calculating free recoil energy

21 March 2004, 07:01

Anybody have a formula or some way of calculating free recoil? I think QuickLoad does it, but I don't have a copy of that software. I'm looking to do a comparison of a few different cartridge bullet combos. If someone does have just the equation, I'm not adverse to using a calculator (HP 32SII)

TIA,

Monte

21 March 2004, 09:09

Tailgunner

MV=MV. mass velocity out the front = mass velocity out the back.

(Bullet weight(gr)/7000** x Bullet Velocity + Powder weight(gr)/7000** x 5200*) / Rifle weight = Recoil velocity.
Free recoil energy = RW x RV x RV /64.32 (gravity constant).

* different sources cite different gas velocities, some use 1.5 times the bullet velocity as this figgure.
** converts weight in grains to weight in pounds.

21 March 2004, 09:11

Ben_Wazzu

Calculating recoil is a momentum balance.

Wg*Vg=Wb*Vb=Wp*Vp

Wg is weight of gun in pounds
Vg is the velocity of the gun, which you will solve for in feet per second
Wb is weight of the bullet converted from grains to pounds
Vb is velocity of the bullet in feet per second
Wp is weight of the powder converted from grains to pounds
Vp is velocity of the powder. An old NRA Rifleman article states that using 4000 fps is a good approximation for most cartridges.

Now that you have the velocity of the gun calculate the kinetic energy of the gun hitting your shoulder.

KEg=0.5*Wg*Vg*Vg

KEg is kinetic energy of the gun

And convert KE of the gun using the gravitational acceleration constant, g=32 feet per second^2 to get units of foot pounds.

KEg/g=recoil in foot pounds

According to an old Col. Whelen book anything over 14 ft lbs will make an average personï¿½s shoulder sore after an afternoon of shooting. If you have Excel you can calculate and compare many different loads and cartridges easily. The general rule is the lighter the bullet and powder load the less recoil.

General numbers off the top of my head:
223 is about 4 ft-lbs
243 is about 7 ft-lbs
308 is about 14 ft-lbs
30-06 is about 17 ft-lbs
300 Win Mag is about 25 ft-lbs

Ben

21 March 2004, 11:03

waitaminit

here's a link to a web calculator

http://wildcatshooting.com/forum/viewtopic.php?t=143

- the text does not say so, but it is there, and, if you go backward to the ballistics page of the site, you'll find the link for the JBM recoil calculator at "sticky-ballistics calculator".

21 March 2004, 11:49

4bambam

Sent you an E-mail that might help in what you was looking for.

21 March 2004, 16:35

milanuk

Thanks, guys.

I had found a website afterwards that explained the formulae, and most of the conversions/shortcuts involved here and crunched the numbers by hand. Later someone sent me an Excel spreadsheet that I'm sure works fine, other than I don't have Excel (on a Mac, w/o M$ Office) handy. Couple website links, all of which matched up w/i one decimal place (I calculated to 3, just for giggles) w/ that I did by hand. Musta done something right.

Thanks again,

Monte

21 March 2004, 18:48

Clark

Quote:

Vp is velocity of the powder. An old NRA Rifleman article states that using 4000 fps is a good approximation for most cartridges.

"Hayes elements of Ordiance" may be where it says that the velocity of the gas is approximated with 1.5 times the velocity of the projectile.

22 March 2004, 01:04

Tailgunner

Quote:

Calculating recoil is a momentum balance.

Wg*Vg=Wb*Vb=Wp*Vp

Ben

You got a sign wrong, it's Wg*Vg=Wb*Vb + Wp*Vp. Which simplified is Mass*Velocity = Mass*Velocity (MV=MV)

22 March 2004, 01:24

irv

The recoil you feel is an Impulse not Energy. Impulse = Momentum. Free recoil is meaningless as
your shoulder mass determines the recoil velocity. If the butt plate dosent move there is no energy
transfer. If you are trying to quantify "Kick" stick with Momentum. Every thing that goes forward has a reaction
back. (Newton).
Good Luck!

22 March 2004, 05:02

458RugerNo1

Go to the Beartooth Bullets forum online and they have calculators for all kinds of stuff... Recoil, bullet energy, TKO, etc. Just plug in the numbers for your cartridge and in an instant you've got the answers.

22 March 2004, 05:19

Sabot

Like most physics problems there is a good shortcut formula that works well on a hand calculator:

1. Bullet weight (grs) times velocity (fps)

2. Powder weight times 4700 fps

3. #1 plus #2 divided bt 7000

4. Number 3 squared (or times itself)

5. Number 4 divided by 640

This gives recoil for a 10 lb rifle. Divide by your rifle weight divided by 10.

22 March 2004, 05:28

<eldeguello>

Go to stevespages.com. There's a good recoil calculator in there! Beats having to fumble around for the rather arcane and complicated formula for computation of free recoil, which can be found in Hatcher's Notebook, as well as other places!

22 March 2004, 05:52

Grandpasez

In step five you could divide the figures you get in

step four, by the rifle wt times 64.

Like 10 lbs x 64= 640 ---20lbs x 64= 1280 --- 15 lbs x

64= 960..Overall this is a fast simple formula that I

use. Ed.

22 March 2004, 07:18

bartsche

Quote:

"The recoil you feel is an Impulse not Energy. "

Two men fire the same rifle same load from the same bench.The first man is 6' tall and weighs 175# The other man is 6' tall and weighs 330#. The first man's body is moved noticeably when he fires. The second man's body moves when he fires also but not nearly as much ( inertia of course).The ENERGY obsorbtion is the same but the period of time of the energy distribution is not the same. The ENERGY IMPULSE would than be measured in ft.#/sec. The MV impulse of which you speak would be #/sec.

Are you saying the energy is not felt. If so why? We are both retired Engineers but I'm still willing for you to teach me. roger

22 March 2004, 08:29

irv

Why do you say the energy transfer is the same, or the duration for that matter. Momentum can consist of a
lighter blow over a period of time (recoil pad). The man who has a weight nearest the weight of the rifle would absorb more
energy (better impedance match). This is the mistake in using recoil energy instead of momentum.
Unless you measure the velocity of the shooters shoulder (and it's temperature rise) you can't quantify
recoil. I'm sure what you feel is an impulse into your shoulder not a temperature rise.
A similar problem occurs with "Knock down power". Bullet penetration depends on Momentum
(mass x velocity). Wound cavity size depends on Energy (mass x velocity squared).
Other errors in the gun rags concern shooting uphill, and bullet drift in the wind. (mucho B.S. on these subjects)
Take Care!

22 March 2004, 12:19

Tailgunner

Not to argue (to much) with you imagineers, but the term "free recoil" implies just that, that the rifle is free to move as far and fast as it wants to. Us technician types would picture it as swinging free at the end of a pendulem rod or string.
What your discribing would better be called "felt recoil", which is totaly different.

22 March 2004, 14:36

irv

I'm new to shooting but don't you hold the butt against your shoulder, and feel the recoil?.
Please correct me if I'm wrong.
Good luck!

22 March 2004, 18:00

Clark

Quote:

weight nearest the weight of the rifle would absorb more
energy (better impedance match).

So many times in so many situations, that is the way to look at it.
Not this time though.
The reason we care about recoil is pain to the shoulder, damage to the shoulder, and how far the scope eye piece will come back.

These things involve the area of the butt and the peak force on it. The compliance of the shoulder, the padding of the jacket, etc. all taken care of with the peak psi at the shoulder.
Recoil pads reduce peak pressure by averaging it over a larger area and over a longer time.
The compliance of the shoulder becomes more important the heavier the rifle and slower the rifle comes back.
This is why we see pictures of little girls shooting 50 BMGs [girl weight = gun weight] with supposedly very large energy numbers.
The heavy and slow moving gun simply pushes the shooter a long ways averaging the force over more time.
Plenty of energy transfer, no pain.

--
A society that teaches evolution as fact will breed a generation of atheists that will destroy the society. It is Darwinian.

22 March 2004, 21:33

Tailgunner

Free recoil is the (for lack of a better term) "magnatude of the energy pulse" caused by the recoil. It can be quantified, as the formulias above show, and as the name (and formulia) implies it does NOT involve the shooter.
Felt recoil is affected by the shooter and the stock design, area and angle that the energy is applied to, hold firmness, technique, position (prone, kneeling, sitting, standing), and can NOT be quantified.
A given bullet, launched at a given velocity, by a given amount of powder, in a gun of a given weight, will yeild the same energy pulse regardless of stock design. How that stock is designed will make a world of differance EX: M-94 Win in 30-30 or a H&R Topper in 410 cause me much more pain than my Mauser 30-06 (The T/C Encore 209x50 muzzle loader hurts more than my CZ 416Rigby), even though the free recoil numbers are higher for the -06 and Rigby due to stock design and fit.
Pliable recoil pads spread the pulse out over TIME, they don't reduce the total force.
Come on up sometime and we'll burn some powder together, doing some comparitive field testing.

23 March 2004, 08:16

bartsche

To bad there isn't a thumps up Icon on this forum.You and Clark did a good job on felt recoil.The simple picture I tried to draw along with the brief expo were not anywhere as effective as the explanations you two gave us.

roger

23 March 2004, 08:23

Clark

Quote:

Pliable recoil pads spread the pulse out over TIME, they don't reduce the total force.

They don't reduce the force - time product [except for some new lossy materials], but they DO REDUCE the peak force.

And the peak force is important as [peak force ]/ area of skin = peak pressure on skin

Peak pressure on the skin is much harder to quantify, but very closly tracks pain.

So Steve's site may have a free recoil calculator and a horoscope calculator, but I don't imagine we will see a peak pressure on skin from recoil calculator soon