Consider the length of the curve as L and radius of the curve as R. For a transition curve, the shift S of a circular curve is :
- AR²/12 L
- BL²/24 RCorrect
- CL³/24 R²
- DL²/12 R
Solution
Concept
Shift of a circular curve for a spiral transition
Formula
S = L² / (24 R)
Step-by-step solution
1. For a cubic parabola/spiral transition of length L between a tangent and a circular curve of radius R, the circular curve is shifted inward by S. 2. S = L² / (24 R).
Explanation
The shift is the distance by which the original circular curve moves inward when a transition curve is inserted. It is proportional to the square of the transition length and inversely proportional to the radius.
Why the other options are wrong
L²/12R is double the correct value, and the other forms have the wrong dimensions of length.
Shortcut
S = L²/24R; tangent length extra = (R + S) tan(Δ/2) + L/2.
Common mistake
Using 12 instead of 24.
Correct answer: B) L²/24 R