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Originally Posted by BrianR
Actually, as the goal has a 30" ID, the very bottom of the goal is at 7' 3".
Assuming that your calculation is for the center of the ball, which has a 7" diameter, it will extend 3.5" below the 7' 9.8", which brings you to 7' 6.3" at the bottom of the ball, which is above the 7' 3" bottom of the goal.
But if you were calculating for the top of the ball, you will have the ball hit the bottom of the goal by 0.2". Whether this makes it in is thus up to the spin you have on the ball, as frontspin would bring it into the goal, whereas backspin would cause it to fall away.
Oh, and another quick note. The goal is slanted forward at a 9 degree angle, which adds another variable into the calculations. Without doing all of the math, this will just make it harder for shots to hit after they have reached their maximum, and will make it slightly easier for shots which are still rising to go in. Just another little trick the GDC threw in to try to deter the really long shots.
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Thanks for the correction. I had misread the arena dimensions and thought the the bottom of the goal was at 8' 6". My calculations were for the bottom of the ball. These are supposed to be the rough estimates which guide the engineering of the shooter. For example the decision of just what range in elevation to try for.
As for the 9 degree forward slant, the "quick" way to account for this is to assume a slightly smaller flat circular opening.