Circular Curve External and Middle Ordinate

E = R (sec \frac{Δ}{2} - 1), M = R (1 - cos \frac{Δ}{2})

T already in the handbook (R tan(Δ/2)). E is PI to curve; M is chord-to-curve at midspan (sight/obstruction). L=R Δ_rad = 2π R Δ°/360.

Step-by-step solved example

R=500 m, Δ=60°. E and M?

External E from PI to the curve; middle ordinate M from the chord.

Answer: E ≈ 77 m, M ≈ 67 m

0/10 correct

1.T =

2.LC long chord =

3.For small Δ, M ≈

4.Degree of curve (arc, English) D =

5.Δ=90°, R=200: T =

6.Stationing of PC = PI − T

7.Sight obstruction uses M compared with

8.Δ in the L=2πR Δ/360 must be

9.If R doubles at fixed Δ, E

10.PI is