# Bullet trjectory

1. Jan 30, 2005

### sirasher

I am doing a science project and need a few questions answered. I am trying to theoretically determine which caliber of bullet is capable of travelling the farthest. I've already assumed that the time each caliber of bullet spends in the air is going to be exactly the same. Therefore, I'm assuming each bullet is shot perfectly horizontally at an altitude of 9.8 m, so each bullet hits the ground in 1 second. To determine the distance each bullet travels, I need the velocity. I'm aware of theexit velocities of each caliber of bullet. But while some bullets may exit the barrel faster than others, drag slows each one down at different rates. I was wondering if anyone could get me an equation that I could use to determine the deceleration due to drag for each caliber of bullet.

2. Jan 30, 2005

### Erienion

It sounds like you're building in an extra lot of work trying to work out the drag on the bullets, you can calculate the trajectories just using the muzzell velocity and the angle from the ground the bullet is fired. The difference between rifle calibers is so small compared to the differences in initial velocity. Just neglect to mention air resistance.

If you really want to calculate the drag i think you can do it by taking the cross sectional area of the bullet and you'll also need a constant to account for the different shapes of the bullets, finally you'll need to find a drag coefficient for air. All this sounds like a real mission to get, maybe someone else thinks of a simpler solution. Also with something like a bullet you'll get into all kinds of complicated rubbish with turbulent flow and shock waves if your bullets are supersonic.

3. Jan 30, 2005

### Andrew Mason

Your time of flight of 1 sec. is incorrect. If you fire at a height of 9.8m, the bullet will drop only half that height in one second ($h = \frac{1}{2}gt^2$).

In order to determine the actual horizontal distance travelled before hitting the ground, you would need to know the horizontal speed as a function of time or distance. The problem is that this is not linear. Drag deceleration is a function of the square of the bullet velocity.

I think you can assume that the drag coefficients of all the bullets are about the same. The distance ultimately depends on the muzzle velocity of each bullet.

AM