1. ## Recoil is Easy..

The question of recoil has come up, oh, a few times on this forum and several times we have refered to an on line calculator for answers. I had just recently completed this simplified version for my book and posted it on another forum so I'll post it here for those adventurous souls who would like to try their own calculations.

Recoil is calculated in three aspects.

Recoil Impulse (RI), Recoil velocity (RV) and Recoil Energy (RE. For best results, in that order.

RI=(Bw*Bv) + (Pw*4400)/225190 - lbs/sec

RV=RI*32.17/Gw - ft/sec

RE=Gw*RV(squared)/64.34 - ft lbs

Bw=Bullet weight in grains.
Bv= Bullet velocity in ft/sec.
Pw=Powder weight in grains
Gw=Gun weight in pounds

4400 is the constant which represents the exit velocity of the powder gasses. (a major part of recoil, I call it the Bill Lear effect)

225190 is the acceleration of gravity (g) 32.17 ft/sec*7000(the number of grains in a pound) This constant gets it back to common units.

g=32.17 ft/sec

g2=64.34 ft/sec

This will provide a close approximation of recoil. We are generally interested in Recoil Energy and Recoil velocity.

A 375 with a 300 grain bullet and 80 grains of powder which gives 2600 fps velocity in an eight pound rifle will produce about 50 ft lbs of RE and an RV of 20 fps.

2. Interesting stuff if your into numbers and I am.

My oldest brother is the "Tim the toolman Taylor" of the shooting world. He is into the "Benford" model when it comes to firepower. He regularly target shoots with a 416 Rigby, 375 HH and a 458 Lott. The harder it belts him the bigger he smiles. The more it devistates a concrete block the better he likes it. When it comes to reloading he doesn't hold back on expense and he knows what he's doing. He often pushes his loads to the limits. He's gonna love this formula.....my guess is that he'll be screwing with a calculator all night.

Just to put things into perspective...big brother is no wimp. He once entered the National arm wrestling contest on a whim and finished second! He's never lifted a weight in his life!

3. Nice work, Murph. There will never be adequate formulas for predicting the effects of stock configuration, shooting position and hold, but you've made it easier to deal with the things we can measure.

I've shot some real boomers, and with the same loads and gun weight, there can be a lot of difference from one model to the next. Even if we can't account for that BETWEEN models, calculating RV and RE make it possible to compare calibers within the same model.

Of all the boomers I've shot, the worst popped up recently (literally). It's a 6-pound 54-caliber muzzleloader with a short barrel. Handy and accurate as the dickens, but with a 120-grain charge and 450 grain bullet, you can't keep the fore end in hand when you touch it off. Add a scope, and you're going to be wearing it, no matter what your shooting position. Yeah, I know that for sure after scoping myself offhand, kneeling and prone. I may be slow, but I ain't stupid. It now wears a receiver sight!

4. ## Numbers...

EKC,

Why am I not surprised that your brother is a "tool man" and a champion arm wrestler!?

I hope he does wring it out as I hope several try it. I wanted the formula evaluated before publishing it. It is my own creation, I mean the simplified version. I'm schooled in physics and math but it's not easy for me to use some of these formulas. Hatchers notebook is pretty tough. I always wanted something more simplified for all the calulations for us gun nuts.

Muzzle Energy and Sectional Density are two that most shy away from and they aren't too bad, but Recoil is a little more complex. I have seen it published in books with obvious errors or without explanations of the constants and it was hard to follow.

BrownBear,

You know, for years I couldn't understand why folks would even ask about recoil. But now I know it's because of the fear of pain! I enjoy the thump of a heavy caliber rifle, oh, I don't want to be maimed and bruised either, but it makes me feel alive when I get thumped. I have shown a cartridge, or mentioned a certain cartridge to hundreds of people and their first reaction 99% of the time is "Boy, I bet that thing kicks!" And, we see the subject here daily, and the many ways to reduce it. Recoil pads, muzzle brakes, mercury reducers, Magna-porting....lots of ink used on those subjects.

Rifle weight is a big factor as one can see by changing that value in the calculations, but I believe that stock design is the real hidden factor in what the shooter feels. I once used six different 30-06 rifles, of about 7 1/2#, for recoil tests for a bunch of guys, good hi-power shooters, and some thought one of the rifles was a 378 Weatherby. Even with the same ammunition, some rifles just maim the shooter.

Some of those old rifles with a lot of drop in the stock and the curved butt plate are real killers on either end. The idea of an ultra light 45-120-540 just doesn't set well with me.

I am a firm believer in proper shooting technique as the best means of reducing recoil and once this is mastered a shooter can shoot the heavies well without being banged and bruised. I can't teach that here on the forum and so many have gone to the brakes, and of course they do work, so that becomes the short cut. I am old school, in this regard, for sure.

Of course, there is nothing in the formula to determine what a shooters personal level of tollerance is and the best way to find out is to shoot the various calibers. A problem with that is that there are so many ill designed stocks made with cheap material that a shooter cannot tell the difference between a crappy 30-06 and a well stocked 470 Capstick!

Everyone should shoot a Dakota rifle in 450 Dakota caliber. It is easier on the shooter than a Remington XCR 30-06. Still we shoot!

5. I would like to add something here. Formulas are wonderful for calculating the amount of recoil but "felt" recoil has other variables.
Stock shape is one as Murphy pointed out but the second one is the shape of the cartridge.
Now, this is just a theory of mine and I realize I have no concrete data to prove it but in my opinion straight wall, or reasonably straight walled cases usually result in more of a shove back, than a hard "snap" from a big bore. It seems the straight wall cases allow everything to move out, then back in an even force. Bottleneck cases seem to have that pressure build up and release that causes that big "snap" backwards.

6. I've wondered about that too Randy, but even after years of shooting I probably don't have enough experience to guess. I resolved it in my mind by realizing that in my straight-walled cases at least, they simply aren't pushing the same bullet weight as fast as a bottleneck usually pushes the same weight.

My original 450 Alaskan doesn't hurt due to great stockwork, but it's sure hard to keep my front foot on the ground when I light it off.

My 50-140 Sharps really moves me around, probably more than the 450, but again, it doesn't hurt due to the stock agreeing with me.

OTH, the 458 Win Ruger #1 rechambered to 460 Weatherby I briefly owned was brutal. I've still got a #1 in 458, and I don't find it painful at all. But add the extra whoomp of the 460, and that same stock design turns into a torture device.

7. Not to argue, but doesn't Bore Diameter need to be included in the calculation? I reference this by Hatcher's Notebook, that on page 256 he used the cross section area of the bore in his calculations.

On page 287 he also states "Thrust = net gas pressure at exit x area of the exit x mass rate of discharge"

In fact, he deals quite extensively with recoil, to the tune of ~54 pages, in his Notebook. It is a very interesting reference to read and worth owning.

8. ## More Numbers and Theories

Ok, thanks guys, for the comments.

In reverse order...
Yes, bore diameter and gas exit pressure do effect the recoil. So does bolt thrust but only a small amount.
Hatcher was really into this but there are mistakes in is work, mostly from a mathmatical perspective. I don't have the good general's note book here but as I recall he did dedicate some time to recoil and I think he was right on this one.

If we think about the gas exit pressure, then consider that all modern cartridges operate at about 60,000 psi. (start the bullet moving with the same pressure) it is the bore swept volume and velocity (actually rate of change of velocity, delta V) that determines the exit pressure. Then it is the exit pressure and gas volume (big cases have more) that determines that jet like thrust. The expansion ratio of a particular caliber takes this all into consideration. Expansion ratio is the ratio of the bore (bullet swept volume of the bore) plus the chamber volume compared to just the bore volume.

If we use the expansion ratio as a multiplier in the RI equation this will satisfy that aspect of it. In my formula I use a constant of 4400 as the gas exit velocity just to make this more user friendly. I have seen others use that as well and the numbers range from 4000 to 4800 fps. My 4400 exit velocity is a pretty good mean and the change it makes with the long way around the barn is about a pound in the RE quantity, so not a big deal. This is a smple and close approximation. I also use constants elsewhere. The 225190 is 32.17 f/s (accelleration of gravity) * 7000 (grains in a pound). But for some reason most folks like to just multiply numbers, rather than use little symbols.

Bolt thrust is peak pressure * the area of the case head. This is what is felt at the bolt as the pressure is trying to push it out of the rifle. This is what starts the rifle moving backwards. This rate of accelleration of the mass of the gun varies with the cartridge head size and the pressure exerted on it. So...it must have an effect on the recoil impulse numbers. Sometime back I messed around with those numbers and I don't recall how significant it was but I have discounted it as insignificant.

Case shape. I used to think that straight walled cases had less bolt thrust (less than the head diameter and pressure would calculate) but Ken Oehler talked me out of that. (I think some of that is on the 24hrcampfire) If that were the case, then it would have a minor effect on recoil as well.

Another aspect of that is pressure is equal in all directions. Pressing against sidewalls, case head, bullet and the shoulder of the case. The push against the case head is rearward agains the bolt, against the gun, against the shoulder. The sidewalls is not along the recoil axis, so would not be considered. Against the bullet, well it will move forward and will determine the opposite and equal force. But what about the shoulder? That gas pressure exerts a force forward on the inside shoulder of the case, the chamber and thus the gun, whch is is 180 degrees from the recoil vector. So.....it would seem that necked down case would have less recoil than straight walled cases given all else being equal. But straight walled cases also will have much higher expansion ratios, but generally lower exit pressures. This may account for that difference in felt recoil due to the straight walled case expansion ratio, a shove rather than a snap, which is probably more significant than anything else that we can feel. So you can see how these opposing and counter opposing forces are at work and how complex the calculations would become. Certainly more than most of us would want to bother with for a pound or two defference in Recoil Energy.

From a shooters perspective none of this amounts to a hill of beans. All we care about is does it hurt the shoulder? And as has already been mentioned, the shape of the stock has a much greater impact (pun intended) than most of the math. Boy ain't this fun? And I need more caffeine before talking anymore on internal ballistics!

9. I bet you do your own taxes don't ya Murphy?

I think I got adult A.D.D...... my mind does not want to concentrate that hard...not on this day anyway.

When Murphy gets bored he delves into formulas. When I get bored I load ammo with the pointy end down. Don't shoot half bad either!

However tomorrow if I wake up on the right side of the bed then I am gonna play with your formula in regards to my 350 mag. I might be able to make sense out of why I think it bites more than my 338 when both are launching 250 grain fodder! In my mind it can't but it does!

10. Here's something else- what about case-pressure needed to achieve a given velocity? Look at Garrett Cartridges' site...they claim that the 45-70 kicks less than the 454 Cassull, when loaded to identical velocity, because it operates at lower pressure levels (due to its larger case).
What do you think? Would a 375 H&H, loaded with a given bullet at a given velocity, kick more than a 378 Weatherby loaded with the same bullet to the same velocity?

11. Originally Posted by go_north
Here's something else- what about case-pressure needed to achieve a given velocity? Look at Garrett Cartridges' site...they claim that the 45-70 kicks less than the 454 Cassull, when loaded to identical velocity, because it operates at lower pressure levels (due to its larger case).
What do you think? Would a 375 H&H, loaded with a given bullet at a given velocity, kick more than a 378 Weatherby loaded with the same bullet to the same velocity?
Yes and no and maybe. Exit pressure, velocity and volume are factors. I'm not sure about how to determine what the exact exit pressure, gas velocity and volume is. I don't think it would be a big difference, that's why I didn't address it in the original formula. I do understand it, very well, but not sure how to quantify all the factors. To quote Ken Oehler; "The moon may also affect it but I can't quantify that."

I'm sure we're splitting hairs here, but the questions show an understanding of the factors involved. I appreciate the interest. When I first posted on this subject way back when I first started posting on this forum, I wrote about the gas effect on recoil. I called it the Bill Lear (inventor of the lear jet) effect. (This is why a muzzle brake works) It was met by the "in the know" crowd as B.S., well I'm pretty comfortable with theories. One guy here actually wrote that gravity had nothing to do with bullet drop! Oh, well!

See below from an earlier post.

If we think about the gas exit pressure, then consider that all modern cartridges operate at about 60,000 psi. (start the bullet moving with the same pressure) it is the bore swept volume and velocity (actually rate of change of velocity, delta V) that determines the exit pressure. Then it is the exit pressure and gas volume (big cases have more) that determines that jet like thrust. The expansion ratio of a particular caliber takes this all into consideration. Expansion ratio is the ratio of the bore (bullet swept volume of the bore) plus the chamber volume compared to just the bore volume.

Here's another little trivet, not that one opinion is better than another but;

Quote: from John Barsness

You can handload the 9.3x62 to basiclaly duplicate the 250-grain .338 Winchester factory load, or the 300-grain .300 H&H factory load, yet recoil will be noticeably less in either case. With the 250's this is due to less muzzle pressure (and hence rocket effect) than the .338; with the 286's it is due to using less powder than the .375. Either bullet weight works great on game.

12. I think that you're 100% correct about the "bill lear" effect. Now that I think about it, it may be the PRIMARY factor in recoil. Why do I say that? Well, I read guys say that a 50 BMG w/a shoe-box size brake on it kicks like a 22 mag. Granted, it may weight 20-30 lb. also, but other than that, the ONLY thing cutting recoil is the brake. Does the brake effect bullet weight? No. Does the brake effect bullet velocity? No. Does the brake effect exiting gas? Yes. If redirecting exiting gas, without effecting any other factor, knocks off x-amount of recoil, than in a universe of cause-and-effect like ours, it's safe to assume that x-amount of recoil was caused by exiting gas alone.
Now if this exiting gas is such a huge factor (huge enough to be the difference between kick like a 50 BMG and kick like a 22 mag), than any other factor effecting said gas should be of supreme import to those concerned with recoil. What other factors effect said gas? Well, barrel-volume to chamber-volume ratio has got to be huge. So does straight-wall vs. bottle-necked cartridges.
As a matter of fact, the two things I just mentioned are identical concepts, if you think about it. It's the difference between holding a fire-cracker on a flat palm or in a tight fist. The gas WILL escape either way, the difference is in how easy its route is.
Imagine filling a wide bucket with gasoline and lighting it. Now imagine filling a narrow-necked bottle with gasoline and lighting it. I'm sure that at the end of the day, the same amount of energy is put out by both; but if these were rifle cartridges, which one would put out that energy with a sharper slap?

13. go_north,

I think you're on to it. I have believed this for many years. In General Hatchers note book he says, in regard to recoil, that it is a significant part of recoil but if a person were to say it is half of recoil he'd be wrong (or words to that efffect) I say no. For some calibers it is more than half! The accepted math does not reflect that, but all the gas factors aren't calculated. That's why the Ultra large cases produce so much more recoil and why (technically) the WSM's generate less. The big problem with it is, recoil is a subjective force, to some shooters it is a lot to another it isn't much. Also the weight and stock design are big factors.

There is a lot to it and we may never know all the answers but it gives us something to talk about in the middle of winter in a frozen world. We just had a 60 degree temperature swing here in 72 hours so I think I'll go out and experience some recoil from a wildcat 375 WSM. HooYah for global warming!!

#1. exiting gas pressure can be reduced by using shorter cartridges, because shorter cartridges use powder more effeciently.
#2 exiting gas pressure can be reduced by using straight or tapered walls, not bottle-necked (remember the bucket/bottle illustration).

Problem- The only way to achieve magnum velocities in a standard length cartridge is to make it fat (like the Dakotas). But fat cartridges need to be necked down (creating the bottle-neck). Of course, the closer the bore-volume to chamber-volume ratio is, the less pronounced the bottle-neck is. But anyways, is there any way to have your cake and eat it too? In other words, a standard length cartridge that doesn't bottle-neck? The closest we can probably come to it is by useing a taper like the H&H. But I don't think there are any fat, standard length cartridges that use an H&H-like taper...one again, the closest thing to it is probably the 375 Dakota, making it so ideal.

Another note- exiting gas pressure is also reduced to the degree that a case is loaded below its max (more room for the gas to expand). Which is why I would guess that a 375 Dakota loaded to H&H velocity would kick less than the H&H loaded with the same bullet to the same velocity.

15. ## clarification

To clarify- the 375 Dakota, loaded to H&H velocity, would probably have slightly greater total recoil, but because of decreased exit pressure it would give off lower amounts of the recoil per unit-of-time (I forget which that is, recoil-impulse or recoil-velocity). Which seems to be the most significant aspect of felt-recoil.

16. Interesting thoughts. I always think back to a friend's 404 Jeffrey I kept, reloaded for and shot for two years.

The 404 has an '06 length case quite a bit bigger in diameter huffing out a 404 bullet. The rifle was a dream to behold, a Griffin & Howe, 22" barrel, scope in claw mounts, minimum steel overall and a really minimum stock of outstanding walnut. Checkered steel buttplate, too. I bet it didn't top 7 pounds with the scope off.

Holy Moly, did that thing kick though! I've always wanted to try the round in about a 9 pound rifle with a straight stock, because along the lines of this end of the discussion, I wonder how it would compare with other rounds yielding similar ballistics.

17. ## It's all Greek to me......

This is getting more like a thesis than just an opinion but I wanted to add to a couple of things being kicked around.

First of all I'm sure case shape has an effect on the recoil numbers but I don't know how to begin to calculate that. Certainly the quantity of powder has an effect and a full case or a half full case (in the same size case) will be different. The problem becomes much more complicated when we start trying to put numbers to it because;

a. we can't know the exact exit velocity of the gas, only that it will be faster or slower.
b.this max rate of discharge and exit velocity must be integrated with time to make it valid.

To integrate with time takes calculus. (e-T/t ) When dealing with the negative exponent of the natural log function most people go to sleep or at least off into dreamland. I've done it and I don't think it is worth it.

Thrust=(Max. rate of discharge*delta V)+(Gas pressure at exit-atmospheric pressure)*area of exit......ad infinitum ad nausem ....e-T/t....let me know when this gets exciting......

Here is a big thing to consider. The powder charge and it's rapidly expanding gas pressure produces more of the recoil than the acceleration of the bullet.

Hatcher's notebook is in error not only mathmatically (he doesn't integrate with time on this formula) but in concept. Using his theory would mean that there would be equal energy in the first half of the bullets travel through the barrel as in the last half. Or that gas exit energy would be the same as it moved down the barrel. That can't be true. Energy is quantified at the square of velocity. Velocity or more correctly, delta V (velocity and the rate of change of velocity) must be calculated with integrated calculas to be correct, here again the tiny little greek symbol epsilon (e) to the exponent of time/tau. (another little greek guy)

To use a John Bercovitz example;

If a car is traveling at 60 mph and the brakes are applied to reduce the speed to 30 mph, and then to to reduce from 30 to 0 mph, that equal energy would be removed from 60-30 as from 30 -0 and that is wrong. Three times the energy is removed from 60-30 than from 30-0. Equal amounts of momentum are removed each time but not energy.

Few of us delve into physics and it's associated math on a routine basis. Most don't even want to try to understand it. It still gives me a headache.

I'd rather talk about which bullet to use in my 38-55 or why did S&W buy T/C? Or will we ever see the M70 again.

18. Go North, I am in 100% agreement with shorter case/ less bottle neck(bottle/bucket illustration) = less pressure = less recoil. However the fact remains that I have a 338 win mag in Ruger 77/wood stock/24 inch tube that bites less than my new stainless synthetic 77 in 350 mag when both are shooting 250 grain bullets. It is a sharp, jabbing kick so it probably has more to do with recoil velocity than recoil energy. The 338 is a full pound heavier but my feeble brain won't let me concider that measley 1 pound as the reason.

Murphy, I am a firm believer in the "Your never to old to learn" theory! You have brought a whole lot of intersting stuff to the forefront on this forum. I promise that I am gonna play with this formula until I'm blue in the face. However today I chased 1's and 0's around eor gates, nor gates and clock timed flip flop circuits until my brain won't cut it anymore. Then you go and make that last post. Ya done left me in the dust on that one! I need a beer!

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