Re: Question: twist rate for .338 bullets
V-Ref,
Thanks for bringing the developments on this thread to my attention. I'll be happy to discuss the questions.
The Greenhill formula was good for the projectiles and mostly subsonic speeds of it's time. In the modern world of pointed, boat tailed bullets fired at 3+ times the speed of sound, the Greenhill formula is simply not very representative, even with the attempts at modern correction factors.
The new standard for practical stability calculation is the method developed by Don Miller. This is the method I recommended for use in Gustavo Ruiez's program: LoadBase2 (mentioned above). Millers stability formula is essentially a curve fit to empirical data (not a direct stability calculation). As such, it has it's limitations, but is quite accurate and very useful for estimating gyroscopic stability. I have written a simple program that calculates stability based on Millers formula that I will be happy to email to anyone interested (free).
The Miller formula is the most practically useful formula for estimating stability, but there are more accurate ways. The McGyro code, developed by Bob McCoy is more accurate, but is still not a direct calculation of bullet stability. It's a more sophisticated empirical estimate that involves more variables, some of which not available or obvious to the average shooter. The JBM twist calculator runs the McGyro stability code, and can be used (for free) at this address:
http://www.eskimo.com/~jbm/cgi-bin/jbmdrag-5.0.cgi
One important note on the use of both the Miller and McGyro programs:
It's a very common mistake to think you can calculate the downrange stability with these programs. The programs are good for calculating muzzle stability only. Even though the JBM implementation of McGyro gives stability factors at what appear to be 'downrange' velocities, that's not the case. When the output says: SG=x.xx at 1300 fps, it means if you fired the bullet with a muzzle velocity of 1300 fps, the SG would be x.xx. It's NOT the SG of the bullet fired that's fired at high velocity and slows to 1300 fps.
Historically, Walt Berger has established the twist requirements for Berger bullets and continues to do so. For the few bullets that have been released in my short time with Berger so far, Walt and I have discussed our independent calculations of twist requirements based on different methods and have found them to be in agreement. My methods are Miller and McGyro. I don't know for sure what Walt's prediction method is based on, but it's agreed with my calculations so far. We always round the number down to the faster twist to be on the safe side, which is why many times (especially at high altitude in warm air) people find they can stabilize bullets with slower than the recommended twist.
Beyond the Miller and McGyro prediction codes you would have to use a direct calculation that requires the actual aerodynamic and mass properties of the bullet (the 6-DOF details that muffcook was describing). These are time consuming and difficult to generate, even for someone with the resources and knowledge to do it. Honestly, the prediction methods (Miller and McGyro) are close enough that a more sophisticated calculation is seldom required, especially since we leave a safety margin.
Moving on...
You can't tell anything about stability from rotational speed (RPM) alone. Calculating RPM's as a means to quantify stability is a common mistake. The gyroscopic stability factor (SG which is calculated by the Miller and McGyro programs) is the real measure of bullet stability. RPM's play a part, but is not the whole picture.
Consider the conflicting influences involved in bullet stability. The <span style="font-style: italic">destabilizing</span> influence exists because the center of pressure (cp)is in front of the bullets center of gravity (cg). Airplanes, rockets, and arrows achieve stability by forcing the center of pressure behind the center of gravity with tail surfaces. Bullets, however, have to <span style="font-style: italic">live with</span> their cp in front of the cg and achieve stability another way. The <span style="font-style: italic">stabilizing</span> influence for a bullet is it's spinning mass. The spinning mass makes the bullets axis rigid, and resistant to the <span style="font-style: italic">destabilizing</span> overturning torque of the cp being in front of the cg.
Deep breath...
Now consider the factors that affect the relative strength of the stabilizing and de-stabilizing influences.
1. Increasing twist rate (while leaving everything else unchanged) will increase the rigidity of the spin axis while leaving the de-stabilizing influences unchanged, so stability is improved.
2. Increasing the length of the bullet will usually increase the distance between the cp and cg which increased the destabilizing torque which has a destabilizing affect. Also, the longer bullet has a less rigid spin axis than a shorter bullet.
3. Increasing the weight of the bullet while leaving everything else the same will increase the rigidity of the spin axis.
4. Now we get to the interesting 'double edged sword': velocity. Increasing the velocity has two effects. First, it will increase the RPM's of the bullet which has a stabilizing effect. Second, it increased the force (aerodynamic drag) that's applied at the cp thus increasing the overturning (destabilizing) torque. The net result is that increased velocity improves stability because the spin axis is strengthened a little more by the extra RPM's than it's weakened by the greater overturning torque. The increase in stability with velocity is far less than a 1:1 correlation with velocity though.
All of the above has been talking about gyroscopic stability, specifically at the muzzle. Gyroscopic stability will generally improve as the bullet flies down range because the forward velocity (a de-stabilizing influence) is eroding faster than the spin rate (a stabilizing influence). If a bullet has gyroscopic stability at the muzzle, it will only grow larger downrange.
It's interesting to note that the gyroscopic stability factor is the ratio of the stabilizing influences to the destabilizing influences. So in theory, this ratio should be greater than 1.0 for the bullet to be gyroscopically stable. In practice, you want SG to be a little greater than 1.0 to allow a margin for error (imperfect calculations, imperfect barrel twist, non-standard atmospheric conditions, etc).
Now to the really interesting question which prompted me to start this thread.
I said earlier that gyroscopic stability only increases with range as the bullet slows down. So why do bullets have <span style="font-style: italic">stability</span> problems at transonic flight speeds? When a bullet has 'trouble' at transonic speeds, it's not for a lack of gyroscopic stability, but rather dynamic stability which is more complicated than gyroscopic stability. I say it's more complicated because the factors required to calculate it are so very hard to predict, that even if you have a 6 DOF simulation, the parts of the aerodynamic model that are important for predicting dynamic stability can only be determined within ~+/- 20%, and in some cases can be as far off as 100%! Transonic aerodynamics is messy business and is a very difficult challenge for modeling and simulation. When I was 'greener', and had more faith in the modeling tools than I should, I was predicting transonic stability for bullets with confidence. It took a few cases of being proven wrong, but I learned the limitation of the modeling tools for this application. The truth is, you just have to try it before you know if a particular bullet at a particular twist, MV, atmosphere, etc will successfully negotiate the transonic regime.
In summary:
We have Miller and McGyro (both free and available) to predict gyroscopic stability at the muzzle. These are predictions, but are accurate enough for selecting a proper twist for gyroscopic stability. The equations of motion in most ballistics programs are direct, exact calculations for ballistic trajectories which are more accurate then commonly believed. The equations assume the bullet is flying point forward, which it will for a broad range of stability, until it approaches transonic. At that point it's a gamble. Generally, heavier bullets (high BC) are able to negotiate this flight regime better than light (low BC) bullets, but there are no hard and fast rules.
I hope this answers more questions than it raises!
Take care,
-Bryan
) Great post, and it did overstimulate my simple mind after the first reading.
