Caliber selection? Kinetic Energy? Oh Dear.

[YoungBlut]

Hi yah guys. I was floating around on several forums the other day and I came across posts asking for a certain amount of kinetic energy needed to knock over the various Silhouettes at a given distance. A hail storm of physics mumbo-jumbo issued forth explaining how kinetic energy doesn’t mean a thing. I don’t discount this statement as it is quite true. I saw one poster explaining the use of a British unit called slugs and he referenced that rams require a certain induction of momentum that equals 1 slug, or essentially 32 pounds per second introduced to the target for a certain length of time. They went onto say those bullets which stick/splatter on the target do not push it as well, which I disagree with. Now given that I am a chemist I have learned a few tricks that allow one to compare multiple vector quantities whose casual relationship is quite complex. I would be happy to pm an explanation to anyone who wants a more technical description of exactly what I am doing.
The result would be to list calibers that can take down the various targets 98% of the time and better at certain distances. This lets folks decide what calibers to get and allows folks who are not so keen on reloading or have a tight budget to find a solution to their woes. The positive effects don’t stop there but I am sure folks will find this information useful in all kinds of ways that I haven’t thought of yet.
Really all I need from you guys is a little info. I would need yall to name the caliber and designate either light bullet or heavy bullet (if it is medium go ahead and call it heavy as this relationship is not quite linear, if you are not sure which it belongs in then just list the weight in grains and I will do the work from there), and the list of ranges that this is reference to. The calibers I want are ones that knock over the targets 50% of the time, and calibers that knock over the target about 95% of the time. So if you were to a caliber/bullet combo and it is a total crap shoot as to if it will knock it down or not, that fits with 50% and if you get a knock down a fair majority of the time that will work for the 90%.
These data points will be compare to another vector quantity, which will be weight in grains multiplied by velocity. A lovely equation relating enzyme kinetics will be helping us make a list of go and no go calibers for the various course ranges that I think will finally end some of the controversy on this subject for good. I will also be able to post margins of statistical error if anyone is interested in seeing how accurate my data is. Thanks for any info you give guys and remember this info is not just for you but for all shooters so any data you have for me to input only makes my job easier and my system model that more accurate by lowering my margin of error.

[260 Striker]

YoungBlut - Interesting study that has been discussed for years. Your comment about "sticking" to the target brings me to ask, should you also ask if a shooter is using jacketed or cast bullets. I shoot a lot of cast bullets and my seat of the pants theory is they hit the target harder given the same caliber, weight, and velocity as a jacketed bullet. Can't substantiate that statement with any scientific data but they sure make a louder sound when they hit steel. Then you open the door to hard cast bullets may shatter more than a softer alloy and you will go down a whole other direction in your study. Sounds interesting but I have seen as many high horsepower loads ring rams and then someone comes along with a mouse load and knocks them over. I'm sure your studay will be a good starting point and will be an interesting read. Sounds like lots of data to collect.

[YoungBlut]

Thanks, I thought about what I posted and I think I was a tad unclear in what data I wanted. A good example would be: Cartridge name, bullet weight, bullet style, bullet material, velocity at the muzzle, ballistic coefficient, and a list of ranges where knocking down each of the 4 target types is roughly a 50/50, the ranges where the combination starts to see occasional knock down failures (as in 1 out of 10 or 1 out of 20 don’t fall down). I also misspoke saying that I would compare momentum to power factor which follow a linear relationship. I will compare momentum in slugs to the probability of knocking the target over. The relationship will be exponential in that as we go higher in slugs we reach a point where the curve will flatten out. This occurs because we know that a 300 win mag will knock the targets down 100% of the time, and so will a 50 bmg, and so would 338 lapua. Thus the value for these calibers will be the same. The problem is that the magical ballpark figure which expresses the minimum momentum in slugs needed to get 100% probability of a knock down including margins of error is somewhere right on that area that flattens out. In its exponential form we can’t extrapolate where that point is. I can use a double reciprocal plot and some tinkering to linearize that data. The Y axis intercept would then be the minimum number of slugs needed to knock over a target 100% of the time.
This would be some really useful data which could save IHMSA folks money on wasted components from testing loads and spare new shooters from eating the cost of a gun that turns out to be too much of a cream puff for the event they want to participate in. Also one would know that instead of trying for full bore rams at 150 meters they could try for half sized rams inside of 100 meters or so on. It could also be used to guess the minimum loading for a given caliber when that velocity component is applied to published load data. This would spare us unnecessary recoil and wear and tear on our guns by firing projectiles which just barely make the cut.
There are some issues with this system primarily because it really only deals with the pushing aspect of a bullet impact and leaves out the torque aspect of things. Moreover in the above proposed relationship folks with lighter weight and thus faster moving projectiles would experience a greater amount of error. My initial estimate shows folks with bullet weights lower than 90 grains experiencing a margin of error of 125 fps while folks with bullet weights of 300 or more experience a margin of 40 fps or less.
I did some test problems to see what I was working with here and I have learned a few things. I still maintain kinetic energy is a bad example to choose a caliber with. As far as things to consider go, momentum is one thing to consider, friction of the base against the stand is another, and inertia of both the bullet in motion and target at rest are important. As for bullet choice, I would say a solidly bonded bullet is your best bet in rifle calibers; they won’t fall apart as easily as they smash into the target and for handgun bullets a harder lead would be best. It will splatter some but less than softer alloys thus more of it is likely to stick.
I have watched several slow motion videos and regardless of bullet construction all bullets seem to do their smashing in about 1 millisecond. The jacket bounces off almost right away and the core is what sticks. Jacketed bullet cores seem to continue pushing for a good 2-5 milliseconds. Logic would say that having more lead to act as that core which will stick and push longer would give an overall advantage. Moreover a metaphorical “slow moving freight train” made of lead would have all the right qualities as its low velocity will destroy the bullet less and its composition would help the bullet stick longer.

[ole95]

Did you use the term :" Dwell time on the target" in all of that

[YoungBlut]

Not in those exact words but i discussed the phenomenon yes. The "dwell time" is the momentum I speak of. Mass x velocity x time affecting target