Re: MAX ball shot trajectory
 

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.

Re: MAX ball shot trajectory
 

Something else teams may want to consider finding... there is a speed for every angle where the ball will "peak" inside of the goal range if fired at that speed. If you try to caculate to have the "peak" as close to the top of the goal as possible, but still able to go in, you get a range where the ball will go into the goal if you fire from anywhere within that range, so long as the angle and speed stay the same.

For example, if your ball leaves your launcher 54" above the floor, fired at 10 m/s and at a 32 degree angle, you can land the ball in the goal anywhere from 6' away to 24' away without having to adjust speed or angle.

That 9 degrees will just have to be accounted for then. I still think at least a few teams will be able to hit the goal from beyond the center line.

Re: MAX ball shot trajectory
 

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.

Re: MAX ball shot trajectory
 

Here's a spreadsheet (that I've posted elsewhere) that allows the user to vary speed, angle, drag coefficient (Cd = 0.41 was measured), etc. The calculation includes air resistance and provides an x-y trajectory plot with the top and bottom of the goal opening indicated. Longest shot is definitely NOT the best trajectory...the parameters in the "as downloaded" shows a wide range for balls in the goal opening.

Re: MAX ball shot trajectory
 

We figured outa formula in excel...

so pretty much at12m/s and 45 degree angle the ball would go its highest at 3.7m and it would fall after 14.7 meters which means the shooter has to be at around 7.3m away from the target