I'll admit that I've only glanced over the OP's conversions (non-SI units make my eyes bleed).  That being said, slugs are a unit of mass, analogous to kg, and are actually in base units of (lb*s^2/ft).  Pounds are a unit of force (e.g., weight), analogous to Newtons.  There are a couple of unholy units (lbm and kgf) that go the other way, but they are almost never used.

Step up 10 bucks for a better controller or dedicated ADC?

The bigger issue is building a full bridge strain gauge circuit in the 1st place, instead of just tapping a pressure transducer. Or hell, even just tapping 2-3 check valved pressure gauges. Any measurement loss can easily be calculated... well, easier for some folks.  and no electronics, circuits, or code to mess up.

That's why this thread has gone as long as it has. OP thinks you can divide twice to get acceleration or that the cubic root of a volume is just one of the original length measurements.  Lots of wtf conversions.  

I'm thinking that's the better plan.  He can't build a true active full bridge circuit anyway: you need 2 gauges in equal compression and 2 in equal tension for that to work, at each axial location on the barrel.  He could throw some dummy gages on there to complete the bridge (making it half-active), but he may as well use fixed resistors at that point.

I didnt have the heart to tell him it would take 20 strain gauges to measure 4 unique points along the barrel if building full bridge circuits. So I went with "just do the math,"  but that didnt work out so well either.

Actually, you cannot easily build a full bridge circuit when you do not have anything in compression.  Everything will be pretty much in tension.  The temperature can be compensated easily by putting everything near the barrel.  In fact the whole apparatus will be in the same room.

To balance the bridges (which is what I would do before starting, since I don't like to rely on code to do this) I would have one variable resistor, two fixed, and the gauge for each.  To amplify the signal, requires an op-amp.  I am in the process of trying to decide on which one would be best for the ADQ chip I found.   I don't care if the signal is linear or not, since I would calibrate the output with the known input.  I would then do a best fit equation in a spread sheet.

If I were bending a bar, then the full bridge would be much better as there would be more signal.  But, I am not bending a bar, I am expanding a tube radially, and slightly compressing it linearly due to Poisson's ratio.  But this compression will be offset just a little by the resistance of the projectile putting the tube in a little bit of tension. If the tube were capped, then there would be significant tension.

Now, I suppose using two gauges at 180 degrees may help give a better signal, and I may wind up doing that.

Do you know the parameters you want for your barrel yet?  I ran some rough numbers on page 1- you may want to try estimating what sort of microstrain you expect the gages to experience and see how that meshes with the precision of the rest of your electronic setup (amplifier, voltage source, ADC, etc.)  It's a good first-order check of what you'll be able to resolve with your measurements.

The "barrel" is a piece of A-513 DOM tubing that is a nominal .380" I.D. and .625 O.D.  I have a stick left over from another project that is 45" long.

I ran the strain numbers once, but I cannot seem to find those notes.  However, I seem to recall that the maximum strain would be about .0008 at 4000 psi.

If I could get a resolution of 10 atm (~150 psi) I would be elated.  Even 15 atm (225 psi) would be more than adequate.  But, the 12 bit resolution might get me quite a bit better than that.

ETA:  I found an online calculator for stress in the tube.  I also found a reference for Young's Modulus which is stress/strain.  Using what I found gives me a strain of about 1.62 x 10^-4 or 162 micro-strain.

The calculator gave me a hoop stress of 4716 psi while the reference for Young's Modulus was 29 x 10⁶ psi.

If I can get a the strain gauge DAQ to differentiate between 10 micro-strain, then that would be about 250 psi increments (though it may well not be linear).  That would be good enough for this purpose.

Using those numbers for the tube, I'm calculating about 180 microstrain at 4000 psi.  FWIW, this also gives a hoop stress WAY below the yield strength on that tube.

As for the ADC, resolution is one thing, repeatability and the noise floor are another.  You can easily (depending on the setup) have multiple LSBs of pure trash being read in.  Having a good amplifier circuit close to the gages will help.  I would recommend digging up one of the specialty low-noise, instrumentation Op-amps designed for bridge measurements.  Couple of bucks on Digikey.

High speed 'One shot' measurements are the nightmare of Analog to Digital Conversion (ADC).
A huge amount of time the 'pulse shape' ends up being determined by the amplifier chain from teh sensor to the ADC.

You can get huge resolutions with repeated measurements at slow sample rates.
A single event measurements at a high sample rate?

How much money do you want to spend?

The bottom bits of all the 'high resolution' ADCs are noise.
Multiple runs let you store it and use Digital Signal Processing (DSP) to average it out.

If you are really smart you can even lear how dither signals and 'Out of Band 'noise injection work.
But again.
Only if you can take multiple measurements of the SAME pulse.

Even running multiple converters in parallel does not work.
Each converter has this nasty thing called 'aperture uncertainty' about WHEN the measurement is taken.

And the uncertainty varies with so many parameters it cannot be determined.

 

As little as possible.  However, $150 would be about my maximum spending limit.  



I gathered that from my initial investigation, which is why I posted the question.  I was hoping that someone would have a "quick and dirty" solution.

I really wish there were an easy way to do the thing strictly analog.  If it were a relatively slow process it would be rather easy.  But, the speed  requires much more involved stuff.

One way to (maybe) do  this with strictly analog equipment is with four old fashioned (non storage) analog oscilloscopes and a very high speed movie camera.  A chart recorder would be way too slow.

A decent rented digital sampling scope will easily measure the pulses and the time between them.
Most have at least two channels and rigging something to just put both pulses on a single channel is easy.
All you have to do is make sure they are large enough to see on the scope.

Any decent high speed scope has more than enough sampling and vertical amp bandwidth.

A 'scope card' in a PC is unlikely to work though.

Yeah, but where to rent such a scope: that is a bit of a problem around here.  The nearest large city is Salt Lake City, UT and it is about a 2.5 hour drive one way from here.

UPS.

Electrorent is the big gun but often has smaller portable 'field' units available for not all that much daily.

ElectroRents isn't cheap in any way that I have ever experienced.

A good 4CH DPO scope with this kind of capability is one way around all the fuss of designing and building your own circuits, but I am thinking they would blow through your budget real fast. They take a big chunk of change out of us for everything we do and we have large accounts with them. No reason not to look into it, but borrowing one from a HAM or other hobbyist may be a better route.

There are plenty of other smaller rental places.
ER has everything but it is often new and expensive stuff.

Bandwidth is the problem.
You need a lot more than a cheap audio scope.

The cheaper the scope the better your dedicated amplifier chain will need to be.