CivilForge

Crest Vertical Curve (SSD Controls)

L = \frac{A S ^{2}}{2158} (S < L, US: S in ft, A in percent)

Length L (ft) of a crest curve when stopping sight distance S (ft) is less than L. A = |g2 − g1| is the algebraic grade break in percent. The constant 2158 comes from eye height 3.5 ft and object height 2.0 ft. Design speed V (mph) is used only to compute S from the SSD formula first. If S > L, use L = 2S − 2158/A. Metric analog: L = A S² / 658 with S, L in m.

L

(ft)

Curve length

A

(%)

Algebraic difference of grades |g2−g1|

S

(ft)

Stopping sight distance

g_{1}, g_{2}

(%)

Initial and final grades

Step-by-step solved example

Grades +2.0% to −4.0%. SSD = 500 ft. Assuming S < L, find crest length L (US customary).

Crest curve: SSD through the high point controls L when S < L.

1. Algebraic difference
A = |−4.0 − 2.0| = 6.0%.
$A = 6%$
2. Length
L = 6×500² / 2158 = 6×250000/2158 = 1,500,000/2158 = 695 ft. Check: S = 500 < 695 = L, so the S<L formula applies.
$L = 695 ft$

Answer: 695 ft

10 practice questions

0/10 correct

1.g1 = +1%, g2 = −3%. A equals

2.The 2158 constant (US) assumes eye and object heights of

3.A = 8%, S = 400 ft, S < L. L is nearest

4.If S > L the US crest formula becomes

5.A larger grade break A, same S < L, makes L

6.Sag curves for headlight sight use a different constant because

7.Metric crest (S < L) uses L = A S² / 658 with S in

8.Design speed V enters the crest-length calculation by

9.A = 4%, S = 600 ft, and S < L. L is nearest

10.A vertical curve is a