拱形弧长计算公式,已知跨度和拱高,求拱形弧长跨度1200,拱高750,求结果

Question

拱形弧长计算公式,已知跨度和拱高,求拱形弧长
跨度1200,拱高750,求结果

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