Nerd Alert - Effect of Upward Force on Barrel and/or Quad Rail

[rraisley]

Okay, in another thread, someone mentioned, again, about drilling out the end cap on the quad rail so that it does not contact the barrel, thereby preventing the barrel being forced upward, and therefore shooting high. I got my 15-22 MOE out, mounted the rather heavy BSA 4-14x44 scope and a full mag, and proceeded to take some measurements. Well, I couldn't really measure any deflection, so the engineer in me decided to do a theoretical analysis of the deflection. I figured if I could calculate what the deflection should be, I could calculate about what kind of effect it would have.

And since I have qualified this post with the "Nerd Alert" tag, I don't mind going into detail.

My measurements indicate that on my MOE, when held by the grip, and with support on the end of the quad rail (just about 11" from the chamber end of the barrel), there was a force of 3 pounds 5 ounces, or 3.3125 pounds. If supported just behind the suppressor, there is a force of 2 pounds 10 ounces (2.625 pounds), at a distance of 15.5" from the chamber end of the barrel.

Now, the formula for angle of deflection, in radians, is:

Theta = P x L^2 / 2 / E / I

where

P = force on the barrel in pounds
L = length from fixed support (chamber) to force location, inches
E = modulus of elasticity (for steel about 30,000,000) lb/in^2
I = area moment of inertia (calculated below), in^4

For a hollow tube (our barrel) I is calculated as:

I = pi / 4 x (r2^4 - r1^4)

I measure the OD of my barrel as 0.672", and will assume the ID as 0.22" (doesn't have much of an effect, so close enough). That means r2 = 0.672 / 2 = 0.336, and r1 = 0.22 / 2 = 0.11

Calculating I, I get I = 0.009895

Okay, first taking the 2.625 pound force on the end of the barrel, the barrel angle deflection is:

Theta = 2.625 x 15.5^2 / 2 / 3e7 / 0.009895 = 0.001062 radians
= 1.062 mRAD = 3.65 MoA = 3.82" high at 100 yards.

Yup, supporting the barrel at the end like this definitely makes the gun shoot high.

Doing the same thing for supporting at the end of the quad rail results in less of an effect:

Theta = 3.3125 x 11^2 / 2 / 3e7 / 0.009895 = 0.000675 radians
= 0.675 mRAD = 2.32 MoA = 2.43" high at 100 yards.

Now, on the one hand, upward deflection of the barrel by supporting the end of the quad rail (say by a bipod) will be somewhat less than this, because the rail has strength too, resisting how far it will push upward, and if there's any clearance, that will have to be taken up before it hits. Still, a definite/possible/probable problem.

If supported by a bipod, or even your hand, I think this is a reasonable value. If you happen to pull down on the front of the rifle, holding it tighter to a bag, or on top of a bipod, you could exert a much larger force, and deflection, causing the problem to be much larger. And of course, it would vary, as your force varies. Worst case would be pulling down on the grip trying to steady the gun. Probably best to just let it rest there, not hold it down.

If you've watched those Top Shot closeups of the barrel when shooting, it's amazing how much up and down movement there is when fired. I'm not talking about recoil; I'm talking about vibration, basically, and it has to affect the accuracy some. Note those barrels /always/ move relative to the stock, never /with/ the stock.

I didn't include deflection calculations here, but I did them, and the normal weight forces indicate the barrel deflects about 0.011" when supported at the end, and 0.005" when supported at the front of the quad rail. So, it shouldn't take much clearance to be sure the rail doesn't hit the barrel when shooting.

So - comments? Corrections? I won't take any "I don't care's", because I did warn you this was a Nerd Post. ;-)

 

[DelFuego]

I knew I should have paid more attention when I took Calculus I.

 

[Guy A]

Interesting--even to a non-nerd like yrs truly.

 

[stickbug1]

I have to admit that about half way through your original post my eyes glazed over an I began to lose what little remaining brain function I have. So I skipped over a lot of it.

One thing I did want to point out to those who may be misled. The idea behind "free float" hanguards it not a matter of preventing transfer of force to the barrel, and thus moving or bending the barrel. It is about the ever elusive barrel harmonics. If you want to geek out and spend hours in theoretical probability, here is your topic. And let me reassure you that I only vaguely begin to understand the topic.

Try this for more in-depth understanding Rifle Accuracy: Barrel Harmonics Effects on Rifle Accuracy Explained
Basically every barrel has an inherent vibration cycle as the bullet travels down the bore. Things touching the barrel can both negatively and positively impact this.

rraisley - I expect to see a full analysis and write up next week

 

[Doug B]

I'm a nerd. Looks like a problem from Mechanics of Solids. Been about twenty years since I did any of that though.

Agree that a bipod or other 'upward' force could-would deflect the barrel and affect accuracy. However, if you attach a scope, and a bipod, and shoot with the same setup each time, you should be able to correct for any deflection by simply zeroing in the scope for a certain distance. There would be a slight difference in weight as the full magazine emptied. The closer the bipod is kept to the magazine, the less bending moment affect.

This discussion also assumes that your barrel nut is nice and tight.

Discussions like this make me want to dig out my Solids book and remember how to calculate and graphically depict the load-deflection-sheer diagrams.

 

[omster]

Thanks for the analysis - and it's nice to see the formulas yield somewhat real world results! I've got some experiments to try next time I'm at the range

 

[Jav]

Wow! The 'nerd alert' title did not prepare me for that post at all hahah. Well, thanks but I'd put down the lead pencil & throw some bulk lead ammo down range!

 

[rraisley]

Agree that a bipod or other 'upward' force could-would deflect the barrel and affect accuracy. However, if you attach a scope, and a bipod, and shoot with the same setup each time, you should be able to correct for any deflection by simply zeroing in the scope for a certain distance.

That is certainly true. But, although I've only shot my new gun with bipod once, so far, I'm sure I have pulled down on it, against the bipod, to some degree, and I'm sure that degree varies quite a bit. When a force of only 3 pounds can move POI 3 inches, it's no wonder that it's hard to group rounds the way we like. I'm shocked just looking at the crosshairs move so much during each heartbeat, for example. Anyhow, consistency, and removing any variables we can from the equation should definitely help. And force on the barrel, especially if it varies, is, I think, worth eliminating.

 

[rraisley]

One thing I did want to point out to those who may be misled. The idea behind "free float" hanguards it not a matter of preventing transfer of force to the barrel, and thus moving or bending the barrel. It is about the ever elusive barrel harmonics. If you want to geek out and spend hours in theoretical probability, here is your topic. And let me reassure you that I only vaguely begin to understand the topic.

Try this for more in-depth understanding Rifle Accuracy: Barrel Harmonics Effects on Rifle Accuracy Explained
Basically every barrel has an inherent vibration cycle as the bullet travels down the bore. Things touching the barrel can both negatively and positively impact this.

rraisley - I expect to see a full analysis and write up next week

I'm only a geek. It takes a super-geek to get into the vibration end of things. But this article highlights a couple things:

1) Anything touching the barrel will change the vibrations, and most definitely more vertically than horizontally, making things more unpredictable.

2) Vibration, as important as it apparently is in these calculations from the above page, are being made by a barrel that, at 1.25" or so in diameter, is over 10 times stiffer than our 15-22 barrels, so we're getting more vibration, and movement, than the target rifles (nothing new, I know).

Anyhow, thanks for listening/reading/glossing-over.

Now, if I can figure out how to remove the compensator without screwing anything else up in the process, I can get my Dremel back out. ;-)

 

[GMC man]

I'm only a geek. It takes a super-geek to get into the vibration end of things. But this article highlights a couple things:

1) Anything touching the barrel will change the vibrations, and most definitely more vertically than horizontally, making things more unpredictable.

2) Vibration, as important as it apparently is in these calculations from the above page, are being made by a barrel that, at 1.25" or so in diameter, is over 10 times stiffer than our 15-22 barrels, so we're getting more vibration, and movement, than the target rifles (nothing new, I know).

Anyhow, thanks for listening/reading/glossing-over.

Now, if I can figure out how to remove the compensator without screwing anything else up in the process, I can get my Dremel back out. ;-)

I agree I think I want to do the same to mine but I am going to watch what gunsmith I take it to..( earlier post on forum gunsmith nightmare )

 

[Gunslinger808]

And don't forget downward forces, most notable are folks that have a tight sling hold.
If you really want to get into the physics, look up hour glass profiled barrels (if you can find articles on it).
Also molecular stabilization and alignment of metal crystals through cryogenics, another good study.

 

[Lock&Load53]

Just my 2 cents worth on accuracy. After shooting paper for accuracy and tigth groups for 30+ years, I know this. Your ammunition has alot to do with your accuracy of YOUR gun.
I am not dismissing any of the information based on math in this thread. I know about harmonics, free floating barrels,etc. from experince.
All I am saying, even though the formula plays a great part in your rifles accuracy, something as simple as changing brand of ammunition, bullet weights, velocity, etc. can and will effect impact as much as free floating a barrel. It is a term known as Standard Deviation (SD) from shot to shot which sets up the vibration in the barrel to start with.
I could go on about this, but it may not even be apporiate for this thread anyway. I found the formula interesting, myself.
Just go shoot those M&P 15 22 and have fun, I sure like mine.

 

[rraisley]

You're certainly correct about ammo being a huge variable. And vibration, etc. must have a lot to do with it, because it's not so much the actual velocity difference that matters. I just calculated the difference in impact at 100 yards of a 3% change in velocity (1222 fps vs 1260), which is quite a lot, and it changed by 0.63". But sure, that's one more variable that we can't really control, outside of using more expensive ammo.

 

[roadkill45]

good calculations, although i didn't understand the most part. agree with above, everything that goes in/out/around/holds the 'gun' will affect any given aspect of shooting. removing the flash hider is easy enough, barrel block, wrench, if too tight heat (they use a dab of blue loctite from factory) I took the step drill and drilled the hole out so that it would free float w/o buying a whole new aluminum expensive already free floated front end since i did not want to put too much into a rabbit/can gun. i don't use a bipod and with the drill out the barrel def does not touch therefore letting the barrel harmonize as much as it wants.
all my predator hunting AR's are free floated AL, but i use shooting sticks, not a perm attached bipod. doesn't matter either way if the FF handguard is tight, consistent shot placement will be the same.

good ammo, good basic trigger/breathing skills, a good optic, and a FF barrel will bring you amazing results. Remember, most guns can out shoot you!

 

[porkchop]

You lost me when you wrote 'Theta'!

 

[rraisley]

My whole purpose in this was not trying to get exact about barrel deflection or any of that, but just to get a ballpark figure of how much effect force on the barrel had. If my calcs had turned out to indicate the force on the barrel ended up moving impact location at 100 yards by only a small fraction of an inch, then I'd have felt that preventing contact by the rail to the barrel didn't matter. But the effect being several inches, and more if excessive force is put on it, then yeah, I think it does matter, and should be eliminated or prevented.

 

[RolandW]

Thanks, rr. Now I can explain to my wife why, after spending all that money, I still missed that groundhog.

 

[BillyJack2012]

EXACTLY what I came up with.