OT: Equation to Solve Arc Height

[Darken99]

Anyone know of a equation for solving arc height based on the diameter/radius and the arc angle?

I know how to solve it in autocad but just wondering if there is an equation to solve it without drawing it.

Thanks

 

[CarlB]

From survey book,

M=R[1 - cos (Delta/2)]

where Delta is the central angle; M is the middle ordinate, the distance from the middle point on the arc to the middle point on the chord.

 

[Darken99]

Great thanks

 

[Darken99]

ok that equation works good for solving things but I have a question about how the math works in reverse when im trying to solve the angle. If I have Cos(delta/2) = .5244 I can not remember how to simplify this equation to solve delta.

Thanks

 

[CarlB]

Take the arccos (also cos -1 on calculators) of 0.5244, get 58 degrees, which id delta/2, so delta is 117 degrees (rounded).

 

[Darken99]

Ok thanks... That is what I did. It just seemed to high of a angle.

Thanks again

 

[CarlB]

The curve diagrams in these pubs may help visualize:

http://www.usace.army.mil/usace-docs/eng-manuals/em1110-1-1005/c-9.pdf

http://www.ctre.iastate.edu/educweb/ce353/lec05/lecture.htm