Ok gang, math time! Can someone tell me how to solve this one? At about 5' high I can clear my obstruction with a 45d angle. I need to figure out the mast height then to get to a 23d angle for the 119 bird. Can anyone give me a good idea how to figure this one out?
Ok gang, math time! Can someone tell me how to solve this one? At about 5' high I can clear my obstruction with a 45d angle. I need to figure out the mast height then to get to a 23d angle for the 119 bird. Can anyone give me a good idea how to figure this one out?
Yes. Call the distance to the obstruction X. The formula for your mast height is:
5 + (X * 0.575)
Show Your Work: Assume for a moment (since you didn't say) that the obstruction is 100 feet from your mast and 105 feet high, giving 45-degree clearance when 5 feet up.
Considering the tangent of 23 degrees is about 0.425, then 100 feet of distance will let you clear 42.5 feet of obstruction. 105-42.5 = 62.5 (gulp) feet high, and that's how high the dish would have to be.
Plug in a 55-foot tree and a 50-foot distance to it. Now 50 feet of distance will let you clear 21.3 feet of tree. 55-21.3 = 33.7 feet high, which is still pretty high for a dish mount.
In general, the pole will need to be
(5 + X) - (X * 0.425).
Shuffle the parentheses and we get
5 + (X * 1) - (X * 0.425).
One more round gives us
5 + (X * (1 - 0.425))
which gives you the formula at the top.