Academic question

[dahermit]

Contention: An M1 Garand produced less recoil than a Mauser 98k, using typical WWII ammunition due to the fact that the M1 is gas operated.

I anyone up to the challenge of proving (as in physics, Newton's laws, Boyle's laws, etc.)

The person claiming the above states that the inertia of the M1 stock (stay at rest), does not allow the stock to recoil until the bullet has passed the gas port.
However, when I look at Newton's Third law:

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

It seems to support the concept that recoil is generated at the instant (the word simultaneously) of firing.

In any event, I would be interested in a non-anecdotal, scholarly explanation of the above contention. At one time I would have attempted to do the math, research on weights of the two rifles, comparative bullet weights comparative chamber pressures, etc., but at 71 I think that would result in a futile exercise.
Can anyone help?

Addendum: M1 Garand 9.5 lbs (empty) M2 Ball ammo:152 grains at 2,805 fps

98k Mauser 7.1 lbs (empty)187 grains at 2,700 fps.

 

[carguychris]

The person claiming the above states that the inertia of the M1 stock (stay at rest), does not allow the stock to recoil until the bullet has passed the gas port.

To use a highly technical and scholarly terminology, this is total horse hockey.

However, when I look at Newton's Third law:

Quote:
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

It seems to support the concept that recoil is generated at the instant (the word simultaneously) of firing.

Correct.

Whenever one body exerts a force on another, it causes a reaction. Even if the reaction is so small that it can't be realistically measured (e.g. the deflection caused by an ant walking across the Brooklyn Bridge), the reaction is there.

There is no way that a Garand has enough inertia that the acceleration of the bullet from zero to ~2,700 fps within a few inches will not cause a measurable reaction.

The Garand rifle will begin to move the instant the bullet does.

 

[dahermit]

Thank you, but that was not really what I was looking for. I was looking for proofs of such as in a physics/math class that an M1 either recoils more or less than a 98k Mauser, using typical WWII ammunition.

 

[Oysterboy]

The moment the explosion occur the action (bullet) and reaction (recoil) happens at the same time. I know that's not what you're looking for but consider the actions of the rifles.

The Mauser is a bolt action rifle so the recoil is from the bullet alone.

The Garand is a semi-auto rifle and the spring being compressed and closing the bolt adds to the recoil.

I noticed when I was shooting my MP15 and the bolt locked open on the last shot the recoil was less. Very slightly less though but it's noticeable.

 

[44 AMP]

Actual and Felt

Understand you are talking about two related, but different things when you talk about the recoil of a rifle.

First, is the actual numbers of energy, generated by the round being fired, and divided by the weight of the rifle to give you an energy/velocity figure for the rifle. You can do the math (I'm not going to either) to get exact numbers, but it should be easy to see that the cartridges are close in energy, but the rifles are not close in weight, the heavier one will have a lower recoil energy.

And then there is the feel of the recoil of the rifle to the shooter. And that is entirely subjective. In general, even with equal recoil energy from the cartridges, AND equal weight rifles, the semi auto will feel like it kicks less.
This is because the moving parts of the semi auto change the feel of the recoil, and the duration of the feel, which most people interpret as "less" recoil.

Comparing the Kar 98K and the M1 Garand, the Garand will have both a lower recoil energy and feel like it has less kick than the Mauser 98k.

 

[JohnKSa]

It seems to support the concept that recoil is generated at the instant (the word simultaneously) of firing.

Recoil begins the instant that the bullet begins to move. As soon as the bullet stops accelerating (when it leaves the muzzle in this case) there is no longer any recoil force acting on the gun and the gun is basically "coasting" backwards on the momentum imparted during the bullet's acceleration down the bore.

M1 Garand 9.5 lbs (empty) M2 Ball ammo:152 grains at 2,805 fps

98k Mauser 7.1 lbs (empty)187 grains at 2,700 fps.

Based on your numbers, the Mauser would recoil considerably more than the Garand. The recoil velocity of the Mauser would be about 58% higher than the recoil velocity of the Garand.

Recoil is basically conservation of momentum. Momentum is mass times velocity. So conservation of momentum says that the momentum of the ejecta (everything coming out the muzzle) is equal to the momentum of the recoil.

It's reasonable in this case to simplify the problem by ignoring the gas that exits the muzzle (since it should be very similar in both rifles) and just focus on the bullet. So take the mass of the bullet times the velocity of the bullet and divide that by the mass of the rifle. The resulting figure will provide the recoil velocity of the rifle.

 

[dahermit]

Thank you John, that is more of what I was looking for. However, my opponent in this matter insists that the gas operation of the M1 makes it recoil less, and I am sure his mind will not be changed by what you have posted, unless it includes some scientific explanation relative to reduced recoil-not reduced recoil due to the gas system. Most likely though, he will not concede given facts that would prove him wrong anyway.

 

[44 AMP]

my opponent in this matter insists that the gas operation of the M1 makes it recoil less, and I am sure his mind will not be changed by what you have posted,

"Never argue with a pig, it wastes your time, and it annoys the pig". If your opponent is in this category, don't waste your time...

IT's not the fact that the Garand is gas operated, its the fact that it is a couple pounds heavier that makes it recoil less. A 9lb BOLT ACTION will have less recoil than a 7lb BOLT ACTION. (shooting the same or equivalent rounds).

The fact that the Garand is gas operated adds to the soft feel, but it is the difference in the weight of the rifles that makes the most difference.

 

[Frank Ettin]

....

M1 Garand 9.5 lbs (empty) M2 Ball ammo:152 grains at 2,805 fps

98k Mauser 7.1 lbs (empty)187 grains at 2,700 fps.

Based on your numbers, the Mauser would recoil considerably more than the Garand. The recoil velocity of the Mauser would be about 58% higher than the recoil velocity of the Garand.

Recoil is basically conservation of momentum. Momentum is mass times velocity. So conservation of momentum says that the momentum of the ejecta (everything coming out the muzzle) is equal to the momentum of the recoil...

Yes. Or to put it another way --

Recoil energy is a precise, physical quantity that is a function of the weight (mass) of the bullet, the weight (mass) of the powder charge, the muzzle velocity of the bullet, the muzzle velocity of the powder gases, and the weight (mass) of the gun. If you have those quantities for a given load in a given gun, you can calculate the amount of recoil energy produced when that load is fired in that gun. And a heavy bullet will produce more recoil energy than a lighter bullet fired from the same gun at a comparable velocity. Note that --

• Recoil energy is directly proportional to the mass of the ejecta, i. e., recoil energy increases as the mass of the ejecta increase. The mass of the ejecta is made up of --
  
  
  • The mass of the bullet; and
    
    
  • The mass of the gases produced by the burning powder (which is directly proportional to the mass of the powder charge).
  
  
• Recoil energy is directly proportional to the velocity of the ejecta, i. e., recoil energy increases as the mass of the ejecta increase. The velocity of the ejecta includes --
  
  
  • The velocity of the bullet; and
    
    
  • The velocity of the burning powder gases.
  
  
• Recoil energy is inversely proportional to the mass of the gun, i. e., as the mass of the gun increases, recoil energy decreases.

If you're interested, you can calculate the recoil energy of a given load using the following formula¹:

WG = Weight of gun in pounds
WB = Weight of bullet in grains
WP = Weight of powder charge in grains
VB = Muzzle velocity of bullet in f/s
I = Interim number (Recoil Impulse in lb/sec)
VG = Recoil velocity of gun (f/s)
EG = Recoil energy of gun (ft lb)

I = [(WB * VB) + (WP * 4000)] / 225218

VG = 32.2 * (I / WG)

EG = (WG * VG * VG) / 64.4

Felt recoil is a subjective matter. It's how you experience the recoil, and it's really something that only you can decide for yourself.

In general, for example, a lighter, fast bullet may produce recoil energy comparable to that of a heavier, slower bullet. But the recoil energy of the load with the lighter bullet will be manifest in a shorter pulse (distributed over a shorter period of time), while that with the heavier bullet will be distributed over a longer period of time. Depending on how you, personally experience these two types of recoil pulses, one may seem greater to you than the other, even though they really have similar recoil energy.
________________________

1. This formula is quite similar to a formula for free recoil set out at http://en.wikipedia.org/wiki/Free_recoil, although I think that the formula from Wikipedia may be a little more precise based on what I've read in Hatcher's Notebook. The formula I've reproduced above, is from the Q&As at http://www.frfrogspad.com/miscella.htm (specifically the question about why some guns of the same caliber kick harder than others). John Schaefer (FrFrog) notes that, "..."4000" is the nominal velocity of the powder gases at the muzzle for commercial smokeless powder and the observed range is between 3700 and 4300 f/s. It is sometimes stated as 4700 in some sources but this is based on observations of artillery, not small arms...." The Wikipedia formula would use the actual powder gas velocity, which may not be readily available.

 

[mete]

Careful definitions are necessary !
Recoil ? Recoil energy ? Recoil velocity ?
A semiauto spreads out the recoil over time therefore giving the feeling that it has less recoil. Punch vs push !!
Here's an interesting example comparing the 338 Win mag and 375 H&H .The 338 has less recoil energy but some shooters prefer shooting the 375 ! Strange ? No it's because the recoil velocity of the 338 is is higher than that of the 375 !

 

[Mike Irwin]

.338s have often tended to be somewhat lighter than rifles chambered in .375.

The Winchester Model 70 Safari in .375 is 9 pounds, while the Model 70 Sporter in .338 is 7 pounds 12 ounces.

That extra weight in the .375 makes a big difference in felt recoil.

 

[45_auto]

If you want the derivations, tell him to read the SAAMI paper on recoil energy here:

http://www.saami.org/PubResources/GunRecoilFormulae.pdf

Then the easiest thing to do is to plug the values for your Garand and Mauser into one of the online calculators like this one:

http://handloads.com/calc/recoil.asp

You'll get this:

As others have stated, you can see that compared to the Mauser, the Garand has 10% less recoil impulse, 33% less recoil velocity, and 40% less recoil energy.

None of these quantities have anything to do with the operation of the weapon. If you actually measured the recoil, the recoil impulse of the Garand would most likely be slightly lower than calculated because the moving parts of the weapon spread the impulse (force in relation to time) over a slightly longer time period.

 

[T. O'Heir]

The person claiming the above is confusing actual recoil and felt recoil. The M1 Rifle produces less felt recoil due to the weight and gas operation, but the actual recoil is still there. The .30 M2 cartridge does produce less actual recoil due to the lighter bullet though. And the recoil starts as soon as the bullet starts moving. Not after some of the gas has been bled off. That's simple physics. There's no magic or long and involved formulas required.
"...spring being compressed and closing the bolt adds to the recoil..." Nope. Some of the energy generated is used to do that. Lessens the felt recoil, but does not add to the actual recoil. The actual recoil is the same in a 1903(close enough to a K98) and an M1 using the same ammo.

 

[Frank Ettin]

The person claiming the above is confusing actual recoil and felt recoil. The M1 Rifle produces less felt recoil due to the weight and gas operation, but the actual recoil is still there....

No, not really. See posts 6, 9 and 12.

The M1 actually produces less recoil energy. It produces less recoil energy because the rifle is heavier than the Mauser and the bullet is lighter than the 8mm bullet fired by the Mauser. Recoil energy is a function of the mass of the firearm, the mass of the ejecta (the bullet, and the gases produced by the burning propellant) and the velocity of the ejecta. The gas operation of the M1 has no effect on the recoil energy.

The gas operation of the M1 might influence the felt recoil, but the fact remains that the recoil energy of the M1 is less than that of the Mauser 98k.

 

[45_auto]

The actual recoil is the same in a 1903(close enough to a K98) and an M1 using the same ammo.

Nope. Have you ever shot a 1903 and a Garand? Newton's laws still apply. A Garand is about 10% heavier (more mass) than an 1903. Therefore the Garand will have less recoil energy and velocity than the 1903. It's obvious by how painful your shoulder is after shooting a Highpower match with a 1903!

Even if you don't understand the math, the third paragraph from my old 1963 "Schaum's Engineering Problems" will hopefully make it clear to you:

"The greater the mass of the gun, the less will be the speed of recoil. Hence the energy to be absorbed by the recoil spring or other devices (such as your shoulder!) will be correspondingly less."



If it's not obvious to you and you don't feel like doing the math, you can always plug the numbers into a website like the one I linked to a few posts above and compare the numbers:

http://handloads.com/calc/recoil.asp

 

[44 AMP]

Originally Posted by t o'heir
The actual recoil is the same in a 1903(close enough to a K98) and an M1 using the same ammo.

Nope. Have you ever shot a 1903 and a Garand? Newton's laws still apply. A Garand is about 10% heavier (more mass) than an 1903. Therefore the Garand will have less recoil energy and velocity than the 1903. It's obvious by how painful your shoulder is after shooting a Highpower match with a 1903!

I think you missed his point. I believe the point was that shooting the same ammo, the recoil is the same, meaning that the energy delivered by the round is the same, no matter the rifle. ALL the energy the rifle has comes from the round, and shooting the same round, its the same for all rifles, be they Encore single shots or M1 Garands.

What the rifle does with that energy is what's different. Recoil of the bullet is the same, but that energy, transferred to the rifle comes to your shoulder differently. The recoil from the round is the same, but the recoil of different rifles from firing the (same) round is different, and what you feel from the recoil of the rifle is different yet.

 

[JohnKSa]

I think you missed his point. I believe the point was that shooting the same ammo, the recoil is the same, meaning that the energy delivered by the round is the same, no matter the rifle. ALL the energy the rifle has comes from the round, and shooting the same round, its the same for all rifles, be they Encore single shots or M1 Garands.

Recoil is based on the bullet momentum, not bullet energy. Recoil is about the recoil velocity (rearward velocity of the rifle) and recoil energy (energy generated by the rearward velocity of the rifle) and both are based, in part on the weight of the rifle.

The fact that two rifles fire exactly the same weight bullet at the same velocity DOES insure that both rifles have the same muzzle momentum. It ALSO means that firing the load in two different rifles will impart the same momentum to the rifles.

HOWEVER, that's where the similarities end. Unless the two rifles weigh the same amount, the recoil velocity and therefore the recoil energy of the two rifles will be different.

For a very simple example, let's say the muzzle momentum (bullet momentum) of a particular loading is 12

Let's say we have 2 rifles, one with a mass of 2 and the other with a mass of 4.

We shoot the same loading in both rifles. Both rifles will have recoil momentum equal to the momentum of the bullet as it leaves the bore--12.

Since momentum is equal to mass times velocity, we can divide the momentum by the mass of each rifle to calculate the recoil velocity of each rifle. We can calculate the recoil energy once we have the velocity since recoil energy is equal to 1/2 x (mass x velocity²).

The recoil velocity of the lighter rifle (mass of 2) will be 12/2 = 6 and the recoil energy will be 36.

The recoil velocity of the heavier rifle (mass of 4) will be 12/4 = 3 with a recoil energy of 18.

Same loading, same bullet energy, same bullet momentum, same recoil momentum but very different recoil velocity and recoil energy.

 

[SaxonPig]

Gun companies selling gas operated rifle and shotguns have long claimed reduced recoil. I'm not a physicist but the concept makes sense. How much felt difference is there is the question. Likely very little.

Weight of the projectile has a big effect on measurable recoil. Weight of the gun has a big effect on felt recoil. Design of the stock can also make a difference.

I can speak from experience having shot both...an issue 98 Mauser with 198 grain service ammo kicks much harder than does an M1 with 150 grain ammo.

 

[Frank Ettin]

Gun companies selling gas operated rifle and shotguns have long claimed reduced recoil. I'm not a physicist but the concept makes sense. How much felt difference is there is the question. Likely very little.

Weight of the projectile has a big effect on measurable recoil. Weight of the gun has a big effect on felt recoil. Design of the stock can also make a difference....

Now you're confusing recoil energy with felt recoil.

Recoil energy is an objective, physical and calculable quantity. It is determined by the mass of the ejecta, the velocity of the ejecta and the mass of the gun. Whether a gun is gas or otherwise operated, the design of the stock and other things have absolutely nothing to do with recoil energy. How recoil energy can be calculated is discussed in posts 9, 12 and 15.

Felt recoil is subjective. It's how the recoil is perceived. Things like a gun being gas operated or the design of the stock do affect felt recoil.

...I can speak from experience having shot both...an issue 98 Mauser with 198 grain service ammo kicks much harder than does an M1 with 150 grain ammo.

Your experience tells you felt recoil. It does not tell you recoil energy. However, as noted in post 12, the recoil energy of the Maser is greater than that of the M1.

 

[jmr40]

There is recoil energy, and recoil speed. And of course felt recoil is much different. Using the exact loads in guns of exact weight actual recoil will be exactly the same. A gas operated semi slows the recoil down and spreads it out over a slightly longer time period. This makes for more comfortable recoil.

Consider this analogy. If I punch your shoulder with 25 ft lps of energy it will hurt much worse than if I place my fist on your shoulder and gradually increase pressure until I reach 25 ft lbs of force. The force exerted is exactly the same, but one will hurt much more.

This is the principle behind gas operated guns. A recoil pad does the same thing FWIW. Both spread out the recoil over a longer time frame.

Also check out the chart from handloads .com posted by 45_auto. It not only lists the recoil in energy, but the velocity of the recoiling gun. If you have 2 guns with exactly the same recoil energy, the one that is recoiling the fastest will hurt more. It is not unusual for a gun to have much less recoil, but recoil faster and it will SEEM to recoil more.