Recoil of .45 ACP vs. 9mm Luger

[klmhq]

I don't believe them.

Don't get me wrong... I'm not saying that they are full of it... yet.

They make some 'interesting' assumptions and stick a lot of stuff in that doesn't seem to apply.

Quoted below is my e-mail to them asking them to explain their formula and such. I may even get an answer... though I doubt it since they sell something. Also, I tend not to ask in the most politic way. Something in my personalilty says, get correct info first, worry about ruffled feathers last.

Anyway, mathematically and physicsally (), I believe that their work is BS, but I'll wait for a response.

Kev

Dear Sirs,

A friend of mine pointed me to your site and asked me to look at how you calculate recoil... we've had quite the discussion on it lately.

If I may ask a couple of questions about your formula...

***FROM www.loadammo.com/Topics/August01.htm
*** (1) I = (Wb*Vb + Wc*Vc)/225400

***Where:
***I = recoil impulse, lb.-sec.
***Wb = bullet weight, grains
***Vb = muzzle velocity of bullet, f.p.s.
***Wc = weight of powder charge, grains
***Vc = velocity of powder gases, f.p.s. (4,000 in these calcs.)
***225400 = unit correction factor (7000 gr./lb.*32.2 f.p.s.2)

***The free recoil velocity of the gun is easily found from the recoil mpulse and weight of the gun:
*** I = Wg/32.2*Vg or rearranging terms:

***(2) Vg = 32.2*I/Wg

***Where:
***Vg = free-recoil velocity of the gun, f.p.s.
***32.2 = acceleration of gravity, f.p.s.2
***I = recoil impulse, lb.-sec.
***Wg = weight of gun, lb.

***The recoil energy of the gun can then be calculated from the kinetic energy equation:
***E = ½*Mg*(Vg)2 or simplifying:

***(3) E = Wg*(Vg)2/64.4

***Where:
***E = free-recoil energy, ft.-lbs.
***Mg = mass of the gun (Wg/32.2)
***Wg = weight of gun, lb.
***64.4 = acceleration of gravity*2, f.p.s.2
***Vg = free-recoil velocity of the gun, f.p.s


1) Impulse in measured in (metric) kilogram meters per second. Here you are using lbs/sec. There is no component for distance as is required. How do you get the impulse then?

2) Why do you have a correction factor and where did it come from? Why is the correction factor 7000 grains/pounds (which doesn't seeem to make sense anyway) * the acceleration due to gravity? Gravity would play litte or no part in a normal one dimesional Newtonian mechanics problems. I realize that recoil isn't purely one dimensional, but your use of 1-d momentum implies that you think it is too.

3) How do derive the 2nd formula? Why is gravity included?

4) Equation 3, where does the 64.4 come from and why? You say that it is accel due to gravity*2, why?

Please tell me how you derived these equations.

Thank you.

[MLB]

KLM,

I haven't really dug through the formula just yet, but I believe "G" is in there to convert to pounds (force) to pounds (mass) to be consistent with grains (mass).

P.S. Impulse is force x time as I recall. No distance required. It's in the acceleration. Metric: (kg x m/s^2)x(sec) or English: (lb-f)x(sec)

Farkin' English system...

[MLB]

tman said:

...


"High velocity .22 centerfire cartridges, such as the .22-250 , will receive as much recoil from accelerating the powder charge as from accelerating the bullet."

...

I missed this tidbit the first read through, and it's an interesting point that I hadn't considered. I believe that what he is getting to is a vaild point.

The powder charge is ignited from the primer of course, and burns forward. It must then "push" or accelerate this mass of yet unburned powder forward as it goes.

With a relatively light projectile like a .223 with a heavy powder charge, the powder charge is probably a significant fraction of the accelerated mass for a while.

Assumptions are a dangerous thing. We are attempting to approximate a dynamic process with static equations. I'm sure we all realize that when we were discussing "force" we were actually referring to "average force" (since it changes from ignition to muzzle), and now we should be aware that "mass" as we discuss it is also a variable.

[TMan]

Is Dr. Dean available? I need a scream. What idiot started this thread? Oh, me again.

Personally, I do believe the guy's formula's because they were consistent with those in the book that I bought. (After I corrected the way the last one was written in the book).

Someone mentioned the value of 4,000 for C, the velocity of the charge. In the book, which incidentally was not written by God, the author states that a value of 4,700 was used for years based on testing with military cannons. Later testing at Aberdeen Proving Grounds provided values varying from 3,710 to 4,115. The U.S. Army Ballistics Research Laboratories came up with numbers of 3,880 to 4,010. These figures were based on smokeless powders. For Black Powder you should use a value of 2,000.

The basic formula for recoil is:

Mg*Vg = Mb*Vb + Mc*Vc

Where:
Mg,Vg = mass and velocity of the gun
Mb,Vb = mass and velocity of the bullet
Mc,Vc = mass and velocity of the powder charge

Since we are dealing with mass not with weight, we must divide the weight by 32.2 (actually 32.17 is more accurate) to get mass. Since there are 7000 grains in a pound we divide grains by 7,000 to get our unit of measure.

The KE formula is: 1/2*MG*(Vg)²

We are dealing with Weight so we divide by 32.2, which yields:
1/2*Wg*(Vg)²/32.2 and getting rid of the leading 1/2 gives us:

Wg*(Vg)²/64.4

[MLB]

TMan knows more than he lets on methinks. Glad you rattled the cage.

[klmhq]

I got a response from the guy at the website.

The method used to calculate recoil, shown in the Topic of the Month discussion, was derived from equations developed by Mr. William C. Davis Jr., the noted ballistic expert that worked on staff for the American Rifleman magazine for many years. For an in-depth review of this equation and how it was developed I suggest you get a copy of Mr Davis's original article that appeared in the February, 1977 (pp 32-34) issue of the American Rifleman. Another good discussion can be found in Julian Hatcher's book "Hatcher's Notebook," pages 283-299.

I think you will find that the 7000 figure is used to convert grains to lbs-weight while the 32.16 figure is used to convert lbs-weight to lbs-mass, a necessary conversion.

Best regards,
Wayne Blackwell
[\quote]

Looks like some more diggin.

I'm fairly sure they all know more about ballistics than me, but when the numbers don't make sense, I have to ask why.

The thing about those conversions still bother me though. If we were on another planet, we would need to convert weight (the force of gravity acting on an object) to mass (how much something contains), but on Earth, they are the same.

Maybe tomorrow...

[TMan]

Oh, Oh, the book I'm reading quotes for William C. Davis Jr. too. I was more comfortable thinking they were different sources coming to the same conclusions.

TMan knows more than he lets on methinks.

Hey MLB, I've been reading and studying a lot here as of late since I bought this book, which was just to learn more about ballistics in general. I didn't realize that it covered recoil until I got to chapter 6, which I seem to be stuck on. To come to think of it - it would be chapter 6 - not a good number.

Kev, it is always good to question. Looking back at times in my life that I took things for granted, I got screwed. There are some things you have to accept or take by faith. I don't believe in gravity. They tell me that we are stuck to this planet because of the large mass of the planet and the small mass we have (well, my mass has been increasing over the years). I don't believe it. Why just because something is big does it attract things that are smaller. I think the reason we don't float of into space is because the earth sucks.

Another thing is: opposites charges attract and like charges repel. So why aren't those protons in the nucleus of the atom repelling each other? Oh because there is energy holding them together and if you break the bond, you release the energy. Where did the energy come from?

I'm going to bed. I have to get up in the morning and dig up the front yard - I have a water leak. Now where is that bottle of aspirin?

[klmhq]

tman said:

There are some things you have to accept or take by faith. I don't believe in gravity. They tell me that we are stuck to this planet because of the large mass of the planet and the small mass we have (well, my mass has been increasing over the years). I don't believe it. Why just because something is big does it attract things that are smaller. I think the reason we don't float of into space is because the earth sucks.

Another thing is: opposites charges attract and like charges repel. So why aren't those protons in the nucleus of the atom repelling each other? Oh because there is energy holding them together and if you break the bond, you release the energy. Where did the energy come from?

I'm going to bed. I have to get up in the morning and dig up the front yard - I have a water leak. Now where is that bottle of aspirin?

Never take something about science on faith. That's what religion is for.. faith. Everything in science can be proven. If you really want to know about gravity, the weak electromagnetic force, or that sort of thing, let me know.

You don't see wind right, but you know it exists. Same thing with gravity and nuclear bombs (protons and breaking nuclear bonds).

[MLB]

klmhq said:

...
The thing about those conversions still bother me though. If we were on another planet, we would need to convert weight (the force of gravity acting on an object) to mass (how much something contains), but on Earth, they are the same.
...

The confusing thing is that they are entirely different, but have the same name. The measured "pound" is a force value, like the metric Newton. The proper English mass unit is the Slug, which is equal to the amount of mass that is accelerated 1 ft/sec^2 by 1 lb of force. So, a slug of mass weighs about 32lbf here on Earth.

Metric is not much better, since people "weigh" themselves in kg rather than the more appropriate Newtons. Of course, it is the mass you are concerned with, not the pressure you impose on the floor I guess. Perhaps we should measure ourselves in slugs, it certainly would make the numbers look better...

[klmhq]

mlb said:

Perhaps we should measure ourselves in slugs, it certainly would make the numbers look better...

It would also be really appropriate for some people I know.

[TMan]

MLB, thanks for the clarification on that. I missed that in his post. I need reading lessons.

Kev, the problem I have with "science" is that there is so much junk science out there. People have to get their PHD's based on some work, and a lot of it would make good fertilizer. Science once said that I should eat margarine because butter was bad for me. I said: margarine tastes like crap and I'm not about to eat it. Now we find out the margarine is worse for you than butter. Had I switched I'd probably be dead by now.

MLB is right about slugs. I'd forgotten that. Sure wish I had some of my old text books that I threw out figuring I'd never need them again. I've recently thrown out nearly all of my computer books too. Had to do it. Needed room for the gun books I've been buying. ;D