Help me out with the math here fellas

C

Clay

New member
I'm helping my son out with his science experiment. In short, I need to know how much "power" in ft lbs. each of these bullets provided when shot from the guns we were using. I've seen some of you geniuses on here show the math.

Distance for all of these is about 5 yards, so not much velocity loss between muzzle and target.

First up is a 22lr. We shot from a Browning Buckmark with a 5.5" barrel using Federal 36gr copper plated hollow points.

Next was a 9mm. We used a Glock 26, 3.46" barrel with 115gr full metal jacket WWB.

Last was a 44 magnum. We used a Taurus 44ss6, 6.5" barrel with 240gr jacketed soft point Winchester.

I realize this won't be "exact", but most importantly I'm looking to show how we got the results, to show the math behind it. Thanks guys
 
You should be able to look up their rated velocities, and the lengths of the test barrels used, from the manufacturer's data and then define adjustments based on the barrel lengths of the pistols under consideration.
 
What you trying for I think is the..

"Kinetic energy" of the bullet,which is the formula:
KE = (Velocity^2)*(mass of bullet)

so you need a chronograph to measure the velocity at the distance you prefer,

convert the weight of bullet from grains to pounds (1 lb / 7000 grains),

now you have the bullet mass = w(gr) / (7000gr / lb)*( 32.3 ft/sec^2)

now the formula is KE = m * (Vel^2) = "x" ft-lb

NOW, if you really want to get intersting (and have your own private range) make a "ballistic pendulum" and fire the bulltes into that, record the maximum swing with video camera, then you can calculate the energy by the displacemnet of the "bob" of the pendulum. Here you know where zero rest is prior to impact and the vertical displacement after impact. Then it a simple work calculation of physics.
 
Energy Equation

After all the units are worked out:

ME (ft-lbs) = velocity (fps) squared x bullet weight (gr) / 450,240

Be careful using published velocity data - barrel length can make a big difference on muzzle velocity (and thus a bigger difference on energy) so either find tables to roughly match your barrel lengths or down-grade the velocities by interpolation (assuming that you don't have a chrono to measure true velocity)

And just a clarification, this is for "Energy", not "Power". The later is the "rate" at which energy is used (or generated), and would be expressed as ft-lbs per second (burn rates of powder, for example, equate to power)
 
For KE the formula is favored to velocity over mass.
Mass means nothing when ultra velocity enters. A .17 Remington will outperform any heavy bullet chosen by the .30-30 crowd.
So what table of ballistics do want to discuss?
Where are you sending the bullet?
If you intend to send it into bone (to brain) or shoulder then you need a .416 Rigby or above (.458).
If you want paper ballistics the answer is there.
If you want something that wins in one shot your choices will always be an elephant gun--a highly disregarded incapacitating rifle albeit rifle.
From what you listed the .44 Magnum is easily easily the winner in a handgun.
What is the point of this query?
 
For KE the formula is favored to velocity over mass.
Click to expand...
The formula for KE is what it is because:

1. The results provided match experimental measurements of kinetic energy and its effects.
2. It can be derived from a knowledge of the interactions of mass, energy, velocity, acceleration and force.

Kinetic energy is a REAL physical value that can be measured and that has measureable effects. The formula wasn't dreamed up by someone who thought terminal performance should be more heavily affected by velocity than mass. It is true that increasing energy will increase kinetic energy more than increasing mass will, but that's NOT because it happens to align with any particular theory of terminal performance, it's because that's the way the real world works.

That said, it is true that one needs to be careful about using simple physical quantities like momentum or kinetic energy as if they tell the whole story of terminal performance. It's far, FAR more complex than that.
 
That said, it is true that one needs to be careful about using simple physical quantities like momentum or kinetic energy as if they tell the whole story of terminal performance. It's far, FAR more complex than that.
Click to expand...

On paper in the field velocity will overcome mass.
Weatherby proved it.
 
The formula is favored to velocity for KE.
Weatherby proved it with his rifle cartridges improving velocity instead of mass. Forget that the ballistics show the same.
 
The formula is favored to velocity for KE.
Click to expand...

I'm afraid I don't understand you either. What does it mean for something to be "favored to" something else?

Perhaps you mean the kinetic energy is more dependent on velocity than on mass because of the squared term? Or that terminal effects are more strongly affected by an increase in velocity than an increase in mass (compared to some baseline)?

- Sr.
 
Perhaps you mean the kinetic energy is more dependent on velocity than on mass because of the squared term? Or that terminal effects are more strongly affected by an increase in velocity than an increase in mass (compared to some baseline)?
Click to expand...
Yes. I found the 6mm Remingtom loaded to over 3600 fps in MV could extemely kill and jelly up a coyote beyond 300 yards using the Sierra JHP in 75 grains.
No other rifle, except perhaps a .257 Weatherby, could approach that damage downrange.
Read the articles concerning game preserve or park rangers having to kill (humanely) livestock or varmints. They did NOT use their .30-30s or .30-06s.
They used a light bullet going very very fast to ensure no ricochet or other hazard. And they killed what they shot dead with one shot.
 
Instead of crunching a bunch of numbers that are already available from the bullet manufacturers, how about making this a meaningful experiment? Why not have your son research and construct a simple ballistic pendulum. Then do some test firing and record the results. Then he can draw his own conclusions from his observations. He'll remember the actual experimenting long after the energy formula is a faded memory, and he'll probably totally impress his teacher.
 
The formula is favored to velocity for KE.
Click to expand...

The formal way of describing this is to say that the velocity term dominates the equations, or that velocity is the dominant term in the equation.
 
extemely kill and jelly up a coyote
Click to expand...

as opposed, of course, to lightly killing and slicing thin.

The OP made it clear he was working on a school physics project, not killing elephants. :)

The ballistic pendulum sounds like a neat idea. Be pretty cool to video that as part of the project.
 
Quote:
On paper in the field velocity will overcome mass.

What does this mean?
Click to expand...

It means, if you can get a bumble bee to fly fast enough, it will stop a fraight train (from my Traffic Accident Reconstruction Days)
 
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