Sag Vertical Curve Length (Headlight)

L = \frac{A S ^{2}}{200 ( h _{1} + S tan α )} (S < L)

Night sag sight is controlled by headlight beam height h1 and angle α. A = |g2−g1| in percent. When S > L a different formula applies. Comfort (centripetal) can also control: L = A V² / (46.5 a) in US units.

$A$: Algebraic grade difference (%)
$S$: Sight distance
$L$: Curve length

Step-by-step solved example

A=6%, S=400 ft, h1=2.0 ft, α=1°. Approximate L (S<L form)? tan1°≈0.0175.

Sag curve: headlight sight controls L at night.

1. Denom
200(2+400×0.0175)=200(2+7)=1800.
2. L
L=6×160000/1800=533 ft. S<L so the form is consistent.
$L = 533 ft$

Answer: 533 ft

10 practice questions

0/10 correct

1.Sag curves are concave

2.Headlight sight matters at

3.A is

4.Comfort criterion uses

5.If S > L you must use

6.Larger A requires

7.Drainage on sags: water

8.g1=−3%, g2=+3%. A=

9.α is the

10.Units in the US formula mix ft and %; keep