Projectile stability, rate of spin, and distance

[Colorado Redneck]

A 22-250 I shot a lot, was perfectly accurate using Hornady 55 gr. spire points. The velocity was about 3600 ft./s. BUT! They were great at 100 yards, but at 250 yds. the groups were scattered, as big as 6-7 inches. I changed scopes, no improvement. I was talking to a gun shop guy I trust a lot, and mentioned that I was thinking of getting rid of the gun and he suggested trying a different bullet. I went to 50 gr. Vmax and the groups at both distances improved a lot. Then with 40 gr. Sierra BK', the groups got even better and more consistent. That round has been excellent for grass rats over 300 yards many many times.

The question this raises in my feeble mind is, as the bullet travels down range, does the rate of spin slow significantly? Just because velocity decreases, I assumed (ASS-umed) spin rate would too.

What do you guys think?

 

[Unclenick]

It slows, but not as fast as forward velocity. If you launched the bullet with marginal stability in the first place, it takes distance for it to start spreading out, and that's what you saw. Not losing spin rate as fast as forward velocity was not enough to make up for that with the marginally stable bullet.

The reason spin doesn't slow as quickly as forward velocity is the rotational surface velocity of the bullet isn't as fast as the forward velocity, so there is less fluid friction to slow it down. The rifling engraving has negligible effect, as it is shallower than the air boundary layer at the surface of the bullet.

An approximating formula Geoffery Kolbe published for spin decay is:

Where:
Nm = the spin rate the bullet had at the muzzle
N = the spin rate of the bullet after your time of flight to the range of interest
t = time of flight in seconds from the muzzle to the current bullet position
d = bullet diameter in inches
e = natural logarithm base, 2.71828…

N = Nm × (-0.035 × t / d)^e

 

[Colorado Redneck]

Thanks for the explanation, Unclenick. The math formula is over my simple mind.

 

[dahermit]

A 22-250 I shot a lot, was perfectly accurate using Hornady 55 gr. spire points. The velocity was about 3600 ft./s. BUT! They were great at 100 yards, but at 250 yds. the groups were scattered, as big as 6-7 inches. I changed scopes, no improvement. I was talking to a gun shop guy I trust a lot, and mentioned that I was thinking of getting rid of the gun and he suggested trying a different bullet. I went to 50 gr. Vmax and the groups at both distances improved a lot. Then with 40 gr. Sierra BK', the groups got even better and more consistent. That round has been excellent for grass rats over 300 yards many many times.

Barrel shot out?

 

[Colorado Redneck]

Barrel shot out?

It is now. Replaced it with a Criterion a few months ago. 9 twist and it shoots 53 g, V-max lights out.

When using the 55 Hornady Sp. Pts the gun was still fairly new to me. I probably shot 900-1000 of those bullets as they were given to me. Was having a hell of a time hitting p. dogs out at distance. Finally took it to the range and eventually figured out the issue---wrong bullets for that gun. After that it was probably another 1500 or so rounds before it started to act like the barrel was going. Last spring it was still getting the rats over 350 yds but missing more as time went on. Took it to the range one last time and it was gone. I don't know haw many rounds down the tube, but it was used when I got it.

 

[Bart B.]

Unclenick, regarding:

N = Nm × (-0.035 × t / d)^e

I assume spin rate (Nm) is in rpm's and time of flight (t) is in seconds; the norm for stating such parameters. And "^e" is ^2.71828… in a spreadsheet formula?

Right?

There's other on line references to Kolbe's formula saying it's:

N = Nm exp(-0.035 t / d)

In Googling the 'net for Kolbe's stuff, I found this most interesting site:

http://www.geoffrey-kolbe.com/external_ballistics.htm

 

[rkittine]

With a 1:9 twist you might do better with a heavier projectile as the faster twist will stabilize it, where some of the lighter projectiles will come apart at distance with the faster twist. Part will depend on how much free bore you have.

Bob

 

[Unclenick]

Bart,

Yes. TOF is in seconds. I'll go back and add that into the original post.

Since the formula just produces a multiplying factor for the spin rate at the muzzle to get the spin rate after the TOF, the unit of spin can be rpm, rps, angular velocity, ω, in radians/s, or whatever else you want to use. You just have to realize the result will be in those same units, whatever they are.

For Excel, actually the easier thing is to use the older exp() notation for e as an exponent. In Excel the calculating cell could then be written:

=Nm*exp(-0.035*t/d)

Excel reads that just fine and you don't have to remember a value for e, as it's built into Excel to (IIRC) 14 decimal places.

The reference is: Geoffery Kolbe, A Ballistics Handbook (Scotland, Pisces Press, 2000, ISBN 0-9537537-0-0), P. 808.

That small book (the page number's first digit is the chapter number and not the actual number of pages in the book up to that point) is full of useful formulae and explanations and various bits and pieces.

Thanks for the link to Kolbe's site. I wasn't aware of it. The stability formula he uses is the one in the Handbook. I've tried to put that formula in Excel before. Kolbe said it's reverse engineered from some software written by Robert McCoy, but a typo of some kind, his or mine, was messing it up and I never got back to it. Nice to see it someplace I can use it.

 

[Colorado Redneck]

Rkitine--Thanks for the suggestion.

So far the 53 grainers have worked like magic. And with the fast twist they literally blow sod poodles to smithereens. Only pushing about 3650-3700 fps. The guy that sold me the barrel talked me into the 9 twist, just for this reason. They didn't have a 12 twist in stock, and I wanted a new tube pronto, so I listened to him, and glad I did. Got it from Northern Shooters Supply, and Jim helped me with the decisions on tools to remove/install and talked to me while I was setting the headspace when installing. Great guy.

I may try longer bullets in the future---only had the tube for a few months. But the way it has performed so far, am satisfied.

 

[Bart B.]

Unclenick, thanks for the info.

Kolbe's software on barrel whipping using finite elements is the first I've seen on line that takes into consideration how the action and stock position and weights effect the barrel's whip frequency and direction. Using Quickload to determine barrel time, one can get a decent idea what's the angle a bullet leaves at on the muzzle whip axis of their rifle barrel.

His formula uses the bore diameter which means small caliber ones with the same outside profile will be stiffer than large caliber ones. A given barrel profile and caliber cartridge based on a .308 Win case will be stiffer than if the cartridge is based on a .338 Lapua Mag case. Less metal is removed at the breech, both in length and diameter. Thinner and longer chamber walls means the barrel's less rigid in that area.