# Calculate the force of an air rifles projectile

I have an air powered rifle and I would like to find a way to calculate the amount of force it produces as well as its velocity. The air rifle can be pumped which increases the pressure which gives the metal bb a lot more energy. I dont think there is any real way I could reliably test for acceleration but it might be possible to find its velocity using a 240 fps camera and enough distance but it will still be tricky.

Another idea I had was to calculate a distance then use a laser level to find where the projectile will hit a target then calculate how much the bb dropped. For example I could use $$H = V_0 t + \frac 12 a t^2$$ then plugin $$0$$ for $$V_0$$ which would remove the first $$t$$ and get me $$H = \frac12 a t^2$$ then put in the height for $$H$$ and gravity for $$a$$ to find the time it took to reach the target. Then I could take the distance traveled with the time to find its velocity (which assumes its constant even though its not due to minimal wind resistance).

That being said what is the best way to find its force? I have no idea how to find its acceleration but could I just use the barrel length with the velocity I calculated earlier to find its acceleration since it started from rest and then use that acceleration with its mass to find force?

If what I said above is correct how can I find the actual force, velocity and acceleration while taking into account wind resistance? I have taken multiple calculus courses but I am not exactly sure the best way to find this value.

• At these speeds you can't neglect air drag. And trust me: that really complicates the math!
– Gert
Mar 14 at 21:39
• You could shoot a target hanging on a string close to the exit of the barrel, like a lump of clay, and see how far it swings up. You could also measure the recoil of the gun, either with a real-time force sensor, or just hang the gun using a string at each end. The lump of clay will be easier. Mar 14 at 21:39
• @tom10 My thoughts entirely. Measurements...
– Gert
Mar 14 at 21:40
• @UnSure No, you use conservation of momentum to calculate muzzle velocity.
– Gert
Mar 14 at 21:44
• en.wikipedia.org/wiki/Ballistic_pendulum
– Gert
Mar 14 at 21:48