Ballistics Formulae: Distance Traveled Without Air Resistance

[Unredeemed]

I'm writing a talk on ballistics and was looking for the formula for the distance traveled by the projectile. However, all the formulae I have found exclude air resistance. I understand that the effect of air resistance depends on how stream-lined the projectile is, but is there not a general formula?

Also, the formula for distance traveled (when air resistance is neglected) changes if the projectile is not traveling over a flat surface. Why is that?

If anyone has the answers to those two questions you'd be a real life saver.

 

[mgb_phys]

The air resistance is generally proportional to area and the square of the speed, since the resitance acts to reduce the speed, the resistance is constantly changing which means the speed is alsways changing - you have to write this as a set of differential equations. If you wanted to do it accurately you also have to account for the different density of air at different heights in the trajectory.

The reason the path only applies to flat ground is simple - sketch the path of the projectile ( a parabola ), now draw the ground where it lands higher - it's obvious that the parabola cuts the ground at a closer point. Imagine if the ground was high enough that it reached upto the maximum height of the projectile - then it would only travle half as far.

 

[Unredeemed]

The air resistance is generally proportional to area and the square of the speed, since the resitance acts to reduce the speed, the resistance is constantly changing which means the speed is alsways changing - you have to write this as a set of differential equations. If you wanted to do it accurately you also have to account for the different density of air at different heights in the trajectory.

The reason the path only applies to flat ground is simple - sketch the path of the projectile ( a parabola ), now draw the ground where it lands higher - it's obvious that the parabola cuts the ground at a closer point. Imagine if the ground was high enough that it reached upto the maximum height of the projectile - then it would only travle half as far.

thanks a lot, that's exactly what I needed to know.