The Radius Equation
This summer, my father undertook the project of making a walking bridge over their fish pond in their backyard. One of the problems he had to solve was what should the radius of the arc be knowing how high you want the bridge off the ground at it's apex, and how far the bridge has to cross over the water.
Though the math was not very difficult, I dug deep into my memory of trigonometry and created him an equation which would give him 'R', knowing the above two values. To make it easier for him to understand, I created a picture for him.
Comments
Would it be possible for you to send me he derivation of this radius equation?
Posted by: alistair | October 24, 2007 05:32 PM
I used the Pythagorean Theorem to solve for R:
R^2 = (R-h)^2 + (c/2)^2
R^2 = R^2 – 2Rh + h^2 + (c/2)^2
R^2 – R^2 = - 2Rh + h^2 + (c/2)^2
0 = - 2Rh + h^2 + (c/2)^2
2Rh = h^2 + (c/2)^2
R = (h^2 + (c/2)^2)/2h
Posted by: cwp | October 24, 2007 08:31 PM