doublegunshop.com - home Forums General Discussion DoubleGun BBS @ doublegunshop.com How to calculate felt recoil

I don't post often but I am always amazed at the wealth of info here. So here goes.

Can you at least estimate differences in felt recoil between two different loads?

Assume same gun/mount etc. Only thing that changes is the load/speed.

Really what I'm after is the difference between say a 1 1/8 oz at 1350fps versus 1 1/4 at 1100?

JW

Many people "Feel" a lot of what they want to feel. As far as "Actual" measurable recoil the wt of both wads & powder would also figure in. However as the shot wt & velocity are the major factors of recoil then (1.125 x 1350) ÷ (1.25 x 1100) = 1.1, so the faster load even though lighter shot wt would have approximately 10% more recoil. Note 1¼ is 11% heaver than 1 1/8 but 1350 is 23% faster than 1100 so more than offsets the heavier shot wt.
The 1¼oz load @ 1100 fps is the "Low Velocity" load of which Burrard in his famous work "The modern Shotgun" spoke of so highly with shot size suitable for the game at hand. For use on birds the size of pheasants, mallards etc he spoke of it with Brit #4s (US #5 equiv) in glowing terms for use in the 2½" British game guns. Recoil was almost identical to the standard British driven game load of 1 1/16oz @ 1300fps.

There are several good recoil calculators on the net, inclduing the one here: http://www.rfgc.org/reload/recoil_calc.htm (For others, just google "recoil calculator".)

You plug in the relevant info (velocity, shot weight, etc.) and it tells you the recoil.

Of course, these do not calculate "felt" recoil, but assuming the same gun the difference in felt recoil should be directly proportionate to the actual recoil.

If you're into self abuse, here's the whole formula.

I=(WbxV+4000xWc)/225,400

Where: I=impulse (lb-sec)
Wb=bullet wt (grains) you'd want to include the wad
V=muzzle vel (fps)
Wc=charge wt (grains)

Then plug that into Vg=32.2xI/Wg
Where Vg is gun velocity (fps) and Wg is gun wt (lbs)

Finally Eg=Wgx(VgxVg)/64.4
Where Eg =free recoil energy (ft-lbs)

If you're completely confused, congratulations!
Pete

I never have been able to use with facility the "gun magazine calculators", probably because they dont name things right, and mash everything into one enormous equation. Its easier to return to your 10th grade high school physics ( or if you are an engineer, what you did at the office yesterday morning ).

Remember that determining free recoil is a two part calculation.

First - you must calculate the velocity of the gun when it recoils and hits your shoulder.

Use the Momentum equation - which merely states mathematically "for every action there is an opposite and equal reaction".

M1V1 = M2V2

M1 is Mass of the ejecta , including shot, wads and powder ( this is one reason Black Powder loads kick so much they really DO have 3 drams of powder -82 grains - rather than 18 grains of Red Dot or somesuch, and all of that has to be included in the "mass of ejecta", but I digress).

V1 is velocity of the ejecta ( muzzle velocity)

M2 is mass of the gun

V2 is velocity of the gun in recoil after firing.

Remember to get Mass from Weight, you must divide by accelleration due to gravity, or "g", which is 32.2 feet per second per second in the English system.

Find M1.

M1 is the mass of the combined ejecta.

Shot weight is 1-1/8 oz. That is 1.125 oz, or 0.0703 pounds.
Divide by 32.2 , and the result is 0.00218 slug.

Wad - Hornady Versalite - weighs 37 grains. Divide by 7000 to convert to pounds = 0.0053. Divide by 32.2 = 0.00016 slug.

Powder - 25 grains Unique. Divide by 7000 to convert to pounds = 0.0036 pounds. Divide by 32.2 = 0.00011 slug

Sum all the numbers
Therefore M1 is (0.00218 + 0.00016 + 0.00011)= 0.00245

Find M2.

Assume gun is 7.5 pounds. Divide by 32.2 and the result is 0.2329. Therefore M2 is 0.2329.

So....

M1V1 = M2V2 ( 0.00245 ) ( 1350 fps) = (0.2329) V2

Rearrange and solve for V2

M1V1 / M2 = V2 or ( 0.00245) (1350) / (0.2329) = 14.20

V2 = 14.20 feet per second in recoil.

Substitute V2 into the Kinetic Energy Equation, Ke = 1/2 MV^2 where V^2 indicates "Vee Squared".

Where M is M2 from above.

Therefore:

Ke = 1/2 (0.2329) ( 14.20^2)= 23.48 foot pounds of Recoil, for a 1-1/8 oz load at 1350 fps in a 7.5 pound gun.

Using the same methodology , given a 1-1/4 oz. shot load, a Hornady Versalite wad, 19.5 grains of GD, for an M1 of 0.00268, and a V1 of 1100 fps,

We arrive at a recoil velocity, V2, of 12.66 fps.

Plugging this into the Kinetic Energy Equation, Ke=1/2MV^2,

we get Ke = 18.66 foot pounds.

CONCLUSION

The 1-1/8 oz load at 1350 fps has 23.48 foot pounds of recoil.

The 1-1/4 oz load at 1100 fps has 18.66 foot pounds of recoil.

The heavy shot charge loading kicks less, and will be a more pleasant companion for a day afield. Burrard discusses this a bit in The Modern Shotgun.


Whether or not the gun "kicks" you badly, includes psychological and physiological factors not subject to easy calculation.

Hope this helps a bit.

Regards

GKT

Good post Greg,

I might add that in addition to psychology it might also include straight physics that are not subject to easy calculation.

Some people think that peak force has as much to do with how much a load "hurts" than total recoil energy.

As seen above it is a straight forward procedure to calculate free recoil energy expressed as foot-pound.

Two gun/ load combinations might produce identical foot-pound recoil (as per the above calculation.) But produce quite different peak force.

No good way to calculate peak force, it would have to be measured...

TH3,

Do you think that calc works well for a 12 gauge bore size? I wonder if the jet effect of the powder though a such large diameter would be discounted more than the above rifle calculation

And where's variable for the reduced venturi effect of long forcing cones?

Folks:

I belive that since the pressure is so low at muzzle, there is negligble gas pressure effect.

Regards

GKT

Here is an easy-to-use calculator I like: http://www.zknives.com/bali/brcstgn.shtml
There IS no way to calculate "felt recoil" of course. That's why all manner of charlatans and snake oil salesmen like to use the term. Some legitimate examples of felt recoil being different from true or calculated recoil are: A fixed breech gun such as an O/U or SxS will produce the same true recoil as a gas operated autolader of the same weight. The gas auto will produce less felt recoil, however, because the recoil is broken up into two or three smaller impacts, whereas the O'U is all at once. Two otherwise identical guns will produce less felt recoil if one has a good recoil pad. Better yet, a shock absorbing mechanism like the Air Cushion or G-Squared device. Some prime examples of highly questionable reducers of felt recoil are back boring, lengthening forcing cones and the typical porting that is usually done. None of the above however, is measurable. That's why the term is often just a smokescreen to make the illogical believable.

Jim,

I know that you know a lot about this stuff.

I understand that it cannot be calculated, however why can't aat least some of those things be measured?

Modern pressure sensing technology has come a long way. I imagine that it will not be long before smart, pressure sensing, fabrics will allow us to measure the force right at our shoulder.

(I heard of a person, recently, experimenting with pressure sensors in gloves to measure handgun recoil force...)

But in the mean time we have all the technology we need to determine what impact such things as forcing cones, back-boring, etc may or may not have on peak force. Of course there is still the human element of determining how differences in force are perceived, but we can at least measure the change (or lack?) in recoil force with these technologies. No? Problem is that mostly it is the companies making the products who also own the measuring technology.

So when a company like Benelli talks about their recoil measuring technology, they are not making up the fact that they own some pressure sensors and a computer.

Graphs such as these

They are not "making the data up." They have actual measurements. Of course we can safely assume that they are not reporting all of their data... http://www.benelliusa.com/firearms/comforTech.tpl

I'm hoping that in his retirement Don Amos will be able to have some data we can trust.