Question regarding "over-stabilization" and twist ratios...

Barrel length is not really a very significant factor in stability. I ran some numbers: For a 168 grain MatchKing at 2550 fps (20" tube) and 2600 fps (22" tube), that 2" barrel length increase only changes the gyroscopic stability factor (s) of a 12" twist fröm 1.708 to 1.719. If, instead, you change the twist of the 20" tube to 10, then the stability factor goes fröm s=1.708 to s=2.460. Like bullet length, twist is a big player in stability, where different bullet weight (for a fixed bullet length) is a middling factor, and velocity for a given rate of twist is the smallest factor.

An important aspect of the over-stabilization issue, in addition to the extra drag due to yawing nose up and the lift it creates that bleeds off energy, is bullet mass symmetry about its spin axis. If the bullet has any imperfection in that mass distribution, the spin is eccentric and wobbles around the line of the trajectory. How much it wobbles depends on the size of the mass distribution error and the rate of spin. The faster it spins, the greater the wobble for a given flaw. Assuming wobble isn't extreme enough to cause the bullet to become totally unstable, it still introduces both added drag and small random deviations in the trajectory (drag noise) that open the groups up at the target. For this reason, better jacket and core symmetry is one of the elements of superior accuracy achieved by match bullet construction.

At the other end of the spectrum is too little spin. Any bullet fired straight with a stability factor of s>1.0 will not become unstable and tumble, but as Sionaphrys said, bullets launch with some degree of yaw, introduced in large part by muzzle blast passing the bullet and pushing on its base. This yaw is not exactly the same, round to round. It is made much greater if either the bullet base or the muzzle crown are not perfectly symmetrical. The yaw and spin combine to rotate the bullet spin axis around its center of gravity and therefore around the trajectory path. This is fast precession (coning motion) and nutation. If s>1.0, this motions irons out and the bullet nose ceases coning and nutating, but it takes time and distance down range to get there. The nearer s is to 1.0, the longer it takes. If s<1.0, instead of ironing out, the circles get bigger and bigger until the bullet is overturned by air pressure and starts to tumble. If s=1.0 exactly, the coning never gets bigger or smaller, so the bullet never "goes to sleep".

You can see the initial helical corkscrew due to coning in the air disturbance caused by a bullet (its wake). At Camp Perry at the 600 yard line and further back that's easy to do standing behind the firing line because you can position yourself to see the bullet wake arc upward against the sky. Harold Vaughn has some computer plots of the nose spiraling inward over distance for different values of s.

In any event, the two extremes of error source are what you are trying to balance when you choose a target value of s by selecting a twist rate for any given bullet. The match bullets are so well made any more that they often will still shoot well at values of s=3 or sometimes greater. If you are benchrest shooting, Harold Vaughn thinks s=1.4 is about the best compromise. Don Miller thinks 1.5 is best. I've seen a best compromise number suggested as high as 1.7, but it really does depend on how well the bullet is made, not to mention assuming a perfect crown on the barrel and a perfect barrel time load for minimum shot-to-shot muzzle disturbance.

If you are missing any one of the above elements, you'll find the best s value changes. For example, a barrel with a slightly eccentric crown will likely do better with a shorter bullet that gets a higher s value fröm its rate of twist. That's because the crown imperfection makes greater muzzle blast induced yaw to recover fröm by the time the bullet gets to the target, so it needs to go to sleep faster. In this situation you will also likely find a faster powder that doesn't push the bullet quite as fast, but that produces less muzzle blast also produces better accuracy. Flat bullet bases that spend less time clearing the muzzle will also be easier to shoot accurately fröm such a gun.

As Homer Powley (I think it was) put it, the aerodynamic forces "conspire" to point the bullet into the trajectory path. There is a constant translation of overturning forces to the opposite side by spin that makes this true. It is why a bullet yawing most extremely after clearing the muzzle has its nose describe a helical path around the mean trajectory path (the coning or precession I mentioned earlier). The degree to which the bullet resists that aerodynamic conspiracy is dependent on how fast it spins, its mass, and how hard the air resistance reaction force is that it experiences. The degree of success they have in resisting the conspiracy is indicated by how far their average nose-up yaw above the line tangent to the trajectory at any given moment in flight. That is a function of the gyroscopic stability factor which takes spin, velocity, atmospheric density, bullet length and mass all into account in one number.

The tendency to nose over does, in fact, occur. Just look at the angled ramp on the back of a Springfield '03 ladder sight to see how much the sight windage has to move to the side to compensate over a long distance. Typically, with normal gyroscopic stability factors, you see around one foot of windage drift at 1000 yards due to this effect.

If you want to calculate change in stability with distance, you can. Velocity loss is in any ballistic tables. Loss of spin is slower (which is why s increases with distance) but there is surface friction slowing it. Geoffry Kolbe has a spin decay approximation of:Davers,

Momentum is not a good indicator of stability because it is the product of velocity and mass which don't have the same effect on stability. The gyroscopic stability factor, which takes all the elements of stability into account, increases directly with mass for a given velocity. So, if you keep the same bullet shape and and add enough powder to keep the same velocity, but increase momentum 67% by increasing the mass 67% by replacing the lead alloy core with tungsten, you increase the stability factor 67%. But if you keep the original bullet and increase momentum 67% by adding enough powder to increase velocity 67% you do not get a 67% increase in stability factor. Only about 19%. The reason is that at the higher velocity, air pressure on the bullet nose is greater, so it takes more spin and momentum to keep the bullet from tumbling under those greater aerodynamic forces. That cancels out almost 70% of the gains from the higher momentum and spin.

For example, we take a 168 grain Sierra MatchKing at 2600 fps in a 12" twist barrel. The gyroscopic stability factor is:

s=1.719

We now increase momentum 67% by increasing mass 67% and keeping velocity the same, so the same size bullet now weighs 280.6 grains:

s=2.871 a gain of 1.152

We now increase momentum 70% for the original 168 grain bullet by increasing velocity 67% to 4342 fps:

s=2.040 a gain of only 0.321

So, momentum was increased 67% in both cases, but did not bring about the same effect on stability. It is still bullet length and rate of twist that matter most, which is why the old Greenhill formula only used those two factors.

Well, again, I suggest taking a look at a Springfield '03 ladder sight. It can't quite be ignored. A foot at 1000 yards is roughly equal to 1 mph wind drift. That gives you a sense of the scale. It's not a lot to most shooters, but it is enough to make a sniper miss a man-size target at that range if he fails to dial it in.


Mike,

you are describing a projectile whose center of pressure is behind its center of gravity. Such shapes are inherently stable. An arrow with feathers is an example. More drag to the rear of the center of gravity points the projectile into the wind because it pivots around its center of gravity.

Most modern pointy shape bullets, however, are the other way around with center of pressure ahead of center of gravity. So, imagine shooting an arrow backward and having to make it spin fast enough to keep pointing straight ahead despite air pressure trying to turn it by it force on the feathers.

If a bullet is spinning fast enough to be stable and has gone to sleep and is flying steady, the upward tipping force (the overturning moment) puts vertical momentum into the bullet by trying to flip it. What stops it fröm flipping the bullet into a tumble is that overturning momentum is translated into the downward direction half a turn later, neutralizing it and that happens faster than the tumble can initiate. This is intrinsic to what defines spinning fast enough to be stable.

The injection of upward momentum and its neutralization by translation is a continuous process for the flying bullet. The faster the bullet spins the more gyroscopic force it has trying to hold its nose up, but that increases the the overturning momentum that gets translated around to the bottom to pull the tip back down.

So, the yaw upward above tangent to the trajectory path is a position representing equilibrium between those two influences: the gyroscopic tendency to fix orientation, and the constant downward translation of overturning momentum due to spinning. The faster the spin, the more the bullet tries to hold its orientation, so the more it is chin up and the more overturning force is applied to create more vertical momentum that is translated down to oppose the upward tipping. The exact value of the neutralizing momentum is always lagging by half a turn, so it is never 100%. Therefore the equilibrium position of the nose is higher for higher gyroscopic stability (faster spin relative to forward velocity), which results in more effect fröm both influences.

Keep in mind we are talking about numbers in thousandths of an inch above the tangent to the trajectory path. IIRC, Harold Vaughn had examples like 0.003" to 0.009" nose up off the trajectory for a range of stability factors. As former head ballistician for Sandia National Laboratories, his book is a worthwhile read on these and other accuracy topics.

MZ5,

I somehow missed that the difference was your only point about affect at that range. For that you are correct, the difference is small. The greater drag from over spinning is another issue, though, as the stability factor jumps quite a bit going from 12" to 10" twist. A lot of Palma rounds have historically been on the ragged edge of staying out of transonic problems at 1000 yards. The Palma shooters go to a lot of trouble to use those 32" broomstick barrels and the three extra grains of case water capacity in Winchester cases to get every little increment of muzzle velocity increase they can muster. The added drag from a faster twist's greater yaw angle would not be welcome. Any extra flight time exaggerates wind drift at that range.

The Palma shooters have had 13", 13.5", and even 14" twists made up because of groups opening up with faster twists. Whether by wind or by wobble probably doesn't matter to them. They are just being empirical. I am curious, though, to see if we don't start to hear of some 12.5" twist Palma tubes showing up with the new, longer shape .5 BC BC Palma bullets from Sierra and Lapua? Time will tell.

It seems to be using a secant rather than tangent ogive. The boattail angle and length also affect it. Sierra told me the new 155, which has a higher BC than the 168 (a 1958 design), is modeled after the secant ogive 175.

The 168's trouble comes from it becoming unstable at the top end of the transonic range, at around 1400 fps. Not even the old M1 173 grain ball bullet from between the world wars did that, much less the last 155 grain Palma design.

When I met Sierra's Kevin Thomas at a long range school at Camp Perry one year, he explained the 168 had originally been designed for 300 meter match shooting. It was just serendipity that it went to 600 with great accuracy for service rifle matches.

The newer 175 grain design doesn't have the instability problem. It flies to 1000 just fine. Unfortunately, Palma rules limit the bullet weight to 155 grains, so they can't swap in something heavier there.

As I said, it seems to be dropping into the top of the transonic range that boogers them. That's about 1400 fps. Simply staying supersonic doesn't cut it with 168's.

When I took Gunsite's PR1 class, we had one popper at 748 yards that nobody could hit on demand. We were using PMC ammo loaded with the 168's that we bought from the school. Paulden, AZ is at about 6.000 feet, so you'd think we had some wiggle room, but the target was across a valley with a 20 mph crosswind, so a bit of extra drag was operating. My rifle has a 22" barrel and even though the wind was quite steady, the rounds would veer off first left, then right. I could see the dust kick up just fine in the mil-dot scope and see exactly how many dots of correction to make, but it didn't work. I hit it once, but it was luck. At the time I thought it was just the wind being crazy further out than I could see the mirage, but I got set straight on that score the next year.

That next year we (I and my dad and one of the guys who'd also taken than PR1 class) attended the Long Range Firing School at Camp Perry, still carrying the 168's. The first range exercise was at 800 yards. This was morning and there wasn't much wind, but we were at near sea level. As the first shots went downrange, up and down the firing line all this moaning and cursing started as .30 cal shooters with 168's were having trouble getting on paper, ourselves included. Reports of keyholes started coming back from the pits.

That's the class Kevin Thomas was in. He explained the 168's limitations and that Sierra had developed the 175 in cooperation with the military specifically to function well through the transonic range and out to beyond 1000 yards. So, we all took our lunch break to run to Commercial Row and buy up HSM and Federal cartridges loaded with the 175's. After lunch, back at the 800 yard line, no more problems. And the case of the hard to hit popper was solved.

Instability from overstabilization?

Apropos of this thread, I have uncovered a possible example of overstabilization actually causing instability:

I was rereading an old thread in which Humpy (post 31, here) described being able to shoot at 1000 yards successfully with the 168 gr. SMK with a very mild .308 load. He was, however, using it out of a 13.8" twist barrel. It was only a 24" tube, but it was from a Palma style blank, being an Obermeyer 5 R 0.2980" bore and .3055" groove tube. So this was tight enough to give him some extra pressure and extra bullet alignment. Nonetheless, his 37 grain 4895 load, from QuickLOAD, would only have had an MV of 2400 or so, depending on some variables. The ballistic charts show you need 2850 fps to keep the 168 supersonic to 1000 yards, so that load would be subsonic long before the bullet arrived. Humpy speculates that they may have been striking the target at an angle, but I doubt it. Being subsonic they should have plenty of retained spin. Even if they did hit sideways, they could not have gone unstable more than about 25-50 yards ahead of impact, because I can tell you from watching through my scope, a 168 spinning head over heels does not remain on trajectory for long.

So, why would these bullets remain stable through the transonic range under those firing conditions when they did not so so for me or any of the other LRFS shooters? AT this point it seems to me likely the extra yaw caused firing these bullets with a 10" twist vs. the 13.8" is the main variable change. The 168's may get more spin from the 10", but apparently their shape just cannot remain equilibrated against the overturning force through the transonic range if they enter it too far nose-up.

Now an experiment needs to be done to prove this. Anyone want to buy me an Obermeyer barrel? I seem to be out of stock.

Incidentally, a 13.8" twist calculates to bring about a stability factor of just 1.244 at 2400 fps. This is below the optimal numbers usually given, and is even below Sierra's recommended minimum of 1.3. That bullet would have taken a long time to go to sleep. But a 10" twist at 2400 fps produces a stability factor of 2.44 with that bullet. Well above the recommended maximum of 1.7 for best accuracy. For Vaughn's ideal of 1.4, a 13.2" twist is needed. For Miller's 1.5, a 12.75" is needed. For the 1.7 recommended number I can't recall the source of, a 12" twist is needed. 12 2/3" is the average for these sources, so if I were building a gun specifically for 168's, I might be tempted to get at 12.5" and call it close enough.

The problem with the above is, the AMU went from 12" to 11" in the M14 to get better performance from the 168 in match shooting to 600 yards. So now there would seem to be a conflict in what does best under what circumstances. I can't really explain that. Something about that bullet's shape.

BAGTIC,

I think you must have responded to something two pages back. A quote would help provide current context.

You are correct about mortars, but in terms of stabilization, whether shape stabilized (as by fins; center of pressure behind center of gravity) or spin stabilized, as Bryan Litz says, a simple definition of stability is that the stable projectile points into its trajectory path. This is called tracing of the trajectory by the projectile. The unstable projectile does not trace. A projectile that presents a large pitched up nose angle to the oncoming airstream has too much air pressure up under its nose for its spin or its fins to oppose overturning. Overturning initiates uncontrolled tumbling.

For a stable, pointed thirty caliber bullet at typical .30-06 velocities, you usually have something on the order of a pound or so of air pressure against the nose pointing into the trajectory. This is called a pound or so of drag, by ballisticians, as if a vacuum applied pulling force instead of pressure on the opposite side causing a reaction force to being pushed, but that's how the convention is, and it's relative, so it doesn't change the result of calculations. But with the less pointy and less symmetrical nose-up profile presented to the airstream, the force (or drag) is much greater and quickly becomes enough to overcome gyroscopic stabilization. Even if the projectile miraculously failed to overturn, it would be slowed dramatically more quickly by the higher drag than is in the more aerodynamic attitude of pointing into the airstream. In other words, it's ballistic coefficient would become dramatically smaller when nose up. It would take much longer to get to the target, and the wind would thus have time to blow it all over the place and it would fall to earth before getting to a long range target.

The high firing angle problem is much more common in artillery than in small arms. If you fire at high enough angle (see Hatcher's experiments with bullets fired straight up and falling to earth) the projectile will have too sharp a turn to make at the apex of the trajectory and will therefore fail to trace. Instead it will fall to earth tail first. That's a disaster for artillery, as the shells don't go as far as they should and the fuses won't impact correctly oriented for firing.

Be aware that conventional small arms exterior ballistics software always assumes tracing and will not correctly predict how a projectile behaves at high discharge angles. At firing angles over about 50° or so, they may be wrong at ranges far enough for the projectile to drop very significantly. In other words, I'd expect their high angle predictions to be close enough at, say, 300 yards, but instability might occur before 1,000 yards for rifle rounds that are fine fired over flat ground.


BTW, Litz's book also mentions the instability problem with the 168 grain MatchKing in the transonic range. He blames the design of the boattail (angle and length).