Force plate acceleration measurement

[PercyShelley]

Inspired by the box o' truth website and a thread here earlier, I have decided that I want to objectively test the recoil of various rifles, and perhaps at some later date see what the effects of muzzle brakes and soforth on rifle recoil are.

Leaving aside issues of stock shape on perceived recoil, this will be a fairly simple exercise. All I need is the right equipment.

Recoil is a fluctuating level of force sustained over a period of time. This fluctuation can be measured by certain equipment, and then represented graphically as the curve of force over time, the integral of which would be the total momentum imparted by the bullet and gases exiting the rifle.

The tool required to measure this is a force sensor or force plate. The guts of such a thing are a piezoelectric cell which is compressed by the system exerting the force. Multi-axis models are used for monitoring athletic performance and industrial equipment, but a single axis model will suffice here, as recoil is primarily a straight-line phenomenon.

Right now, I just need to figure out which model of force sensor to use. Back in High School we used Vernier brand force plates; which are simple and intuitive to use, and interface with TI-brand calculators. The only problem with using Vernier in this experiment is that their sensors are complete and utter garbage, and will lack the necessary fidelity, range and reliability to complete the tests.

So, I'm looking at other brands, and I really have no idea what would be suitable. Futek? Kistler? Bertek? What brand is good? I'm also at something of a loss as to how to interpret the model parameters given at these manufacturers websites.

Back of the envelope calculation: a .30-06 with a high-pressure 180 gr loading will produce just short of 10 newton-seconds of recoil from bullet mass alone. Gas recoil will drive that up significantly. A .22 lr will produce less than a tenth of that.

Since the .30-06 has a muzzle velocity of 878 m/s, its average velocity in the muzzle is on the order of 439 m/s (assuming uniform acceleration, which I know isn't the case, but this is just preliminary work), meaning it will clear a 24 inch barrel in no less than .0013 of a second. Peak recoil of a .30-06 could well exceed 7 kilonewtons based on those numbers!

Therefore, I need a single-axis force sensor sensitive to thousandths of a second which can accurately measure forces from under a kilonewton to well over twenty. Finally, I need a brand that can somehow be interfaced with a windows computer or a TI calculator.

Again, Vernier force plates would be perfect if they weren't such outstanding garbage.

Anyone in manufacturing who knows of something along these lines?

 

[Fast Frank]

I don't have any idea about getting sensors, but I thought I would mention that your measuring rig needs to simulate the "Give" in a shooter's shoulder.

Attempting to measure recoil with the sensor attached to a fixed object will produce higher force rates for shorter times.

I know this because I witnessed a kid that put a 12GA against the concrete of a bridge and pulled the trigger. It broke the stock.

Figuring out how much weight and drag to use so that the sensor will move about the same distance as the shooter's shoulder might prove to be in an interesting experiment of it's own.

 

[fletcher]

What kind of price range are you looking for?

Figuring out how much weight and drag to use so that the sensor will move about the same distance as the shooter's shoulder might prove to be in an interesting experiment of it's own.

A good chunk of rubber should suffice.

 

[Smitty in CT]

http://www.shootingsoftware.com/recoil.htm

 

[boilingleadbath]

Looking at the 30-06 situation:
11 gram bullet
4 grams powder
2500 gram gun (with 20" long bore)

We find that the gun has moved backwards about .104" while the projectile is in the barrel, calculations performed by assuming the center of mass of the system is stationary. (assumes the gases are distributed equally along the bore - probably not quite true)

We might assume that just about all the gas has left the bore in a millisecond... and at that time the gun should have moved less than .28"

That's not a very large distance, so it may be a fair enough approximation if you just make a ballistic pendulum of the gun... hang it from some ropes and let it swing.
Although it might give you less interesting data.
************************

Alternatively, mount the force plate between the recoil pad and the rest of the stock, and fire it normally... lets you use a plate with a lower max force.

 

[Jimmy Newman]

One thing to note is that your force plate will need an exceptionally high sample rate to get any kind of useful data (read, an expensive one).

Also, I think you would want the butt directly against the force plate. If you put rubber or something in between, the gun will still exert the same amount of force but the cushion will act to "smooth it out" and you won't get an actual reading of the force that the gun exerts on the shoulder.

Interpretation of how that force acts on the shoulder is tough/complicated, but just sticking some rubber in front will give you skewed numbers that may or may not really have anything to do with what you're looking for.

 

[SprayAndPray]

The first thing that came to mind was a heavy (maybe 10 kilos or 20 or more?) sled in which you mount the rifle, the tracks can be slightly angled, then just measure how far it moves up the tracks. Sensor somewhere in between sled and rifle.

 

[Owen]

if you could find a way to mount the gun so it could move freely, you could mount a piezo accelerometer, and get free recoil velocity indirectly.

Once you have the free recoil velocity curve, you can get the momentum of the rifle. If you have the momentum of the rifle, you can determine the velocity of the bullet at any point in the barrel (momentum = 0), and you can generate a force curve.

momentum=impulse

mv=ft

Kaman Aerospace makes these really neat linear bearings...

 

[PercyShelley]

Was Kaman the company that made the helicopter with twin intermeshing rotors?

That's not a bad idea; although one could accomplish something similar by progressively chopping the barrel down and recording the difference in velocity with a chronometer if I read you correctly.

Would get sketchy with rifle cartridges down in the 3'' barrel lengths or less though.

Can anyone raise any methodological objections to simply wedging the force plate between my shoulder and the butt of the rifle, as boilingleadbath and others have suggested, aside from the fact that I won't have the same mass or mass distribution as other shooters?

Really, if measuring the precise force/time curve is too technically challenging, then I might as well look into a methodology that will give a set of measurements that aren't uniform with other measurements, but are at least internally consistent and comparable. Ballistic coefficients, for example, are based off a large series of arbitrary standard atmospheric conditions, fixed velocities and standard projectiles, but the end result is a useful number that you can compare to other ballistic coefficients and derive useful load and bullet flight data from.

 

[Dave P]

aside from the fact that I won't have the same mass or mass distribution as other shooters?

This method is full of big variables, namely how tight you pull it in, and how much force your shoulder is applying. What are you really wanting to know?

QuickLoad is a great internal ballistics calculator that also gives you recoil values.

 

[jrfoxx]

couldnt you just put the force plate between he butt of the ifle, and your shoulder? might be a little uncomfortable, but it will eliminate trying to simulate a shooter, and you get the fun of firing the gun...just a thought, I know nothing about force plates.

 

[Owen]

Yes, Kaman makes the Port/Starboard intermeshing helicopters

http://www.kamanaero.com/helicopters/kmax.html

The thing you are going to have to watch for is the sampling rate. the recoil peak is very, very short, on the order 1 millisecond. You are going to want a sample rate at least twice that, and preferably 10 times that. If the forceplate you use has a 1millisecond sample rate, you are going to have to shoot multiple times to ID the peak, and you'll never be sure if you actually caught it.

Second, don't get stuck on "force plate" terminology. A force plate is simply a couple of load cell held in a frame, with some built in amplifiers and such.

I wonder how hard it would be to use an aftermarket, slip on, buttplate as a receiver for you loadcells/forceplate?

 

[PercyShelley]

I wonder how hard it would be to use an aftermarket, slip on, buttplate as a receiver for you loadcells/forceplate?

Assuming I could get a suitable power supply next to it slicklike, and a suitable data recorder or cable attached unobtrusively as well, that would be a very good setup.