How Do I Factor in Air Resistance for Projectile Motion?

[mabramovich]

Hi:

I'm to write a program ("game") in which two tanks take shots at each other, with a user who inputs firing angle, gravitational acceleration and the like, I'm sure you've all heard of it.

Anyway, I'm having trouble in dealing with air resistance. Without knowing too much on the subject (not covered in any particular detail at the grade 11 level) the equation for drag is of course:

$$F_{D} = \frac{1}{2}C\rho\\Av^2$$

The problem I have is for calculating velocity for use in that formula. First of all, I would I assume I would take both the x-component and y-component of velocity and vector-add them to get a composite velocity, but the formulae normally given for a velocity at time, $$t$$, ignore air resistance, for example:

$$V_{y} = sin\theta\\-gt$$

There is of course no problem if a constant air resistance, $$F_{air}$$, is used, but air resistance is directly proportional to velocity, so I'm in a bit of a loop here, do I not have a problem of requiring velocity to calculate air resistance and air resistance to calculate velocity?

Any help is greatly appreciated, and of course not just a formula but an explanation.

Thank-you.

 

[robphy]

You might find this helpful:
http://wwwmaths.anu.edu.au/comptlsci/Tutorial-Gravity/tutorial_projectile.html

 

[Q_Goest]

I'd assume your game calculates the position of the projectile at distinct points in time, such that the entire flight of the projectile is broken up into small bits in time.

You'll need a mass for the projectile. Apply F=ma and determine acceleration. The force on the projectile is the force due to air resistance per your equation above. The accelleration is then a=F/m. Assume this acceleration (decelleration) is applied during the time step. The velocity at the beginning of the time step is V1 and at the end is V2. I'd assume the time steps are going to be very small, a fraction of a second. So now determine velocity V2 from V2=V1+at where acceleration is negative because the force is slowing the projectile down.