Feasibility of Using a Constant Acceleration Rate for Freeway Entrance Ramp Acceleration Lane Length Design

When estimating the required acceleration length of vehicles accelerating from a stopped position, a constant acceleration rate is sometimes assumed for the sake of simplicity. Nevertheless, to date there is no clear-cut evidence showing whether a constant acceleration rate is reasonable in providing appropriate acceleration lengths. In this paper, the estimation errors associated with the constant acceleration assumption were investigated. For each sample, a piecewise-constant acceleration model was used to figure out the vehicle’s speed versus location profile; accordingly, the constant acceleration rate was calculated. Using this constant acceleration rate, speeds at the predetermined locations were calculated and compared to the results that were generated by the piecewise-constant acceleration model. Based on the statistical analysis of 575 individual vehicle-accelerating trajectories, it was found that the constant acceleration model failed to reproduce the field-observed acceleration profile. Therefore, simply using a constant rate cannot accurately estimate the required acceleration lengths at various freeway design speed scenarios. This indicates that when adopting the constant acceleration assumption for each design speed scenario, it is necessary to use an appropriate acceleration rate that fits for this design speed. Finally, this paper revealed that normal acceleration rate ranges from $1.31\mathrm{m}/{\mathrm{s}}^2$ ($4.3\mathrm{ft}/{\mathrm{s}}^2$) at $64\mathrm{km}/\mathrm{h}$ (40 mph) to $1.8\mathrm{m}/{\mathrm{s}}^2$ ($5.9\mathrm{ft}/{\mathrm{s}}^2$) at $32\mathrm{km}/\mathrm{h}$ (20 mph).