Here's the link if interested. The description has the info, but I'll post it too. The formulas for the energy calculations will be posted soon.

https://youtu.be/MWClcGXqnN4

115 gram lead sling bullet

Momentum=4.79 kg×m/s

Velocity  = 41.71 m/s

Ft lbs of energy = 74

Area=.8"

Length=2.9"

Pressure=92.5 psi

Pressure?  How is this calculated and to what is it referring?

IronGoober wrote on Jul 31^st, 2022 at 11:11pm:


Pressure is a direct reference to an objects penetration qualities in correlation to the projectiles widest point. The formula to calculate this is as follows:
Pressure=Force/Area.

Example A: 35.67 gram Arrow (550 grains) from 40# recurve bow at 30 inch draw

Velocity=145 FPS
Mass=35.67 g
Area=.309 (of an inch)
KE=26Ft Lb

P=26/.309
P=84.14 PSI

The arrows total KE is divided by the arrows widest penetrating point, the shaft.

Now lets apply this to a 1 inch ball bearing

66.8 gram steel ball
Velocity=150FPS
Mass= 66.8gram
Area=1.00
KE=52FtLb
P=52/1.0
P=52PSI

Momentum is also very important but I'll be posting an in depth explanation later, however based off this we can see that at each projectiles widest point, despite the ball having way more energy, it only has a little more than half the psi of the arrow, even excluding the pressure of its tip. The ball is 1 inch all around so has no better penetrating point than anywhere else on it.

Ok, but the values you are using are energy/area. In the calculation you just gave, you would have (ftlb/in^2) instead of psi. It is not quite the same thing.

Energy/area is still useful for ballistic calculations, but not the same concept as pressure. I just want to make sure we are all on the same page.


To calculate a value for pressure, you would need to know the rate at which the projectile decelerates (giving you the force, F=ma) and only if the deceleration was constant would you get a constant pressure value (which is not usually what happens in a real situation).  You can make assumptions about deceleration though, like assuming that it happens in a single camera frame, or something like that (1/30th of a second). As long as you are consistent with the assumption, it should give you something useful to compare different throws/ammo.