How does bullet weight relate to recoil?

[SC4006]

I have wondered this for awhile, lets use for example .40 S&W. Why do the 155 grainers produce more felt recoil than maybe a 180? And I know this isn't the rifle forum but I must include that with rifles, it seems to be the opposite, the heavier the bullet the more recoil. Can someone clarify this?

[HK_Flo]

The 155 are higher velocity.

Energy = mass*speed

If you are trying to find a round with lower recoil, you need to look at the ft/lbs which is a measure of the bullets energy. Less energy, less recoil.

[Merad]

For every action there is a second action, equal in magnitude but opposite in direction (Newton's 3rd law).

The amount of recoil depends on how much energy the bullet has when it leaves the barrel. In general, if muzzle velocities are similar, you can expect the heavier bullet to produce more recoil. However if the lighter bullet has a significantly greater muzzle velocity, it can easily produce more recoil.

[Verbal Clint]

HK...you are correct in that both mass and velocity play a part in kinetic energy. However, the equation for kinetic energy accounts for mass and the SQUARE of velocity. Lets say for example that mass doubles and causes velocity to be cut in half. Your overall energy is cut in half because of the big loss due to velocity. All ballistics information should give you weight, velocity, and energy.

There are some things you can do to compensate for the recoil though. I'm not a pro on them, so I'm not even going to offer a suggestion

[481]

I have wondered this for awhile, lets use for example .40 S&W. Why do the 155 grainers produce more felt recoil than maybe a 180? And I know this isn't the rifle forum but I must include that with rifles, it seems to be the opposite, the heavier the bullet the more recoil. Can someone clarify this?

It is all about the conservation of momentum also known as Newton's third law of motion- MV = MV

In a nutshell, the rearward velocity of a gun (R in fps) of a given mass (M in pounds) is equal to the combined forward mass and velocity (V in fps) of the bullet (B in pounds) and the propellant (P in pounds).

Rearranging the equation the solution can be written like this-

(BV + PV) ÷ M = R

So, a 2 pound gun firing a 230 gr. (0.0329 pound) @ 835 fps with a 5 grain (0.000714 pound) charge of propellant @ 4,500 fps would have a rearward velocity of....

[(0.0329 lbs x 835 fps) + (0.000714 lbs x 4,500 fps)] ÷ 2 lbs = 15.34 fps.

You can also figure out the KE of the recoiling gun by using the equation ½mv² which gives you-

½mv² = 7.31 fpe

[SC4006]

Interesting, I wasn't looking for a round with less recoil necessarily, just curious.

[Bongo Boy]

Here's a handy little table for 40SW load data. It shows a few loads each using a different bullet weight, but having a muzzle velocity so as to produce the same power factor. Power factor is the product of the bullet weight in grains and the muzzle velocity in feet per second (sometimes then divided by 1000). Power factor is proportional to momentum.

The table also includes the resulting muzzle energy of the same loads. This is the actual mass of the bullet (converted from weight in grains to mass in lb-m, or 'pound mass'), multiplied by the square of the muzzle velocity in fps.

You can see that energy increases dramatically with velocity even though bullet weight is decreasing. GPerceived recoil may be driven by other factors including gun mass, etc., but recoil is proportional to energy, and keeping such factors the same across these loads shows the bigger bullet will be more comfortable.



You have to keep something the same to show this--so I chose power factor because the whole issue of attaining a target power factor with minimum recoil comes up a lot in the action games (IDPA< USPSA etc). Often, beginning shooters who understand this will strive to get the heaviest bullet they can, but other practical matters come into play--cycling time, available recoil springs, reliable cycling and general feeling of responsiveness. So, in many cases very good shooters will back down from what appears to be the Holy Grail of low recoil, accept more recoil and compensate with incredible skill. I am not one of them.

[Jim Watson]

No.
After you tabulate it, you still miss the point.
Recoil is a momentum balance, which is represented by power factor.
Muzzle energy does not determine Newtonian recoil.

It can affect felt recoil.
Most shooters agree that the slow heavy bullet thumps them less than the light fast one, even though the computed recoil is the same.
I think the muzzle blast of the high velocity round plays a part on the senses of the shooter. Then you can get into bullet and gun acceleration and the rate of change of acceleration ("surge" or 4th derivative.)

[Noreaster]

I know one manufacturer that uses 155 grain 40 S&W when they want to bring a gun to it's breaking point. Faster wear and tear.

[Colorado308shooter]

I much prefer shooting 180 grain loads out of my XD-40. The 155's are really snappy and unpleasant.

The 180's give more of a thump.....than a snap.

I've also found that the 168 gr loads in my .308 have a nicer felt recoil than the 155's. The 155's really snap into my shoulder, where-as the 168's give me more of a "thump".

[481]

Originally Posted by SC4006:

Interesting, I wasn't looking for a round with less recoil necessarily, just curious.

Oh, I didn't think that you were.

Originally Posted by Sc4006:

Why do the 155 grainers produce more felt recoil than maybe a 180? And I know this isn't the rifle forum but I must include that with rifles, it seems to be the opposite, the heavier the bullet the more recoil. Can someone clarify this?

Just answered your question and left you with the equations that'll allow you to find the answers to any further questions you might have.

Hope it helped.

[Bongo Boy]

A simple explanation, which of course may be incorrect, would seem to be offered by the fact (I assume it's a fact) that what we experience is the impulse required to provide the momentum change.

Given perceived recoil is the kind I...perceive...then that's pretty important to explain in getting a handle on why heavier bullets have a nicer [perceived] recoil.

One reasonable explanation would be that, for two otherwise identical situations where two bullets achieve the same peak momentum, the heavier one achieves it over a longer period of time. With that impulse duration being larger, and in the denominator, the impulse peak is likely lower.

It seems these differences (in impulse duration and peak) would be miniscule, but it at least seems reasonable that we're sensitive to small changes in the way the energy is delivered--especially changes in acceleration as you mentioned.

Conservation of momentum alone doesn't explain anything, near as I can tell, especially since the examples I selected were specifically chosen to reflect that while the change in momentum (power factor) is the same in all cases, experience says perceived recoil isn't (again, perceived is kind we're discussing).

Where's my thinking all fouled up?

[Frank Ettin]

Originally Posted by SC4006

...lets use for example .40 S&W. Why do the 155 grainers produce more felt recoil than maybe a 180?...

There's a difference between recoil energy and felt recoil.

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.

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.

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

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

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.

[1911Tuner]

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.

There's another factor in play. The rate of acceleration and the force requirement...or the force applied...to achieve that rate.

Force forward=Force backward.

If the force requirement to accelerate a 185 grain bullet to 1100 fps is greater than the force requirement to accelerate a 230 grain bullet to 830 fps, the force backward with the lighter, faster round will produce more recoil...or vice-versa.

Something else that is only occasionally considered is that the recoil generated in an autopistol doesn't behave the same was as it does in a revolver or single-shot/fixed breech pistol. Most of what we perceive as recoil is muzzle flip, which is actually momentum. We don't perceive much of the actual recoil impulse...not that we're fully aware of. It's over before our brain can process that something happened to our hand.

With the autopistol, the disconnect is even wider. In these, the gun is comprised of the barrel and breechblock...the slide...and the frame is essentially no more than the gun mount...and the only connection between the gun and the mount is through springs. With the auto, about 90% of the muzzle flip happens when the slide impacts the frame...and by the time that happens, the bullet is about 20 yards downrange...and the original action/reaction that took place when the round fired is long since over...relatively speaking.

[481]

Whoa, Frank!

Didn't think that I could learn more about the topic 'til you posted. I was wrong.

Thanks.

[SC4006]

thanks for all of your input guys, especially Frank, I understand a little more now.

[darkgael]

I am always interested in discussions such as these. Nice....nice to read accurate info from people who know what they are talking about.
FYI - there is a handy little recoil/velocity program available online.
http://www.handloads.com/calc/recoil.asp

I have found that it correlates well with my manual calculations done using the formulae cited in previous posts.
One neat feature of this program is that, in addition to free recoil figures, it supplies both the recoil velocity of the firearm being used as well as the time of the recoil pulse. These two are a great help in understanding felt recoil.
For instance - without going through all of the data - I have a T/C Encore and when shooting a kinda goofy almost wildcat, a 50/70 case loaded with 690 grain BMG bullet at 900 fps, the recoil velocity is 18.12 fps. This is a substantially faster recoil velocity than my .375 H&H model 70 firing 300 grainer at 2400 fps, even though the free recoil of the .375 is substantially more than the 50/70/690.
The Encore, so loaded, is a more uncomfortable gun to shoot.
Pete

[Dashunde]

Why do the 155 grainers produce more felt recoil than maybe a 180?

There are a lot of great responses here, the non-scientific answer is simply this...
The heavier bullet puts up more resistance to being set in motion, that extra resistance translates into rearward recoil.

[1911Tuner]

Just for giggles, let's toss somethin' else on the stove.

Recoil is nothing more than backward acceleration in response to an applied force. With a given weight/mass, the faster the rate of acceleration desired or required, the higher the level of force that's required...and as that unwritten and often not considered part of Newton 3 states...Force forward is force backward. Muzzle velocity, while related, isn't the sole determining factor in the rate of backward acceleration...aka recoil.

Let's do a hypothetical.

As with most hypotheticals, we'll have to assume a few things that probably won't or can't happen in the real world.

We have two .44 Magnum revolvers. These revolvers are identical in every way except for the barrel lengths. One has a 10-inch barrel, and the other is a stubby 2-incher. Both these revolvers weigh exactly 45 ounces...or about the weight of a 4-inch Model 29 Smith. (Hypothetical...remember?)

Both these revolvers will fire 240-grain bullets. The cartridge in the 10-inch gun will be loaded with Grievous SlowPowder and shorty will be firing one loaded with Grievous QuickPowder...the two extreme numbers in the Grievous powder lineup. (Think Bullseye vs 2400)

Both guns produce identical 1200 fps muzzle velocities.

We have to assume that QuickPowder doesn't blow up the gun.

For simplicity, we'll assume that the rate of acceleration is linear.

The rate of acceleration in the 10-inch barrel is 120 fps per inch...and in order for the 2-inch gun to match the 1200 fps muzzle velocity...the rate of acceleration is 600 fps per inch. The force requirement for that to happen will necessarily be off the scale.

In this hypothetical...which revolver will be reasonably pleasant to shoot...and which one will wreck your wrist in short order?

Just listen to the wheels turn!