Horizontal-Curve Middle Ordinate (Sight)

M = R (1 - cos \frac{Δ}{2}) = R (1 - cos \frac{S}{2 R})

Lateral clearance M from the chord (or from the travel-lane centerline, with the Handbook figure) to an obstruction. If M available is less than required for SSD, the curve is sight-limited. Δ = S/R in radians for the arc of length S.

$M$: Middle ordinate / clearance
$R$: Radius
$S$: Sight distance along the curve

Step-by-step solved example

R=800 ft, S=400 ft. M required (use Δ=S/R rad)?

Middle ordinate M = R(1−cos(Δ/2)) for lateral clearance.

1. Angle
S/R=0.50 rad = 28.65°. Δ/2=14.32°.
2. M
M=800(1−cos14.32°)=800(1−0.9689)=24.9 ft.
$M = 24.9 ft$

Answer: 24.9 ft

10 practice questions

0/10 correct

1.M grows if R

2.If an obstruction sits inside the curve closer than M

3.For small S/R, M ≈

4.SSD on a horizontal curve uses the

5.Δ in M=R(1−cos Δ/2) is the

6.Clearing on the inside of the curve is

7.R=500 m, S=150 m. S/R=0.3 rad. M≈

8.Spiral transitions affect

9.Barrier on the inside must be checked because

10.Units of M are