Question

For a horizontal curve, the radius of a circular curve is 300 m with the design speed 15 m/s. If the allowable jerk is 0.75 m/s$^3$, what is the minimum length (in m, integer) of the transition curve?

Hint:

For transition curves by jerk criterion: $L=\dfrac{v^{3}}{C R}$ (SI units). Keep $v$ in m/s for a direct result in metres.

Answer 1

Step 1: Use the jerk (rate of change of radial acceleration) criterion.
For a transition curve, the minimum length based on allowable jerk $C$ is \[ L_{\min}=\frac{v^{3}}{C\,R}, \] where $v$ is speed (m/s) and $R$ is radius (m).

Step 2: Substitute the data.
Given $v=15$ m/s, $R=300$ m, $C=0.75$ m/s$^3$: \[ L_{\min}=\frac{15^{3}}{0.75 \times 300} =\frac{3375}{225}=15~\text{m}. \] \[ \boxed{15} \]