Now that you mention it, I could measure bolt retractions for tight and loose holds.
Another good idea from the hive mind.
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Mass in motion has kinetic energy (K.E.), it doesn’t contain it, and can not (or be thought to) store it. The K.E. of the BCG overcomes the potential energy (P.E.) of the buffer spring, as well as the P.E. of trigger spring, as well as the inertia of the buffer, as well as the frictional forces of the sliding of the BCG inside the upper receiver, as well as the (could list more) … Then if the AR were aimed downward (upward), then gravity will be a factor, but not significantly. But, it is the near instantaneous build-up of pressure that has to overcome all the inertia of the masses being moved, along with the P.E. of the springs, and of course the frictional forces.
BTW, since v is so much smaller than c, Einstein won’t be involved.
This is a good illustration of why this sort of thing is better expressed in mathematics than in words.
But if a mass (BCG) receives kinetic energy from a transient phenomenon (gas expansion), and then later transfers energy to other parts in a way vital to functioning, I think "stores" is the most descriptive word. You mentioned flywheels, which are an excellent example.
BCG k.e. doesn't overcome the buffer spring potential, it adds to it, it is changed into it, since BCG energy decreases during the retraction part of the cycle as the BCG does work on the spring, and the spring potential increases. If these two energies were the only relevant ones, I would be using the model
k.e. + spring potential = C
.5*m*v^2 + .5*k*(retraction + installation compression)^2=C
where C is a constant. "installation compression" is the distance that we have to compress the recoil spring during installation into the RE, and the other variables have been defined in previous posts. Note that when the first term increases, the second decreases, and vice versa.
You are correct that the BCG k.e. will be transferred to many different places and forms (including into the shooters body :)), that it will increase the hammer spring potential by cocking the hammer and that it will be dissipated into frictional heats in several places.
But kinetic energy is usually not thought to "overcome" the inertia of another mass, but rather to be partly transferred into the kinetic energy of the other mass. The inertia of the other mass would be represented by m2 in the equation (for an elastic collision)
k.e. of mass 1 + k.e. of mass 2 = C
.5*m1*v1^2 + .5*m2*v2^2=C
I have been loosely referring to the BCG/buffer mass as just the BCG mass, since I am assuming that they remain in contact during the cycle. I have also been ignoring energy dissipations due to inelastic collisions of the sliding masses inside the buffer.
In my thinking I have been arbitrarily lumping these other energies into a 20% overhead, as I mentioned in post #33, mostly because they are more difficult to estimate. I don't think that this will be a problem, since I am mostly interested in the relationship of *changes* in gas port radius, buffer mass, and BCG retraction.
But it really shouldn't be hard to roughly estimate hammer cocking energy, so I'll do it.
ETA: [It takes an average of about 4 pounds of force on the tip of the hammer to cock it, and the hammer tip moves about 1.5 in. during cocking. This gives a hammer cocking energy of 6 in.lbs, higher than I thought it would be. I am neglecting energy dissipated by friction and hammer bounce (if any).]
I'm glad that people are thinking about this stuff.
Well said, I was being facetious in my "relativistic" comment.
We are getting a bit off track here, and I'm sure the discussions of basic physics and engineering philosophy are trying the patience of many readers. I'm going to reduce posting until I have hard retraction data to present (should be a few weeks).
I'm an engineer so I can say engineers suck. I am just kidding though and do appreciate your efforts. There is usually a huge difference in the shop guy and the engineer guy but I am both unfortunately.
I have something similar to your rig. I built a pneumatic AR. all the problems I encountered ended up making me sensor the end points for travel. The next time I rebuild it I feel like using a PLC.
*If the term for Dwell is used for barrel length after port then what do you call the straight area of the carrier that dwells before action. I wish that was ironed out because I now have corrected someone for using could have been the correct terminology.
A useful tool from this I hope can be pulled together one day, but it is basically an open source application run by the old phone like the android OS. It would take lots of time and inputs to make it useful but I would like to see a "heath meter" out of it, it would almost need a proximity for rearward travel, and ofcourse a few variables should be input including ammo and everything else. If all variables were input correctly it should be able to determine if the weapon is as "reliable" as it could be.
The stroke travel is pretty interesting, more than anything I think the world improperly diagnoses the magazine as the failure too often, is it the magazines fault if it didn't stroke and give enough time for the round to be in the pickup position? If you find a finicky magazine and it is working in other weapons, do you have a timing issue with the interaction of the two because of stroking difficulties? If so what is to blame.
I'm interested in magazine timing too. I've been doing some work on the time interval between next round release on the rear-moving part of the cycle (when the bolt lugs release the case head) and round pickup on the forward moving part. I call it the follwer rise time (FRT).
A BCG/buffer that has excess initial velocity and so bounces off of the rear wall of the receiver extension, say with 10% of its original energy or 30% of the original velocity, significantly reduces this interval. I assume that the bounce preserves 20% of energy or 45% of velocity. Here are the results of a simple Euler integration of some stripped down equations of motion:
BCG just kisses rear wall of RE: FRT = 28ms
BCG hits rear wall with 10% energy: FRT = 18ms
But if you look into the ejection port while manually retracting the BCG, you can see that the next round doesn't pop up much when the bolt lugs release it. The main part of the "pop up" is when the round leaves the magazine during feeding.
rounds only feed to the bottom flat portion on the carrier after the rounds above are stripped from the mag, then upon rearward motion, the bolt drags and releases from the top of the cartridge at the rear rim, then the cartridges head nose up but with a good mag they will level out a bit before hitting the lips, but generally the front portion of the cartridge hits the lips first.
I've always viewed the system in simple terms of a closed constant potential and kinetic after separation, variables of mass and spring constant disregarding gravity. Supersonic and choking conditions are great study but high speed video is your friend in those regards. Your frame rate has to be freaking amazing, like 10k/sec minimum.
I would work until you have the old schools agreeing with the outputs, not necessarily the parameters for models/equations. Equations are not something most people know even how to plug in variables. They are not stupid by any means and have more knowledge than imaginable but just in a different format accessed by a different vocabulary.
It may have already been said, but I'll mention it now just to be sure.
I am fairly certain that the frictional forces applied to the bottom of the bolt carrier group during recoil by the round stack in the magazine are not the same when the magazine is fully loaded as opposed to when it is nearly empty (30 rounds versus maybe 5 rounds).
SS, this may be worth measuring as well. I have seen cyclic rate tests done where the cyclic rate seems to rise as the magazine empties when the gun is fired full auto. I'm guessing that this could be caused by reduced friction from less pressure supplied by the round stack in the magazine.
Also the rate at which the friction decreases may or may not be linear.
Food for thought. Great thread, btw.
BufordTJustice,
truest thing ever written, that is why all analysis should take this into account, even the videos showing bolt bounce are greatly influenced by this, it really gets different on monster magazines.
there is only so much force an AR can use to strip the round from the mag so the force has an upper limit.
Wrong.
K + U = C
1/2m(v^2) + 1/2k(x^2) = C
C equals initial state conditions. Since v is zero, K(initial) is zero. If the spring were in an uncompressed or non-stretched state, U(initial) would be zero, and C would equal zero. This is not the case.
Therefore C would equal 1/2k[x(initial state)^2].
This is from the conservation of mechanical energy.
Also, you can’t combine an initial state position with a final state position, as in
[x(i) + x(f)]^2.
Seriously, one last time, then you are on your own; KE is dependent on velocity, if mass is constant (non-relativistic), so how is velocity stored in the mass?