
06586004
j
2016d.00878
Pakdemirli, Mehmet
Mathematical design of a highway exit curve.
Int. J. Math. Educ. Sci. Technol. 47, No. 1, 132139 (2016).
2016
Taylor \& Francis, Abingdon, Oxfordshire
EN
M55
I75
N45
kinematics of motion
calculus
curve design
highway exit
doi:10.1080/0020739X.2015.1044045
Summary: A highway exit curve is designed under the assumption that the tangential and normal components of the acceleration of the vehicle remain constant throughout the path. Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived. The equation and initial conditions are cast into a dimensionless form first for universality of the results. It is found that the curves are effected by only one dimensionless parameter which is the ratio of the tangential acceleration to the normal acceleration. For no tangential acceleration, the equation can be solved analytically yielding a circular arc solution as expected. For nonzero tangential acceleration, the function is complicated and no closedform solutions exist for the differential equation. The equation is solved numerically for various acceleration ratios. Discussions for applications to highway exits are given.