Sometimes the transition curves discussed above can not meet other conditions such as slickness, fairness, and then the functional of transition curve is built as Eq.
Transition curve design is important to transmission performance.
The transition curve needs to meet some conditions according to the specific circumstances.
Usually the door speed of opening and closing is designed quickly and smoothly for the convenience of passengers, so the transition curve should be first-order continuous at the two connection point at least.
45 kilometers; geometry correction curves consisting of extended arc transition curves
for optimal speed on curves, cleansing or restoring drainage ditches side (deep drainage in areas of its occurrence), improving the bottom of the ditch with the relevant slants roadside ditch at a total length of 46.
The most important property of the transition curves is the curvature change which directly depends on the curvature length l.
The most experienced transition curves among these recommended curves in the open literature are clot-hoid, lemniscates, cubic parabola, cubic spiral sinusoidal, bloss and 2R radius circles (Can et al.
On the other hand, the obtained new transition curves are compared with the most used transition curves (clothoid, sinusoidal and bloss) in highways with regard to curvature change, angle of deviation, superelevation, lateral acceleration and total curve length.
Determination of other elements of G1 and G2 transition curves
The tangential angle at any point of transition curves
The Cartesian coordinates (X, Y) of the transition curves are calculated via using Fresnel integral (Jeffrey, Dai 2008).
Shift of the transition curves in the all transition curves is given as follow, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].