Gravity: Thou art a _ _ _ _ _

I've made progress in my 3D Turret program. I've (unfortunately for my poor brain) decided to include gravity in my calculations. Mainly because I'd prefer for my calculations to not shoot off into the sky without ever coming down again. Gravity's good for that sort of thing. Unfortunately, it's also good at making you do a bunch of calculations for determining maximum distance, terminal velocity, and a few other things. I did have a model that was close to what it should be, but the calculations it was making wasn't quite right. (Specifically it was 2 seconds later in hitting the ground than it should have been)

So I decided to peruse Wikipedia a little, specifically the free fall, projectile motion, and trajectory pages. They're plenty of nice equations ready to use. And although I was slightly saddened that I had admitted defeat in a way and just looked up the answer. The equation's were very similar to the ones I had devised. I had a big comment written at the top of my code that GRAVITY IS M/S^2, but for some reason I didn't square the time in my calculation for figuring the new z position of the projectile. But besides that, my equation was correct.  My velocity updating line of code was correct though, so I was quite happy. From this figuring out the maximum distance was a matter of either running trials of different time increments or solving an equation. Or the third option not allowed by any homework ever done by a person. Look up a calculator on the internet that displays all the information when you enter the right numbers. I opted for the third approach and then tested it against my code by running the simulation to that time and making sure the z went to 0.

The only thing I'm still unsure of, is terminal velocity. Which is, unfortunately, rather annoying to figure out when you have no idea what the dimensions of your hypothetical projectile is. So I had to determine what I was actually firing (a small bullet with a mass of .04 kg is what I believe I decided on, with a cross section of 50mm^2, traveling through  standard sea level air density (1.5 kg/m^3) with a drag coefficient of (.1) (a small ball by the examples I found, although it had a bullet (.3)) it gave a ridiculous terminal velocity (small that is not large) so I decided to go with my turret firing perfectly round projectiles.

So, after all that and 1 and a half cramped notebook pages later, I have an update position function I feel like I can rely on for my calculations.

Tommorow, after doing some trivial work (required course work for a required class which pertains to my major in no way), I'll start working on the estimation process and how it leads it's target through 3 dimensions. But for now, more reading Gödel, Escher, Bach by Douglas Hoftstadter (I'm a little more than halfway through the book )