Impact on metal targets

Question
Hi Doug,
I'm a USPSA shooter and would like to know if it is possible to calculate the force at impact of 2 different bullets.

We use power factor (GR x FPS/1000) to compare loads. So in 9mm, I reload either 147GR bullets @ 930FPS or 124GR bullets at 1100FPS, both loads giving 136PF.

It looks like it's easier for the 147GR to knock the metal plates down but if I do the maths (Energy = ?x KG x meter/second^2) I have more energy in the 124GR since mass is linear and speed exponential.

The only variable I cannot find anywhere is the deformation of the bullet when hitting the plate (both bullets are from same company, same recipe for the lead, round nose NOT hollow point)

Any ideas ?

Thanks

Roger

Answer
Roger,

The formula you used is the same as mine, energy deliver is essentially computed by taking half the mass and multiplying it by the velocity of the bullet, squared.  There is a constant that is sometimes applied that deals with the force that gravity exerts on the mass of the bullet as it travels, but honestly, at typical pistol ranges, this would be negligible in my opinion.

Regarding the issue to it appearing that the 147 grain bullet knocks the plate down more easily, there is another factor to consider, that of 'force of impact' which is not related to just the energy alone.  Force of impact relates to the weight of the object, how fast it is traveling and how quickly it stops.  Based on the formula which you can find here:  http://hyperphysics.phy-astr.gsu.edu/hbase/carcr2.html

While the example they use is the effect on a driver involved in a car crash, the math still works for this problem  as it factors in deceleration.

But again according to the math, the smaller bullet traveling faster should deliver more energy.  

The thing I can't find is something that factors in the surface area of the projectile once it expands.  I wonder if the fact that the surface area of the larger bullet provides more leverage in overcoming the inertia of the plate.  Think about the idea of pushing a door open with your fingertip, vs pushing it open with your palm.  Perhaps this is a direction to consider.

Since I will be the first to admit that Physics is NOT my strong point, I am way out of my expertise here.  Still I thought it was an interesting question and thought I'd take a stab at it...

Hope this provides you with some food for thought.

Doug