Assuming your shotgun is the same size as a Winchester 1887:
![[Image: eq.latex?\begin%7Balign%7Da&=\frac%7Bv%5E2%7D%7B2s%7D\...end%7Balign%7D]](http://www.codecogs.com/eq.latex?\begin%7Balign%7Da&=\frac%7Bv%5E2%7D%7B2s%7D\\&=\frac%7B(300\times%200.3045)%5E2%7D%7B2\times%200.508%7D\\&=8229.6\%20ms%5E%7B-2%7D\end%7Balign%7D)
![[Image: eq.latex?\begin%7Balign%7DF&=ma\\&=0.00012\t...end%7Balign%7D]](http://www.codecogs.com/eq.latex?\begin%7Balign%7DF&=ma\\&=0.00012\times%208229.6\\&=0.987552\%20N\end%7Balign%7D)
So it's hitting with a force of about 1N.
What might be more useful is the stress:
![[Image: eq.latex?\begin%7Balign%7D\sigma&=\frac%7BF%7D%7BA...end%7Balign%7D]](http://www.codecogs.com/eq.latex?\begin%7Balign%7D\sigma&=\frac%7BF%7D%7BA%7D\\&=\frac%7B4\times%200.987552%7D%7B0.06%5E2\pi%7D\\&=349.2750719\%20Pa\end%7Balign%7D)
The stress is only rough because the area of the BB that hits is alot smaller than the area I used here (just taking it's diameter). I'm not sure how much stress hurts, but I've seen somewhere that 20 psi (= 6894.757 Pa) bruises the skin.
But I could be totally wrong.
So it's hitting with a force of about 1N.
What might be more useful is the stress:
The stress is only rough because the area of the BB that hits is alot smaller than the area I used here (just taking it's diameter). I'm not sure how much stress hurts, but I've seen somewhere that 20 psi (= 6894.757 Pa) bruises the skin.
But I could be totally wrong.