Calculating Recoil Forces in Firearms: How to Choose the Right Damper or Spring

[ELPicos]

Hi all,
I do not know if I'm in the right place to ask this question ..? I am on a small project concerning a machine to sight the firearms and this machine will be provided with a shock absorber as well as a spring in compression in order to absorb the recoil of the weapon. I do not have the training to calculate the strength of the damper and the spring in question, so I need help for that. Here's my question, if a rifle has a recoil force of 30 foot pounds (41 NM) and an acceleration of 15 feet (4.5 meters second) what damper force will stop the recoil of the weapon in a 3-inch stroke (75mm) long or what spring force will do the same job? I include 2 links, one for the table where I took my data and the other showing the type of damper I will use, they are available in various lengths and forces. The strength of the dampers are given only in Newton and not in Newton / meter, I understand that either the damper or the spring will have the same forces but I am confused with the conversion of Newton only and / or the Newton / meter or the ft / lbs. Could someone help me or tell me where I can find help on this? Thank you for your attention!
http://www.chuckhawks.com/recoil_table.htm
https://www.amazon.com/dp/B077GL5KGG/?tag=pfamazon01-20

 

[jedishrfu]

Why not just prepare for 20 to 40 ft/lbs to cover all types of weapons and loads?

From your first reference:

t is worth remembering that the majority of authorities agree that recoil of over twenty foot pounds will cause most shooters to develop a serous flinch, which is ruinous to bullet placement (the prime component of killing power). Fifteen foot pounds is probably about the maximum recoil energy most shooters feel reasonably comfortable with, particularly at the shooting range, where most serious marksmanship practice occurs.

With respect to spring force, often the formula is Hooke's law ie $F = k * x$ where F is the force when the spring is stretched or squished and x is the stretching distance. So in your example, you have F at 30 Newtons and x, the recoil distance at 0.07.62m (3 inches) and then look for a spring with a k of $(30 N) / (0.0762 m) = 393.70 N/m$

https://en.wikipedia.org/wiki/Hooke's_law

Google can help with the conversion of N/m to English units.

Here's one such calculator:

https://www.convertunits.com/from/Newton+meters/to/foot+pounds

 

[ELPicos]

Thanks to answer me, I'm french Canadian, I will try to explain at my best my project,
I want to mount the system with a shock and 2 compression springs, shock and one spring will be installed to counter the recoil and the other spring in the same direction as the recoil of the weapon, these 2 springs will be adjustable with screws in compression. That way I will not have to change anything to take the smallest calibres up to 50BMG. The shock will have a resistance situated approximately to the median force between the smallest calibers and the 50BMG, and with the small calibers I will compress the spring in the same direction that the recoil and with the big calibers I will do the opposite and compress the spring installed in the same direction as the shock. The purpose of mounting it this way is to always have a recoil stroke of about 2 or 3 inches regardless of the caliber without changing anything just changing the springs adjustment, with no significant impact on the weapon stock and rifescope. 30 foot pound is the medium recoil.

 

[jedishrfu]

Okay you'll have to wait until an engineer member sees your post. Perhaps @russ_watters can provide a better answer.

 

[ELPicos]

Ok Thank You!

 

[berkeman]

The shock will have a resistance situated approximately to the median force between the smallest calibers and the 50BMG, and with the small calibers I will compress the spring in the same direction that the recoil and with the big calibers I will do the opposite and compress the spring installed in the same direction as the shock. The purpose of mounting it this way is to always have a recoil stroke of about 2 or 3 inches regardless of the caliber without changing anything just changing the springs adjustment, with no significant impact on the weapon stock and rifescope. 30 foot pound is the medium recoil.

Have you surveyed the existing products that are used for this purpose? It looks like many do not use springs for much of the damping -- they just use hydraulic dampers...

https://ads.midwayusa.com/product/397047/hyskore-gas-dampened-dlx-precision-shooting-rest?utm_medium=shopping&utm_source=google&utm_campaign=Shooting+-+Rests%2C+Bi-Pods+%26+Benches&utm_content=397047&cm_mmc=pf_ci_google-_-Shooting+-+Rests%2C+Bi-Pods+%26+Benches-_-Hyskore-_-397047&gclid=EAIaIQobChMIhMe3y4mZ2QIVjIp-Ch3ibAxbEAQYAyABEgLmP_D_BwE

 

[ELPicos]

Yes, I know well these machine from Hyskore, they need 3 dampers force to deserve all calibers. I'm machinist, these rifle rest are really toys compared to the one I'm going to build. These rifle rests are rough on rifle, I want a system adjustable with fine tuning for any pressure. I will use linear bearing and guide and much nice stuff to mount that, Thanks for your attention!

 

[berkeman]

Yes, I know well these machine from Hyskore, they need 3 dampers force to deserve all calibers. I'm machinist, these rifle rest are really toys compared to the one I'm going to build. These rifle rests are rough on rifle, I want a system adjustable with fine tuning for any pressure. I will use linear bearing and guide and much nice stuff to mount that, Thanks for your attention!

Are you a marksman as well? I'm a pretty good shot, but my best friend has been a professional marksman for decades. What issue can you see with your plan of using spring resistance to the recoil? There is a very important potential problem with that...

 

[ELPicos]

I'm a long range target shooter and I want to eliminate the human factor to develop the best hand loads possible for me and others. I don't see issue with a damper and two spring front to front to fine tune, do you see problems with that? My problem is more to have a starting point to choose a right shock to start with. When I see exemple, 30 foot pound and 15 feet second of acceleration, it's impossible for me to know which force of shock will absorb that in 3 inches stroke approxymately. I think that if I have good force of shock it will be possible to make ajustments with springs each side of this force.

 

[berkeman]

I'm thinking that you should try to emulate the human shoulder as best you can in absorbing the recoil. I guess if you are just using the rest to measure groups with different hand loads it may not matter. But if you are wanting to sight the rifle in the best you can to match how it will shoot with you instead of the rest, it seems that hydraulic damping would be a closer match to your shoulder than adding springs into the mix. Good for you being a long-range shooter tuning up your hand loads!

 

[ELPicos]

The shock on the link above is an hydraulic shock, I will use this type with a 6 inches possible stroke, If I use spring with that the hydraulic effect will be again there, in hydraulic shock you have a spring. I think that my method will imitate human shoulder at best, the hyskore machines are bad, the damper effect work in short stroke and it's not good for rifle stock and riflescope.

 

[sophiecentaur]

It surprises me that no one has brought up Conservation of Momentum into this discussion. If you launch a projectile of mass m at velocity v then momentum mv of the projectile will be transferred to the gun / mounting / Earth, whatever else you can say about the situation. Dealing with recoil has to be a matter of making the gun's mass slow down from its initial velocity over a suitably long time (i.e. so it loses its backward momentum over an acceptable time against a spring or damper or someone's shoulder).
I know that this thread is essentially a Practical Discussion but we could at least describe the quantities correctly, if we want a reliable answer out of the exercise. I realize that people get guns to do what they want, very successfully, but that is in spite of the miss-used units and quantities of the non-Pghysics approach.
For instance, the OP says

if a rifle has a recoil force of 30 foot pounds (41 NM)

Foot Pounds and Nm are units of Energy (a force times a distance = work), not Force.
We also read

an acceleration of 15 feet (4.5 meters second)

Feet per second is the unit for Velocity, not Acceleration.

The strength of the dampers are given only in Newton and not in Newton / meter, I understand that either the damper or the spring will have the same forces but I am confused with the conversion of Newton only

This is actually right. The damper will produce a retarding Force (usually depending on the velocity it's being compressed) and it will dissipate energy by the movement:
Work = Force times Distance again. I would think that a more relevant quantity would be the Change of Momentum which would be this Force times the time it's applied for. That's a quantity called Impulse. You would actually know the momentum you have to deal with because
Momentum of recoiling gun = - momentum of bullet
Mass_gun times speed_gun = -mass_bullet times speed_bullet
and you will know the two masses involved and the speed of the bullet(?) so you can easily work out the recoil speed.

If I have introduced more confusion than light into this then I apologise - but at least I have given a reason for dampers being specified in Newtons
I think it could help somewhat if @ELPicos tries to approach this with a bit more genuine Physics because it could well help to get a better grasp of what's actually going on than just by looking at the figures in that table (useful as they are). IT would definitely be worth while reconciling the two approaches; clearly the practical based approach gets results so there's no point in chucking out the baby with the bathwater. (Ancient English expression - lookitup)

 

[ELPicos]

Look this recoil calculator : http://www.shooterscalculator.com/recoil-calculator.php

 

[berkeman]

Look this recoil calculator : http://www.shooterscalculator.com/recoil-calculator.php

The units look reasonable at the calculator page. Are you saying that you got your units that @sophiecentaur corrected from that page?

 

[ELPicos]

Bullet Weight: (gr) 250
Bullet Velocity: (fps) 2700
Powder Charge Weight: (gr) 65
Firearm Weight: (lbs) 8.5
Recoil Impulse (lbs.sec) 4.44
Recoil Velocity (fps) 16.81
Recoil Energy (ft.lbf) 37.31

With these values is it possible to calculate the right force damper to stop the recoil in 3 inches approx?

 

[sophiecentaur]

@ELPicos It's not your fault but why don't you guys a better system of units? SI is so much more straightforward. I did start off with feet and inches etc, when at school so I am putting my money where my mouth is. "Grains" fgs!
But at least that list does use Impulse, so all is not lost.
For a first stab, you only need a subset of those figures.
Energy to dissipate is 37.31 ft lbf.
Work is force times distance and required distance is 0.25feet so required damper force is 37.31 / 0.25 lbf
This assumes that the force will be constant throughout the process but it would give a good ball park answer. If there is a spring involved, that force would increase as the distance increases. It isn't surprising that the figures you are finding are based on actual measurements because the 'real' equations would be pretty complicated.
PS The 150lbf result seems quite high. That could hurt your shoulder and it could imply you move back by more than 3". Can that be right?

 

[ELPicos]

Yes it is possible, these values are for a big magnum caliber, I am a 130 kilos guy and this caliber push me back about 4 inches, the riflestock is provided with a generous rubber recoil pad otherwise it could be injury.
I will order a damper according to the given strength and I will do a practical test, this kind of damper is available at Amazon or Aliexpress and not very expensive. Thank you very much for taking the time to help me, I will let you know the results of my test. ELPicos.