Join Date: Nov 2001
Location: Atlanta suburbs
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To paraphrase, "It is better to be thought a fool and remain silent, than do math in public and remove all doubt." But, that being said, I'll take a crack at it.
Recall (in a nightmare sense) from trig, the "Rule of Sine". If you have a triangle with angles a, b and c, and sides of length a', b', and c' where a' is the side across from angle a, b' across from angle b, etc.. then a'/sin(a) = b'/sin(b) = c'/sin(c).
If you know the length of one side and 2 of the angles, you can compute the length of the other 2 sides using the rule of sine.
In your example you referenced the FireHawk which has a half gain angle on 28 degrees, so there is one angle. You also said that your straight line of seats would be 12 feet back, so we know one side. And since the line of seats is straight, there is our 2nd anlge, 90 degrees. Since all the angles of a triangle add up to 180, we know that that last angle is 62 degrees.
So using the rule of sine, 12/sin(62) = x/sin(28). Solve thru and you get x=4.3 feet. So, if you move 4.3 feet in either direction off dead center AT 12 FEET back, the picture you see will be 1/2 as bright as dead center. Since you said your row of seats was 96 inches long, no one will see less than half gain, but the far left and far right person will be very close.
Now take the GrayHawk in the same scenario. Its half gain angle is 48 degrees. That makes its equation 12/sin(48) = x/sin(42). Solving thru you get x = 10 feet. That means with the GrayHawk AT 12 FEET BACK you have to get 10 feet off center to see half the brightness from dead center. So in your 96 inch seating example, since the furthest person is going to be 4 feet on each side of center, they still see a picture that is approximately 75% as bright as on center.
And I'll finish that off with, I think that's right?