Thread: The Maths of Recoil

Originally Posted by 257weatherby

You people make it hard - more bang juice= bigger bang = more recoil. Equation solved, now off to go find a life.......

Not the first time a 243 user has been referred to as a philistine

Originally Posted by Sideshow

NO Sorry @Cordite it wont work! Why you ask? Because she and hers will bring in a law where by you will have to wear lycra to shoot it...and I aint doing that...leave the fish cakes out on the road ah.....(why fishcakes? cause thats what they look like after you hit one)

Is that you, @kotuku???

An aside: why do 1oz 12g slug loads seem to kick harder than 11/4oz no.5 shot loads?

Higher velocity?

Originally Posted by Micky Duck

I specifically kept velocity and projectile weight the same..... definately agree longer barrels are MUCH nicer to shoot.

Greetings Micky Duck and others that may be interested,
Sorry Micky I had not answered your question so now, fortified with a night of slumber, a bowl of muesli and a large cup of tea, I will attempt to address it a bit better.
First I looked at the powder charge needed to produce the 2,500 fps velocity. The Hodgdon data for AR2208 and the .303 with the 150 grain projectile. Next I looked at velocity loss from the 24 inch test barrel to 14 inch. Using the lower end of the often quoted 20 to 25 fps per inch this works out to a loss of about 200 fps. The increase of velocity form 24 inches to 30 inches will be less so lets say a gain of 50 fps. AR2208 needs about 1 grain more powder to increase velocity by 50 fps in a 24 inch barrel so to achieve 2,500 fps the 14 inch barrel needs 44 grains, the 24 inch 40 grains and to 30 inch only 39 grains.
Now to recoil energy. The recoil generated by the projectile is the same for each barrel length. The velocity of the powder mass in high power rifles was given as 1.75 times projectile velocity. This is a rough average and the longer barrel will deliver less and the shorter one more. The formula for energy is 0.5 times mass times muzzle velocity squared so even the same powder charge will produce greater recoil in the shorter barrel than either of the longer barrels. The extra powder needed to achieve the same velocity in the shorter barrel makes this even worse.
So should we all ditch our shorty barrels and screw in 30 inch ones? Probably not. But we do need to remember that short barrels come at a cost, both velocity and recoil.
Regards Grandpamac.

Originally Posted by grandpamac

Greetings Micky Duck and others that may be interested,
Sorry Micky I had not answered your question so now, fortified with a night of slumber, a bowl of muesli and a large cup of tea, I will attempt to address it a bit better.
First I looked at the powder charge needed to produce the 2,500 fps velocity. The Hodgdon data for AR2208 and the .303 with the 150 grain projectile. Next I looked at velocity loss from the 24 inch test barrel to 14 inch. Using the lower end of the often quoted 20 to 25 fps per inch this works out to a loss of about 200 fps. The increase of velocity form 24 inches to 30 inches will be less so lets say a gain of 50 fps. AR2208 needs about 1 grain more powder to increase velocity by 50 fps in a 24 inch barrel so to achieve 2,500 fps the 14 inch barrel needs 44 grains, the 24 inch 40 grains and to 30 inch only 39 grains.
Now to recoil energy. The recoil generated by the projectile is the same for each barrel length. The velocity of the powder mass in high power rifles was given as 1.75 times projectile velocity. This is a rough average and the longer barrel will deliver less and the shorter one more. The formula for energy is 0.5 times mass times muzzle velocity squared so even the same powder charge will produce greater recoil in the shorter barrel than either of the longer barrels. The extra powder needed to achieve the same velocity in the shorter barrel makes this even worse.
So should we all ditch our shorty barrels and screw in 30 inch ones? Probably not. But we do need to remember that short barrels come at a cost, both velocity and recoil.
Regards Grandpamac.

That is a very clear way of explaining it GPM and would have Sir Isaac thinking. What interests me is if I am going to build a lightweight rifle in 6.5 mm that achieves 3000 fps with a 100 grain Barnes and have clean slate to start with, which calibre do I go with?. As an example only, I could go with a 6.5-284 and load it down or a 6.5 x 47 with a normal load. The 6.5 x 284 will need more powder and create more recoil to reach the same velocity with the 100 gr Barnes.

Originally Posted by Finnwolf

An aside: why do 1oz 12g slug loads seem to kick harder than 11/4oz no.5 shot loads?

Higher velocity?

Yes. Recoil increases in proportion to projectile mass but in proportion to the square of velocity. Those slugs are going a lot faster.
Grandpamac.

Originally Posted by Moa Hunter

That is a very clear way of explaining it GPM and would have Sir Isaac thinking. What interests me is if I am going to build a lightweight rifle in 6.5 mm that achieves 3000 fps with a 100 grain Barnes and have clean slate to start with, which calibre do I go with?. As an example only, I could go with a 6.5-284 and load it down or a 6.5 x 47 with a normal load. The 6.5 x 284 will need more powder and create more recoil to reach the same velocity with the 100 gr Barnes.

Greetings Moa Hunter,
Thanks for your kind words. I suspect that other considerations will come well ahead of recoil in your choice but the 6.5-.284 Lapua loaded down will have a little more recoil than the 6.5 x 47 due to the increased powder charge. As you are building a lightweight rifle you may be looking at a short action which would rule the 6.5-.284 out. The curmudgeon in me would suggest that the 6.5 mm Creedmoor could be considered as well but that may not be what you are looking for. As I said other considerations.
Regards Grandpamac.

Quickload provides a recoil estimation based on the load you have plugged in at the time and the mass of the rifle. Don’t know how accurate it is but the numbers change in the direction you would expect if you alter relevant parameters. Felt recoil will be affected by stock design and fit as others point out.

Originally Posted by Plinky

Quickload provides a recoil estimation based on the load you have plugged in at the time and the mass of the rifle. Don’t know how accurate it is but the numbers change in the direction you would expect if you alter relevant parameters. Felt recoil will be affected by stock design and fit as others point out.

Greetings Plinky,
Quickload has all the data needed to calculate recoil energy. They also have the ability to model a better figure for the recoil energy from the powder charge. The trick is how well they do it. Some of the Quickload data I have seen is dangerously hot especially with Barnes projectiles. It is just a matter of how good their model is. Still it will give you a rough comparison at worst.
Regards Grandpamac.

Timely to bring Chuck Hawks ( is there really a guy named such) in.
https://www.chuckhawks.com/rifle_recoil.htm

Check out his table. It's been around a long time. Does his info match QL calcs?

I'm a fan of QL but also treat some of its outcomes with scepticism......ah make that all outcomes until you have real world data to correlate.

Originally Posted by Moa Hunter

... and would have Sir Isaac thinking.

I doubt it. Turning in his grave more likely. Recoil calculations are based on conservation of momentum.

Originally Posted by Puffin

I doubt it. Turning in his grave more likely. Recoil calculations are based on conservation of momentum.

Quite Right Puffin,
Thanks for pointing that out. I shouldn't have mentioned the energy formula. I blame brain fade and the almost 50 years since sixth form physics. I was aware that the calculations for recoil were based on momentum but was trying to get the basic relationship between barrel length and recoil and why short barrels boot much more than longer ones for the same performance. Free recoil energy is still expressed in foot-pounds force or in metric Joules so introducing momentum, although correct, does not help basic understanding. I take no credit for disturbing Isaac Newtons slumber rotary or otherwise.
Regards Grandpamac.

I disagree. Basic understanding on recoil necessarily begins with balancing momentum.
The article the OP linked to contained all that was needed for him to answer his own question without being mislead.

Originally Posted by Puffin

I disagree. Basic understanding on recoil necessarily begins with balancing momentum.
The article the OP linked to contained all that was needed for him to answer his own question without being mislead.

I too disagree, I have not been mislead. Although the article contains all that I needed to answer the question opening the topic for discussion potentially has some benefit for other members. Newtons third does not allow for the propellant gas being diverted through a break or muffler from my understanding ?

Originally Posted by Moa Hunter

I too disagree, I have not been mislead. Although the article contains all that I needed to answer the question opening the topic for discussion potentially has some benefit for other members. Newtons third does not allow for the propellant gas being diverted through a break or muffler from my understanding ?

It would seem difficult to do a straightforward calculation based on Newton's laws even with a normally crowned muzzle as some of the propellant gas will get vented at 90deg to the bore axis and will therefore not contribute to rearwards recoil. Some of the gas will exit at 90 degrees to the barrel, some at 45 degrees, some straight ahead, causing increasing rearwards recoil (rocket effect).

Interestingly, a muzzle brake like on the Lee Enfield No 5 directed most of the escaping gases straight ahead (think rocket nozzle!) and increased recoil compared to without the flash hider. It was really not a flash hider but a blast forwarder, the figure I have for forward venting muzzle brakes is that they halve the sound hitting the shooter compared to a bare barrel.