Hi there

I have a problem which I thought would be quite easy when I was out on site.

I have a curved bridge which I am assuming is part of a circle.

I measured the arc length AL and by pulling a string taught and dropping a ruler down measured the distance from the centre of the arc to the chord which I call h.

I thought that these two measurements must define an individual circle, and did not make an attempt to measure the chord length.

I am now trying to define the radius and angle etc. of the arc but cannot do this algebraically. I could probably attack this iteratively to find the particular solution using excel but I'd like to know if there is a direct equation to solve this.

I have been through a few sides of A4 trying to solve this and suspect I do not have enough information, so here is some of my equations I have written but cannot see how to combine them to get r the radius or theta alone.

r = radius

theta = half the included angle

AL = arc length

CL = chord length

h = Arc Height ( max distance from chord to Arc)

r*cos (theta) = r-h

CL = 2*r*sin( theta )

AL = r * theta

r^2 = (CL/2)^2 + (r-h)^2

What approach should I be taking?

(I have found an online calculator that has given me a result but I am frustrated with my own attempts to solve it directly)

Any help would be most appreciated.

Thanks

Matt