Projectile trajectory formulas with air resistance

[Babillon]

I've been working on making a package of Java classes to use in developing programs/games using actual physics instead of 'best guess'.

The problem is I'm pretty rusty with the whole subject, and am lost trying to get a formula for projectile trajectory with air resistance taken into account. I found this, https://www.physicsforums.com/showthread.php?t=27331&page=1&pp=15&highlight=projectile+trajectory, set of formulas which seem to have helped the person who asked the same question as me, but the thing is, it's completely lost on me.

If anyone could explain the formulas mean and how they work I'd be very appreciative.

Also, if anyone knows of any other resources or projects similar to what I'm working on, I'd very much like a point in that direction.

Thanks!

 

[jim mcnamara]

If you google for 'external ballistics' you'll find a range of stuff, including some examples in Fortran and C.

 

[SergejVictorov]

You need to set up the differential equation of motion in two dimensions. In a simple model there are only two forces involved: gravity, which is constant and air resistance, which is proportional to velocity squared. There is no analytical solution, therefore you have to integrate the equations numerically. If you restrict the air resistance to only the x-direction (that is, the horizontal one), an analytical solution can be found which is pretty accurate for small launch angles. If you need help with doing the derivations, just ask.