Circular Curve: Tangent and Length

T = R tan (Δ/2) L = R Δ_{rad} C = 2 R sin (Δ/2)

Δ is the deflection (intersection) angle. T is PI to PC (or PT). Arc length L uses Δ in radians (or L=2πR Δ°/360). Chord C joins PC to PT. Degree of curve D=5729.58/R (arc definition, R in feet).

$R$ (ft or m): Radius
$Δ$: Intersection angle
$T$: Tangent length
$L$: Arc length

Step-by-step solved example

R=400 ft, Δ=40°. T and L?

T = R tan(Δ/2), L = R Δ with Δ in radians.

1. T
T=400 tan20°=400×0.3640=145.6 ft.
2. L
L=400×40×π/180=279.3 ft.
$T = 145.6 ft$

Answer: T=145.6 ft, L=279.3 ft

10 practice questions

0/10 correct

1.T equals

2.L in radians form is

3.If Δ is in degrees, L=

4.Chord C=

5.PC is

6.PT is

7.Larger Δ at fixed R makes T

8.Station of PT = station of PC +

9.External distance E=

10.Middle ordinate M=