# Airsoft - range and energy question

1. May 4, 2016

### Mos

Hey guys.

I play a lot of airsoft, I also like physics, in airsoft LOADS of physics is in place there.

Basically, it's paintball, with realistic guns, shooting plastic BBs.

So, the question, if I shoot a 0.4g BB at 284 it will create I think 1.49 joules of energy.

When said BB is travelling in the air, if it was a 0.2g BB at the same joules of energy, which would go further?

I think it's the BB. At 0.4g as it keeps it's inertia and energy is not lost through particles of dust. Question two, is it the more energy something has, the further it will go?

Thanks guys,

2. May 4, 2016

### Staff: Mentor

You could compare this to shooting an arrow. for the same pullback distance a lighter arrow will travel farther and faster than a heavier arrow. Because you pullback the bow to the same distance then the energy imparted will be the same. Some Airsoft guns use a spring mechanism that works in a similar fashion.

The 284 you mention must be 284 ft/sec and the 0.4g mass which you'd need to convert to MKS units if you want the answer in joules.

The equation $KE = 1/2 m v^2$ sums it up nicely but I'll leave it to you to go from here.

More on Airsoft guns:

https://en.wikipedia.org/wiki/Airsoft_gun

3. May 4, 2016

### jfizzix

In the overly ideal case of 2D kinematics (no drag and so forth) the maximum range of a BB is given by

$r_{max} = \frac{v_0^2}{g}$
where you aim it 45 degrees above the horizon.
The initial kinetic energy is
$E_0 = \frac{1}{2}m v_0^2$

Putting this together, you can get the max range in terms of the initial kinetic energy:
$r_{max} =\frac{2 E_0}{m g}$

Therefore, in this case, if you have the same initial kinetic energy, but a smaller mass, the max range of the BB will be farther because it will have had to travel faster initially to have that same kinetic energy. Drag or no drag, the initial velocity of the smaller BB will be faster at the same initial energy.

Including drag into the situation is a more complicated issue, as solving the range is done by computer (it turns out to be a transcendental equation, and cannot be solved by algebraic methods), but in the approximation that the BB is light and traveling slow enough initially, that at the end of its flight it's just falling straight down at terminal velocity, you can show that
$r_{max}\approx \frac{v_0 m}{b}$
where $b$ is the drag coefficient of the armophere.

Combining this with the formula for the initial energy, we find:
$r_{max}\approx \frac{1}{b}\sqrt{2 m E_0}$

In this case, we see that if the initial energy is the same, but the mass is smaller, the range actually goes down due to drag.

What ends up happening in the field is somewhere between these two extremes.
If the final horizontal velocity is pretty much the same as your initial horizontal velocity, then drag isn't important, and you can use the first formula.
If your final horizontal velocity is near zero, then drag is dominant, and you should use the second formula.

If you're not accustomed to using a computer to solve equations, field testing in a large enough safe space would probably be easiest.

4. May 4, 2016

### Mos

This wasn't homework or coursework.

But thank you.
So to sum up, if a mass of 0.4g leaves the barrel with an energy of 1.49 joules
Though a 0.2g mass leaves the barrel also with 1.49 joules

The latter will go further?

5. May 4, 2016

### jfizzix

The latter will go further if it doesn't lose much horizontal velocity by the time it hits the ground again.
The former will go further if it does lose most of its horizontal velocity by that time.

f you're somewhere in between, you'll need to know what the terminal velocity of these BBs are (what their max falling speed is due to drag) to figure out which'll go further.

I can't imagine these BBs go very fast compared to the muzzle velocity if you just drop them from a large height, so my gut says drag will dominate, so that the former will go further.

To really be sure, you'll have to do your own tests. Experimental data trumps theoretical guesswork.

6. May 4, 2016

### Mos

Awesome, I will do some tests.

Thank you, my guess is the heavier BB will go further, due to airsofters research.

7. May 4, 2016

### Staff: Mentor

Okay I removed the warning.