Most accurate length and barrel contour

[Lemonaid]

I came across this article at the Lilja website about rigidity. It may be of use in selecting your next barrel.
An Ar may have even more problems with long heavy barrels than other platforms due to the short amount of barrel in the receiver.
There is the trade off between velocity of a longer barrel and it's rigidity as pointed out in the article.
Using the formulas in the article someone with better math skills and inclination than me should be able to get a petty good idea of ideal barrel length, diameter and contour.
I would very much like to hear any empirical evidence the hoard might have, I know there are some pretty accurate short barreled rifles out there.

https://riflebarrels.com/a-look-at-the-rigidity-of-benchrest-barrels/

[grayfox]

Reading it now.
My question, that has rattled around in my head for a while, is related to whether there is a point of diminishing returns for an OBT calculation (barrel length and MV vs nodes) compared to overall length of a (not-skinny contour) medium to heavy but useable barrel.
Part of me wants to say that if the barrel gets below x inches in length, or "short enough" (whatever that means) for say at least 0.700" nominal muzzle diameters, maybe the OBT calcs don't have much bearing and you only need to shoot for the best group... maybe barrel whip/harmonics is all you need.
This could be possible if stiffness becomes the controlling factor in muzzle position at bullet exit, rather than longitudinal pressure wave.
If this makes any sense.
Anyway, not trying to distract from the thread, but maybe these 2 thoughts are related. I don't know. Just thinking.

[grayfox]

Do we know how "un-stiff" is still a very good barrel? ie, there are practical limits - unlimited stiffness is not necessary to be a good barrel... or?

[grayfox]

One advantage an AR or any "straight back barrel-to-shoulder" rifle is that the vertical torque could be lower since the thrust axis is closer to 'centerline of the stock' (probably more accurate is 'center of gravity of the rifle system'...?).

[Lemonaid]

Do we know how "un-stiff" is still a very good barrel? ie, there are practical limits - unlimited stiffness is not necessary to be a good barrel... or?

Excellent question, I was wondering that as well. If I understood the article, the calculated muzzle deflection should tell how far the bullet will travel vertically, total of - to + in the vibration. You should be able to calculate how much that would translate to at 100 yards. That should give you the worst case accuracy due to the barrel stiffness/elasticity. I would think it would be something like: Long pencil thin barrel 2 inch spread, very stiff short barrel 3/4 inch spread.
In both cases tuning the load can get much better accuracy but the short stiff barrel starts out a lot better.
I'll look at the formulas and see If I can give some calculated examples.

EDIT: MATH Guru's Help! This is what I calculated but must be wrong. Deflection in inches x 12 (1 foot) x 300 feet (100 yards)

Max heavy varmint blank 18 inch .00509 x 12 x 300 = 18.3
Light varmint 23.88 inch .01879 x 12 x 300 = 67.64

If the decimal is moved one place left it would make more sense, 1.83 inches vs. 6.76 inches

[grayfox]

I've done a lot of those projections, basically look at it as a rt triangle, where angle x is very very small.
for very small angles, sin x = x.
sin x=opp (the deflection)/hypotenuse (L).

So vertical deflection =L*sin x, or L*x at 24" (I have a 24" barrel).

But we already know the "sides" of the barrel-triangle... the vertical is 0.0012" for a 24" (rounded up) barrel.

If I got this correct, so 24" barrel, deflection of 0.0012" (rounding up for a 24" barrel) for his 5 lb 4 oz barrel and 1 lb weight deflection, (all of which does not reflect, I think, the actual barrel condition at the shot, but anyway...)

Or, 0.0006"/ft travel. Total displacement across 100 yds, or 300 ft, would be proportional.

Deflection (1-way) at 300 ft = 0.0006*300 = 0.18".
For the 2-way deflection it would be 2x, or 0.36", and I would assume ctc.

Of course, we don't know if our real barrel has a 1-lb "weight" for the deflection/torque, and we don't have his exact barrel dimensions on our rifle, so ours might behave differently.