Degree of Curve (Arc Definition)

D = \frac{5729.58}{R} (R in ft, D in degrees)

Arc definition: D is the central angle subtended by 100 ft of arc. Derived from 100 = 2π R (D/360), so D = 18,000/(π R) = 5729.58/R. Chord definition (some railroads) uses a 100 ft chord and is slightly different. Curve length L = 100 Δ/D = R Δ_rad with Δ the intersection angle.

$D$ (deg / 100 ft arc): Degree of curve (arc)
$R$ (ft): Radius
$Δ$ (deg): Intersection (central) angle
$L$ (ft): Length of curve

Step-by-step solved example

A circular curve has R = 1,910 ft. Find D (arc definition) and the length if Δ = 24°.

Arc definition D = 5729.58/R (R in feet, D in degrees).

1. Degree
D = 5729.58/1910 = 3.00°.
$D = 3.0 0^{\circ}$
2. Length
L = 100 Δ / D = 100×24 / 3.00 = 800 ft (or L = R Δπ/180 = 1910×24×π/180 = 800 ft).
$L = 800 ft$

Answer: D = 3.00°, L = 800 ft

10 practice questions

0/10 correct

1.R = 2865 ft (arc definition). D is nearest

2.A sharper curve (smaller R) has

3.L for D = 4°, Δ = 20° is

4.The 5729.58 constant equals

5.D = 6° (arc). R is nearest

6.Metric practice usually specifies

7.Tangent T of a circular curve is

8.Chord definition of D (railroad) compared with arc definition at the same R is

9.Δ = 36°, D = 3°. L =

10.External distance E = R (sec(Δ/2) − 1) is the