Recoil Calculator


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Jaywalker
September 25, 2003, 03:21 PM
For those of us who don't always have access to the web, here's a compact application that allows us to calculate recoil energy and recoil velocity from our own computers. Enter the info requested then press your <Return> key.

The calculation is based on Harris' articles in "The American Rifleman" in the late 70's.

Powder weight in the cartidge is a part of the recoil energy, so you'll have to estimate factory powder weight for factory loads. I use 58 grains for my .270, for instance, and 45 g for the 7mm-08 Rem 140 g bullet, 43 g for the .260 Rem 140 g bullet, and 39 g for the .243 Win 100 g bullet. YMMV, and feel free to choose a better powder weight. More powder means more mass exiting from barrel, at an estimated 4,000 fps. (I think this estimate is fine, since most of the gas is behind the bullet, which is around 3,000 fps, with smaller amounts of gas at a higher velocity both before and after the bullet. I believe it's varying gas velocity estimates that lead to varying recoil energy results from different recoil calculations.) Larger amounts of powder definitely mean more recoil energy, however.

This app's optimized for smokless powder. Since blackpowder's gas velocity is about half that of smokeless powder gas, this application will yield erroneous results for bllackpowder. (I do have a slicker program that does both, and has great windows and choices. It takes up 5 megabytes of space, though, instead of this simple one's 99 kilobytes, and therefore isn't great for downloading over a dial-up line.)

Good Luck. Post questions, if necessary.

Jaywalker

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jsalcedo
September 25, 2003, 05:16 PM
good program

It seems to be right in line.

Jaywalker
September 28, 2003, 09:35 AM
jsalcedo,

I appreciate your comments, since I coded the app. People like a little validation before they trust, these days.

I just thought I'd respond to your comment that the app is in line with other recoil calculators. It is, of course, and I think the reason is that the others may have got it from me, at least indirectly.

Back about five years ago I went looking on the web for a recoil calculator and wasn't able to find a good one. The few that were there were "estimators," or calculators that didn't show the recoil velocity component, which describes how "sharp" the recoil feels. I had an old set of American Rifleman magazines and vaguely recalled that one of them had a recoil calculation, so I searched for it. I finally found it in a 1979 issue, but it didn't appear to be accurate. Finally, in 1999 (I think), I was browsing through a 1980 American Rifleman, and found a correction to the 1979 article. Well, that fixed it, so I sent a spreadsheet with the calculations embedded (and visible) to a few shooting and hunting websites, but I had to keep resending them to folks who had overwritten the formulas on the spreadsheets. To save myself work, I then coded it into the current version and started distributing this one instead.

Later, I started seeing lots of sites that clearly used the same calculation I had distributed previously in spreadsheets. Since all of them now included the "recoil velocity" component, too, I at least suspect I'm the intermediate source (American Rifleman's Harris was my source) for the current web recoil calculation.

Patting-self-on-back mode off. ;)

Jaywalker

jsalcedo
September 28, 2003, 01:47 PM
Great work!

I spent at least 2 hours yesterday weighing my rifles and calculating
the recoil using info from my handloads.

Tomorrow I'm doing pistols.

The info is going to help me calculate new loads to work up for my son and nephew who are both young and recoil sensitive.

discusser
November 3, 2004, 02:24 AM
Thanks for the recoil calculator. :)

Will this work for shotguns too?

taliv
November 3, 2004, 09:25 AM
i'm rather fond of this program that i use on my palm pilot. very handy.

it does that recoil calculation, and also reload and cartridge costs, and required twist rate on barrels and bullet drop, speed of sound, etc.

pretty snazzy

and portable

(be advised, it works in treo300s but causes my treo600 to crash and requires a hard reset and file wipe)

Tony Williams
November 4, 2004, 03:53 AM
OTOH, for those who like to pound out the sums on their pocket calculators, this is from the article on 'Basic Ballistics' on my website:

"The recoil force generated by firing a gun has two components; the momentum of the projectile, and of the escaping gas. Projectile momentum is easy to calculate; just multiply the projectile weight by its muzzle velocity (so a cartridge firing a 10g bullet at 1,000 m/s should have the same bullet momentum as one firing a 20g bullet at 500 m/s). Note that this is a different calculation from muzzle energy, as bullet weight and muzzle velocity are of equal value. This explains why in different bullet-weight loadings of the same cartridge which generate the same muzzle energy, the heavy bullet loading will produce heavier recoil.

The recoil caused by the escaping gas - a kind of "rocket effect" - is much more difficult to calculate because it depends on the relationship between the burning characteristics of the propellant and the length of the barrel. If you assume two rifles firing the same cartridge, one with a barrel of optimum length and the other with a much shorter barrel, the optimum length one will produce the higher muzzle velocity and therefore the greater recoil through bullet momentum. However, in the short-barrel gun the gas will be at a higher pressure when the bullet leaves the muzzle, and will therefore expand more violently, causing more muzzle blast and flash and generating a stronger "rocket effect". In this case, a higher proportion of the recoil will be generated by the expanding gas than with the optimum barrel.

For this reason, there is no simple ratio which will tell you exactly what proportion of the recoil is generated by the escaping gas as opposed to the projectile. However, a good approximation can be made, based on the weight multiplied by the velocity of the propellant compared with the weight multiplied by the velocity of the projectile. In a large number of empirical tests, the velocity of the gas escaping from the muzzle of a rifle has been determined to be 1,200 m/s (4,000 fps) plus or minus 10%. In larger high-velocity military weapons, which can operate at very high pressures and velocities, the escaping gas velocity may be significantly higher.

It is therefore fairly simple to work out what proportion of the recoil impulse is generated by the escaping gas. Take for example the 7.62x51 NATO military rifle/MG cartridge in M80 ball loading. This uses 3.0g (46 grains) of propellant to fire a 9.5g (146 grain) bullet at a muzzle velocity of 840 m/s (2,750 fps). The calculation goes like this (the units of measurement don't matter as long as they are used consistently):

Bullet momentum: 9.5 x 840 = 8,000 (rounded). Propellant momentum: 3.0 x 1,200 = 3,600. So the total recoil momentum is 8,000 + 3,600 = 11,600, of which the gas produces 3,600 / 11,600 x 100 = 31%

This figure of around 30% is typical for a medium-velocity rifle cartridge. In a higher-velocity rifle like the 5.56mm NATO it is in the region of 35-40%. In handguns it is much lower, in the region of 10-15%, although in the big Magnums it can exceed 20%. In powerful military cannon it can be as high as 50%."

"So far I have only discussed the "recoil force" as opposed to the recoil experienced. This is because the recoil experienced depends on the weapon, and on the mounting. In the case of a rifle or handgun, the weight of the weapon has a significant effect. Momentum works both ways, equally (you can't defeat Newton's law of equal and opposite reactions!), so the rearwards momentum of the gun matches the forwards momentum of the bullet plus the expanding gas. It therefore follows that the heavier the weapon, the more slowly it will move backwards under recoil, giving a smooth push rather than the sharper kick of a lighter weapon firing the same ammunition. The recoil momentum experienced by the firer is the same, but it is delivered in a different way; the lighter weapon, recoiling more quickly, has the same momentum but higher energy and is perceived to "kick harder".

For instance, let's take our 7.62x51 NATO cartridge and work out the recoil energy it would generate in different rifles. As we have seen, the cartridge generates a total recoil impulse of 11,600 (grams per metre per second). If a rifle weighs 4.0 kg (8.8.lbs) or 4,000g, it will therefore be pushed back at 11,600 / 4,000 = 2.9 metres per second. 4.0 kg at 2.9 m/s = 17 joules (whereas the cartridge develops 3,350 joules - which shows the importance of velocity in calculating energy). If a lightweight rifle of only 3.0 kg (6.6 lbs) is used to fire the same cartridge, it will be pushed back at 11,600 / 3,000 = 3.9 m/s, producing 23 joules muzzle energy - an increase in recoil energy of 35%, even though the recoil momentum is the same.

To translate this into practical consequences, the 7.62x51 NATO cartridge generates only about double the recoil momentum of the 5.62x45 NATO, but in rifles of the same weight this translates to double the rifle recoil speed, therefore four times the recoil energy. An intermediate military rifle cartridge like the Russian 7.62x39 used in the famous Kalashnikov AK 47 rifle fits about half-way between the 7.62x51 and 5.56x45 in recoil generated; regarded as around the maximum for (just about) controllable automatic fire in a military rifle."

In the new book 'Assault Rifle: the Development of the Modern Military Rifle and its Ammunition' by Max Popenker and myself, I have calculated the recoil impulse generated by a large number of cartridges, service and experimental, and included this in the ammo table.

Tony Williams: Military gun and ammunition website (http://www.quarry.nildram.co.uk) and discussion
forum (http://forums.delphiforums.com/autogun/messages/)

WYO
November 5, 2004, 08:57 AM
I have been using the recoil calculator at http://sst.benchrest.com but I can't vouch for its accuracy.

Moparmike
November 5, 2004, 11:58 PM
Hmm. It gives me some huge number when I put in the following:

Bullet weight: 923567gr
Velocity: 98765464194
Powder: 1gr
weight of firearm: .5 lbs


It then spits out that the gun will be moving at 26,061,863,848,361.1 ft per second which comes out to 1.77694526 × 10^13 miles per hour (which is about 26497 times the speed of light), and that the recoil energy will be somewhere around 5,273,453,006,603,364,010,000,000 ft/lbs, or 1.0546906 × 10^28 ft / tons.

Its no wonder that people end up on Alpha Centauri every time they shoot my gun....:uhoh: :scrutiny:

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