拱跨径L=3米,高H=0.75米,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)
=0.75/2+3^2/(8*0.75)
=1.875米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((3/2)/1.875)
=106.26度
C=PI*R*A/180=PI*1.875*106.26/180=3.477米
拱跨径L=3米,高H=0.75米,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)
=0.75/2+3^2/(8*0.75)
=1.875米
A=2*ARC SIN((L/2)/R)
=2*ARC SIN((3/2)/1.875)
=106.26度
C=PI*R*A/180=PI*1.875*106.26/180=3.477米