) 800 1000 100% 80% 60% 40% 20% 0% (a) crest combinations (files 003, 017, 018). o O O Rp, Animations - o Rp, Images o O o O 1 1 1 1 1 1 1 1 1 1 200 400 600 Sight Distance (m) 800 1000 (b) sag combinations (files 024, 038, 039). Figure 4.18. Effect of Sight Distance on Perceived Horiz.Curve Radius (Rp = R a c t)- Phase I. Rp > Ract 100% 80% 60% 40% 20% ORp, Animations o Rp, Images o o O 200 400 600 Sight Distance (m) 800 1000 (a) crest combinations (files 003, 017, 018). 100% 80% 60% 40% 20% m Rp < Ract O Rp, Animations o Rp, Images 200 400 600 800 Sight Distance (m) 1000 (b) sag combinations (files 024, 038, 039). F i g u r e 4 .19 . E f fec t o f S igh t D i s t a n c e o n P e r c e i v e d H o r i z . C u r v e R a d i u s ( R p oppos i t e to expec ted) - P h a s e I. Rp > Ract 80% -I 60% 40% 20% A 0% O Rp, Animations o Rp, Images o O o O o O Mnt Sky Background Image Sky#2 (a) crest combinations (files 003, 019, 020). Rp 1* Ract 80% 60% 40% 20% 0% O o O o O o ORp, Animations o Rp, Images Mnt Sky Background Image Sky #2 (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 Mnt Sky Background Image Sky #2 (a) crest combinations (files 003, 019, 020). 80% 60% 40% 20% 0% O Rp, Animations o Rp, Images o O o O o O i i i Mnt Sky i Sky #2 Background Image (b) sag combinations (files 024, 040, 041). Figure 4.21. Effect of Background on Perceived HorizXurve Radius (Rp = Rac*)-PhaseI. Rp < Ract 80% 60% 40% 20% 0% O Rp, Animations o Rp, Images Mnt Sky Background Image Sky #2 (a) crest combinations (files 003, 019, 020). Rp < Ract 80% 60% 40% 20% -j 0% o O O Rp, Animations o Rp, Images o O Mnt Sky Background Image Sky #2 (b) sag combinations (files 024, 040, 041). Figure 4.22. Effect of Background on Perceived Horiz.Curve Radius (Rp opposite to expected) - Phase I. 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 test-curve 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 response frequency of R p = Ract for files 001- 020 should be considerably less than the sum of R p < RaCt and R p « Ract responses. For files 022 through 041, the frequency of responses for R p = Ra C t should be considerably less than the cumulative R p > Ract and R p » Ract 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 increases from 500m 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 response frequency as R increases from 500m 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 to R o a d I m a g e (S ta t i c ) P r e s e n t a t i o n s - P h a s e I I I M A G E S Files 001 - 020 have an overlapping crest curve and files 022 - 041 have an overlapping sag curve. Sample Size 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 File No. 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 A % 4 4 4 4 4 2 6 8 4 4 4 4 4 4 4 4 4 4 4 4 K 100 100 100 100 100 100 100 100 50 75 125 100 100 100 100 100 100 100 100 100 Lv R 400 300 400 400 400 500 400 600 400 700 200 500 600 500 800 500 200 500 300 500 500 500 400 300 400 500 400 700 400 500 400 500 400 500 400 500 400 500 400 500 1* e 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 4 200 8 200 6 200 6 200 6 200 6 Sight Distance 1000* 1000' 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 1000* 100 300 1000* 1000* Rp = Ract, "T" 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 Rp < Ract , "M" 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 Rp < K Ract, "B" 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 ). | Sample Size 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 File No. 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 A % 4 4 4 4 4 2 6 8 4 4 4 4 4 4 4 4 4 4 4 4 K 50 50 50 50 50 50 50 50 25 75 125 50 50 50 50 50 50 50 50 50 Ly 200 200 200 200 200 100 300 400 100 300 500 200 200 200 200 200 200 200 200 200 R 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 L H e 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 6 200 4 200 8 200 6 200 6 200 6 200 6 Sight Distance 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100 300 1000 1000 Rp = Ract, "T" 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 0.37 J.57 0.43 0.32 0.42 Rp > Ract, "M" 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 0.33 §J3 : > Ract, "B" 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 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 File Number 13 15 17 (b) sag combinations. Figure 4.23. Effect of Vertical Alignment on Perceived Horizontal Curve Radius - Phase II. 80 1.0 0.8 l%ofT's |D%(M + B) S 0.6 o 2 0.4 0.2 0.0 111 300 400 500 600 Horizontal Curve Radius (m) 700 (a) crest combinations (files 001 - 005) • %ofT's • %(M + B) 300 400 500 600 Horizontal Curve Radius (m) 700 (b) sag combinations (files 022 - 026) Figure 4.24. Effect of Horizontal Curve Radius on Curve Perception - Phase II. 81 1.0 0.8 a o.6 m =) 5T 0.4 -\ 0.2 0.0 2 B%ofT's • % ( M + B) 8 A ( % ) (a) crest combinations (files 006, 003, 007, 008) 1.0 0.8 I 0.6 4 a* S 0.4 0.2 4 0.0 • %ofT's • % ( M + B) 4 6 A(%) 8 (b) sag combinations (files 027, 024, 028, 029) Figure 4.25. Effect of Vertical Curve Parameter A on Curve Perception - Phase II. 1.0 0.8 1 0.6 m or1 ^ 0.4 l%ofT's |D%(M + B) 0.2 0.0 _______ |i 1.0 0.8 1 0.6 6 0.4 P H 0.2 0.0 50 75 100 125 K (a) crest combinations (files 009, 010, 003, 011) • %ofT's • %(M + B) 25 50 75 125 K (b) sag combinations (files 030, 024, 031, 032) Figure 4.26. Effect of K on Curve Perception - Phase II. 83 1.0 0.8 I 0.6 3 t 0.4 fe 0.2 0.0 • %ofT's • %(M + B) 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 0.8 3 0.6 a* e 0.4 0.2 0.0 • %ofT's • % ( M + B) 4 6 e (%) (a) crest combinations (files 015, 003, 016) 1.0 0.8 A S 0.6 m cr 2 0.4 0.2 0.0 4 H%ofT's • % ( M + B) e (%) (b) sag combinations (files 036, 024, 037) Figure 4.28. Effect of e on Curve Perception - Phase II. 85 1.0 0.8 g 0.6 8 0.4 tin 0.2 0.0 l%ofT's • %(M + B) 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 0.8 1 0.6 -I cr 2 0.4 0.2 0.0 • %ofT's • %(M + B) Mnt Sky#l Background Picture Sky#2 (a) crest combinations (files 003, 019, 020) r/oofT's | d % ( M + B) Mnt Sky#l Background Picture Sky#2 (b) sag combinations (files 024, 040, 041) Figure 4.30. Effect of Background on Curve Perception - Phase II. 5.0 D A T A ANALYSIS & DISCUSSIONS 87 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 p and actual horizontal curve R. Section 5.2.2 provides calculations similar to section 5.2.1 but for the adjusted Rp. Section 5.2.3 tests the 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 85th percentile values rather than mean values to evaluate situations, using 85th percentile values 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 p = 200m, R p = 250m or R p = 300m. The perceived horizontal radius R p = 200m represents the 0 - 30th percentile, Rp = 250m represents the 40th - 60th percentile, and Rp = 300m represents the 70th - 100th percentile. Therefore, it was deemed appropriate to use the mean perceived radius R p . As depicted in Figure 4.23, the mean value of perceived radius R p was consistently smaller than the actual horizontal radius Ract when a horizontal curve was overlapped with a crest curve, and R p was consistently larger than the actual horizontal radius when a horizontal curve was overlapped with a sag curve. To test the significance of the difference between R p and Ra C t , SPSS was used to perform a one-sample t-test on the collected data with the null hypothesis, Ho: R p = RaCt. 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 p , is statistically significant. 5.2.2 Hypothesis Testing - Modified Data The setup for Phase II was based on assumptions from the 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 C t and R p as determined in section 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 p ' = Ract • 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 RaCt, and the adjusted perceived horizontal curve radius Rp' , is still statistically significant. 90 Table 5.1. Test of Hypothesis on the Mean Value of Perceived Radius Standard V e r t i c a l F i l e Pa rame te r Sample M e a n Dev ia t ion C u r v e No . Tested Size Ract RP RP ta a'(%)b 0) (2) (3) (4) (5) (6) (7) (8) (9) 001 R 90 300 252 41 -11.0862 0.00% 002 R 90 400 308 82 -10.6153 0.00% 003 R 90 500 429 85 -7.9252 0.00% 004 R 90 600 527 86 -8.1034 0.00% 005 R 90 700 620 85 -8.9220 0.00% 006 A = 2% 90 500 427 85 -8.2298 0.00% 007 A = 6% 90 500 431 80 -8.1457 0.00% 008 A = 8% 90 500 417 88 -9.0113 0:00% 009 K = 50 90 500 424 89 -8.0466 0.00% Crest 010 K = 75 90 500 429 84 -8.0510 0.00% 011 K - 125 90 500 411 84 -10.0318 0.00% 012 LEFT TURN 90 300 248 44 -11.1868 0.00% 013 LEFT TURN 90 500 400 91 -10.4040 0.00% 014 LEFT TURN 90 700 628 87 -7.8353 0.00% 015 e = 4% 90 500 432 82 -7.8538 0.00% 016 e = 8% 90 500 422 87 -8.4692 0.00% 017 SIGHT = 100m 90 500 449 74 -6.5692 0.00% 018 SIGHT = 300m 90 500 430 85 -7.7766 0.00% 019 BACKGROUND 90 500 421 87 -8.6264 0.00% 020 BACKGROUND 90 500 443 77 -7.0263 0.00% 022 R 90 300 391 83 10.4159 0.00% 023 R 90 400 511 85 12.3449 0.00% 024 R 90 500 634 81 15.7559 0.00% 025 R 90 600 729 80 15.3479 0.00% 026 R 90 700 833 79 15.9463 0.00% 027 A = 2% 90 500 618 77 14.4579 0.00% 028 A = 6% 90 500 642 76 17.6591 0.00% 029 A = 8% 90 500 632 76 16.4650 0.00% 030 K = 25 90 500 637 74 17.4914 0.00% Sag 031 K = 75 90 500 639 76 17.3400 0.00% 032 K = 125 90 500 634 75 16.9621 0.00% 033 LEFT TURN 90 300 388 82 10.1713 0.00% 034 LEFT TURN 90 500 593 83 10.6430 0.00% 035 LEFT TURN 90 700 807 88 11.4430 0.00% 036 e = 4% 90 500 619 87 12.9234 0.00% 037 e = 8% 90 500 608 90 11.3321 0.00% 038 SIGHT = 100m 90 500 566 82 7.5542 0.00% 039 SIGHT = 300m 90 500 580 80 9.5338 0.00% 040 BACKGROUND 90 500 612 87 12.2108 0.00% 041 BACKGROUND 90 500 588 85 9.8465 0.00% Calculated value of the t -statistic. b Level of signif icance for accepting the nul l hypothesis H„ : Rp = R^ . 91 Table 5.2. Test of Hypothesis on the Adjusted Mean Value of Perceived Radius Adjus ted S tanda rd V e r t i c a l F i l e Pa rame te r Sample M e a n Dev ia t ion C u r v e N o . Tested Size Ract Rp* RP' ta a'(%)b 0) (2) (3) (4) (5) (6) (7) (8) (9) 001 R 90 300 261 55 -6.7121 0.00% 002 R 90 400 323 105 -6.9277 0.00% 003 R 90 500 459 117 -3.3340 0.12% 004 R 90 600 551 113 -4.0893 0.01% 005 R 90 700 646 115 -4.4796 0.00% 006 A = 2 % 90 500 439 100 -5.7849 0.00% 007 A = 6% 90 500 464 115 -2.9217 . 0.44% 008 A = 8% 90 500 448 123 -4.0307 0.01% 009 K = 50 90 500 456 122 -3.4592 0.08% Crest 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% 018 SIGHT = 300m 90 500 457 114 -3.5993 0.05% 019 BACKGROUND 90 500 446 115 -4.4796 0.00% 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% 027 A = 2 % 90 500 613 86 14.0443 0.00% 028 A = 6% 90 500 636 92 12.7237 0.00% 029 A = 8% 90 500 624 93 13.8177 0.00% 030 K = 25 90 500 630 89 14.7751 0.00% Sag 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% 035 LEFT TURN 90 700 790 113 -8.1821 0.00% 036 e = 4 % 90 500 606 110 8.5287 0.00% 037 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% Calculated value of the t -statistic. b Level of signif icance for accepting the nul 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 p = RaCtiwas tested at a level of significance of a = 5%. For example, if the value of K doesn't have a significant effect on the perception of horizontal curvature, than the mean values of R p (n = 90) for files 9, 10, 3, & 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. A N O V A A n a l y s i s D a t a S e t u p O v e r l a p p i n g C r e s t C u r v e O v e r l a p p i n g S a g C u r v e 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 of files 27, 24, 28, 29 Effect of K, compare Rp of files 9, 10, 3, 11 Effect of K, compare Rp of files 30, 24, 31, 32 Effect of LT Turn, compare Rp of files 12, 1 Effect of LT Turn, compare Rp of files 33, 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 of files 35, 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 of files 24, 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 A n a l y s i s : E f f e c t o f O v e r l a p p i n g V e r t i c a l A l i g n m e n t o n R p . ANOVA: Single Factor Groups Count Sum Average Variance Column 1 (files 001 - 020) 1800 Column 2 (files 022 - 041) 1800 769250 1103500 427.36 613.06 14861.01 17467.03 Column 1 has overlapping crest curves. Column 2 has overlapping sag curves. ANO\ \ Source of Variation SS df MS F P-value F crit Between Groups 31034184 Within Groups 58158160 1 3598 31034184 16164.02 1919.95 0 3.84 Total 89192344 3599 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 p should be captured better. Equation Forms: y = aixi + a2x2 + a3x3 + anxn + c (5.1) y = x,al * EXP(a2x2 + a3x3+ anxn + c) (5.2) The results of the regression analysis show that models in the form of equation (5.1) have a higher adjusted r2 value than when in the form of equation (5.2). However, the advantage of equations in the form of (5.2) is that the perceived radius Rp will equal zero when the actual radius is equal to zero (Rp = 0 when R = 0). This is not the case for equations in the form (5.1) 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 t-statistic denoted t_. The details of each regression model are presented in Appendix C. Sag Curve Equations: R p = 1.078 Xi + 3.737X2 + 26.094X6 + 42.088, r 2 = .744 (Ml) f, = 53.391, f 2 = 2.047, t6 = 4.446, t. constant = 3.140 736 (M2) r, = 51.929, t2 = 1.909, t6 = 3.727, tt constant = 7.289 Crest Curve Equations: R p = 0.956 Xi - 50.778, 747 (M3) = -3.724 R p - Xi 1.113 * 0.4118, 722 (M4) / i = 34.161, c^onstant = -4.407 Where X] = R, X 2 = A, and X 6 = turning direction. 96 Table 5.5. Variables used in Regression Model Development Trials. Dependent Variable: Y = Perceived horizontal curve radius, Rp (m) XI = Horizontal curve radius, R (m) X 2 = Vertical curve parameter A (%) X 3 = Vertical curve parameter K X 4 = Superelevation rate e (%) w -898* e (0.0064A+0.0401T + 0.782), f 2 _ y^ft (M2) 99 Where T = 0 for a turning direction to the left and T = 1 for a turning direction to the right, A = (|gi - g2|) and R = curve radius in meters. For 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 p = 0.956 R - 50.778, r2 = .747 (M3) R p = 0.4118 R 1 1 1 3 , r2 = .722 (M4) 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. Also, many of the subjects verbalized their difficulty in perceiving a difference between comparison images in Phase II. This issue may be related to difficulties in depth perception of the computer-generated images and should be addressed in future work. 101 As always, sample size and diversification could be improved. One possibility is to publish a web based presentation. Also, some of the parameters tested, such as left-turn, A, and K may have been under represented in the experiment. For example, the values of K that were tested were K=25, 50, 75, 100 and 125. 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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 DETAILS 108 Table A . l . Sample Characteristics - Phase I G = General Publ ic E = Engineer T = Transportation Engineer Sample No. Population Type L . 41 S S u o '41 i t * = il rs '7 it a Wear (.kisses u B * 1) " ft. X ' t d tt s IE a * B <-o •> '•G CS U '3 " S T Ui ' U ) B . 'Z p * = s '.©-TV, , fl s er n u fa- Duration on ll\v>s Sample No. Population Type o •o B V O it en < it a a a 4), cn > , SB-5. <• S5 ,41 Xiii 'u 5 41. at _ B IE A :1 , B »T5 W" 6 1 B> !E *c "TT ~K x~ s c ^. u B ii s .»er» 91 fa Duration on llw\s 1 G F B VANCOUVER Y i i Y D B 18 G F B VANCOUVER N 12 N B B 2 E M B VANCOUVER Y 8 N A A 39 G M B VANCOUVER N 14 N B A E M B VANCOUVER Y 9 N B B 40 G F B VANCOUVER N 13 Y B A 4 G F B BURNABY TM 16 Y D D 41 G M B VANCOUVER Y 15 Y C A 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 43 G F D NORTH VAN. Y 45 N D A G M B VANCOUVER Y 15 N B A 44 G F B NORTH VAN. N 13 N C A " 8 G F B VANCOUVER Y 17 N D B 45 G M D NORTH VAN. Y 43 N B A 9 E M A •N. 7 N E C 16 G M B NORTH VAN. •N 13 N B A 10 E M C VANCOUVER Y 17 N C A 47 G M B VANCOUVER N 12 Y D A 11 E M A Y 7 Y B A 48 G F B VANCOUVER N 16 Y C A 12 E M B VANCOUVER N 9 N D D 49 G M B VANCOUVER Y 15 Y D B P E M A VANCOUVER Y 5 Y C B 50 G F B NORTH VAN. N 15 TM B A 14 -E • F A Y 6 Y C A 51 T M D VICTORIA Y Is T F A NORTH VAN. N 7 Y A A 52 G M D VANCOUVER N 50 "IM C C Ifi E M e N 25 Y A B 53 G M C NORTH VAN. Y 24 TM A A 17 E F B VANCOUVER N 14 N C A 54 G .F B VANCOUVER Y 9 TM E A 18 E F A VANCOUVER Y i;5 Y C A 55 G F B NORTH V A N "NT 10 N B A 19 E F G VANCOUVER Y 20 -N D A Sfi G F B VANCOUVER Y 16 Y C A '20 E M B VANCOUVER Y 15 Y C A 57 G M C VANCOUVER Y 43 Y C A 21 G F A VANCOUVER N 8 N D E ^8 G F C VANCOUVER Y 40 TM E G 22 E M B VANCOUVER Y 7 Y A B s9 G F B VICTORIA N 0.5 Y C A 23 G F B VANCOUVER N 9 Y C A 60 G M B VICTORIA N 10 N A A 24 T F A VANCOUVER Y 6 N D A 61 G F B VANCOUVER Y 10 Y e B 2^ T M B VANCOUVER . N 10 Y D B 62 G M A VANCOUVER 0 3 26 T M B BURNABY Y 14 Y B B 63 G F C VANCOUVER N 38 N D B 27 G M B VANCOUVER N 17 Y D A 64 G F B VANCOUVER Y 13 Y E B 28 G M B VANCOUVER Y 10 Y C A 65 E F A VANCOUVER Y 6 Y B B 29 G F B VANCOUVER N N D A 66 G F B VANCOUVER Y 8 Y D B 30 G F B N N D A 67 G F B N N B B 31 T M B Y 15 N B A 68 G M B N TM C A *2 G F D VANCOUVER N 50 Y D C 69 G M B N N D A V , G M D VANCOUVER Y 50 N D A 70 G M B B A G M B VANCOUVER Y 12 Y C A 71 G F A TM N D A i S T F A COQUITLAM Y 5 N B B 72 G F B Y N C A 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 Table A . l . Cont. Sample No. Population Type a = O en < ' 41 u 'it -"O n •cc if C« r m CS it £• u v >u B" S 9 s Sample No. Population Type it •3 z 4> en it ^ „ = it «. it ^ •s* 4f yi* o « it Driving Expericnci B 03 U S t3 et, 5 * '>. Q * -X'-E O .«-. CJ S 41 s L . I t . Duration on Hww 75 G M C Y Y B A 83 M B R I C H M O N D Y 12 Y C A . 7ft G F B N N C A 84 F C V A N C O U V E R Y 24 Y B B 77 T M A P O R T M O O D Y N 8 N A A 85 M B S U R R E Y Y 20 N A A 78 T F A V A N C O U V E R Y 7 Y B A 86 F B N A N 1 A M O Y 21 N B A 79 G M B V A N C O U V E R Y 20 Y D D 87 M 80 G F B V A N C O U V E R Y 14 Y D C 88 F C V A N C O U V E R N 12 N E C 81 89 M B V A N C O U V E R Y 4 Y 82 M B V A N C O U V E R Y 10 N C A «0 F D V A N C O U V E R •N 30 N B B 91 M D V A N C O U V E R Y 47 Y C B 110 Table A.2. Experimental Data: Animated Crest Combinations - Phase I M = > R ' S = ' V = R " L = " Rp < R " O v e r l a p p i n g C r e s t C u r v e - A n i m a t i o n F i les H i '•m ssfs I I iSH mm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 S S L L M L L L L L S L L S S L S S L S 2 L L L L L S L S L L L S L L L L S L L L 3 S L L L L S L L L L L L L L L L S S L S 4 S L L L L L L L L L L L L L L L s L L L 5 L L L S L S L L L L S L L L L M L L L L 6 M L S M L L M L L L M M M M L M- M L L L 7 M L L S L L S S S M S S S S L L L L S M 8 L S L L M S M L L M L L M M S L S M M M 9 M M M M M M M M M M M L M S M M S M L M 10 M M L L M L M M L L M M M M M L S M M M 11 S S S M L S M S S M S S S S S M L L M M 12 M S S L L S . M L L L s L L s L L S L L L 13 L M M L S s L L M M L S L L M M M M S L 14 S S M L M M M L L M M S M M M S S L L M 15 S S M M L S S L L S M s S L M S S S M S 16 M S L L L L L S L L L M L L S L S L L L 17 L L L L L L L L L L L L L L L L S L L L 18 S L S L L S S S L L S L L L S S S S S S 19 L M S L L M L M L S L L M L L L S M S 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 S S L S L s S L S 22 L L L S S S L L L S S L L L s L s S L s 23 M M M M M S M M M M L M M M M M s M L M 24 S S L L S M S M L M L S S M S L s S L L 25 L L S S S S S S L S M L M S S L s S S M 26 M M M L S s L M L M L L L S M M s S M L 27 M M M M M s M M M M M M M M S M s S M M 28 M M M M S M M M M M M M M M M M s M M M 29 30 L L L L L L 31 L S S L L L M L M L S S S L L M s L M S 32 L L L L L L L L L L M S L L L L . s S M S 33 L L L L L L L L L L L L L L L L s L L s 34 L L L L L L L L L L L L L S L L s S L L 35 S M S S S S L S L M L S S L S S s S M s 36 L L L L L M L L L S L L L L L L s L L L 37 L L L S L S L L L L L S M M S L s S M M 38 S S L L L S L L L L L L L L L L s L S L 39 L L L L L L M L L L L L L L M M L L M L 40 M S L M L L S L M S L S S M M S M M M M 41 L S L S M L M L L L M L M L M S M L L L 42 M M M M L S M L L M L 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 45 L M S L M S S . L L M S L L L M M S: S S S 46 M L L L L L L L L L s L L L L L s L L L 47 L L L L L L M L L L s L M L M L s L L L 48 L S L L L S L L L L s S L L L L s L L L 49 M ivi M S S S S M S L L M S M S M s L S S 50 M L L L L L L L L L L L L L L M M L L M 51 52 L s S M S S M M M M S S L L S S M S S S 53 S s S S S S M S M M s s S S S S S S M S 54 S s s M s s M L S M s s S S M S S L S L 55 M L L L L L L L L L L L L L L S S L L S 56 S s s S M L M L M M L L M L M S S M M s 57 M M M M M M M M M M M M M L S M s M M M 58 M S M L S S S S S M M M S L M S M S S S 59 S S- S L L S L S s L L S S S L L S S S S 60 L s L L S L L L L L L S L L L L S L L L 61 S s M S S M L M S M L M M S L S s M M M 62 S s L S L S S S s S S L S L S L s S S L 63 L L L L L L L L L L L S L L L L s L L L 64 M S S S S S L M L L S M S S S S s S S S 65 L M M M M M M L M M M L M M M M s S L M 66 M S L S L S M L M M M M L L L S s M M S 67 L s L L L S L L L S L L S L S L s L S L 68 S L L L L L L L L L L S L L L L s L M L 69 L S L L L L S L L L S L L L L S s M L S 70 L L L L L L L S L S L S S L . S L s L .S L 71 S S L L L L S L S L S S L S L S s S L S 72 L S S S L S L L L L s L S S L L s S L S L' 73 L L L L S L L L S L L L L S L S s S L 74 L L L L S L L S L S L M S S L L L L S L 75 S L L L L L L L L L L S L L L L s S s L 76 S L L L L L L L S L L S L L L L s L s M 77 L M S L L M L L L L M s L L L L s M M L 78 L M L S L M L L L L L L L L L L s S L L 79 M M M S . L L S L L S S L L S S S s S S S 80 L L L s S S M • L S S S S M S S S s L S S 81 L L L L L L L L L L L L L L L L s L L L 82 S L L L L L S L L L S L L L L L s S L L 83 S S L L L S L L L L L S L S S L L S S L 84 85 86 87 88 s L L L L L L L L L M L L L L L M L L L 89 90 91 112 Table A.3. Experimental Data: Animated Sag Combinations - Phase I M = " R p > R " S = "Rp = R " L = " R p < R " O v e r l a p p i n g S a g C u r v e - A n i m a t i o n F i les Hi H I 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 M M M M M S M M M M S M L M M S S S M M 4 L M M M M M M M L S M L S M S M S L M M 5 M M M M M S M M M M M M M M M M S M M M 6 L M M M M M M M M M M M M M M M M M M M 7 M M M S M L M M M M M S S L L M L M L M 8 S M S L L L L M M M M S L L M • M S L L L 9 •L L L L L L L L L M L L L L L L S L L L 10 M M M L M S M M M S M M M M S M s M M M 11 S M M S S M M M S S S S S S M M s L M M 12 M M M M M S M M M M M M M L M M L M M M 13 L S S S L S L L L L M L M L M L L L S M 14 M S M M M S M M M M M L M M M L M M L M 15 S M S M M S M M M S M M L M S S S S M L 16 M S M S M M M M M M M M M M L S s M M M 17 M L M L M L M M M L L L M M M L L L L M 18 S S S S M S M M M S M L • M S S M S L L M 19 M M M S M M M M M M L M S M L M M L M M 20 L M M M M M M M , M S M S M M M S S M M M 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 23 L L M L M S L M L L M M L M L M S M L M 24 M L M L M M M M M M S L M L M M S M M M 25 S M M M S M M M M S S M S S S S S M M L 26 M M S L S M S L S M M S S L L M S S L M 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 29 30 S S S S S S 31 M M M M M M S M M S S S S S M M S M M M 32 S M M M M S M M M M S M M S M M s S M M 33 M M M M M M M M L M M M L M M M s M M M 34 M M M M M S M M M S M M M M M M s M M M 35 S M S L L M M M S S S S S M M L s M M M 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 s M M M 38 M M M M M M M M M M M M M M L M s S M M 39 L L L L L L L L L L L L M M L L L L L L 40 M M M M L L L M L M M S M M S M S M M L 41 M M M M M M M M M M M M M M M M L M M M 42 L M L M M M M M M M M M M M M M L L M L 113 Table A.3. Cont. 43 S M... M S M M M M M M M M M M M M M M M M 44 S L S M S S S M S S S S M S L M S s S L 45 s M M M M M M M M S M M M M M M L L S M 46 s S M M S S S M M M S S M M M M S M M M 47 M M M M M M M M M M M M M M M M S L M M 48 M M S M M S M M M S S S M M M M s S M M 49 S L L L M S M M M M M S L L L S s L M S 50 S M M L S M M M M M M S M M M M s S M M 51 52 S M S M M M M L L M M S M L M L L L L M 53 S S S M S S S S S S S S S S S S S S S M 54 M M M M S S M M M s S S s S M M s . S S M 55 S M M M S M M M M M M S M M M M s s M M 56 L M S S M S M M L M S L L M L S s s M M 57 M M M L M L M M M M M L L L M M s L M M 58 M S M M M S S M M S S S S S M S s S S S 59 S M. S M. M s M M M S S S S M M M s L S S 60 M M M M M s M M M s ' M M M M M M s L M M 61 S M S S L L L S S M L L S L S L M M M L 62 S S L S S S M S M S M M S S L M S L M M 63 L L L L L L L L L L L L L L L L L L L L 64 M S S M M S M S S M M S M S M S L S M S 65 M M M M M M M M M M M M M M M M L S M M 66 L M M M M S M M M M S L M M L M S L M L 67 M M M M M M M M M S M M S M S M S M S M 68 S M M M M M M M M M M S M M M M S M M L 69 M M M M M M M M M M S M M M M S S M M M 70 M M M M M M M S M M M S M M M M M M M M 71 M S M M M M S M S M S M M M M M S S M M 72 M S S S M M M M M M s M S M M M S S M M 73 M M M M M M M M M L M M M S M M S S M M 74 M M M M M M M S M M M S S M M M M M M M 75 M M M M M M M M M M M M M M M M S S M M 76 S M M M S M M M M M M S M S M M S M M M 77 S S M M L S M M M M S S S L M M S M S M 78 M M S M M S M M M M S M M M M M S S S M 79 S S M M S S S M S S S L S M M S S S M M 80 L L L M. M M M M M M M S S S M M S M M L 81 M M M M M M M M M M M M M M M M S M M M 82 M M M M M S M M M M M M M M M M S S M M 83 M M S S M M M M M M M S S S M S S S S S 84 85 86 87 88 M M M M M M M M M M M M M M M M L M M M 89 90 91 114 Table A.4. Experimental Data: Image Crest Combinations - Phase I M = " R p > R " S = ' V = R " L = " R p < R " O v e r l a p p i n g C r e s t C u r v e - Image Fi les isS&SS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 L L L L L L L L L L L M L L L L S M M M 2 L S L S L S L L L L L L L L L L S L L L 3 L L L L L L L L L L L L L L L L S S L L 4 L L L L L L L L L L S S L L L L S L L L 5 L S L L L S L L L L L L L L L L M L L L 6 M M L M L S M L S M S L L L L L L M L M 7 M M M M M M S M S M S M L M M M S M S M 8 S M M S L S M M M S s M M M M M s M M M 9 M M M M M S M M M M M M M M M M s M M M 10 L M S M L S L L M L S L L M L M s M M M 11 M S M S M s M M M S M M L M S M s M M S 12 L S S S S s S L S S S S L L S L s M S S 13 M M L M . M M M M M M M M L M L M s M M M 14 L L L L M S L L L L L L L L M L s M L L 15 S M S S S S S L M M S S S L M M s M S S 16 L M L L L L L L L L L M L L L L s L L L 17 S M L S L S L L L L L L L S L M L L L L 18 M S S S M S M M M M S M M M S S s M S S 19 M L L L L L S S S L s L L S S S s S S S 20 M S M M L S S M S L s M M L L L s L L L 21 L L L L L L L L L L s L S L L L s L L L 22 L L L L L L L L L L s S L L L L s S L L 23 M S L S M S L S L M L L L M M M s L L M 24. L S L S L s L L L L L L L L L L s L L S 25 M L L L L s S L S L L M S L S S s S S S-26 M M L L L s M M M M L M M L L M s L M S 27 M M M M M s M M M M S S M S M M s S S M 28 M M M M M s M L M M S M M M M M s M M M 29 L L L L L L L L L L L L L L L L s L L L 30 L L L L L L L L L L L L L L L L s L L L 31 M S S S L L L M L M L L M S L M s L S L 32 L L L L L L L L S L L M L S L L s S L L 33 M L L L L L L L L L L M L L L L s L L L 34 L L L L L L L L L L L L L L L L L L S L 35 S S S S M S M M M L M L M M M M s M M M 36 M L L M L M L L L S L L L L L L s S S S 37 M L M L M M L M L S S M M S M M s M S M 38 S M M M M S M M M S s S M S M L M M S M 39 M L L L L L L M L M L L L L L L M M L L 40 S S M S L S M M L S S S L L M L S M S S 41 S S M S L L M M M L S S S S M S S M M S 42 L M L M M . L M M M S M M M L M M M M M M 115 Table A.4. Cont. 43 L S L L L S L S L L L L L L L L S L L L 44 S S S S M S M S M S S S S S S S S M M S 45 S M M M M S L M S S L L L L S L S M L S 46 M S M S S S S M S s S M S M s S S S S M 47 M M M M L M M M M M M M M M M M s L M M 48 L L S S L S L S L S S S L L L S s L M L 49 S S S L M L M L S L S S L L M S s S L L 50 M M M M S L S L L L S M L S L L s S L L 51 S S S L S M M S L S L S L L S L s S S S 52 S M M M M M M M M s M S M S S M s S M S 53 S M S M M S M M M M S M S M s M s S S s 54 S S S M M S M S M M S S S S s S s M S s 55 M s S S S L S L L L S S L S L L s S L L 56 M M M M S S M M M M S S M M S M s M S S 57 M M M M M S M M M M S M M S M M s M M M 58 M S M M M S M M M M M M M M M M s S M M 59 L L L L L S L L L L L L L L L L s L L L 60 L L L L L S S L L L L S L L L S s M L L 61 M L M M L S L M L M M S M M M M s M M L 62 L S M S M S M L M S S s M S M S s M S M 63 M M M M M M M M M M M M M M M M s M M M 64 S L L L L S M S M M S S L M L S s M M M 65 M M M M M L M M M M M s M M M M s S M M 66 M M M M M S M M L M S M M L L M s M M M 67 L S L L L s L S L S L L S L S L s L S L 68 S L L L S L L L L L L S L S M L s L M L 69 L S L L L L S L S L S L L L L S s M L S 70 L L L L L S L S L S L S S L S L s L S L 71 S S L L L L L L L L S S L S L S s S L S 72 L S M S L S S L S L S L M L L M s s L M 73 L L L L S L S L S L L L L S L S s s L S 74 L L L L L L s S L S L S S L S L s L S L 75 S L L L L L L L L L L S L L L L s S S L 76 S L L L L L L L S L L S L L L L s L S M 77 M M S L L M M L M L L M L L L M L M M L 78 S L L L L S L L L L L L L L L L s L L L 79 M M M S s M S M S S S S S S S S s S S S 80 L L L L L S S L M L S M M s M L L M L S 81 L L L L L L L L L L L L L L L L M L L L 82 L L L S L L L L S L L L L S L L s L L L 83 L S L S L L L L L S L L L L L L s L L L 84 L ' S L L L S L L S S S L L S S L s S L S 85 L L L S L S L L L s S L L L L S L L S S 86 L S -S s S L M L S L L L M S M L s S S s 87 S s S s L S S L L S S L S S S S s L L L 88 L s s L L L L L L L L L L L L L s L L L 89 L L M L L M M M L L L L M L S S L M M M 90 S M L . L M S M M L L M L , M L M M S M M M 91 M M L L L M M M M M M M M L M M L M M M 116 Table A.5. Experimental Data: Image Sag Combinations - Phase I M = " R P > R " S = = R " L = " Rp < R " O v e r 1 a p p i n g S a g C u r v e - Image Fi les ? \ 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 1 M M L M M S M M M M M M M M M M S M M M 2 M M M M S S M M L M M S M M M S s M L M 3 L M M M M M M M M M M M M M M M s S M M 4 S M M S L S M M M M M M M M S M s S L M 5 M M M M M s M M S M M M M M L S M M S M 6 M M M M M M M M M M M M ' M M M M s M M M 7 M M S S M S S S M M M S S L S S L L S S 8 L L L M L S M M L M M L L L L M s L L L 9 L L L L L L L L L L L S L L L L S S 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 S M M S S M L S S S M L 12. M S M M M M M M M M M S M M M M M s M M 13 L S L L M S L L S S S L L L M S S L L L 14 M M S M M S M M M M M M ' M M M M S M M M 15 M M S M M S M M L S M M M M M S S L M L 16 L L M L M S M L S S M M M L M S s S L M 17 S M S M M S M M M M S M L L M M s M L M 18 M M M M M M M M M S M S M M S M s S S M 19 S S S L S S S S S M S L M M L S s M S L 20 S S S M M S M M S S s L M M L S s M S L 21 M M M M M M M M M s M M M M M M s M M M 22 M M M M M M M M M s S M M M M M s S M M 23 M M M M M S M M M M L M M M M M s M L L 24 M M M M M M M M M M M M M M M M s M M M 25 L L L L L S S S L L S S L L L M s S L S 26 M M M S L M S M S S S M L S S M s S S M 27 L L S M M L L L S L L L L L M L s L L L 28 L L . L L M L L L M M S L L L M L s L M L 29 M M M M M M M M M M M M M M M M s M M M 30 M M M M M M M M M M M M M M M M s M M M 31 S S M S S S M S M M L S M S M M s S M M 32 M M M M M M M M M M S M M M M M s L M M 33 S M S M M M M M S M M M S M M M s S M M 34 M M M M M S M M M M S S M M M M s S M M 35 M M S S M S M M M S S s- M L M S s s S M 36 M M M M M M M M M ' M M M M M M M s s M M 37 S S S M L S S S L S M S L M S M s s L L 38 S S S M M S M M M S S M L M S S s L M M 39 L L M L M M L L L L L M L L M M L M L L 40 M M M M M M M M L L S • S M S M M s L M M 41 M M L S M M M M M M M M M M M M s L M M 42 L M S L M M S M M M . M S L M M M s L M L 117 Table A.5. Cont. 43 S M M M M S M M S M M M M M M M S M M M 44 S S S S S S S S M S S S M S M S S s S M 45 M M M M M M M M M S M M M M M M M - s M M 46 S S M M S S S S S S S S S S M S S L S S 47 S M M M M M M M M M M L M M M M L M M S 48 M S S M L S M M M S M M M S M M S L M M 49 L S L M M S L L M M S M S s L M S S M M 50 S S M M M S M M M M S M M M S M s M M M 51 S S M M M L L M M S s L L L M M s S L L 52 M L L L M M S L L S L S M M S L M L L L 53 S S S M L S S S S S S S S S s S S M S M 54 S M S S S S S S M M s S s M s S s M M M 55 S s M M M S M M M M s M M M s M s M M M 56 L s L L S M M M S M s L L M s S s L L M 57 S s M M M M M M M M M M M M M M s S M M 58 S s S S M S S S L M L M S S S S s ' L L L 59 M M S M M S S M M M S S M M M S s M M M 60 S M M M M M M S M M M S M M M S s M M M 61 M M M S M S M M M M M M M M M s s S S M 62 S S M S M s M M S S S S M M M M s M S M 63 L L S M M L L L M L L L L L M L s L L L 64 M S S M M S M M S M S M M M M M s S M M 65 M M M M M M M M M S M S M M M M s M M M 66 M M L S M M M L M L M M M M S L s L M M 67 M M M M M M M S M S M M S M s M s M S M 68 S M M M M M M M M M M S M M s M s M M M 69 M M M M M M M M S M S M M M M S s M M M 70 M M M , M M S M S M M M S S M M M s M M M 71 M S M M M M M M M M S M M M M M s S M M 72 M S S M M M S M S M s M S M M S s S M M 73 M M M M M M s M M M M M M S M S s S M S 74 M M M M M M s M M M M S S M M M s M M M 75 M M M M S M M M M M M M M S M M s S M M 76 S M M M M M M M M M M S M M M M s M M M 77 S M S M S S L S L S S M M L M S s M M S 78 M S M M M L M M M M M M M M M M s S M M 79 L M M M M M S S M S M S L M M S L M S M 80 S M S S M S M M M S M s S M S M s M S S 81 M M M M M M M M M M M M M M M M s M M M 82 M S M M M M S M M M M M M M S M L S M M 83 M S M M M S M M M S S S M M M M s L M M 84 S S S S M S S M S M ' S S S S M M s S M S 85 S M S S M M M S S s M S M M M M s S M M 86 M S S M S S M M s M M S M S M S s M L S 87 S S S S M S S M M S M s S s S S s S S S 88 M M M M M M M M M M M M M M M M s M M M 89 M M M M M M M L L M M L M M M L s M M M 90 S M S M M S M L M M L L M M S L s L L L 91 M M M M M M M M M M M M M M M M L M M M 118 Table A.6. Experimental Data: Crest Combinations Summary - Phase I M = > R " S = •Rp = = R " L = " Rp < R " O v e r 1 a p p i n g C r e s t C u r v e s Test-Curve No . | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | 19 | 20 \n in ia t ions IfiJJlL Total # of " L " Total # of " S " Total # of " M " 36 24 22 34 31 17 49 17 16 48 20 13 49 20 12 34 34 13 44 15 23 55 13 13 55 13 13 46 13 23 39 26 16 37 29 15 43 20 19 48 21 12 39 25 17 42 22 17 7 65 9 34 37 36 31 24 27 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 % of L's % o f S ' s % of M's 4 4 % 4 1 % 6 0 % 59% 6 0 % 4 2 % 54% 6 8 % 68% 5 6 % 4 8 % 4 6 % 5 2 % 59% 2 9 % 3 8 % 2 1 % 2 5 % 2 5 % 4 2 % 18% 16% 16% 16% 3 2 % 36% 2 4 % 2 6 % 2 7 % 2 1 % 2 0 % 16% 15% 16% 2 8 % 16% 16% 2 8 % 2 0 % 19% 2 3 % 15% 4 8 % 5 2 % 3 1 % 2 7 % 2 1 % 2 1 % 9% 80% 11% 4 2 % 4 6 % 4 4 % 3 8 % 30% 3 3 % 2 0 % 2 5 % 2 2 % Images mis! '+ * Total # of " L " Total # of " S " Total # of " M " 37 22 32 33 30 28 47 17 27 42 25 24 54 11 26 32 47 12 40 17 34 47 11 33 44 .18 29 44 23 24 39 39 13 36 28 27 50 13 28 48 24 19 44 20 27 42 19 30 8 78 5 31 37 37 23 27 26 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 % of L's % o f S ' s % of M's 4 1 % 36% 5 2 % 4 6 % 59% 3 5 % 4 4 % 5 2 % 4 8 % 4 8 % 4 3 % 4 0 % 5 5 % 5 3 % 2 4 % 3 3 % 19% 2 7 % 12% 5 2 % 19% 12% 2 0 % 2 5 % 4 3 % 3 1 % 14% 2 6 % 3 5 % 3 1 % 3 0 % 2 6 % 2 9 % 13% 3 7 % 36% 3 2 % 2 6 % 14% 3 0 % 3 1 % 2 1 % 4 8 % 4 6 % 2 2 % 2 1 % 3 0 % 3 3 % 9% 34% 4 1 % 4 1 % 86% 2 5 % 3 0 % 2 9 % 5% 4 1 % 30% 3 1 % Average ||jI|P§ff|f|g I B j j t % of L's % o f S ' s % of M's 4 2 % 3 9 % 56% 5 3 % 60% 3 9 % 4 9 % 6 0 % 58% 5 2 % 4 6 % 4 3 % 54% 56% 4 8 % 4 9 % 9 % 3 8 % 4 3 % 4 3 % 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 % 24% 8 3 % 3 2 % 30% 3 1 % 3 1 % 2 6 % 2 5 % 2 1 % 2 2 % 15% 3 3 % 2 6 % 24% 2 7 % 17% 2 4 % 2 7 % 18% 2 5 % 2 7 % 8% 3 0 % 2 7 % 2 6 % 119 Table A.7. Experimental Data: Sag Combinations Summary - Phase I M > R " S = ' R p = R" L = " Rp < R " O v e r l a p p i n g S a g C u r v e s Test-Curve N o . 1 22 1 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 J 40 | 41 ISlffiimatibiis jjBil > Total # of " L " 13 12 7 14 9 12 9 7 11 8 9 16 11 14 16 10 13 22 13 15 Total # of " S " 26 15 21 15 14 30 9 8 10 21 24 31 23 16 10 16 59 23 11 6 Total # of " M " 43 55 54 53 59 39 63 66 60 52 48 35 47 51 55 55 9 36 57 60 Sample Size 82 82 82 82 82 81 81 81 81 81 81 82 81 81 81 81 81 81 81 81 % of L's 16% 15% 9% 17% 11% 15% 1 1 % 9% 14% 10% 11% 2 0 % 14% 17% 2 0 % 12% 16% 2 7 % 16% 19% % o f S ' s 3 2 % 18% 2 6 % 18% 17% 3 7 % 11% 10% 12% 2 6 % 3 0 % 3 8 % 2 8 % 2 0 % 12% 2 0 % 7 3 % 2 8 % 14% 7% % o f M ' s 5 2 % 6 7 % 6 6 % 6 5 % 7 2 % 4 8 % 78% 8 1 % 74% 64% 59% 4 3 % 5 8 % 6 3 % 6 8 % 6 8 % 1 1 % 4 4 % 70% 74% Images s i USUI Total # of " L " 14 10 12 11 8 6 9 12 12 7 • 9 12 16 14 8 8 6 20 19 18 Total # of " S " 29 28 29 16 10 42 20 17 21 28 32 33 15 15 20 28 81 33 17 11 T o t a l * of " M " 48 53 50 64 73 43 62 62 58 56 50 46 60 62 63 55 4 38 55 62 Sample Size 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 91 % of L's 15% 11% 13% 12% 9% 7% 10% 13% 13% 8% 10% 13% 18% 15% 9% 9% 7% 2 2 % 2 1 % 2 0 % % o f S ' s 3 2 % 3 1 % 3 2 % 18% 11% 4 6 % 2 2 % 19% 2 3 % 3 1 % 3 5 % 36% 16% 16% 2 2 % 3 1 % 8 9 % 3 6 % 19% 12% % of M's 5 3 % 58% 55% 70% 80% 47% 68% 68% 64% 6 2 % 55% 5 1 % 6 6 % 6 8 % 69% 60% 4 % 4 2 % 6 0 % 68% • \ \ c ragc Spit % of L's % o f S ' s % of M's 16% 13% 11% 15% 10% 11% 11% 11% 13% 9% 11% 16% 16% 16% 14% 11% 1 1 % 2 5 % 18% 19%! 3 2 % 2 5 % 2 9 % 18% 14% 4 2 % 17% 14% 18% 2 8 % 3 2 % 3 7 % 2 2 % 18% 17% 2 5 % 8 1 % 3 2 % 16% 10% 5 3 % 6 3 % 6 0 % 6 7 % 7 6 % 4 8 % 7 3 % 7 5 % 6 9 % 6 3 % 57% 4 7 % 6 2 % 6 6 % 6 9 % 64% 8% 4 3 % 6 5 % 7 1 % Table A.8. Sample Characteristics - Phase II G = General Publ ic E = Engineer T = Transportation Engineer 11 s J? \ ** 1 "c. | Population Type _t id s i a * mi mt c mt tf* ex > s tf» m* w mt I S • fi P i tea* Population Type a mt mt illliiliii^ llililiiii x it r y it mi mt m* «* tf* *s ..mm-. > mi mt mi 1 G F B NORTH V A N . N 13 N c A 38 T F A VANCOUVER Y 7 Y A A 2 G M B WILLIAMS L A K E Y 15 N A B 39 T M A PORT MOODY N 7 N A A 3 G F B VANCOUVER N 15 Y 40 E M B VANCOUVER N 8 N D C 4 M B VANCOUVER Y 9 N B B 41 E M B VANCOUVER Y 8 Y C B 5 M VANCOUVER Y N C A 42 E F A VANCOUVER N 7 Y C A 6 F B NAN1AMO Y 21 N B A 43 E F A VANCOUVER Y 1 Y C A 7 M 44 E F A NORTH V A N . N 7 Y A A 8 F C VANCOUVER Y 24 Y B B 45 E M A SURREY N 4 N A B 9 E M B VANCOUVER Y 4 Y 46 E F B RICHMOND Y 6 Y A A 10 G F D VANCOUVER N 30 N B B 47 T M A VANCOUVER Y 8 Y C B 11 G M D VANCOUVER Y 47 Y C B 48 E M B VANCOUVER N 11 Y E E 12 T M A VANCOUVER N 2 Y C A 49 E F A COQUITLAM Y 4 N A A 13 T M 50 E F A VANCOUVER Y 6 N C B 14 T M B 51 G F B VANCOUVER Y 17 N E D 15 T M 52 G M B VANCOUVER N 12 Y C A 16 E M B VANCOUVER N 11 Y B B 53 G F B VANCOUVER Y 12 Y D B 17 E M B BURNABY Y 15 Y B B 54 G M B VANCOUVER Y 15 N B A 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 21 E M B NORTH V A N . Y 7 Y A A 58 E F A VANCOUVER Y 8 N C A 22 T M C VANCOUVER Y 18 Y C A 59 E M A VANCOUVER N 6.5 N B B 23 G M C ARMSTRONG N 37 N A A 60 E M B VANCOUVER N 20 N E C 24 G M D VANCOUVER N 43 Y A A 61 E M C VANCOUVER N 29 Y A B 25 G M B PEMBERTON Y 5 Y C A 62 E M A VANCOUVER Y 5 N E E 26 G F C ARMSTRONG N 20 N A A 63 E M A VANCOUVER N 7 Y A A 27 G M C VERNON Y 38 N C D 64 E M C RICHMOND N 23 Y B A 28 G F B K E L O W N A 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 V A N . 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 31 T F A VANCOUVER Y 6 N C A 68 G M B VANCOUVER Y 20 N C C 32 T F A VANCOUVER Y 5 Y B B 69 G F B D E L T A N 14 N A A 33 G F B VANCOUVER Y 14 Y E B 70 G M D NORTH V A N . Y 42 N B A 34 E M A VANCOUVER Y 4 Y B A 71 E M A VANCOUVER Y 6 Y C A 35 G M B VANCOUVER Y 11 Y B A 72 E M B VANCOUVER Y 17 N A B 36 G F A VANCOUVER N 9 Y D A 73 G F B VANCOUVER Y 9 Y D A 37 T M C BURNABY Y 28 Y B B 74 G M B VANCOUVER Y 10 Y B A 121 Table A.8. Cont w 1 r l i a H B s B . o Cu y Cl t * ii l o t B i i -o ^ B M I mi mv f * * l %af '> ' E I Q l 1 IMP SC s "> b o mi X B M sk e r » y. * X • s t g « ,-Sl S Sir t e a l iVjM CU a H B a o CL 4* 4* SC r * «* ii Q 0£ *r w zr i* £ , s $ ICS* 75 E F c VANCOUVER N 10 Y C A 83 G F B VANCOUVER Y 12 Y c A 76 E M A VANCOUVER Y 6 Y E B 84 G F A VANCOUVER N 0 N F 77 E M A VANCOUVER N 7 Y D A 85 G M B VANCOUVER Y 13 Y D B 78 G M C VANCOUVER Y 31 N B A 86 G F A VANCOUVER N 8 N D B 79 G M C VANCOUVER N 17 Y C A 87 E M A ALDERGROVE N 9.5 N A B 80 G F B VANCOUVER Y 8 Y D B 88 E M A COQUTTLAM Y 7 N B A 81 T M B VANCOUVER N 11 N D D 89 G M C VANCOUVER Y 38 Y D G 82 G M B VANCOUVER Y 12 N B A 90 G F C VANCOUVER Y 35 Y D Table A.9. Experimental Data: Image Crest Combinations - Phase II 1 2 2 O v e r l a p p i n g C r e s t C u r v e z i fes. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 300 400 500 500 600 500 300 300 400 500 400 300 500 700 400 500 500 300 400 300 2 300 200 300 500 600 500 500 500 500 500 400 200 400 600 500 500 300 500 500 500 3 250 300 400 600 500 500 400 300 300 500 300 300 300 600 500, 400 500 500 500 500 4 250 200 300 600 600 500 400 300 400 400 500 200 300 700 400 300 400 400 500 500 . 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 9 200 300 500 600 700 500 500 500 500 400 400 300 300 500 500 300 500 500 500 400 10 200 200 300 400 500 300 500 300 300 300 300 250 300 600 400 400 500 500 500 500 11 250 200 400 500 500 400 300 400 300 300 400 200 300 700 500 300 400 400 300 300 12 300 300 500 500 500 500 500 500 300 500 400 200 400 700 500 400 300 500 300 500 13 300 400 300 600 700 500 300 300 400 500 500 200 500 700 500 500 500 400 500 400 14 250 300 400 400 600 300 400 300 400 400 300 200 400 500 400 400 500 300 300 400 15 300 400 500 600 600 500 500 300 400 300 500 200 500 700 300 500 500 500 500 500 16 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 300 500 500 500 17- 250 400 500 600 700 300 500 300 500 500 500 300 500 700 500 500 300 500 500 500 18 300 200 300 600 700 500 400 300 ,500 . 500 300 200 500 700 500 500 300 500 500 500 19 200 300 500 600 700 500 500 300 500 300 500 300 300 500 300 300 500 400 500 400 20 300 200 500 600 700 500 500 400 300 500 500 300 500 700 500 300 500 500 500 500 21 300 200 300 400 700 300 400 400 500 400 300 250 300 700 500 300 400 400 400 500 22 200 200 300 400 500 500 300 300 500 300 300 200 300 700 400 300 400 300 300 300 23 300 300 500 500 700 300 400 400 300 300 500 200 300 500 500 500 500 500 400 300 24 200 200 500 400 700 400 400 400 500 500 500 250 300 700 300 400 500 300 300 500 25 300 200 400 400 700 400 400 400 300 500 400 200 400 700 300 500 300 500 400 300 26 200 200 500 600 600 500 400 300 300 300 300 250 400 500 500 300 500 400 500 500 27 250 400 500 400 700 500 400 300 500 400 400 300 300 600 500 500 400 400 500 400 28 200 400 300 600 500 300 300 500 500 500 300 200 300 500 300 300 400 300 300 300 29 200 300 400 600 700 500 400 500 500 300 500 200 500 700 500 500 500 500 400 500 30 250 400 400 500 500 400 300 500 500 300 500 250 400 700 400 300 300 300 400 300 31 200 200 300 400 700 500 300 300 300 500 • 4 0 0 300 300 700 300 300 500 500 300 500 32 200 200 300 400 700 300 500 500 300 500 300 300 300 500 500 500 400 500 300 300 33 250 300 300 500 500 400 400 500 500 500 300 300 500 600 500 500 500 500 500 500 34 200 300 300 400 700 500 500 400 300 300 300 250 300 500 300 500 500 300 300 400 35 200 300 500 400 700 500 500 400 500 400 500 250 400 700 400 300 400 300 300 300 36 200 200 300 400 500 300 300 400 300 300 300 200 300 500 300 300 500 300 300 400 37 250 400 500 600 700 500 300 500 300 400 500 300 500 700 500 500 500 500 500 500 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 . 500 400 300 300 300 400 400 42 250 400 500 600 500 500 500 500 500 500 500 300 500 600 500 " 5 0 0 500 300 400 400 123 43 300 300 400 600 700 500 44 300 300 400 400 600 300 45 250 400 400 600 700 500 46 200 300 300 400 700 300 47 300 400 500 600 700 500 48 200 200 500 600 500 400 49 200 400 500 400 700 300 50 300 300 500 500 600 400 51 300 300 500 400 500 500 52 250 400 500 400 700 300 53 250 300 300 400 500 300 54 250 400 500 600 700 500 55 300 400 500 500 700 400 56 300 300 400 500 600 400 57 250 400 500 600 600 500 58 300 200 500 600 700 300 59 200 300 500 600 600 500 60 250 400 500 400 700 500 61 300 300 500 500 700 400 62 200 200 500 600 600 500 63 300 200 300 600 700 300 64 250 400 500 600 700 500 65 300 300 400 500 600 400 66 250 400 500 600 700 400 67 200 300 500 600 600 300 68 250 200 300 600 500 400 69 250 400 500 600 700 300 70 200 400 500 400 500 500 71 200 400 500 600 600 500 72 250 300 400 400 700 500 73 200 200 300 500 500 300 74 300 400 500 600 500 500 75 300 400 300 600 700 300 76 250 300 500 600 600 400 77 300 400 400 600 700 400 78 300 200 300 600 500 500 79 250 300 400 600 700 500 80 300 300 500 500 500 500 81 300 300 500 600 700 400 82 300 200 300 600 700 500 83 250 200 400 500 700 300 84 250 400 500 500 600 300 85 300 400 500 600 700 500 86 250 400 500 600 700 500 87 200 300 500 500 600 400 88 200 400 400 600 500 500 89 300 300 500 600 500 500 90 200 400 400 600 600 400 Table A.9. Cont. 500 500 500 400 500 200 300 500 500 500 500 500 250 300 500 500 500 500 500 300 500 400 400 300 500 500 200 400 400 500 300 500 400 300 500 300 400 400 500 300 250 400 500 500 300 500 400 300 500 500 500 500 400 400 300 400 400 400 400 500 400 250 500 400 500 500 500 500 250 300 500 500 500 400 400 200 400 500 300 500 500 500 300 500 500 500 500 400 400 200 500 500 500 400 300 500 300 500 400 500 500 500 300 300 500 400 300 400 300 300 250 300 500 500 300 500 500 300 500 300 300 500 500 500 300 300 500 300 500 400 500 250 400 500 500 400 500 500 200 300 500 500 300 500 400 200 500 500 500 300 500 300 250 500 400 400 500 400 400 250 400 500 500 500 500 500 200 500 500 500 500 500 300 200 300 300 400 500 500 400 200 400 300 500 300 300 300 250 500 500 300 300 300 400 200 300 500 300 500 500 400 200 500 500 500 500 400 500 250 500 300 400 400 400 500 300 300 500 500 500 500 300 300 300 500 500 400 300 500 200 300 500 500 500 500 400 200 500 500 300 400 500 500 300 500 300 400 500 500 300 200 300 500 500 300 300 300 300 300 400 500 500 500 300 200 500 500 300 500 500 300 200 500 500 300 500 500 500 200 500 500 500 500 500 300 200 500 300 500 500 400 500 300 300 400 500 500 500 400 300 300 500 500 500 500 500 300 500 400 500 500 300 500 300 400 400 500 300 300 400 200 400 300 500 300 400 400 250 500 500 300 300 300. 400 300 500 600 400 500 500 500 400 500 700 500 400 400 500 300 500 700 500 300 500 500 500 500 500 500 400 500 300 300 300 600 500 300 500 500 300 500 700 300 400 500 500 400 500 500 500 500 400 400 300 500 700 500 400 500 500 400 500 700 300 400 500 500 500 500 600 500 500 500 300 500 500 500 300 400 500 500 500 500 700 500 500 500 500 500 500 700 500 500 500 500 500 400 700 500 400 500 500 400 400 600 500 500 500 500 400 500 700 500 300 400 300 500 500 700 500 500 500 500 500 400 700 500 300 400 300 300 500 500 400 400 500 500 400 500 500 300 500 500 500 500 500 500 300 500 400 400 500 500 700 500 500 400 500 500 500 600 400 300 400 400 300 400 700 500 500 500 500 500 500 500 500 500 500 300 300 300 700 300 500 500 500 500 300 500 500 500 400 300 300 500 700 400 500 400 400 300 400 500 400 500 500 500 400 500 500 500 500 500 500 500 500 700 300 400 500 300 300 300 500 500 300 500 500 500 500 600 500 500 500 400 500 300 700 400 500 500 500 300 400 700 500 500 500 300 500 400 700 300 400 300 400 500 500 700 500 500 500 400 500 500 700 300 500 500 300 400 300 600 500 500 300 500 500 500 700 500 500 500 500 500 500 500 500 500 500 300 300 500 700 400 300 500 500 500 500 700 400 500 500 500 500 500 700 500 500 500 500 500 500 600 400 400 400 400 500 400 600 400 500 400 500 500 500 700 500 400 400 300 300 400 500 400 300 500 300 400 400 124 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 1 500 600 700 800 900 700 700 500 700 700 700 400 600 800 700 700 600 500 600 500 2 300 600 600 800 800 600 600 700 600 600 600 300 500 700 700 500 700 500 700 500 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 10 500 600 600 700 900 700 600 700 600 700 700 400 500 900 500 700 500 500 500 500 11 300 500 600 800 900 700 700 700 700 700 500 500 700 700 600 600 700 500 700 500 12 400 400 700 .600 800 700 700 700 600 700 600 500 700 700 700 700 600 500 700 600 13 300 600 700 800 800 700 700 700 600 700 700 500 700 900 700 700 600 700 700 700 14 300 400 700 600 700 500 500 500 500 500 500 500 500 800 500 500 700 600 500 500 15 400 500 600 800 900 700 700 700 700 600 700 300 700 800 500 700 500 700 500 600 16 300 600 700 800 800 700 700 700 700 600 600 300 700 800 500 700 700 600 700 500 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 20 400 500 700 800 900 700 700 600 700 700 600 300 500 900 700 500 500 500 500 600 21 300 500 600 800 700 500 700 700 600 700 600 400 500 800 500 500 500 600 600 600 22 400 400 500 700 700 600 700 500 600 600 500 400 600 700 500 500 700 500 500 600 23 500 600 700 800 900 500 700 700 600 600 500 400 600 900 700 600 500 600 500 600 24 400 600 500 800 900 600 700 700 700 700 700 500 600 700 600 700 700 700 700 600 25 300 400 500 700 700 500 500 600 500 700 700 400 500 900 700 500 500 600 700 500 26 500 400 600 800 700 600 700 700 700 700 600 300 600 800 500 700 500 700 600 600 27 400 600 700 600 800 700 500 700 600 700 700 400 700 900 500 500 600 700 600 500 28 500 600 700 800 900 700 700 700 600 700 700 300 700 700 500 500 500 600 700 700 29 300 500 500 700 900 700 500 700 700 700 700 300 500 900 700 500 500 600 700 700 30 300 500 600 600 800 600 700 500 600 700 700 300 500 700 700 700 600 700 500 500 31 500 600 600 800 900 700 600 700 700 700 700 400 700 700 500 500 500 600 700 500 32 300 600 600 800 900 500 700 500 700 600 600 500 700 800 700 600 500 700 700 700 33 400 600 700 700 900 600 700 600 700 500 500 300 600 700 700 600 500 600 700 500 34 400 400 500 800 900 600 600 600 700 . 700 600 500 500 900 600 600 500 500 500 500 35 300 400 700 600 700 600 500 500 700 500 700 400 600 700 700 700 500 500 500 500 36 400 600 700 700 700 500 600 700 600 600 700 500 700 700 700 600 500 700 700 700 37 300 400 500 600 700 500 700 700 500 500 500 300 600 700 700 600 500 500 500 500 38 400 600 600 800 800 600 600 500 500 600 600 500 500 900 500 600 500 700 700 700 39 500 500 500 700 800 600 600 700 700 700 600 300 600 700 500 700 500 600 500 500 40 500 600 700 800 700 700 700 700 700 700 700 300 700 900 700 700 500 600 700 700 41 500 400 500 600 800 700 700 500 700 700 700 300 700 900 500 500 700 700 500 500 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. 43 500 600 700 800 900 700 700 700 600 700 700 500 700 900 500 700 500 500 700 700 44 500 600 700 700 900 600 700 700 700 700 700 400 500 900 700 700 600 700 600 700 45 300 500 700 700 900 700 600 600 600 700 600 500 500 900 700 700 700 700 700 700 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 48 400 500 600 600 900 600 700 700 700 700 600 300 700 900 700 600 500 600 600 600 49 400 600 700 800 700 700 700 600 600 600 700 300 600 900 700 700 600 600 500 700 50 300 500 700 700 900 700 700 600 700 700 700 400 600 700 700 500 500 500 500 500 51 300 600 700 800 900 600 700 700 700 700 700 300 500 900 700 500 500 500 700 500 52 500 500 700 600 900 700 700 700 700 600 700 400 700 700 700 700 500 500 700 700 53 300 500 700 700 900 700 600 600 700 500 700 400 500 800 600 600 600 600 600 500 54 500 400 500 800 900 600 700 600 700 600 700 300 500 900 600 700 700 600 700 700 55 500 400 700 700 900 700 700 600 500 600 700 500 600 700 600 600 700 700 700 700 56 500 500 500 600 900 700 700 600 700 700 700 400 700 800 700 500 500 500 600 500 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 63 300 600 500 700 800 500 700- 700 700 700 700 400 500 800 700 600 600 600 700 500 64 500 600 600 800 700 700 700 600 500 700 700 400 700 800 500 700 500 600 700 700 65 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 500 700 700 700 66 300 600 700 800 900 700 700 700 500 500 700 300 700 900 500 700 500 500 700 500 67 300 500 700 800 800 600 700 700 700 700 700 400 700 700 700 700 600 700 600 600 68 400 400 500 800 900 700 500 500 500 700 700 300 600 900 600 500 500 500 700 600 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 72 400 400 700 800 800 600 600 600 600 700 700 400 500 700 500 500 500 600 600 500 73 300 600 600 800 800 700 700 700 700 600 500 300 500 700 700 600 600 500 600 500 74 300 500 700 600 800 500 500 600 700 600 600 500 600 900 700 700 500 500 500 700 75 300 600 700 800 900 700 700 600 700 700 500 500 500 900 700 700 600 500 700 700 76 500 600 700 700 800 600 700 700 500 500 700 300 700 700 700 500 500 700 700 500 77 300 500 600 600 800 500 700 500 600 500 700 500 500 800 500 700 600 600 500 700 78 500 400 700 800 900 600 700 700 700 700 700 300 500 700 600 700 500 500 500 700 79 500 600 700 800 900 "700 700 700 700 700 700 500 600 900 700 700 700 700 700 700 80 500 400 600 600 900 600 600 600 600 700 600 500 500 700 500 500 700 600 500 600 81 400 400 700 700 700 500 500 700 600 600 700 400 600 900 700 500 600 500 500 700 82 400 400 600 700 700 600 600 600 600 600 600 400 500 700 600 500 500 600 500 500 83 300 400 500 800 900 600 700 600 600 500 600 300 700 700 700 700 500 500 500 600 84 400 600 700 800 900 600 500 500 600 500 700 400 600 800 700 700 500 500 500 500 85 300 500 600 800 900 600 500 500 500 600 500 300 500 800 700 500 500 500 500 500 86 500 600 700 800 900 700 700 600 600 700 700 400 700 900 700 700 500 700 700 600 87 400 500 700 600 900 600 600 700 700 600 500 500 600 900 600 600 500 500 600 500 88 500 600 700 800 800 600 700 600 700 700 700 300 500 900 700 700 600 500 600 600 89 300 400 700 800 900 600 700 700 600 500 500 300 700 700 700 500 700 500 700 500 90 400 600 700 800 900 700 700 . 700 700 700 700 500 700 700 700 700 500 600 600 500 126 Table A . l l . Experimental Data: Crest Combinations Summary - Phase II O v e r l a p p i n g C r e s t C u r v e s 300 400 500 600 700 500 500 500 500 500 500 300 500 700 5 Ki 500 500 500 500 500 R p : "T" = 300 400 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 " M " = 250 300 400 500 600 400 400 400 400 400 400 250 400 600 400 400 400 400 400 400 "B" = 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 Test-Curve No. 2 3 4 5 6 7 8 9 10 11 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 Total» o f T" 32 34 49 48 43 47 47 43 49 48 37 33 37 50 49 46 57 50 45 54 Total # of "M" 29 29 18 18 22 20 24 19 14 20 26 20 16 15 21 18 20 17 19 21 Total# of "B" 29 27 23 24 25 23 19 28 27 22 27 37 37 25 20 26 13 23 26 15 %ofT's 36% 38% 54% 53% 48% 52% 52% 48% 54% 53% 41% 37% 41% 56% 54% 51% 63% 56% 50% 60% % of M's 32% 32% 20% 20% 24% 22% 27% 21% 16% 22% 29% 22% 18% 17% 23% 20% 22% 19% 21% 23% % of B's 32% 30% 26% 27% 28% 26% 21% 31% 30% 24% 30% 41% 41% 28% 22% 29% 14% 26% 29% 17% % (M + B) 64% 62% 46% 47% 52% 48% 48% 52% 46% 47% 59% 63% 59% 44% 46% 49% 37% 44% 50% 40% R a n 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 Ave. R p 252 308 429 527 620 427 431 417 424 429 411 248 400 628 432 422 449 430 421 443 STDEV 41 82 85 86 85 85 80 88 89 84 84 44 91 87 82 87 74 85 87 77 VAR 1711 6793 7246 7371 7236 7146 6437 7697 7935 7021 7066 1961 8315 7647 6703 7591 5448 7292 7527 5854 127 Table A.12. Experimental Data: Sag Combinations Summary - Phase II O v e r l a p p i n g Sag C u r v e s Ract 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 Rp: "T" = 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 "M" = 400 500 600 700 800 600 600 600 600 600 600 400 600 800 600 600 600 600 600 600 "B" = 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 Test-Curve No. 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 16 14 15 15 36 34 32 27 33 51 39 29 38 Total # of "M" 28 24 21 26 24 34 22 29 29 25 29 29 28 20 19 17 19 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 39% 31% 21% 21% 20% 22% 17% 18% 16% 17% 17% 40% 38% 36% 30% 37% 57% 43% 32% 42% CO 81 % of NTs 31% 27% 23% 29% 27% 38% 24% 32% 32% 28% 32% 32% 31% 22% 21% 19% 21% 33% 23% 28% Ul a o % of B's 30% 42% 56% 50% 53% 40% 59% 50% 52% 56% 51% 28% 31% 42% 49% 44% 22% 23% 44% 30% Q. CO tl) % ( M + B) 61% 69% 79% 79% 80% 78% 83% 82% 84% 83% 83% 60% 62% 64% 70% 63% 43% 57% 68% 58% or Rac, 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 83 85 81 80 79 77 76 76 74 76 75 82 83 88 87 90 82 80 87 85 VAR 6886 7291 6553 6347 6292 5973 5838 5804 5494 5774 5654 6703 6921 7820 7617 8141 6778 6337 7602 7152 Table A.13. Modified 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 Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 2 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 3 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 4 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 5 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 6 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 7 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 8 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 9 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 10 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 11 200 200 300 400 500 300 300 •300 300 300 300 200 300 500 300 ' 300 300 300 300 300 12 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 13 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 14 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 400 300 300 300 15 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 400 300 300 300 16 200 200 300 400 500 300 300 300 300 300 300 200 .300 500 300 300 400 300 300 400 17 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 400 300 300 400 18 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 400 300 300 400 19 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 400 300 300 400 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 22 200 200 300 400 500 300 400 300 300 300 300 200 300 500 400 300 400 300 300 400 23 200 200 300 400 500 300 400 300 300 400 300 200 300 500 400 300 400 300 300 400 24 200 200 400 400 500 400 400 300 300 400 300 200 300 500 400 300 400 400 300 400 25 200 200 400 500 500 400 400 300 300 400 300 200 300 500 400 300 400 400 300 400 26 200 200 400 500 600 400 400 300 300 400 300 200 300 600 400 300 400 400 300 400 27 200 200 400 500 600 400 400 300 300 400 300 200 300 600 400 400 400 400 400 400 28 200 300 400 500 600 400 400 300 400 400 400 200 300 600 400 400 400 400 400 400 29 200 300 400 500 600 400 400 400 400 400 400 200 300 600 400 400 400 400 400 400 .30 250 300 400 500 600 400 400 400 400 400 400 200 300 600 400 400 400 400 400 400 31 250 300 400 500 600 400 400 400 400 400 400 200 300 600 400 400 400 400 400 400 32 250 300 400 500 600 400 400 400 400 400 400 200 300 600 .400 400 400 400 400 400 33 250 300 400 500 600 400 400 400 400 400 400 200 .300 600 400 400 400 400 400 400 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 36 250 300 400 500 600 400 400 400 400 400 400 200 300 600 400 400 500 400 400 400 37 250 300 400 500 600 400 400 400 400 400 400 200 300 600 400 400 500 400 400 500 38 250 300 400 500 600 400 400 400 400 400 400 250 400 600 400 400 500 400 400 500 39 250 300 400 500 600 400 400 400 400 400 400 250 400 600 400 400 500 400 400 500 40 250 300 400 500 600 400 400 400 400 400 400 250 400 600 400 400 500 400 400 500 41 250 300 400 500 600 400 400 ' 400 400 400 400 ' 250 400 .700 400 400 500 500 400 500 42 250 300 500 500 600 400 400 400 500 400 400 250 400 700 500 400 500 500 400 500 129 Table A.13. Cont. 43 250 300 500 600 600 400 400 400 500 500 400 250 400 700 500 400 500 500 400 500 44 250 300 500 600 600 500 500 400 500 500 400 250 400 700 500 400 500 500 400 500 45 250 300 500 600 600 500 500 400 500 500 400 250 400 700 500 500 500 500 400 500 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 51 250 300 500 600 700 500 500 500 500 500 400 250 400 700 500 500 500 500 500 500 52 250 300 500 600 700 500 500 500 500 500 400 250 400 700 500 500 500 500 500 500 53 250 300 500 600 700 500 500 500 500 500 400 250 400 700 500 500 500 500 500 500 54 250 300 500 600 700 500 500 500 500 500 500 250 500 700 500 500 500 500 500 500 55 250 300 500 600 700 500 500 500 500 500 500 250 500 700 500 500 500 500 500 500 56 250 300 500 600 700 500 500 500 500 500 500 250 500 700 500 500 500 500 500 500 57 250 400 500 600 700 500 500 500 500 500 500 250 500 700 500 500 500 500 500 500 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 63 300 400 500 600 700 500 600 600 600 500 500 300 500 700 500 500 500 500 500 500 64 300 400 600 600 700 500 600 600 600 600 500 300 500 700 500 500 500 500 500 500 65 300 400 600 600 700 500 600 600 600 600 500 300 500 700 500 500 500 500 500 500 66 300 400 600 600 700 500 600 600 600 600 500 300 500 700 500 500 500 500 500 600 67 300 400 600 600 700 500 600 600 600 600 500 300 500 700 600 600 500 600 500 600 68 300 400 600 600 800 500 600 600 600 600 500 300 500 700 600 600 500 600 500 600 69 300 400 600 700 800 500 600 600 600 600 500 300 600 700 600 600 500 600 600 600 70 300 400 600 700 800 500 600 600 600 600 500 300 600 700 600 600 500 600 600 600 71 300 400 600 700 800 500 600 600 600 600 500 300 600 800 600 600 500 600 600 600 72 300 400 600 700 800 500 600 600 600 600 500 300 600 800 600 600 500 600 600 600 73 300 400 600 700 800 500 600 600 600 600 500 300 600 800 600 600 500 600 600 600 74 350 400 600 700 800 500 600 600 600 600 500 300 600 800 600 600 500 600 600 600 75 350 400 600 700 800 500 600 600 600 600 500 300 600 800 600 600 500 600 600 600 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 79 350 500 600 700 800 500 600 600 600 600 600 350 600 800 600 600 500 600 600 600 80 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 500 600 600 600 81 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 500 600 600 600 82 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 500 600 600 600 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 87 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 600 600 600 600 88 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600. 600 600 600 600 89 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 600 600 600 600 90 350 500 600 700 800 600 600 600 600 600 600 350 600 800 600 600 600 600 600 600 Table A.14. Modified Data: Image Sag Combinations - Phase II O v e r 1 a p p i n g S a g C u r v e o Z ii "EL £ 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 1 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 2 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 3 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 4 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 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 10 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 11 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 12 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 13 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 14 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 15 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 16 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 17 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 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 21 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 600 700 700 700 22 500 600 700 800 900 700 .700 700 700 700 700 500 700 900 700 700 600 600 700 700 23 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 600 600 700 700 24 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 600 600 700 700 25 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 600 600 700 700 26 500 600 700 800 900 700 700 700 700 700 700 400 700 900 700 700 600 600 700 700 27 500 600 700 800 900 700 700 700 700 700 700 400 700 900 700 700 600 600 700 700 28 400 600 700 800 900 700 700 700 700 700 700 400 700 900 700 700 600 600 700 600 29 400 600 700 800 900 700 700 700 700 700 700 400 600 900 700 700 600 600 700 600 30 400 600 700 800 900 700 700 700 700 700 700 400 600 900 . 700 700 600 600 700 600 31 400 600 700 800 900 700 700 700 700 700 700 400 600 900 700 700 600 600 700 600 32 400 600 700 800 900 700 700 700 700 700 700 400 600 900 700 700 600 600 700 600 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 35 400 600 700 800 900 700 700 700 700 700 700 400 600 900 700 700 600 600 700 600 36 400 600 700 800 900 700 700 700 700 700 700 400 600 900 700 700 600 600 700 600 37 400 600 700 800 900 600 700 700 700 700 700 400 600 900 700 700 600 600 700 600 38 400 600 700 800 900 600 700 700 700 700 700 400 600 900 700 700 600 600 700 600 39 400 500 700 800 900 600 700 700 700 700 700 400 600 800 700 700 600 600 700 600 40 400 500 700 800 900 600 700 700 700 700 700 400 600 800 700 700 500 600 700 600 41 400 500 700 800 900 600 700 700 700 700 700 400 600 800 700 600 500 600 600 600 42 400 500 700 800 900 600 700 700 700 700 700 400 600 800 700 600 500 600 600 600 131 Table A . H . Cont. 43 400 . 500 700 800 900 600 700 700 700 700 700 400 600 800 700 600 500 600 600 600 44 400 500 700 800 900 600 700 700 700 700 700 400 600 800 700 600 500 600 600 600 45 400 500 700 800 900 600 700 700 700 700 700 400 600 800 600 600 500 600 600 600 46 400 500 700 700 900 600 700 600 700 700 700 400 600 800 600 600 500 600 600 600 47 400 500 700 700 900 600 700 600 700 700 600 400 600 800 600 600 500 600 600 600 48 400 500 700 700 900 600 700 600 600 700 600 400 600 800 600 600 500 600 600 600 49 400 500 700 700 800 600 700 600 600 700 600 400 600 800 600 600 500 600 600 600 50 400 500 700 700 800 600 700 600 600 700 600 400 600 800 600 600 500 600 600 600 51 400 500 600 700 800 600 700 600 600 600 600 400 600 800 600 600 500 600 600 600 52 400 500 600 700 800 600 700 600 600 600 600 400 600 800 600 600 500 500 600 600 53 400 500 600 700 800 600 700 600 600 600 600 400 600 800 600 600 500 500 600 500 54 400 500 600 700 800 600 600 600 600 600 600 400 600 800 600 600 500 500 600 500 55 400 500 600 700 800 600 600 600 600 600 600 300 600 800 600 600 500 500 600 500 56 300 500 600 700 800 600 600 600 600 600 600 300 600 800 600 600 500 500 600 500 57 300 500 600 700 800 600 600 600 600 600 600 300 500 800 600 600 500 500 600 500 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 62 300 500 600 700 800 600 600 600 600 600 600 300 500 700 600 500 500 500 500 500 63 300 400 600 700 800 600 600 600 600 600 600 300 500 700 600 500 500 500 500 500 64 300 400 600 700 800 600 600 600 600 600 600 300 500 700 500 500 500 500 500 500 65 300 400 600 700 800 600 600 600 600 600 600 300 500 700 500 500 500 500 500 500 66 300 400 600 700 800 600 600 600 600 600 600 300 500 700 500 500 500 500 500 400 67 300 400 600 700 800 600 600 600 600 600 600 300 500 700 500 500 500 500 500 400 68 300 400 600 700 800 600 600 600 600 600 600 300 500 700 500 500 500 500 500 400 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 72 300 400 500 600 800 500 600 600 600 600 600 300 500 700 500 500 500 500 500 400 73 300 400 500 600 700 500 600 600 600 600 600 300 500 700 500 500 500 500 500 400 74 300 400 500 600 700 500 600 600 600 600 600 300 500 700 500 500 500 400 500 400 75 300 400 500 600 700 500 600 500 600 600 600 300 500 700 500 500 500 400 500 400 76 300 400 500 600 700 500 500 500 600 500 500 300 500 600 500 500 500 400 400 400 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 79 300 300 500 600 700 500 500 500 500 500 500 300 400 600 400 500 500 400 400 400 80 300 300 500 600 700 500 500 500 500 500 500 200 400 600 400 500 500 400 400 400 81 200 300 500 600 700 500 500 500 500 500 500 200 400 600 400 400 500 400 400 400 82 200 300 500 500 700 500 500 500 500 500 500 200 400 600 400 400 500 400 400 400 83 200 300 500 500 700 500 500 500 500 500 500 200 400 600 400 400 500 400 400 400 84 200 300 500 500 600 500 500 400 500 500 500 200 400 600 400 400 500 400 400 400 85 200 300 500 500 600 500 400 400 400 500 500 200 400 600 400 400 400 400 400 400 86 200 300 400 500 600 500 400 400 400 500 500 200 400 600 400 400 400 400 400 400 87 200 300 400 500 600 400 400 400 400 400 400 200 400 600 400 400 400 400 400 400 88 200 300 400 500 600 400 400 400 400 400 400 200 400 600 400 400 400 400 400 400 89 200 300 400 500 600 400 400 400 400 400 400 200 400 600 400 400 400 400 400 400 90 200 300 400 500 600 400 400 400 400 400 400 200 400 600 400 400 400 400 400 400 132 Table A.15. Modified Data: Crest Combinations Summary - Phase II C, = Assumed response (and value) i f subjects were given this option. Based on Phase I percentage of responses opposite to what was expected. O v e r 1 a p p i n g C r e s t C u r v e s Ract 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" = 250 300 400 500 600 400 400 400 400 400 400 250 400 600 400 400 400 400 400 400 "B" = 200 200 300 400 500 300 300 300 300 300 300 200 300 500 300 300 300 300 300 300 Test-Curve No. 1 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 #of^ 17 14 27 22 23 11 30 28 28 27 12 14 22 20 24 24 5 24 22 25 # of True "T" 15 20 22 26 20 36 17 15 21 21 25 19 15 30 25 22 52 26 23 29 Total # of "M" 29 29 18 18 22 20 24 19 14 20 26 20 16 15 21 18 20 17 19 21 Total # of "B" 29 27 23 24 25 23 19 28 27 22 27 37 37 25 20 26 13 23 26 15 (0 o %of^ 19% 16% 30% 24% 26% 12% 33% 31% 31% 30% 13% 16% 24% 22% 27% 27% 6% 27% 24% 28% (A c % of True T's 17% 22% 24% 29% 22% 40% 19% 17% 23% 23% 28% 21% 17% 33% 28% 24% 58% 29% 26% 32% od % of M's 32% 32% 20% 20% 24% 22% 27% 21% 16% 22% 29% 22% 18% 17% 23% 20% 22% 19% 21% 23% 10 o % of B's 32% 30% 26% 27% 28% 26% 21% 31% 30% 24% 30% 41% 41% 28% 22% 29% 14% 26% 29% 17% a: %(M + B) 64% 62% 46% 47% 52% 48% 48% 52% 46% 47% 59% 63% 59% 44% 46% 49% 37% 44% 50% 40% 300 400 500 600 700 500 5 0 0 500 500 500 500 300 500 700 500 500 500 500 500 500 Adj. Ave. Rp 261 323 459 551 646 439 464 448 456 459 424 256 424 650 459 449 454 457 446 471 STDEV 55 105 117 1 13 115 100 115 123 122 116 103 56 123 1 12 111 117 81 114 115 105 VAR 3021 11022 13684 12864 13295 10044 13328 15107 14856 13459 10632 3115 15126 12640 12336 13763 6553 13045 13295 11066 Sample Calculation: using Test-curve file 001 Results from Phase I Results from Phase I I : Average % of sample with " L " resp. = 42 % Average % of sample with " S " resp. = 27 % Average % of sample with " M " resp. = 3 1 % No. of " T " responses by sample = 32 % of sample with " T " responses = 36 % where: " L " resp. s Rp < R " S " r e s p . = Rp = R " M " r e s p . s R p > R where: " T " resp. = RV = R £ = M / (S+M) = 3 1 % / (27% + 31%)= 54.7 % (proportion of " T " resp. that are actually Rp > R) True " T " = S / (S+M) = 2 7 % / (27% + 31%) = 46.3 % (proportion of " T " resp. that actually are R p = R) The no. of assumed C, responses by sample = 32 * 53.7 % = 1 7 No . o f assumed True T responses by sample = 32 * 46.3 % = 15 ( instead of 32 ) 133 Table A.16. Modified Data: Sag Combinations Summary - Phase II C, = Assumed 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 l a p p i n g S a g C u r v e s Ract 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 R P: t> 200 300 400 500 600 400 400 400 400 400 400 200 400 600 400 400 400 400 400 400 »X" = 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 "M" = 400 500 600 700 800 600 600 600 600 600 600 400 600 800 600 600 600 600 600 600 "B" = 500 600 700 800 900 700 700 700 700 700 700 500 700 900 700 700 700 700 700 700 Test-Curve No. 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 # o f £ 10 12 5 9 7 4 6 7 6 4 4 11 14 15 12 10 6 17 15 25 # of True "T" 25 16 14 10 11 16 9 9 8 11 11 25 20 17 15 23 45 22 14 13 Total # of "M" 28 24 21 26 24 34 22 29 29 25 29 29 28 20 19 17 19 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 m o % o f £ 11% 13% 6% 10% 8% 4% 7% 8% 7% 4% 4% 12% 16% 17% 13% 11% 7% 19% 17% 28% vt c %of True Ts 28% 18% 16% 11% 12% 18% 10% 10% 9% 12% 12% 28% 22% 19% 17% 26% 50% 24% 16% 14% P ° % of M's 31% 27% 23% 29% 27% 38% 24% 32% 32% 28% 32% 32% 31% 22% 21% 19% 21% 33% 23% 28% Ifl o % of B's 30% 42% 56% 50% 53% 40% 59% 50% 52% 56% 51% 28% 31% 42% 49% 44% 22% 23% 44% 30% cc % (M + B) 61% 69% 79% 79% 80% 78% 83% 82% 84% 83% 83% 60% 62% 64% 70% 63% 43% 57% 68% 58% 300 400 500 600 700 500 500 500 500 500 500 300 500 700 500 500 500 500 500 500 Adj. Ave. Rp 380 498 629 719 826 613 636 624 630 634 630 376 578 790 606 597 559 561 596 560 STDEV 100 107 93 99 95 86 92 93 89 86 85 100 106 1 13 110 108 91 105 113 119 VAR 9933 11456 8594 9864 9115 7461 8385 8609 7966 7452 7292 9958 11186 12820 11991 11562 8291 10943 12789 14112 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 of files 22, 23, 24, 25, 26 Effect of A, compare Rp of files 6, 3, 7, 8 Effect of A, compare Rp of files 27, 24, 28, 29 Effect of K, compare Rp of files 9, 10, 3, 11 Effect of K, compare Rp of files 30, 24, 31, 32 Effect of LT Turn, compare Rp of files 12, 1 Effect of LT Turn, compare Rp of files 33, 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 of files 35, 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 of files 24, 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 22-41 136 Table B.2. A N O V A : Effect of R. (a) Crest Combinations sii\i\um Groups Count Sum Average Variance Column 1 (file 001) 90 22650 251.6667 1710.6742 Co lumn 2 (file 002) 90 27700 307.7778 6792.7591 Co lumn 3 (fi le 003) 90 38600 428.8889 7245.9426 Co lumn 4 (file 004) 90 47400 526.6667 7370.7865 Co lumn 5 (file 005) 90 55800 620 7235.9551 ANOVA: Single Factoi overlapping crest curves Source of Variation SS 4f MS F P-value F cm Between Groups 8292755.556 4 2073188.889 341.4779408 4.0308E-134 2.391985277 Wi th in Groups 2701694.444 445 6071.223471 Total 10994450 449 (b) Sag Combinations SUMYlAin Groups Count Sum Average Variance Column 1 (file 022) 90 35200 391.1111 6886.3920 Co lumn 2 (file 023) 90 46000 511.1111 7290.8864 Co lumn 3 (file 024) 90 57100 634.4444 6553.0587 Co lumn 4 (file 025) . 90 65600 728.8889 6347.0662 Co lumn 5 (file 026) 90 75000 833.3333 6292.1348 ANOVA: Single Factor overlapping sag curves Source of Variation SS df MS F P-value F cm Between Groups 10964088.89 4 2741022.222 410.7072468 7.4762E-148 2.391985277 Wi th in Groups 2969888.889 445 6673.907615 Total .13933977.78 449 137 Table B.3. A N O V A : Effect of A. (a) Crest Combinations SUMM \R> Groups Count Sum Average Variance . Column 1 (file 006) 90 38400 426.6667 7146.0674 Co lumn 2 (file 003) 90 38600 428.8889 7245.9426 Co lumn 3 (fi le 007) 90 38800 431.1111 6436.9538 Co lumn 4 (file 008) 90 37500 416.6667 7696.6292 A N O V A : Single Factor i overlapping crest curves Source of Variation SS df MS F P-value F crit Between Groups 10972.22222 3 3657.407407 0.51285979 0.673661786 2.629988671 Wi th in Groups 2538777.778 356 7131.398252 Total 2549750 359 (b) Sag Combinations SI M M A i n Groups Count Sum Average Variance Co lumn 1 (file 027) 90 55600 617.7778 5972.5343 Co lumn 2 (fi le 024) 90 57100 634.4444 6553.0587 Co lumn 3 (fi le 028) 90 57800 642.2222 5837.7029 Co lumn 4 (file 029) 90 56900 632.2222 5803.9950 ANOVA: Single Factor overlapping sag curves^ Source of Variation SS df MS F P-value F cm Between Groups 28111.11111 3 9370.37037 1.550917795 0.201060846 2.629988671 Wi th in Groups 2150888.889 356 6041.822722 Total 2179000 359 138 Table B.4. A N O V A : Effect of K . (a) Crest Combinations S U M M \ R V Groups Count Sum Average Variance Column 1 (file 009) 90 38200 A2AAAAA 7935.0811 Co lumn 2 (file 010) . 90 38600 428.8889 7021.2235 Co lumn 3 (file 003) 90 38600 428.8889 7245.9426 Co lumn 4 (file 011) 90 37000 411.1111 7066.1673 ANON \ overlapping crcsl curves Source of Variation ss df MS F P-value Fcrit Between Groups 19111.11111 • 3 6370.37037 0.870613661 0.456446522 2.629988671 Wi th in Groups 2604888.889 356 7317.10362 Total . .2624000 -359 (b) Sag Combinations sii.vivnm Groups Count Sum Average Variance Co lumn 1 (file 030) 90 57300 636.6667 5494.3820 Co lumn 2 (file 024) 90 57100 634.4444 6553.0587 Co lumn 3 (fi le 031) 90 57500 638.8889 5774.0325 Co lumn 4 (file 032) 90 57100 634.4444 5654.1823 A N O V A overlapping sag curves. Source of Variation SS df MS F P-value F cm Between Groups 1222.222222 3 407.4074074 0.069417854 0.976208089 2.629988671 Wi th in 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 S U M M A R i Groups Count Sum Average Variance Co lumn 1 (file 015) Co lumn 2 (file 003) Co lumn 3 (file 016) 90 90 90 38900 38600 38000 432.2222 428.8889 422.2222 6702.8714 7245.9426 7590.5119 A N O V A overlapping crest curves * Source of Variation SS df MS F P-value F crit Between Groups Wi th in Groups 4666.666667 1917000 2 267 2333.333333 7179.775281 0.324986959 0.722822182 3.029597906 Total 1921666.667 269 (b) Sag Combinations S I ' M M \ R \ Groups Count Sum Average Variance Co lumn 1 (file 036) Co lumn 2 (file 024) Co lumn 3 (file 037) 90 90 90 55700 57100 54700 618.8889 634.4444 607.7778 7616.7291 6553.0587 8141.0737 A NOV \ overlapping sag curveV Source of Variation SS df MS F P-value F cm Between Groups Wi th in Groups 32296.2963 1985666.667 2 267 16148.14815 7436.953808 2.171339041 0.116034223 3.029597906 Total .2017962.963 269 140 Table B.6. A N O V A : Effect of Sight Distance. (a) Crest Combinations S U M M A R i Groups Count Sum Average Variance Co lumn 1 (file 003) 90 38600 428.8889 7245.9426 Co lumn 2 (file 017) 90 40400 448.8889 5448.1898 Co lumn 3 (file 018) 90 38700 430.0000 7292.1348 A N O V A overlapping,crest curves Source oJ Variation SS df MS F P-value F crit Between Groups 22140.14014 2 11370.37037 \.106121466 0.183432274 3.029597906 Wi th in Groups 1778777.778 267 6662.089055 Total 1801518.519 269 (b) Sag Combinations S U M M A R Y - -Groups Count Sum Average Variance Column 1 (file 024) 90 57100 634.4444 6553.0587 Co lumn 2 (file 038) 90 50900 565.5556 6777.7778 Co lumn 3 (file 039) 90 52200 580.0000 6337.0787 WON \ o\erlapping sag curves Source of Variation SS df MS F P-value F crit Between Groups 237555.5556 2 118777.7778 18.11749397 4.18519E-08 3.029597906 Wi th in Groups 1750444.444 261 6555.971702 Total 1988000 269 141 Table B.7. A N O V A : Effect of Background Image. (a) Crest Combinations S U M M A R Y I! Groups Count Sum Average Variance Column 1 (file 003) 90 38600 428.8889 7245.9426 Co lumn 2 (file 019) 90 37900 421.1111 7526.8414 Co lumn 3 (file 020) 90 39900 443.3333 5853.9326 \ V > \ \ merlapping.crest curves Source of Variation SS df MS F P-value F crit Between Groups Wi th in Groups 22888.88889 1835777.778 2 267 11444.44444 6875.572201 1.664507929 0.191241806 3.029597906 Total 1858666.667 269 (b) Sag Combinations SUMMAKN Groups Count Sum Average Variance Co lumn 1 (file 024) Co lumn 2 (file 040) Co lumn 3 (file 041) 90 90 90 57100 55100 52900 634.4444 612.2222 587.7778 6553.0587 7601.7478 7152.3096 A N O \ \ o \ e i lapping sag curves Source of Variation SS df MS F P-value F cm Between Groups Wi th in Groups 98074.07407 1896333.333 2 267 49037.03704 7102.372035 6.904318275 0.001192496 3.029597906 Total 1994407.407 269 142 Table B.8. A N O V A : Effect of Turning Direction, R = 300m. (a) Crest Combinations si M M \ n Groups Count Sum Average Variance Co lumn 1 (file 012) Co lumn 2 (file 001) 90 90 22300 22650 247.7778 251.6667 1961.2984 1710.6742 A.NON \ overlapping crest curves Source of Variation ss df MS F P-value F crit Between Groups Wi th in Groups 680.5555556 326805.5556 . 1 178 680.5555556 1835.986267 0.370675733 0.543412375 3.894228939 Total .327486.1111 179 (b) Sag Combinations Sl'MMAKN Groups Count Sum Average Variance Column 1 (file 033) Co lumn 2 (file 022) 90 90 34900 35200 387.7778 391.1111 6702.8714 6886.3920 ANON \ overlapping sag curves. Source of Variation SS df MS F P-value F cm Between Groups Wi th in Groups 500 1209444.444 1 178 500 6794.63171 0.073587506 0.786497584 3.894228939 Total .1209944.444 179 143 Table B.9. A N O V A : Effect of Turning Direction, R = 500m. (a) Crest Combinations S U M M A R Y Groups Count Sum Average Variance Column 1 (file 013) 90 36000 400.0000 8314.6067 Co lumn 2 (file 003) 90 38600 428.8889 7245.9426 ANON \ Source of Variation SS df MS F P-value F crit Between Groups 37555.55556 1 37555.55556 4.827021823 0.029308478 3.894228939 Wi th in Groups 1384888.889 178 7780.274657 Total - 1422444.444 179 (b) Sag Combinations S U M M A R \ Groups Count Sum Average Variance Co lumn 1 (file 034) 90 53400 593.3333 6921.3483 Co lumn 2 (file 024) 90 57100 634.4444 6553.0587 ~ j. * *~ * I I I I II [ M I U H I M — -Source of Variation SS df MS F P-value F crit Between Groups : 76055.55556 1 76055.55556 11.28889095 0.000953979 3.894228939 Wi th in Groups 1199222.222 178 6737.203496 Total .1275277.778 179 144 Table B.10. A N O V A : Effect of Turning Direction, R = 700m. (a) Crest Combinations SUMMARY Groups Count Sum Average Variance Column 1 (file 014) Co lumn 2 (file 005) 90 90 56500 55800 627.7778 620.0000 7646.6916 7235.9551 NNON \ ... Source of Variation SS df MS F P-value F crit Between Groups Wi th in Groups 2722.222222 1324555.556 1 178 2722.222222 7441.323346 0.365825015 0.546059089 3.894228939 Total 1327277.778 179 (b) Sag Combinations SUMMAKN Groups Count Sum Average Variance Column 1 (file 035) Co lumn 2 (file 026) 90 90 72600 75000 806.6667 833.3333 7820.2247 6292.1348 ANON \ Source of Variation SS df MS F P-value Between Groups Wi th in Groups 32000 1256000 1 178 32000 7056.179775 4.535031847 0.034582149 3.894228939 Total 1288000 179 145 Table B . l l . A N O V A : Effect of Overlapping Vertical Curve. S U M M A R \ Groups Count Sum Average Variance Co lumn 1 (files 001 - 0 2 0 ) 1800 769250 427.3611 14861.0146 Co lumn 2 (files 022 - 0 4 1 ) 1800 1103500 613.0556 17467.0342 Co lumn 1 has overlapping crest curves. Co lumn 2 has overlapping sag curves. WON \ Source of Variation SS df MS F P-value F crit Between Groups 31034184.03 1 31034184.03 1919.954047 0 3.8440362 Wi th in Groups 58158159.72 3598 16164.02438 Total .89192343.75 3599 APPENDIX C: REGRESSION ANALYSIS DETAILS 147 Table C l . Summary of Regression Variables Dependent Var iable: Y = Perceived horizontal curve radius, R p (m) X I = Horizontal curve radius, R (m) X 2 = Ver t ica l curve parameter A (%) X 3 = Vert ical curve parameter K X 4 = Superelevation rate e (%) X 5 = 0, overlapping sag curve 1, overlapping crest curve X 6 = 0, left-turn 1, right-turn Vi 0, 1000m sight distance 1, mountain background (base case) . 03 i X 7 = 1, 300m sight distance X 8 = 2, sky photo background > c nt 2, 100m sight distance 3, sky computer generated Independs X 9 = 0, male 1, female X l O = 1, 16 - 25 yrs o ld 2, 26 - 40 yrs old 3,41 - 6 0 yrs old X l l = 0, doesn't wear corrective lenses 1, wears corrective lenses 4, 61+ yrs o ld X 1 2 = Dr i v i ng experience (yrs) X 1 3 = 0, N o dr iv ing school education 1, Dr i v ing school education 148 Table C.2. Regression Analysis Trials Summary - Combined Curve Equations Test-Curve Files Variables 5 — Crest Combinations Sag Combinations SPSS scti o Z !s *£ f-T 00 ~-T T SO ON Tf SD T T • 7 J X •Tt X V0 so X X X Os X — X X (S X ro X Adjusted R 2 1 s • • • • • • • • • • • s/ • • 0.703 1 2 y • • • • • • • • • • • • • • • • • • • • 0.705 1 7 y • • • • • • • • • • • y_ 0.723 1 1 y • • • • • • • • y y • • • • • • • y y • • y • • • 0.726 4 4 10 20 14 38 • • • • y • s/ • • • • y y V • • y y • • y • • • • • • • • • y • • • • • • • • • • • y • • / V 0.737 0.739 0.754 4 19 y • • • • y • • • • • • • • • 0.758 4 13 • • • • • • • • • • y • • • • y • • ' y 0.760 13 42 • y • y • • • • • • • • 0.772 10 37 • V • • y • • • • • • • • • • y 0.774 14 52 y y • • y y v- • • y_ • 0.777 14 13 50 41 V y • y • y y y • • • • • • • • • y s y • • • • • y • 0.779 0.784 14 51 y • y • • • • • • 0.798 14 49 y • • • • • • y_ • • • 0.799 7 32 • • • y • • • 0.806 7 26 V • • • • • • • • y • y 0.808 7 31 V • • • y • • 0.827 7 25 y y • y • • y • • 0.829 of Included in Stepwise Regression Analysis _. Significant Predictor Table C.3. Regression Analysis Trials Summary - Sag Curve Equations Test-Curve Files Variables - Crest Combinations Sag Combinations o Z 33 -» T T SD 00 r*N f*N * O Tt > —i X z —1 r\ w m M <* X VN SO X X X 00 X ON X — X X f S X m X R 2 3 11 • • • • • • • y y_ • • y • 0.604 3 12 • • • y • • y • • • • y 0.610 3 5 • • y y • • y • y • • y • y / / • •/ • y 0.626 3 6 y y y y • • y • • y • • • y • • • y • y 0.631 12 47 y y y y y • y_ y_ • • y 0.643 12 48 y y y y • y • y y • / y 0.646 12 45 y y y y y y • y S • y y y • y 0.655 12 46 y y y y • y y y y y y y y_ • • y y y 0.656 6 23 v * y y y ~y[ y y y_ 0.666 6 24 y y y y y y y_ • • y y 0.669 6 17 y y y y • • y • • • y • • y • y 0.676 6 18 y y y y • y y y • • y_ • y • • y 0.679 15 15 9 54 53 36 Model |M2, Model (Ml) • • y y y • • • y y • y_ y y_ y • • • 0.735 0.744 0.774 9 30 y • y y_ • • y 0.782 9 35 y • • •j • 0.793 9 29 y • • y • • y • • y 0.799 149 Table C.4. Regression Analysis Trials Summary - Crest Curve Equations — Test-Curve Files Variables 5 Crest Combinations Sag Combinations 3 t IX ci Z c CO o CN so1 o irj o cN fN Cl m en m — Adjusted SPSS IS !• H T t I t T m T t f f t t t f CN C- O r«~i SO 00 rN rs rn o m m * > z —i > LNX X v~> vo X X X 00 X o X — X X rN X X R 2 2 10 • • • V • ./ • • 0.539 2 4 • • • • • • • / • • • • • • £ • 0.548 2 9 • • • • • • • • • • • • 0.550 2 3 V • • • • • • • £ £ • £ • 0.559 5 22 .- • • • • • • • • 0.590 5 16 • • V • • • • • • £ • • 0.597 5 21 • • • • • • • • • 0.604 5 15 V • V • • • • • • • £ £ • 0.612 11 44 • • £ £ 0.658 11 40 • • • £ £ • • • 0.663 11 11 43 39 • • • • • • • • £ £ £ • £ V 0.677 0.682 8 34 Model (M4) 0.722 8 28 V V £ • • • • 0.729 oo oo 33 27 • Model (M3) • • • • • • • • 0.747 0.754 / Included in Stepwise Regression Analysis £ Significant Predictor 150 Table C.5. SPSS Regression Results for Model (Ml) \ ar'iablesT- ntiied Mode l Variables Entered Method 1 2 3 R turning direction A Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil i ty-of-F-to-remove >= .101). Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil ity-of-F-to-remove >= .101). Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil i ty-of-F-to-remove >= .101). a. Depe ndent Var iable: Perceived Radius K H 8 9 B I ^ ^ Mode l R R Square Adjusted R Square Std. Er ror of the Estimate a. Predictors: (Constant), R b. Predictors: (Constant), R, turning direction c. Predictors: (Constant), R, turning direction, A l a 2 b 3 C 0.8589 0.8624 0.8630 0.7377 0.7437 0.7448 0.7375 0.7432 0.7441 82.2887 81.3801 81.2490 ' - ^, * W / ' ^ l A N O V A d i Mode l d f Mean F Sig. Sum of Squares „ n Square Regression l a Residual Total 18818000 . 6690172 25508172 1 988 989 18818000 6771 2779.0294 0.0000 Regression 2 b Residual Total 18971542 6536630 25508172 2 987 989 9485771 6623 1432.3063 0.0000 Regression 3° Residual Total 18999199 6508973 25508172 3 986 989 6333066 6601 959.3531 0.0000 a. Predictors: (Constant), R b. Predictors: (Constant), R, turning direction c. Predictors: (Constant), R, turning direction, A d. Dependent Var iable: Perceived Radius 1 151 Table C.5. SPSS Regression Results for Model (Ml) Cont. ( o e f f i c i c n t s ' 1 Mode l Unstandardized Coefficients Standardized Coefficients Beta t S ig . B Std. Error (Constant) R 77.374 1.078 10.552 0.020 0.859 7.333 52.717 0.000 0.000 (Constant) 2 R turning direction 57.037 1.078 27.963 11.257 0.020 5.807 0.859 0.078 5.067 53.305 4.815 0.000 0.000 0.000 (Constant) 3 R turning direction A 42.088 1.078 26.094 3.737 13.404 0.020 5.870 1.826 0.859 0.072 0.033 3.140 53.391 4.446 2.047 0.002 0.000 0.000 0.041 a. Dependent Var iable: Perceived Radius 1 SSS^SSffles^ Mode l Beta in t S ig . Partial Correlat ion Col l inear i ty Statistics Tolerance 1* A turning direction 0.045 0.078 2.746 4.815 0.006 0.000 0.087 0.151 1.000 1.000 2 b A 0.033 2.047 0.041 0.065 0.976 a. Predictors in the Mode l : (Constant), R b. Predictors in the Mode l : (Constant), R, turning direction c. Dependent Var iable: Perceived Radius 152 Table C.6. SPSS Regression Results for Model (M2) \ .iii.ihles 1 ntcrcd ! Mode l Variables Entered Method 1 2 3 L N R turning direction A Stepwise (Criter ia: Probability-of-F-to-enter <= .100, Probabil ity-of-F-to-remove >= .101). Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil i ty-of-F-to-remove >= .101). Stepwise (Cri ter ia: Prbbability-of-F-to-enter <= .100, Probabil i ty-of-F-to-remove >= .101). a. Depe ndent Var iable: Natural log of Perceived Radius : V . ^ « ^ r V ^ f j ^ M o d e l Summan 1 Mode l R R Square Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), L N R b. Predictors: (Constant), L N R, turning-direction c. Predictors: (Constant), L N R, turning-direction, A l a 2 b 3C 0.8549 0.8575 0.8580 0.7308 0.7353 0.7362 0.7306 0.7347 0.7354 0.1499 0.1488 0.1486 Mode l d f Mean F S ig . Sum of Squares „ M Square Regression l a Residual Total 60.3134 22.2146 82.5280 1 988 989 60.3134 0.0225 2682.4548 0.0000 Regression 2 b Residual Total 60.6792 21.8488 82.5280 2 987 989 30.3396 0.0221 1370.5654 0.0000 Regression 3° Residual Total 60.7597 21.7683 82.5280 3 986 989 20.2532 0.0221 917.3733 0.0000 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 Var iable: Natural log o f Perceived Radius I Table C.6. SPSS Regression Results for Model (M2) Cont. ^^^^^^^^^^^^^^^^^^^^^^^ejenis^^^^^^^^^^^^^g Mode l Unstandardized Coefficients Standardized Coefficients Beta t S ig . B Std. Error (Constant) L N R 0.8118 0.9021 0.1077 0.0174 0.8549 7.5383 51.7924 0.0000 0.0000 (Constant) 2 L N R turning direction 0.8027 0.8985 0.0432 0.1069 0.0173 0.0106 0.8514 0.0667 7.5111 51.9188 4.0651 0.0000 0.0000 0.0001 (Constant) 3 L N R turning direction A 0.7820 0.8977 0.0401 0.0064 0.1073 0.0173 0.0107 0.0033 0.8507 0.0618 0.0316 7.2893 51.9290 3.7274 1.9091 0.0000 0.0000 0.0002 0.0565 a. Dependent Var iable: Natural log of Perceived Radius | l ^ ^ ^ ^ ^ ^ ^ ^ c l J ^ ^ ^ r i f i l e s , • Mode l Beta in t S ig . Partial Correlat ion Col l inear i ty Statistics Tolerance l a A turning direction 0.0411 0.0667 2.4977 4.0651 0.0127 0.0001 0.0793 0.1283 0.9990 0.9973 2 b A 0.0316 1.9091 0.0565 0.0607 0.9753 a. Predictors in the Mode l : (Constant), L N R b. Predictors in the Mode l : (Constant), L N R, turning direction c. Dependent Var iable: Natural log o f Perceived Radius 154 Table C.7. SPSS Regression Results for Model (M3) V ariables Entered 1 Mode l Variables Entered Method 1 R Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil i ty-of-F-to-remove >= .101). a. Depe ndent Var iable: Perceived Radius Modi l Sum man Mode l R R Square Adjusted R Square Std. Er ror of the Estimate a. Predictors: (Constant), R l a 0.8646 0.7474 0.7469 78.7269 A NOV V h Mode l Sum of Squares df Mean Square F S ig . Regression l a Residual Total 8217778 2776672 10994450 1 448 449 8217778 6198 1325.8909 0.0000 a. Predictors: (Constant), R b. Dependent Var iable: Perceived Radius CoeifficKnts ! Model Unstandardized Coefficients Standardized Coefficients Beta t S ig . B Std. Error . (Constant) R -50.7778 0.9556 13.6359 0.0262 0.8646 -3.7238 36.4128 0.0002 0.0000 a. Dependent Var iable: Perceived Radius Table C.8. SPSS Regression Results for Model (M4) 155 \ ariables Entered1 Mode l Variables Entered Method 1 L N R Stepwise (Cri ter ia: Probability-of-F-to-enter <= .100, Probabil ity-of-F-to-remove >= .101). a. Depe ndent Var iable: Natural log of Perceived Radius M S I Mimmar> Model R R Square Adjusted R Square Std. Error of the Estimate a. Predictors: (Constant), L N R l a 0.8501 0.7226 0.7220 0.2079 Model Sum of Squares df Mean Square F S ig . Regression l a Residual Total 50.4429 19.3649 69.8077 1.0000 448.0000 449.0000 50.4429 0.0432 1166.9788 0.0000 a. Predictors: (Constant), L N R b. Dependent Var iable: Natural Log of Perceived Radius Mode l Unstandardized Coefficients Standardized Coefficients Beta t S ig . B Std. Error . (Constant) L N R -0.8871 1.1133 0.2013 0.0326 0.8501 -4.4065 34.1611 0.0000 0.0000 a. Dependent Var iable: Natural log of Perceived Radius