BULLET STABILITY AND OPTIMUM SPIN RATE

[Trace]

There is an old thread in rec.guns by Steve Faber with contribution from Bart Bobbitt which says that the important thing for accuracy is each bullet needs to be spun in the narrow RPM range for that bullet.

Too slow, the bullet won't stabilise. Too fast, the nose won't follow the arcing trajectory.

Bart offered this formula:
MV x 720
--------------- = RPM
Twist in inches

He also gave a list of min and max spin rates for .308 SMK's, e.g., the 190SMK, 160000 to 190000.

If this is correct, it is possible to calculate optimum Twist for a given MV and MV for a Twist.

Sierra's test barrel for the 300 WIN MAG was 24" and had a 1:10 twist. So, if Bart's formula and spin rates are applied, the minimum accurate MV for the 190SMK in that barrel would be 2222 and the maximum 2639.

Sierra's "Accuracy Load" is 2900!

My questions are:
1. Is Bart's formula valid?
2. What is current position on the relationship,s) between twist, MV, spin rates and accurate stability?

Trace.
17.04.08

 

[Bryan Litz Ballistics]

Don Miller has created and published a simple, and surprisingly accurate formula for twist rate in Precision Shooting.

The equation is:

S =,30*m)/,t^2*d^3*L*,1+L^2))

S is the gyroscopic stability factor. This is the measure of static stability and 1.4 is the minimal,optimal) value.

m is the bullet weight in grains

t is the twist rate in calibers per turn,for example, a 1:13" twist .308 barrel has t = 13/.308 = 42.2 calibers per turn.

d is the bullet diameter

L is the bullet length in calibers.

This equation is very accurate for a wide range of bullets, velocities and twists. There are corrections for non-standard atmosphere and velocity corrections,the equation is built around MV = 2800 fps). The effect of different muzzle velocity is not as important to stability as most people think.

Anyway, that's the equation I use, exclusively, for calculating static stability. Don's really given us a gem.

Take care,
-Bryan

 

[CPorter]

Spin rates for the 190 SMK can be higher than optimum and still maintain accuracy. What happens is the more the bullet's center of gravity is offset from the center of rotation then the more the faster RPMs will hurt accuracy. Sierra's bullets are pretty good so the offset is usually small and the bullet still shoots well. On the lower side of the equation the bullet will yaw severely if the RPMs are to low and the effect is much more noticeable than the one from having more RPMs than necessary

 

[Trace]

Bryan.

Thank you.
My problem is that I am not familiar with keyboard characters used for mathematical symbols. I would be grateful if you would provide the source of this "code".

Trace

 

[Bryan Litz Ballistics]

Trace,
Send me an email: bsl135@yahoo.com and I'll reply with an excel spreadsheet attached with the equation in it.

Donovan,
In theory, the 1.49 gyroscopic stability factor is best. HOWEVER, there is such a small variation from 1.49 to 1.59 that it's very unlikely you'll see a difference in accuracy due to the barrel twist for your example. As Cporter said above, bullets are balanced pretty good, and dispersion doesn't suffer significantly by going a little over Sg=1.4. If you had a combination that exceeded Sg=2, then it might be worth thinking about going to a little slower twist.
Typically, I use Sg as the variable to identify gyroscopic stability. I was inconsistent in my post above when I used 'S'. I was transcribing directly from Don's PS article which uses 'S'.

Take care,
-Bryan

 

[Trace]

Bryan.

I love it when it's simple! But then I seem to complicate it.
The equation assumes a MV of 2800.
The best SG is 1.49.
How much extra SG should be allowed if MV is, say, 2600?

Trace.

 

[Bryan Litz Ballistics]

Trace,
I'm emailing you a modified spreadsheet that includes the effects of velocity,other than 2800 fps) and atmosphere.
I left these out initially because, as you'll see, the effects aren't that drastic. I guess it's good to be able to confirm though.
One note about using Don's twist rule:
Like most formulas in ballistics, this is an approximation. It's intended for use as a guideline to make decisions not to split hairs with. I mean, don't run the numbers, then call Bartlein and change the twist in the barrel from 1:7.5" to 1:7.4999" just to get Sg = 1.40000 in the equation. In other words, don't get carried away!

PS to all,
If anyone else would like this spreadsheet, please email me,bsl135@yahoo.com) and I'll reply with the spreadsheet attached. It's nothing special, just Mr. Miller's formula mechanized in Excel.

 

[Trace]

BRYAN

BRAVO