Question

拱形弧长计算公式,已知跨度和拱高,求拱形弧长

Answer 1

跨度L=1200,拱高H=750,求弧长C?

弧半径为R,弧所对的圆心角为A.

R^2=(R-H)^2+(L/2)^2

R^2=R^2-2*R*H+H^2+L^2/4

2*R*H=H^2+L^2/4

R=H/2+L^2/(8*H)

=750/2+1200^2/(8*750)

=615

A=2*ARC SIN((L/2)/R)

=2*ARC SIN((1200/2)/615)

=154.639度

C=π*R*A/180=π*615*154.639/180=1659.86