Pellet Twist Rate and Stability
This time we’re investigating pellet twist rate and stability.
Last month I wrote about the two types of stability, Gyroscopic and Dynamic. I should start off this month by saying that I am not aware of any twist calculators that will work for Diabolo (waisted) pellets!
If you input the dimensions they will return an answer that in most cases is too fast a pellet twist rate for best accuracy. They simply are not intended to be used for a drag stabilized pellet.
Even for slugs, most of the online calculators produce flawed results. For the most part, they are intended for Supersonic velocities, and may produce incorrect results below Mach 1.
The only one I use is by Dr. Geoffrey Kolbe, PhD, which is based on the work of Robert McCoy from the Aberdeen Proving Grounds. The Kolbe Twist Calculator can be found online at: http://www.geoffrey-kolbe.com/barrel_twist.htm
Once you input the dimensions of your slug, and optionally the twist rate of your barrel, the Kolbe calculator uses the “McGyro” program to produce a chart showing the optimum twist rate plotted for various velocities, like this:
(Sorry, the x axis graduations do not reproduce very clearly online. In all the graphs for this article, they start at 500 FPS and rise to 4,000 FPS, in increments of 500 FPS).
The optimum twist rate plotted will produce a Stability Factor (SF) of 1.5. This is the recommended twist rate for the best compromise between static stability and dynamic stability.
If you optionally put in the twist rate of your barrel, you will see another chart, which plots the SF vs the muzzle velocity, which looks like this:
A Stability Factor of less than 1.0 means that the slug in unstable and will tumble.
Recent work by famed ballistician Bryan Litz has shown that between 1.0 and 1.5, bullets will tend to wobble a bit. This increases their drag, and hence an SF below 1.5 reduces their Ballistics Coefficient (BC). He therefore recommends an SF = 1.5 as being the optimum.
Dynamic Stability and Aerodynamic Jump
You will remember from the previous article on Aerodynamic Jump that the longer the slug, and the faster the spin rate, the more vertical jump occurs in a crosswind. This means that spinning a slug too fast will increase the vertical deflection you will see in a crosswind.
For this reason, some benchrest shooters intentionally use a slightly slower twist rate, trying to get an SF of 1.2-1.3. They are willing to give up a bit of BC to get less jump in a crosswind.
The military tend to use greater stability, with an SF = 2.0-2.5 being common. Short, light slugs shot from a barrel intended for longer, heavier ones will also have higher Gyroscopic Stability.
Spinning a slug (or pellet) faster than necessary can, however, lead to Dynamic Instability and spiraling. It is generally accepted that an SF greater than 4.0 is asking for trouble. It is a balancing act, particularly if you wish to shoot a variety of slugs.
Since the RPM of slugs decreases very slowly as the slug travels downrange (typically about 95-98% of the RPM remains at 100 yards) the SF increases as the slug travels further. A slug that is gyroscopically stable at the muzzle will remain so as it slows down, with one exception.
The Transonic Problem
You may have heard that slugs or pellets falling back through the speed of sound may become unstable.
“May” is the key word here, but it can definitely happen if the twist rate is marginal.
The classic example of this was when they first used the longer 40 gr. “long rifle” bullet in .22 rimfires in the 18 inch twist of the earlier barrels which worked OK with the shorter 29 gr. bullets from the “short” and “long” cartridges. Here is what happened:
Note that the stability of the .22LR bullet was near perfect when Supersonic. However, just as it dropped below Mach 1, the SF dropped below 1.0, and the bullet tumbled.
By comparison, subsonic “Target” ammo, which started out at about 1050 fps, was stable (barely) and continued to be so as the bullet slowed going downrange. The solution, of course, was to increase the twist rate to a 16 inch twist, which is the standard used in .22LR barrels today.
This gave the following results:
As you can see, this avoids the instability as the bullet falls through Mach 1. It is a classic example of how the wrong choice of twist rate can ruin accuracy.
A Caveat about the Kolbe Calculator
I have used the Kolbe Twist Calculator a lot over the past few years, while developing my “Bob’s Boattails” airgun slugs. It has a built in correction for boattail bullets, which shows that they need a faster twist rate than an otherwise identical flat-based bullet would require.
I suspect that McCoy’s program assumed that boattail bullets had a smooth transition from the cylindrical bearing area to the tapered portion of the boattail.
My designs use what is called a “rebated boattail”, where there is a small step down in diameter where the boattail starts. This is not unlike the step near the base in a gas-checked slug design.
From testing of gas-check style slugs (without the gas check installed), there appears to be no increase in spin required, even though the base is slightly smaller than the caliber. Testing of my rebated boattail designs has shown that while they may need a faster twist than a similar length flat-based slug, they can use a slower twist than Kolbe’s prediction.
Some twist rate in between appears indicated, at least at typical airgun velocities of 900-1000 fps.
Roundball and Pellet Twist Rate
I would like to conclude this article with some comments about suitable twist rates for Diabolo pellets and roundballs.
It has been known for more than a century that a roundball will gain in accuracy if spun slowly, instead of shot from a smoothbore. This is likely because the deflection that might be caused by any slight imperfection is “evened out” by the rotation.
I mentioned briefly before that the required twist rate for a given shape is calculated in “calibers” before being converted to inches. I would suggest to you that roundballs do not need to be spun faster than 1 turn in 100 calibers, and possibly even slower.
That means a 30 inch twist for a .30 caliber roundball, a 45 inch twist for a .45 cal and a 58 inch twist for a .58 cal roundball. Even slower twist rates may work, but I can see no reason to go faster.
Although I have no concrete proof (yet), and there may certainly be exceptions, I think that perhaps the same criteria can be used for pellet twist rate. This could apply to the majority of airgun pellets.
If their shape is such that they are truly “Drag Stabilized”, then why not spin them slowly, like a roundball? In addition to the twists rates given above for roundball, that would mean about an 18 inch twist for a .177 cal. pellet, about 22 inch for a .22 cal. and about a 25 inch twist for a .25 cal pellet.
Such slow twist rates would minimize aerodynamic jump, and decrease the likelihood of spiraling. The high drag pellet would still see an increase in gyroscopic stability as it travels downrange.
It will be interesting to look back from a few decades in the future to see if this suggestion/prediction becomes the norm…
Next month I intend to start dealing with the drag and Ballistics Coefficients.