While taking the stopping sight distance into consideration, when L > SSD, then the general equation for length L of the parabolic curve is :
- AL = N S² / (√2H + √2h)²Correct
- BL = 2 N S² / (√2H + √2h)
- CL = N S² / (√H + √h)²
- DL = N S² / (2√H + √h)²
Solution
Concept
Length of summit curve when L > S (IRC)
Formula
L = N S² / (√(2H) + √(2h))²
Step-by-step solution
1. For a summit parabolic curve with deviation angle N and sight distance S, when L > S: 2. L = N S² / (√(2H) + √(2h))², where H is the height of the driver’s eye and h is the height of the object. 3. With H = 1.2 m and h = 0.15 m this reduces to L = N S²/4.4.
Explanation
The sight line is a chord of the vertical curve; the geometry of a parabola gives the length in terms of the deviation angle, sight distance and the two heights. This is the IRC expression for summit curves.
Why the other options are wrong
The other expressions change the factors (2 in the numerator, or the square-root terms) and do not give L = N S²/4.4 for standard heights.
Shortcut
Summit curve: L = N S² / (√2H + √2h)²; for SSD ≈ N S²/4.4.
Common mistake
Mixing up with the formula for L < S.
Correct answer: A) L = N S² / (√2H + √2h)²