# A Comparison of Friction Supply, Friction Demand, and Maximum Design Friction on Sharp Horizontal Curves with Steep Grades

Open Access

- Area of Honors:
- Civil Engineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Eric Todd Donnell, Thesis Supervisor
- Eric Todd Donnell, Honors Advisor
- Patrick Reed, Faculty Reader

- Keywords:
- Friction
- Friction Supply
- Friction Demand
- AASHTO
- Design Side Friction
- Factor of Safety

- Abstract:
- The American Association of State Highway and Transportation Officials (AASHTO) have a set of recommended parameters to use for horizontal curve design. In their publication A Policy on Geometric Design of Highways and Streets (commonly referred to as the Green Book), design guidelines are outlined based upon a roadway’s design speed, maximum superelevation, the radius of the curve, and the maximum design side friction. These values are considered to be very conservative as they are based on driver comfort studies and not the physics of the vehicle. It is important that these criteria do in fact have a large factor of safety. Otherwise the probability of vehicle skidding or rollover will increase, leading to an increased probability of crashes upon the roadway. The calculations that are commonly used to find friction supply and friction demand are simplified. Friction supply calculations ignore the effects of grade, rolling resistance, aerodynamic resistance (drag), and longitudinal acceleration/deceleration. The friction demand calculations assume some terms are small enough to be considered zero. In this thesis, these calculations are compared to their “modified” calculations which do not ignore any of these components. This is done to ensure that these modified friction calculations do not exceed those used by AASHTO. AASHTO has also never differentiated the maximum design side friction values for two-lane or multi-lane highways. Intuitively the pavement characteristics and driver tendencies vary between these two facility types. These variations could contribute to a difference in friction supply or friction demand that could merit different design criteria for the different facility types. The data analyzed for this thesis were acquired from two different reports: FHWA Information Report to Achieve Target Speeds on Rural and Suburban Highways, and NCHRP Report 15-39: Superelvation Criteria for Sharp Horizontal Curves on Steep Grades. These reports included curve radii, superelevation and vehicle speed for passenger cars and trucks, as well as friction readings as generated by field testing equipment. These data were utilized in the calculation of simple and modified friction demand and supply. The analysis of the data showed that simple and modified friction demand were nearly identical. At the upper end of the speed range, simple friction demand was slightly higher than modified friction demand. At 15 out of 24 sites, simple friction demand was greater than simple friction supply for some portion of the speed range. In all cases, modified friction supply was less than simple friction supply, but it was always higher than the AASHTO recommended maximum design side friction values. Five of the 7 multi-lane facilities had comparable simple friction supply values as the two-lane facilities, but the other 2 multi-lane facilities had higher values. The friction demand values at the two-lane sites were consistently higher than at the multi-lane sites. Based on these results, it can be concluded that the AASHTO maximum recommended design side friction values incorporate some factor of safety across the range of feasible vehicle speeds. AASHTO is also justified in using its simplified friction demand model since it is slightly more conservative than the modified model at higher speeds. At many of the sites, a small proportion of drivers are choosing speeds which require a higher friction demand than the roadway can supply. The comparison of friction supply values on multi-lane and two-lane facilities was inconclusive, but the comparison of the friction demand values showed that the two-lane facilities consistently demand more friction than the multi-lane facilities. The collection of more data from a large variety of sites would lend more credence to this conclusion.