# Ballistics Formulae: Distance Traveled Without Air Resistance

• Unredeemed
In summary, the formula for the distance traveled by a projectile is dependent on the shape of the trajectory and the density of air at different heights.
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.

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.

mgb_phys said:
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.

## What is the formula for calculating the distance traveled without air resistance?

The formula for calculating the distance traveled without air resistance is d = v * t, where d is the distance, v is the initial velocity, and t is the time.

## How does air resistance affect the distance traveled?

Air resistance slows down the object and reduces its distance traveled. The greater the air resistance, the shorter the distance traveled.

## What factors affect the distance traveled without air resistance?

The factors that affect the distance traveled without air resistance include the initial velocity, the angle of launch, and the mass and shape of the object.

## Can the formula for distance traveled without air resistance be used for all objects?

No, the formula d = v * t is only applicable for objects moving in a straight line with a constant initial velocity. For more complex movements, additional factors and formulas may be needed.

## How accurate is the calculation of distance traveled without air resistance?

The calculation is only an estimate and may not account for external factors such as wind or changes in air density. It also assumes a vacuum-like environment with no air resistance, which is not always the case in the real world.

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