Ballistics/Physics Question

[JonMA1]

This is kind of an obscure topic even for the Grill Room, but here it is.

 Today was the end of Muzzleloader season in Northern Michigan. As is always the case, I had to discharge my inline muzzleloader and decided to shoot at a target. I found an old BK cup in the back of my truck (damned kids!), placed it on a log upside down, not affixed to anything, and took a shot at it from about 30yds. 

When the smoke cleared, I thought I’d missed as the cup was in the same position. But when I walked up to it, I was surprised to see the round had hit but not dislodged the empty paper cup.

A charge of 100 gr of triple seven with a 240 gr 45 cal saboted bullet will produce a muzzle velocity of somewhere around 1900 fps. I don’t know what the energy is, but it's got to be pretty high.

I’ve done a fair amount of shooting at the range using various targets and I know bullets don’t always knock heavier objects over. But this was an empty paper cup! 

I'm a dumb-a$$ when it comes to physics, but it just seemed surprising. Was this an anomaly, or is the fact that the paper offered such little resistance that the energy wasn't transferred as the bullet went through?

 

[Chris E]

Hey man, just enjoy your hobby. Thinking is hard. 

[Missouri Swede]

Sounds like a kid's science fair project just waiting to happen!  "What's the coefficient of static friction ..."

[JonMA1]

1 minute ago, Missouri Swede said:

Sounds like a kid's science fair project just waiting to happen!  "What's the coefficient of static friction ..."

Yeah, I'll bring that up to the school board. They're pretty cool about firearms in the classroom these days. C'mon Swede, it's not like I live in Missouri.

56 minutes ago, Chris E said:

Hey man, just enjoy your hobby. Thinking is hard. 

Wow. Kind of bored tonight Chris? I think there's some controversy brewing over in the Tiger Woods thread. Maybe you should mosey on over there. This is the Grill Room, after all. Have you looked at some of the threads in here?

---

I know, it's a stupid topic and question to most. It was directed more towards those who are into shooting.

[Lihu]

1900fps from a muzzle loader!?! Wow!

My old https://en.wikipedia.org/wiki/.30-06_Springfield rifle (Typically used stock 150 Winchester or Remington rounds) was able to do that with empty aluminum cans. Never tried a cup, but I'd imagine it would go clean through as well.

It's not an energy thing more than a pure velocity thing. The inertia of the cup just has to be higher than the penetration energy of the bullet into the cup. The higher the velocity the higher the chances of penetration without knocking the cup over.

I could probably work out the equations, if someone hasn't already. . .googled this topic and got https://en.wikipedia.org/wiki/MythBusters_%282006_season%29

 

 

 

[JonMA1]

9 minutes ago, Lihu said:

1900fps from a muzzle loader!?! Wow!

My old https://en.wikipedia.org/wiki/.30-06_Springfield rifle (Typically used stock 150 Winchester or Remington rounds) was able to do that with empty aluminum cans. Never tried a cup, but I'd imagine it would go clean through as well.

It's not an energy thing more than a pure velocity thing. The inertia of the cup just has to be higher than the penetration energy of the bullet into the cup. The higher the velocity the higher the chances of penetration without knocking the cup over.

I could probably work out the equations, if someone hasn't already. . .googled this topic and got https://en.wikipedia.org/wiki/MythBusters_%282006_season%29

Thanks Lihu. I almost expected someone to call BS on me because it seemed so odd.

I normally can't stand the Mythbusters show, but they did an episode where they debunked the "guy getting blown backwards through the saloon door scene" in Western movies. Everyone knows that's Hollywood BS.

That I get. Even if I don't understand the science, it seems like common sense. But the paper cup staying put kind of surprised me. I mean, a slight breeze would have knocked it over.

Regarding the muzzle velocity... the new inline muzzleloaders are a bit different than the old flintlocks and muskets. While often referred to as "black powder" firearms, that's not necessarily the case. You might find some of this interesting:

http://www.chuckhawks.com/difference_black_powders.htm

 

[Lihu]

36 minutes ago, JonMA1 said:

Thanks Lihu. I almost expected someone to call BS on me because it seemed so odd.

I normally can't stand the Mythbusters show, but they did an episode where they debunked the "guy getting blown backwards through the saloon door scene" in Western movies. Everyone knows that's Hollywood BS.

That I get. Even if I don't understand the science, it seems like common sense. But the paper cup staying put kind of surprised me. I mean, a slight breeze would have knocked it over.

Regarding the muzzle velocity... the new inline muzzleloaders are a bit different than the old flintlocks and muskets. While often referred to as "black powder" firearms, that's not necessarily the case. You might find some of this interesting:

http://www.chuckhawks.com/difference_black_powders.htm

 

Wow, they've come a long way, and certainly not like my old (design) Hawken 50. . .Nice!

[iacas]

Think more along these lines:

[JonMA1]

1 hour ago, Lihu said:

Wow, they've come a long way, and certainly not like my old (design) Hawken 50. . .Nice!

There's a muzzleloader club up here at one of the ranges. They use Hawkens, flintlock or cap locks. They frown upon those new fangled inlines, however.

34 minutes ago, iacas said:

Think more along these lines:

Makes sense. 

I saw it happen and figured it had to be the speed of the bullet combined with the material the cup was made out of, but I still wouldn't have expected it. If it were a plastic bottle, I don't think there's any way it would have stayed upright. Maybe I'd be wrong about that as well. 

But even on the test above, doesn't the fact that the objects have some weight make a difference. In other words, to accomplish the tablecloth trick with an empty paper cup, I assume you'd have to pull the cloth that much faster.

[turtleback]

13 hours ago, iacas said:

Think more along these lines:

 

Anyone remember the game, :Pull the Rug Out".?

http://www.samstoybox.com/toys/PullRugOut.html

[dak4n6]

It's all about the strength of the cup material. The bullet has to push the entire cup to knock it over but if the cup material is too weak it won't transmit the bullet's energy to the rest of the cup.

It's actually a pretty complex problem involving the bullet's size and momentum, the cup material tensile strength, the mass of the cup (inertia), and other factors like where the bullet struck the cup. 

As someone ^^ said, sometimes it's much easier to just go 'wow' and not try to understand....

[JonMA1]

20 hours ago, dak4n6 said:

It's all about the strength of the cup material. The bullet has to push the entire cup to knock it over but if the cup material is too weak it won't transmit the bullet's energy to the rest of the cup.

It's actually a pretty complex problem involving the bullet's size and momentum, the cup material tensile strength, the mass of the cup (inertia), and other factors like where the bullet struck the cup. 

As someone ^^ said, sometimes it's much easier to just go 'wow' and not try to understand....

Good explanation in terms most people can understand, at least in what factors are involved (I'm glad you didn't offer a differential equation).

I was just curious if this was an anomaly or if repeated ten times, might the same result have occurred again. Sounds like there's a good chance based some of the replies. As I said previously, I half expected someone to call BS on it.

As far as not questioning weird stuff... sadly the older I get, the more I seem to do just that.

[Lihu]

22 hours ago, dak4n6 said:

It's all about the strength of the cup material. The bullet has to push the entire cup to knock it over but if the cup material is too weak it won't transmit the bullet's energy to the rest of the cup.

It's actually a pretty complex problem involving the bullet's size and momentum, the cup material tensile strength, the mass of the cup (inertia), and other factors like where the bullet struck the cup. 

As someone ^^ said, sometimes it's much easier to just go 'wow' and not try to understand....

The only way I could see solving it is taking lots of data the Mythbusters way!

It certainly could be fun, then you work out some "simple" equations describing the penetration energy and lateral force on the cup at different penetration energies.

It'd take more than a lifetime to find analytical solutions. . .if even possible.

[dak4n6]

37 minutes ago, Lihu said:

The only way I could see solving it is taking lots of data the Mythbusters way!

It certainly could be fun, then you work out some "simple" equations describing the penetration energy and lateral force on the cup at different penetration energies.

It'd take more than a lifetime to find analytical solutions. . .if even possible.

Correct, you would have to make many measurements incrementally changing one of the variables while holding the others constant, then move on to the next variable, etc. If done with strict controls, one could develop an equation that would predict the threshold values of each variable (given values for other variables) at which the cup would fall over.

1 hour ago, JonMA1 said:

Good explanation in terms most people can understand, at least in what factors are involved (I'm glad you didn't offer a differential equation).

I was just curious if this was an anomaly or if repeated ten times, might the same result have occurred again. Sounds like there's a good chance based some of the replies. As I said previously, I half expected someone to call BS on it.

As far as not questioning weird stuff... sadly the older I get, the more I seem to do just that.

I'm getting the same way, and I am a scientist! I used to want to get to the bottom of stuff that made me go, 'huh?' But now, I'm more inclined to go, 'Hmmm that was weird, but I got a tee time in 1 hr, so whatever...'

[JonMA1]

47 minutes ago, dak4n6 said:

Correct, you would have to make many measurements incrementally changing one of the variables while holding the others constant, then move on to the next variable, etc. If done with strict controls, one could develop an equation that would predict the threshold values of each variable (given values for other variables) at which the cup would fall over.

The thing about loading ammunition is how much control you have over those variables, considering the velocities involved. I'm not talking about a muzzleloader, but hand-loaded brass cartridges.

I've seen a friend work up different loads and then measure the results with a chronograph that were surprisingly predictable.

You have the weight of the bullet and the velocity at a given yardage down-range (there are lookup tables). It should be easy to calculate the energy at impact, correct? In other words, the ballistics part of the equation would be under strict control.

Placing shots at different positions on the cup (you had mentioned that in a previous post) would be easy.

As far as the properties of the target (tensile strength, weight, etc. of the paper cup), I don't know how those are measured. Would it be difficult to gather that info?

[dak4n6]

3 minutes ago, JonMA1 said:

The thing about loading ammunition is how much control you have over those variables, considering the velocities involved. I'm not talking about a muzzleloader, but hand-loaded brass cartridges.

I've seen a friend work up different loads and then measure the results with a chronograph that were surprisingly predictable.

You have the weight of the bullet and the velocity at a given yardage down-range (there are lookup tables). It should be easy to calculate the energy at impact, correct? In other words, the ballistics part of the equation would be under strict control.

Placing shots at different positions on the cup (you had mentioned that in a previous post) would be easy.

As far as the properties of the target (tensile strength, weight, etc. of the paper cup), I don't know how those are measured. Would it be difficult to gather that info?

Wait, so an inline muzzle loader uses brass cartridges? With primers and all? So what's the difference between this rifle and a regular modern one? 1900 fps is a heck of a velocity for a .45 projectile. That's about the same as a .44 mag from my 16" lever action carbine, which will leave my shoulder bruised if I shoot more than 30 rounds in a session. I love that little carbine, but it kicks my a$$ because it's so light.

So, the variables are: terminal bullet velocity, shot placement, shot angle, cup wall strength, and cup weight (I'm probably missing a couple). The wall strength would be the hardest to quantitate. You could devise something where you put a bullet at the end of a force transducer and measure the force while you push the bullet through the cup wall. Then you would have to create a whole series of cups with walls of incremental strengths. Then, there is the difficulty of being able to have walls of differing strengths while maintaining the same weight, and vice versa - walls of the same strength while varying the weight.

Much easier to just go, "Wow, that was weird!"

[JonMA1]

No @dak4n6, sorry. I meant the control would be easier if we switched from a muzzleloader to a rifle with brass cartridges. While you could vary the loads in a muzzleloader, it's a pain in the butt as often as you have to clean them. Your .44 mag would be a good substitute.

Spoiler

To clarify, a 45cal saboted round from a  Thompson Omega Muzzleloader using 100 grains of pyrodex pellets yields a muzzle velocity of 1840 fps. These rifles are capable of handling the pressures of 150 grains

Agreed, it's just easier to just accept it.

Edited December 17, 2015 by JonMA1