Recoil Calculation

For those that may have been following the conversation on recoil calculation in another thread, I thought I would describe the procedure here.

Recoil is reported as an energy value. It is the kinetic energy of the gun. Kinetic energy is the energy of a moving body. The formula for kinetic energy is ½mv2. The first problem is that we do not know the velocity of the gun to use in the formula.

We can determine the gun velocity by looking at the momentums involved. One of Newton’s Laws talks about action and reaction, and that’s what we’re dealing with here.

The momentum of the gun must equal the momentum of the ejecta (everything going out the barrel). Momentum is the mass of an object times the velocity of the object. Velocity is in feet per second and the mass is in slugs (Imperial units).

For an example we’ll look at a 9mm Luger with the following stats:

Bullet weight = 124gr
Bullet velocity = 1,100 fps
Powder charge = 3.5gr
Gun weight = 2.5 lbs.

To determine the mass, in slugs, we take the weight in pounds and divide by the gravitational constant = 32.173 fps2 – This gives;

Bullet mass = 124/7000 pounds, divided by 32.174 = 0.00055 slugs = mB
Powder charge – 3.5/7000 divided by 32.174 = 0.0000155 slugs = mP
Gun mass = 2.5/32.174 = 0.0777 slugs = mG

The momentum balance is expressed as;

mGvG = mBvB + mPvP or vG = (mBvB +mPvP)/mG

Plugging in the values from above;

vG = (0.00055 * 1,100 + 0.0000155 * 4700) / 0.0777 = 8.73 fps

Now, having the gun velocity, we can use the energy formula;

Free Recoil Energy (FRE) = ½mGvG2 = 2.96 ft-lbs

The 4,700 fps for the gas velocity comes from Hatcher’s Notebook.

SAAMI uses the British Textbook of Small Arms formula where the gas velocity is a function of the bullet velocity. In this instance, the SAAMI formula would multiply the muzzle velocity by 1.5, giving a recoil value of 2.56 ft-lbs.

I hope this helps those interested.

I never worry much about pistol recoil, but normally calculate ft-lbs of recoil with steel butt-plate rifles by measuring the size of the bruise on my shoulder when I get home from the range. So 2.96 ft-lbs x 3" bruise = medium pain.

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Gary
SWCA 2515

Perhaps there is some use for calculated textbook recoil figures, but it seems to me that subjective (actual) "felt" recoil is more important and that's different to different shooters. Maybe calculated figures are best used for the purpose of comparison, but, how useful is such information?

I have never cared about the numbers. Like you said, felt recoil is subjective.

You can shoot a revolver with small service grips and consider it hard to shoot because of the felt recoil. Change the grips to a softer rub l and larger to fill the hand and then it feels like a different gun. The recoil numbers did not change but the felt recoil did.

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Freedom is never free!!
SWCA #3437

Now turn this into a Dynamics problem for an automatic

You would start with the slide and barrel locked together moving back against the recoil spring, the barrel unlocks and stops and the slide continues, and finally the slide hits the frame after going against the spring some more.

What would the formula be to calculate the momentum of the slide from t=0 to the time it hits the frame and stops?, and what would the force passed to the shooter by the pistol, and all it's parts, be?

33 years ago when I had to pass Dynamics (what was ME302 IIRC, at UW-Madison) I could come up with something to get enough credit and pass with a decent grade, these days, can still do it, just not in the 90 minutes given for an exam

PS. Don't take this remark too seriously and go too deep into this. We can get into all kinds of little details like is the thing loaded up with 115gn or something heavier and how many rounds are left, and have this turn into a game of wack-a-mole

I have always wondered if there is a difference in recoil from using a fast powder
vs a slow powder in a gun.
One would think that a faster powder would have less recoil.........
and that only the fps of the bullet would be the main component in the recoil methods used.

I don't worry much about rifle recoil but do get involved when I go from a L frame down to a light
J frame airweight when shooting +P ammo !!

I have worked on light and SD loads for two years, developing loads for all family members
to try to make their shooting, more enjoyable and less painful, in studing
how powders and bullet weights and fps, work together in 16 oz. revolvers.

One reason I took on the 38 special, 130 gr bullet, for use as a SD loading
over the 135 Gold Dot and 158 "FBI" load.

In the end, it all comes down to what load will hit at POA or that you fell happy with.........
darn the recoil.

Less powder, less recoil. Since fast burning powders tend to use less powder than slow burning powders, we do see differences.

Competitive shooters found that a heavy bullet using a fast powder, compared to a lighter bullet with more powder, gave less felt recoil even when the numerical recoil is the same (power factor).

But, if we look at the above example, but change to 5.0gr of powder (a a slower powder), the recoil changes to 3.24 ft-lbs.

I find shooting more fun than thinking about shooting.

You jumped over too many steps for me to keep up. Just like in school.

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"Don't Give Up the Ship"

Where did you get lost? I did not intend to skip steps.

I agree, often in school too many things were "intuitively obvious" - but they weren't obvious to me.

I got lost at step 1. Something about "slugs"? And ""mb"? I hated math in school because of the step skipping and the spotlighting in class if I asked for explanations. I loved Geometry and Psych.

__________________
"Don't Give Up the Ship"

I will have to say that perceived, or "felt" recoil has way more to do with recoil velocity, rather than foot pounds of energy. I have both a 577 Nitro Express, and a 340 Weatherby Magnum. The fast sharp jab of the 340 is considerably more brutal than the slow but substantial push of the 577, despite it launching a projectile about 3 times heavier than the 340.

Don't know much about History... Don't know much Biology.
Don't know much about a Science book... Don't know much about the French I took.

But I do know that Buffalo Bore's Heavy 357 Magnum 180gr LFN-GC Outsdoorsman is going to have a bit more (felt?) recoil in a J-frame than I'm gonna want'a deal with on a regular (or irregular) basis! OW!

CHEERS!

Yeah - slugs is one of those fairly ugly things about Imperial units compared to metric units. Slugs are units of mass, translating to (working from memory (dangerous)), (pound-mass x seconds squared) / (pound-force - foot).

The term mb, or mg are variable names for the masses of the bullet (B0, gas (G) and such.

I have not shot a 577, but I have shot a wide variety of cartridges. I fully agree that the larger magnums, such as 416's and such, are more comfortable to shoot than the middle bore magnum like the 300's. I think it's simply that there is so much recoil that your body has to move with it while the smaller magnums do their thing and done, and your body is still trying to react to it.

A lot of years ago a friend of mine had a program in His Tandy 286 computer to find 'recoil factor'. Enter firearm weight in lbs, bullet weight in grains and powder weight in grains, hit enter. 10 lb 30-06 came up 12, 460 weatherby came up 110, My 475 Linebaugh revolver came up 110. Remember Tandy. I think 1986-87 maybe. I think a model 29 came up around 30. Recoil never bothered Me so I never tried any more of that stuff.

Many years ago there was program put out for those that shot a shotgun with all types of
programs and data by a gentleman named Lowery.

It is just too bad that the new PC's will not accept the old CD...........

I think they have CD's for metalic now ................. ?
Just that I am too cheap to buy them and to old to really care now.

I need more explanation of the measurement units for this:
Free Recoil Energy (FRE) = ½mGvG2 = 2.96 ft-lbs

½m (is that half the mass weight of the gun?) x Gv (gun velocity) x G2 (what is G2?)

It been fun following the math formula through to the end.

I would think the recoil energy result would have unit of time linked to it.
A pulse of energy that is expressed as per second per second.
Like acceleration as used in the gravitational constant.

The kinetic energy formula is one half the mass times the velocity squared. I suspect the "G2" was a corruption of the squared notation.

So, one half times the mass of the gun (in slugs) times the gun velocity times the gun velocity.

Units work out to foot-pounds.

I am not much into pain, however, my friend Jim isn't happy unless he has red, black & blue marks on his shoulder from rifle and swollen wrist from pistol.

Me, if the 1st shot hurts I quit and give the ammo to Jim.

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Who are? "They"

I don’t believe the FRE in an automatic (assuming all else being equal) would be any different in a revolver or single-shot. The felt recoil would be less because it took place in stages over a longer period of time.

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and what his trumpet saith

Actually the recoil(?) of the say 416 or 577 NE IS much heavier than say a 300 Weatherby. Time is subjective but not much difference in time of recoil(Hundredths or thousandths of a second?). There is one thing that seems to make a difference is the sound of the shot and the gas coming from the muzzle. Especially the venturi effect of all that gas coming from the smaller bore. I can say with no doubt that my 10 ga Ithacas and Remingtons had way more recoil than my 3 in 12 ga 1100. And when I worked on guns I mounted many scopes on slug guns and then sighted them in for customers. Those 7/8 and one ounce slugs were no fun. Shooting at a deer? Heck, you hardly felt it. Shot 2 grizz that had bad intentions. One with a 41 mag... the other with my 375 H&H. never felt any recoil. A friend hunted Africa took 2 Cape Buffalo with his 416 Remington. 6 rounds on one...one on the 2nd with a follow up JIC Said he never felt the recoil