24 Desired Speed
24.1 Horizontal Curves
For very low-speed horizontal curves, such as at arterial intersections, the desired speed is set in the same manner as for a tangent link (see section below). For higher-speed horizontal curves, such as on freeways and two-lane highways, the process for setting the desired speed is as follows.
A modified version of the horizontal curve speed model developed by Bonneson, Pratt, and Miles (2007) is implemented in SwashSim. Since the simulation tool models multiple driver types, it was desirable to implement the model such that there was range of curve speeds selected by drivers. The easiest way to create this range of speeds was to create a distribution from the 85th percentile and average curve speeds predicted by the Bonneson, Pratt, and Miles (2007) model. The original equation from the model is as follows.
\[ {V_{c,a}} = {\left( {\frac{{15.0{R_p}(0.112 - 0.00066{V_{t,a}} + 0.000091V_{t,a}^2 - 0.0108{I_{tk}} + e)}}{{1 + 0.00136{R_p}}}} \right)^{0.5}} \]
where:
\({V_{c,a}}\) = average curve speed (mi/h),
\({V_{t,a}}\) = average tangent speed (mi/h),
\({R_p}\) = travel path radius (replaced by curve radius in modified model) (ft),
\({I_{tk}}\) = indicator variable for heavy vehicles (1.0 if model is used to predict heavy vehicle speeds, 0.0 otherwise), and
\(e =\) superelevation rate (decimal)
The modified version of the equation substitutes the curve radius for the travel path radius (\({R_p}\)). In order to integrate the model into the simulation tool (SwashSim), some assumptions had to be made regarding the average and 85th percentile tangent speeds. The average tangent speed for passenger cars (\({V_{t,a,PC}}\)) was assumed to equal the FFS input in the simulation tool. Based on the findings in the Bonneson, Pratt, and Miles (2007) study, the average tangent speed for heavy vehicles (\({V_{t,a,HV}}\)) was assumed to be 97 percent of \({V_{t,a,PC}}\). For both passenger cars and heavy vehicles, the 85th percentile tangent speed was assumed to be 11 percent higher than the average tangent speed. This was also based on findings in the Bonneson, Pratt, and Miles (2007) study.
The curve speeds were assumed to follow a normal distribution. The mean was set equal to the average curve speed, and the standard deviation was estimated from the average and 85th percentile curve speeds. The standard deviation was then used to calculate the 15th percentile curve speed. This distribution was applied to the 10 (default) driver types in the simulation tool. The 15th percentile curve speed was assigned to driver type 1 (the most conservative driver), and the 85th percentile curve speed was assigned to driver type 10 (the most aggressive driver). The curve speeds for the other driver types were linearly interpolated between these two speeds. If the driver’s desired speed on the curve exceeded its desired speed on the tangent, the desired curve speed was set equal to the desired tangent speed.
24.2 Tangents
The desired speed for a vehicle is calculated per the following equation.
\[DesiredSpeed_{ij}=LinkFreeFlowSpeed_{j}\times DesiredSpeedMultiplier_{i}\times VehicleTypeDesiredSpeedProportion_{k}\]
where:
\(Desired Speed_{ij} = \text{desired speed for vehicle/driver } i \text{ on link } j \text{ (ft/s)}\),
\(LinkFreeFlowSpeed_{j} = \text{free-flow speed for link } j \text{ (ft/s)}\),
\(Desired Speed Multiplier_{i} = \text{multiplier for driver type } i \text{ (unitless)}\), and
\(VehicleTypeDesiredSpeedProportion_{k} = \text{multiplier for vehicle type } k \text{ (unitless)}\).
The desired speed multiplier value (as a function of driver type) and desired speed proportion value (as a function of vehicle type) can be changed in the Settings. The link free-flow speed is coded by the user in the network setup.
Additional information about desired speed determination for passing maneuvers on two-lane highways is discussed here.
24.2.1 Heavy Vehicles
Bonneson, Pratt, and Miles (2007) showed that the desired speeds of heavy vehicles on level grade tangents are generally lower than those of passenger cars. This relationship was incorporated into the simulation tool by using a desired speed proportion variable that is a function of the heavy vehicle type. This value is multiplied by the passenger car free-flow speed to get a heavy vehicle free-flow speed. Free-flow speed data collected from two-lane highways in North Carolina, Oregon, and Montana, were used to obtain estimates of these desired speed proportions (Washburn et al. (2018)). The following table presents these values.
| Heavy Vehicle Type | Desired Speed Proportion |
|---|---|
| Single-Unit Truck | 0.98 |
| Intermediate Semi-Trailer Truck | 0.95 |
| Interstate Semi-Trailer Truck | 0.95 |
| Double Semi-Trailer Truck | 0.93 |