id: 06586004
dt: j
an: 2016d.00878
au: Pakdemirli, Mehmet
ti: Mathematical design of a highway exit curve.
so: Int. J. Math. Educ. Sci. Technol. 47, No. 1, 132-139 (2016).
py: 2016
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: M55 I75 N45
ut: kinematics of motion; calculus; curve design; highway exit
ci:
li: doi:10.1080/0020739X.2015.1044045
ab: 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 closed-form solutions
exist for the differential equation. The equation is solved numerically
for various acceleration ratios. Discussions for applications to
highway exits are given.
rv: