Originally Posted by Burncycle
If you had an arbitrary set of specifications, such as
"One inch expansion and a total of 13" Penetration through calibrated ballistics gel"
Is there a formula to calculate the ratios of diameters, masses, weights, and velocities that would work to achieve that performance, assuming the metallurgy knowledge was there to tune the HP to expand predictably and consistently?
Obviously the more the round expands the more it experiences drag (like a parachute) and the more quickly it loses velocity in tissue which can lead to less penetration... increasing overall velocity may compensate somewhat assuming the bullet doesn't over expand or tear itself apart, so maybe increased mass (and therefore momentum / inertia) would be superior in achieving the depth of penetration with that kind of expansion. The bullet would have to be designed and tuned to those tolerances and particular velocity ranges.
Basically if you were to come up with a novel cartridge design from a clean sheet (not just a wildcat unless that would meet your criteria) just as a thought exercise, how would one go about calculating it so that it's in the ballpark?
Here is another book
that contains the formulas (or formulae, if you like
) that would allow you to make calculations like those. I also found the presentation of the formulas to be much clearer and more usable than in Bullet Penetration
where you must first find them and then put them into more usable form.
There are also lots of examples (two whole chapters worth) that will help you use the equations, too.
From the website:
QUANTITATIVE AMMUNITION SELECTION presents a mathematical model that allows armed professionals and lawfully-armed citizens to evaluate the terminal ballistic performance of self-defense ammunition using water as a valid ballistic test medium.
Based upon a modified fluid dynamics equation that correlates highly (r = +0.94) to more than 700 points of manufacturer- and laboratory-test data, the quantitative model allows the use of water to generate terminal ballistic test results equivalent to those obtained in calibrated ten percent ordnance gelatin.
The quantitative model accurately predicts the permanent wound cavity volume and mass, terminal penetration depth, and exit velocity of handgun projectiles as these phenomena would occur in calibrated ten percent ordnance gelatin and soft tissue.
The quantitative model is concisely explained using plain language and illustrated with clearly presented computational examples that provide guidance in every aspect of the model's application.
Besides including a variable for the density of soft tissue, the quantitative model employs a material strength variable within its governing expression that allows for the computational evaluation of any type of soft tissue. Within a confidence interval of 95%, the quantitative model predicts the terminal penetration depth of projectiles in calibrated ordnance gelatin with a margin of error of one centimeter.
There is also a couple of models near the end of the book that can be used to calculate penetration through clothing and sheet steel panels. (Very easy to use, too.