John, you need a cheap scientific calculator that has the sine function on it. The button will have "sin" on it. I recommend the TI-30Xa for my math students. It is less than $10 at Target, Wal-Mart, K-mart, etc. You might even have one at home.

What am I thinking, you are on your computer, bringup the calculator and click view, then scientific.

The sine of an angle is the hypotenuse (the width of the control surface) divided by the movement. Suppose your elevator is 2 inches wide and you want to know the movement for 10 degrees. Sine 10 = x/2, or 2 sin 10 =x.

On the calculator, enter 10, press the sin button, then times 2 and =.

This gives .347 inches or just under 3/8 inch. Here's the key sequence again:
10
sin
* (times)
2
= (or Enter on your computer)

Hope this helps.