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Old October 14, 2014, 08:16 PM   #1
choppero
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Recoil testing device needs math help

I have a device (fixture, sled, gizmo) that will measure recoil by pushing a sled (loaded with 50 lb weight) mounted on rails a measured distance. An older (spring loaded) version can be seen on my web site http://hudsontradingpost.com/pages/P...le%20Break.htm
I decided on weight vs spring for consistancy of measurement.

How can I calculate the force required to move a distance. The weight is known (50 lb with rifle). The factory ammo specs are known in this case 338 Win Mag 200 gr Muzzle energy 3890. Distance moved without break 3 7/8 in. and with break it moves 2 9/16 in. The sled moves on Nylon (cutting board material) channels and Delrin rails. Unloaded it slides very free.

It will be great to know what kinds of energy reductions different breaks produce.
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Old October 14, 2014, 09:17 PM   #2
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Ah, unistrut. Wonderful stuff. Is that a fish scale I see in there? Is it free recoiling on bearings? Do you have a Utube video?
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Old October 15, 2014, 03:18 AM   #3
hartcreek
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Hmmm me thinks you might be doing it the hard way. Just use Newtons third law and figure F = MA
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Old October 15, 2014, 07:10 AM   #4
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I'm not sure that you can come up with a formula that will relate distance moved vs. recoil force without somehow factoring in the friction in the system, and I wouldn't know where to begin with that. What might be possible, though, is to establish an empirical relationship between force and distance by measuring the distance moved with a few different loads, and then either graphically or mathematically relating them.

You'll need to do your own reloading and will need a chronograph, which you may already do/have. The procedure would be to, for example, set up a factory dupe load, fire it (good idea to do it several times and use the average), and then measure the distance moved (call it y), then calculate the free recoil of the load (look up "free recoil" on Wikipedia and use the "momentum short form" formula - be sure to factor in the weight of the powder charge and add the weight of your sled to that of the rifle) and call that x. Do the same thing with two or more (more is better) reduced loads and graph the results of x (in ft-lbs) vs y (in inches). If you're lucky, that relationship will form a straight line, but even if not you can still use it by drawing a smooth curve through the points.

Once you've got your line or curve, you can fire the same load with and without a muzzle brake and relate the difference in distance moved to the reduction in free recoil using your graph. Or, if you want to be more elegant, you could relate the two variables mathematically (easy if a straight line, less so if not) and calculate the difference.
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Old October 15, 2014, 08:08 AM   #5
griz
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^ Exactly what he said. You are effectively calibrating your test fixture. You'll want a range of recoil, hopefully above and below what you want to test, to get the slope of the line.
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Old October 15, 2014, 08:23 AM   #6
mehavey
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(Ignoring the static friction force req'd to break the sled into motion at start)

Work = Force X Distance
Force = Friction Resistance (once moving)

- Put the gun on the sled
- Pull the sled with the fish scale and measure the Spring Force (lbs) to keep it moving once started

RECOIL (Work) = That Spring Force (lbs) X Distance Moved (feet) when fired
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Old October 15, 2014, 08:46 AM   #7
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use a bathroom scale at the butt, pull the trigger and record the poundage on the scale
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Old October 15, 2014, 09:36 AM   #8
mehavey
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^^ That ^^ is not Work/Energy
(even if you could record it fast)
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Old October 15, 2014, 09:50 AM   #9
g.willikers
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Since there's no telling the caliber and weight of the rifle a customer might be using the brake on, for advertising purposes, why not keep it simple.
Just compare the amount the apparatus moves, both with and without the brake, as a percentage improvement.
In this case, it will be a 49% reduction.
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Old October 15, 2014, 10:00 AM   #10
mehavey
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^^^ That 2 ^^^
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Old October 15, 2014, 10:03 AM   #11
choppero
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Some thing I have done

The original sled recoiled by use of an old Rem 11 Barrel stub, mag tube and cut down recoil spring and was measured with a push on a rod and old Bridgeport quill scale. the results are


the base of the sled is secured to the bench.

I realized that the spring will have more and more counter force making the results a bit less compairable. I am sure that by maintaining a constant 50 lb weight (including rifle) it will be apples and apples. So far all rifles were 7 lb and results are:
W/O Brake W/Brake %
308 factory 180 gr 1.75 in 1.1875 in 38.3%
30/06 factory 180 gr 3. in 1.625 in 59.59%
338 factory win mag 200 gr 3.875 in 2.5625 in 40.78%

Any comments on how to improve on this sled would be helpful

Friction of nylon on delron is pretty low and should be pretty constant.

Last edited by choppero; October 15, 2014 at 11:54 AM.
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Old October 15, 2014, 10:28 AM   #12
2damnold4this
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What about mounting the rifle in some sort of ballistic pendulum? That would solve the friction problem.
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Old October 15, 2014, 11:32 AM   #13
mehavey
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I'm confused.

Does the current sled have a spring on it to resist the recoil ?

Or now no spring, and recoil resistance is purely a matter of sled friction ?
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Old October 15, 2014, 11:44 AM   #14
choppero
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No spring. Friction and Mass

Last edited by choppero; October 15, 2014 at 11:55 AM.
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Old October 15, 2014, 11:50 AM   #15
choppero
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"What about mounting the rifle in some sort of ballistic pendulum? That would solve the friction problem. "

I'm going for ease of setup. I have to discount friction as there is no way to calculate that. The sled, without weight slides very easy on its delrin plastic rails. then add 50lb and.....well I'm no engineer.
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Old October 15, 2014, 12:51 PM   #16
mehavey
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Quote:
No spring. Friction and Mass
Then straightforwardly from #6 above:

1. Put the gun on the sled
2. Pull the sled with the fish scale and measure the Spring Force (lbs) to keep it moving once started
3. Fire the rifle and measure the Distance moved from firing it.

RECOIL (Work) = That Spring Force (lbs) X Distance Moved (feet) when actually fired
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