Upper Receiver Flex Testing - Part Two

[jmart]

From a purely theoretical point of view, it should be relatively trivial to determine flexure based on the numbers already posted. Torque is Torque and torque generated by a force perpendicular to the axis is the same as torque generated by a VHG...the amount of force required by the VHG will just be different. It's been a few (read: 15) years since I took my engineering statics class, but once I pull out the old books, I'll post a result.

Considering a VFG, how much of the force vector is perpendicular to the HG (deflection/torque) vs how much is along the axis of the fore end (compression)? When I think of a VFG, I think of the user pulling back against it to get the butt solidly positioned in the user's shoulder. Only a small fraction is used to pull down to combat muzzle rise. Same thing with a NM sling on a Service Rifle -- the shooter is looped up and the force of the sling, attached to the upper arm, is primarily pulling the weapon in tight into the user's shoulder. This force is applied more "along axis", in compression, rather than in a perpendicular direction to the handguard.

[edhresko]

Considering a VFG, how much of the force vector is perpendicular to the HG (deflection/torque) vs how much is along the axis of the fore end (compression)? When I think of a VFG, I think of the user pulling back against it to get the butt solidly positioned in the user's shoulder. Only a small fraction is used to pull down to combat muzzle rise. Same thing with a NM sling on a Service Rifle -- the shooter is looped up and the force of the sling, attached to the upper arm, is primarily pulling the weapon in tight into the user's shoulder. This force is applied more "along axis", in compression, rather than in a perpendicular direction to the handguard.

Correct, but the thing to remember is that any weight or pressure (depending on where you're doing the measuring) will generate both a force and a moment. A moment is essentially torque. A moment will be generated for any force that's not in line with the point being measured.

Keep in mind that these calculations are not meant to be something you could design around to determine failure points. It's really more just to get a rough (within 10%) idea of the types of forces on a VFG you'd need to get an amount of flex similar to the experiment KL did.

A few simplifications need to be made to do this in any simple matter, and since it's been years since I've taken calculus, simple = good.

Simplifications:
1) The barrel and handguards are massless. Otherwise, we'd need to weigh them and determine their CG.
2) The barrel and handguards are rigid. While this is obviously not true, taking into account the deformation of the handguards would increase the complexity of the calculations quite a bit, and really would make very little difference. Probably less than 5% difference.

First, to determine the forces and moments, we need to simplify the gun a bit. Since we're measuring from the barrel nut, we can simplify it to a cantilevered beam with the nut fixed and the muzzle hanging out in space.

Now, for the example that KL ran, there will be a moment (i.e. torque) and a shearing force. The shearing force will the same as the weight that was used, since we're considering the assembly massless.

For the torque, M =Force * Distance

so for the 20 lb example,
M = 20 * 7.5" = 150 inch-lbs

So now we want to find out how much force on a VFG will have the same amount of flex. Again, we'll simplify and assume that all the force is pulling back.

I made a few measurements, and my TangoDown VFG is 4.5" from the centerline of the bore. So with a 4.5" moment arm,

M= Force * Distance

150 = Force * 4.5
Force = 150/4.5
Force = 33 1/3 lbs

In general, with a 4.5" VFG, It should take about 1 2/3 times the force parallel to the bore axis.

However, in real life, the person shooting the gun doesn't apply all the force at the end, but closer to the middle or even the top of the VFG. If the pressure was applied all parallel to the bore at 2" down, then the force would be around
75 lbs!

Again, this is a simplification, but I think if KL were to do the experiment, he'd find numbers that were similar (but not exactly equal) to these calculations.

Also, if anyone out there can find a major fault in my logic, I'd like to hear it. I haven't done any static equiliberium calculations in a long, long time...

[bigbore]

seems more posts are being deleted here as often as arfcom. I wait a minute for the page to load only to see its no longer here?

[Thors ~ Hammer]

seems more posts are being deleted here as often as arfcom. I wait a minute for the page to load only to see its no longer here?

Trolling and personal attacks will not be allowed. If that means I delete posts to keep the thread on track well thats whats going to happen.

I'll say it again please keep this on topic.

[Nitrox]

Trolling and personal attacks will not be allowed. If that means I delete posts to keep the thread on track well thats whats going to happen.

I'll say it again please keep this on topic.

If you're deleting off topic posts then why leave all the off topic reminders?

[STAFF]

When posts go off topic with either personal attacks and or innacurate information, we have two options. We can leave the posts as is and then the entire thread as a whole does down hill. The other option is to correct the few posts that are out of line and salvage the discussion as best we can.

We know that people don't like to have their comments removed, but if they stayed on topic and saved the personal attacks for offline, we wouldn't have to do anything.

Other forums suffer from constant bickering, name calling and personal attacks. These things do not add to a technical discussion in any way and is why we do not permit it to happen here.

[KevinB]

I did the edit and cut's -- IF you have issues with this method please PM me and we can discuss this rather than derail a good thread.

[K.L. Davis]

Again, this is a simplification, but I think if KL were to do the experiment, he'd find numbers that were similar (but not exactly equal) to these calculations.

My tests were not as "scientific"... we made a scale sort of thing and simply had guys shoulder and stress the rifle with the rear pin out

If you would like to discuss it off line, I would be happy to... but as stated, for all intents and purposes, this test and the thread are over -- I have asked the staff to lock it.