DESIGNING  HORIZONTAL  CURVES

FOR  LOW-SPEED  ENVIRONMENTS

(MBTC 2019)

 

J. L. GATTIS, Ph.D., P.E.,

B. F. VINSON, III, and

L. K. DUNCAN

 

 

 

 

 

 

 

 

The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof.

 

 

 

                                                                                                                                                                                         

                                                                                                                                       Technical Report Documentation Page    

1. Report No.

   

2. Government Accession No.

3. Recipient's Catalog No.

4. Title and Subtitle

   DESIGNING HORIZONTAL CURVES FOR LOW-SPEED

   ENVIRONMENTS 

5. Report Date                                                                                         FEBRUARY  2003

6. Performing Organization Code

  

7. Authors

   J. L. GATTIS, Ph.D., P.E., B. F. VINSON, III, and L. K. DUNCAN

   

8. Performing Organization Report No.

 

    MBTC FR 2019

9. Performing Organization Name and Address

   MACK-BLACKWELL RURAL TRANSPORTATION CENTER

   UNIVERSITY OF ARKANSAS

   4190 BELL ENGINEERING CENTER

   FAYETTEVILLE, AR  72701

10. Work Unit No. (TRAIS)

 

11. Contract or Grant No.

   DTRS99-G-0025

12. Sponsoring Agency Name and Address

 

   ARKANSAS STATE HIGHWAY & TRANSPORTATION DEPARTMENT

   P. O. BOX 2261

   LITTLE ROCK, AR  72203

  

 

13. Type of Report and Period Covered

   FINAL REPORT

   JAN. 2001 -- JAN. 2003

14. Sponsoring Agency Code

15. Supplementary Notes

   SUPPORTED BY A GRANT FROM THE U.S. DEPARTMENT OF TRANSPORTATION UNIVERSITY CENTERS

   PROGRAM

 

16. Abstract

            This project was a pilot study to explore alternative criteria for the geometric design of low-speed urban horizontal curves.  Low-speed was defined as 70 kilometers per hour (km/h), or 45 miles per hour (mph), or less. The researchers collected data and then developed alternative low-speed urban horizontal curve design paradigms.  The study considered factors such as curve radius, pavement cross slope, vehicle speed within the curve, and vehicle speed in advance of the curve.  The results were compared with the practices in the current American Association of State Highway and Transportation Officials A Policy on Geometric Design of Highways and Streets (Green Book).  The data indicated that a driver’s speed in advance of a curve can influence speed within the curve, and that a portion of drivers exceed the low-speed urban side friction factors in the 2001 Green Book.  During the process of conducting the research, and number of observations were made which could be useful to those conducting related research in the future.    

 

 

 

 

17. Key Words

    HORIZONTAL CURVE, RADIUS, URBAN, LOW-SPEED, CROSS SLOPE

   

18. Distribution Statement

    NO RESTRICTIONS.  THIS DOCUMENT IS AVAILABLE FROM THE

    NATIONAL TECHNICAL INFORMATION SERVICE,

    SPRINGFIELD, VA.  22161

19. Security Classif. (of this report)

    UNCLASSIFIED

20. Security Class. (of this page)

    UNCLASSIFIED

21. No. of Pages

     

22. Price

    N/A

 

Form DOT F 1700.7    (8-72)                      Reproduction of completed page authorized

 

 

 

 

 

 

 ACKNOWLEDGEMENTS

The support of the Arkansas State Highway and Transportation Department (AHTD) and the Mack-Blackwell Rural Transportation Center made this research possible.  The authors appreciate the computer programming performed by Mr. David Li.

 

 

DISCLAIMER

The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the information presented herein.  The contents do not necessarily reflect the official views or policies of the Arkansas State Highway and Transportation Department or the Federal Highway Administration.  This report does not constitute a standard, specification, or regulation.

This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange.  The U.S. Government assumes no liability for the contents or use thereof.

 

 

 

 

 

DESIGNING HORIZONTAL CURVES FOR LOW-SPEED ENVIRONMENTS

by

J. L. Gattis, Ph.D., P.E., B. Finley Vinson III,

Mack-Blackwell National Rural Transportation Study Center, and

Lynette K. Duncan, Center for Statistical Consulting,

University of Arkansas

 

TABLE OF CONTENTS

Chapter                                                                                                                                                       page number

1...................................................................................................................................................... INTRODUCTION ..................................................................................................................................................................................  1

Background ......................................................................................................................................................  1

Goals of this Project............................................................................................................................................ 3

2............................................................................................................................................ LITERATURE REVIEW ..................................................................................................................................................................................  5

............................................................................................................................................................ Earlier Research................................................................................................................................................................................... 5

........................................................................................................................................................... Recent Research................................................................................................................................................................................... 5

....................................................................................................................................................................... Summary................................................................................................................................................................................... 7

3........................................................................................................... SELECTING AND SURVEYING TEST SITES................................................................................................................................................................................... 9

Criteria for a Suitable Test Site............................................................................................................................ 9

Identifying Possible Test Sites............................................................................................................................. 9

......................................................................................................................................... General Surveying Procedure................................................................................................................................................................................. 11

Surveying Individual Sites.................................................................................................................................. 14

4................................................................................................................................................ DATA COLLECTION........................................................................................................................................................................ 17

General Procedure............................................................................................................................................ 17

Cosine Effect................................................................................................................................................... 17

Distances from Beginning of Curve.................................................................................................................... 17

Distances from Points Within the Curve............................................................................................................. 18

.......................................................................................................................................... The Data Collection Process ................................................................................................................................................................................  18

5..................................................................................................................... DATA REDUCTION AND ANALYSIS................................................................................................................................................................................. 23

......................................................................................................................................................... Curve Calculations................................................................................................................................................................................. 23

.............................................................................................................................................................. Data Reduction................................................................................................................................................................................. 25

................................................................................................................................................................ Data Analysis................................................................................................................................................................................. 28

....................................................................................................................................... Data Analysis by Vehicle Type................................................................................................................................................................................. 43

6............................................................................................................................. SUMMARY AND CONCLUSION................................................................................................................................................................................. 45

Summary of Procedures.................................................................................................................................... 45

Observations and Questions .............................................................................................................................. 45

Conclusion........................................................................................................................................................ 46

REFERENCES.......................................................................................................................................................... 47

 

LIST OF FIGURES

Figure 4-1: Data Collection ......................................................................................................................................... 19

Figure 5-1: Raw Data Sample..................................................................................................................................... 25

Figure 5-2: Advance Speed vs. In-Curve Minimum Speed ............................................................................................ 29

Figure 5-3: Advance Speed vs. Speed Change.............................................................................................................. 30

Figure 5-4: Advance Speed vs. Speed Change in Percent.............................................................................................. 31

Figure 5-5: Minimum Speed vs. Speed Change............................................................................................................. 32

Figure 5-6: Sorted Speed Data..................................................................................................................................... 33

Figure 5-7: Radius vs. e+f........................................................................................................................................... 35

Figure 5-8: Radius vs. e+f  (Linear)............................................................................................................................. 36

Figure 5-9: Curve Speed vs. Friction Factor.................................................................................................................. 38

Figure 5-10: In-Curve Speeds vs. Radius...................................................................................................................... 44

 

LIST OF TABLES

Table 3-1: Sites Considered for Study.......................................................................................................................... 10

Table 3-2: Suitable Study Sites..................................................................................................................................... 11

Table 3-3: Summary of Curve Data...........................................................................................................................   12

Table 4-1: Distance from Observer to Curve Reference Point....................................................................................... 19

Table 5-1: Curve Radii and Cross Slope....................................................................................................................... 24

Table 5-2: Design Speeds vs. Recorded Speeds............................................................................................................ 34

Table 5-3: Percentage of Vehicles That Exceeded Green Book f-Values....................................................................... 37

Table 5-4: Comparison of f90 Values ........................................................................................................................... 39

Table 5-5: Confidence Intervals About the 10% and 90% In-Curve Minimum Speeds..................................................... 42

Table 5-6: In-Curve Speed by Vehicle Type................................................................................................................. 43

 

DESIGNING HORIZONTAL CURVES FOR LOW-SPEED ENVIRONMENTS

by

J. L. Gattis, Ph.D., P.E., B. Finley Vinson III,

Mack-Blackwell National Rural Transportation Study Center, and

Lynette K. Duncan, Center for Statistical Consulting,

University of Arkansas

 

CHAPTER 1

INTRODUCTION

 

          This project was a pilot study to explore alternative criteria for the geometric design of low-speed urban horizontal curves.  The researchers collected data and then developed alternative low-speed urban horizontal curve design paradigms.  The study considered factors such as curve radius, pavement cross slope, vehicle speed within the curve, and vehicle speed in advance of the curve.  The methods derived and values found were compared with the practices in the current American Association of State Highway and Transportation Officials (AASHTO) A Policy on Geometric Design of Highways and Streets (Green Book).  Following Green Book (2001, p. 72) practice, low-speed was defined as 70 kilometers per hour (km/h), or 45 miles per hour (mph), or less.

 

BACKGROUND

          Many factors are considered when designing a horizontal curve.  One of these factors is the minimum acceptable radius of the curve, or “what is the smallest acceptable radius”?  The minimum radius of a curve is normally equal to minimum radius that allows the driver to comfortably traverse the curve at the designated design speed.

          When a vehicle traverses a curve, the driver evaluates his or her speed with respect to the radius of the curve.  All other things being equal, the smaller the radius, the more likely it is that a driver will choose a lower speed.  Two other factors affect this relationship between curve radius and speed: side friction and cross slope (or superelevation).

Side Friction

          Side friction is the friction force created by the contact between a vehicle’s tires and the road.  It is this force that counteracts the centrifugal force and keeps the vehicle on the road.  A coefficient called side friction factor (f ) is used to quantify this force.  The side friction factor is a unitless value and is equal to the friction force required by the vehicle divided by the component of the vehicle’s weight that is perpendicular to the pavement surface. 

          Observers have noted that drivers typically do not operate at the speed at which side slip is impending, but rather operate vehicles in curves at speeds well below the threshold of impending side slip.  The friction factor used for design of horizontal curves is based on this threshold of driver discomfort rather than the point of impending slip of the vehicle.  Tables in the 2001 Green Book list, for a given velocity, the design side friction factors above which a driver is no longer comfortable traversing a curve (pp. 145, 197, 201).

Cross Slope

          Cross slope is the slope of the pavement surface perpendicular to the direction of travel.  The superelevation of a road refers to a cross slope that has been modified from its normal “shape”, to aid the vehicle in negotiating the curve successfully.

          The Green Book suggests that superelevation not be used in low-speed urban areas.  This means that the design criteria for low-speed urban curves call for a vehicle’s centrifugal force to be completely counteracted by side friction until the maximum side friction value has been reached; only then would superelevation be used.  This method is chosen because in many urban environments, superelvation  can create a number of aesthetic and operational problems.  The maximum value assumed for safe side friction factors is pivotal in the design of low-speed urban curves. 

Relating Factors to Design a Curve

          The current edition of the AASHTO Green Book contains an equation (pp. 133 ff.) that can be used to calculate the minimum radius of a curve, based on the design speed. This equation relates the velocity of the vehicle (V), the curve radius (R), side friction (f), and superelevation or cross slope (e).

                                                                                                                                                                          (metric) 

                                                                                                                                                                       (standard) 

 

 

The “friction factors” are listed in tables in Chapter 3 of the Green Book.  One table contains friction factors for urban, low-speed situations, while another table applies to rural and high-speed urban situations.

 

Alternative Method

          The second method for assessing the speed suitable for a given curve is that of using a ball bank indicator.  A ball bank indicator is a device that consists of a steel ball and some damping fluid located inside of a sealed glass tube.  Both ends of the tube are curved upward so that the position of the ball in the tube can be converted to an effective angle in degrees (o).  The device is used by mounting it inside the car and measuring the maximum angle that the steel ball reaches while the vehicle is within the curve.  The ball bank indicator has been used to determine the advisory speeds posted below warning signs in advance of curves. 

 

GOALS OF THIS PROJECT

          The maximum side friction factors listed in the current Green Book are based upon research that was performed decades ago.  Given the fact that vehicle components (i.e., suspension components) are constantly being improved, drivers may be willing to accept much higher side friction factors than those listed in the Green Book.  Furthermore, the emphasis of much of the research was on high-speed environments such as highways and arterials, and not on low-speed urban situations.

          This research was conducted to reconsider the side friction factors for low-speed, urban, horizontal curve design.  In addition, alternative design approaches were also investigated.

Design Speed Concept

          The selection of any side friction factor reflects implicit assumptions about design.  Many design decisions in recent decades have been predicated on an assumed design speed.  That is, based on informed experience, the designer identified the speed at which drivers were likely to want to drive the roadway being designed.  Then, various design elements such as the horizontal curve radius were selected so that drivers could safely maintain this speed.

          But in reality, the combination of different drivers in vehicles with different characteristics and capabilities results in vehicles operating over a range of speeds for any given situation.  If a design is created so that almost all drivers can operate at the design speed, then many vehicles will be traveling in excess of the design speed.  This philosophy seems appropriate on busy highways where the roadway will at some times be operating near capacity, for if only one vehicle cannot maintain a minimum speed, then traffic flow on the facility may break down.  However, on lower speed, lower volume urban roadways, there may be merit to designing so that most vehicles will not exceed a certain speed, and will fall within a desired range of speeds.

 

 

 

 

 

 

 

 

 

 

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CHAPTER 2

LITERATURE REVIEW

 

          Methods to design horizontal curves for railroads and roadways have been discussed for decades.  There is a growing interest in reexamining the design of horizontal curves on roadways.

 

EARLIER RESEARCH

          One of the first resources on the topic of horizontal side friction (Barnett, 1936) assumed a safe side friction factor of 0.16 for all speeds up to and including 60 mph.  For speeds above 60 mph, the friction factor decreased by 0.01 for every 5 mph increase above 60 mph.  This friction factor was found by determining the safe speed around various curves, where the safe speed was defined as “…the minimum speed at which the centrifugal force, created by the movement of a vehicle around the curve, causes the driver or passenger to feel a side pitch outward.” 

          Another source (Moyer, 1940) described a different method of determining safe side friction factors.  Moyer used the ball bank indicator to determine safe side friction factors.  By surveying all of the existing 48 states, he found that most engineers considered a maximum ball bank indicator reading of 10O to be satisfactory.  However, their research indicated that this could lead to unsafe friction factors for speeds above 60 mph due to small path variations or driver error.  Furthermore, for speeds below 30 mph, a ball bank angle of 12O to 14O was recommended due to the fact that control was easier to maintain at lower speeds.  The safe speed values listed were all intended for favorable street conditions.  The author, however, expected that drivers would realize the need to lower their speed under wet or icy conditions. 

 

RECENT RESEARCH

          The current AASHTO Green Book lists low-speed urban side friction factors ranging from 0.16 to 0.31, depending upon design speed (30 km/h to 70 km/h, or 20 mph to 45 mph, respectively).

          In 1983, a study was released (McLean, 1983) that criticized the use of the friction factor as a design criterion.  This study noted that the friction factor’s relationship with speed is only valid for vehicles driving at or below the design speed.  Furthermore, the study suggested that friction factor had no direct influence on a driver’s curve speed.

          A recent work (Mudry, 1999) recognized the lack of research conducted in a low-speed environment, and conducted a study of observed friction factors on low-speed urban curves.  The study used twenty-one sites, each with between 70 and 120 vehicle observations.  Using a magnetic speed measuring device, vehicle speeds were measured at the point of curve (PC), the midpoint, and the point of tangency (PT).  It was assumed that the 85th percentile side friction factors were representative of driver comfort.  Mudry found that in most cases (56 out of the 63 test sites) the 85th percentile friction factor exceeded the AASHTO friction factor design values for low-speed urban streets.

          Other recent literature also recognized the shortcomings of the current AASHTO standards.  (Bonneson, 1999) found a correlation between side friction factor and vehicle approach speed, indicating that drivers will accept higher side friction factors on curves with higher speed reductions.   This suggests that current Green Book standards may be overly conservative.  Bonneson also referred to the Green Book background literature, pointing out that there was little agreement upon what driver reaction constituted a maximum side friction factor.  This maximum friction factor has definitions ranging from the point at which drivers become aware that they are on a curve, to the point of impending slip. 

          In a recent National Cooperative Highway Research Program (NCHRP) report (Bonneson 2000), Bonneson formulated a new model for side friction factor recognizing the following phenomena.  There is a decrease in side friction demand with an increase in approach speed, and there is an increase in side friction demand with an increase in speed reduction.  In developing the model, the testing included a range of approach speeds from 40 km/h (25 mph) to 120 km/h (75 mph).  Computer monitored sensors on the pavement were used to determine the vehicle’s speeds.  A laser-gun was used, however, when traffic volume was too heavy to install the pavement sensors.  The speed, leading headway, following headway, and vehicle classification were recorded.  Linear regression analysis was used to arrive at the equation.

 

where:

          fD, 95, PC = maximum design side friction factor

          Vα, 95 = 95th percentile approach speed, km/h

          dv95 = 95th percentile speed reduction

          Vc,95= 95th percentile curve speed

          ITR = indicator variable (1 for turning roadways; 0 otherwise).

 

 

          The report acknowledged that both the 85th percentile and the 95th percentile values could be reasonable for use in curve design.  However, the 95th percentile was recommended for use in developing maximum side friction factors.  The reason for this was that side friction factor is dependent upon only one variable (speed).  This is in contrast to something such as stopping distance, where many variables (reaction time, deceleration rate, and speed criteria) must all be at or below their worst-case in order for failure to occur.  Therefore, failure is more likely to occur in maximum side friction factor design.

          Fitzpatrick (2000) measured drivers speeds through a horizontal curve.  She found that for most drivers, the speed through the curve reached its nadir somewhere between the half-way and two-thirds point along the length of the curve.

 

SUMMARY

          There is a lack of current information on the design of low-speed urban horizontal