If bearing surface length were important to stability, why would we bother shooting diabolo pellets through rifled airgun barrels?
Surely something with such a negligible bearing surface couldn't possibly engage the rifling efficiently?
But it does. Because, as HodgdonExtreme notes, there is no slippage. In part because rotational speed does not instantaneously go from zero to 150,000 RPMs. Even with a long-throated barrel, bullet velocity will ony be a couple hundred fps when it first strikes the rifling. Which works out about 200 revs/second in a 1:12 barrel, maybe 350 revs/second in a 1:7. One inch down the barrel and the bullet is not yet moving 1000 fps but it is fully engraved, yet it barely has rotated 50° since the primer broke (or even just 30° in the case of a 1:12).
So I think you're radically overestimating how traumatic it is to the bullet.
Your second mistake is believing bullet weight has anything to do with stability. A common misunderstanding that stems from the way we tend to talk about bullets.
No one goes to Gander Mountain to buy a box of 1.215" SMKs, we go for a box of 168-grainers. Bullet
length doesn't enter the considerations. So we take for granted the reason a 175-gr SMK is harder to stabilize than the 168 is because it's heavier (by 6 grains). But that's wrong. It's harder to stabilize because it's longer (by 0.051"). Even though it's lighter than either SMK, the 155-gr Lapua Scenar is harder to stabilize than even the 175 because it's longer, 1.291" (thanks to an exquisitely streamlined 10.68 ogive number).
So bullet weight isn't what determines minimum twist. Weight
distribution, however, is king dog shit.
But you're in good company, Fluffy. We all know bullets need to be spun to be stable, but very few shooters understand why. What specifically is it that's wrong with bullets that keeps them from being stable in the first place? Understanding that, IMHO, is the key to understanding every other aspect of bullet stability.
Truth is, we deliberately fuck 'em up. It's what bullet designers do to bullets in the interest of aerodynamic efficiency that makes them unstable to start with.
I already introduced the subject of airgun pellets, and this is an apt point to get back to them. Here's a shot of the cross-section of a bunch of diabolo pellets:
Unlike high-velocity bullets, diabolo pellets inherently have positive longitudinal stability. They're perfectly stable, the pointy end remains pointed downrange, whether they're being spun or not. You could throw a handful of them into the air, and provided you threw them high enough, every last one would strike the ground nose-first. Every kid who ever owned a Crosman Powermaster 760 pump BB gun knows pellets don't need no stinkin' spin. Yes, they're more
accurate if they're fired from a rifled barrel, just like an arrow flies truer if the flethcings have just a touch of 'helical' to them, but that's a completely separate issue from stability.
If you think about it, the general layout of the diabolo pellet is a lot like this thing:
It's a badminton birdie (or a shuttlecock, if you live in San Francisco). No matter how hard you whack one of these things, regardless of the angle you hit it from, within a foot of it leaving the face of the racket, it's always back to flying nose-first (although sometimes with a little accompanying oscillation). It has tremendously strong positive longitudinal stability.
Why?
Because of weight distribution. Remember me writing earlier that weight distribution is king dog shit? This is my proof. Or to be more comprehensive, I should say it's the relationship of weight distribution to drag distribution.
In the case of both the diabolo pellet and the badminton birdie, the designer crammed all the weight he could as near to the nose as he could. And then he added some fiddly bits at the ass end to create a lot of drag, way, way in the back.
Static stability is a wresting match between these two forces. Weight distribution versus drag distribution. A moving object that is traveling with its Center of Mass (CG) in front of its Center of Aerodynamic Pressures (CP) tends to have positive longitudinal stability. The nose naturally wants to continue pointing forward. In a sense, it's like the object is most stable if the CP can get behind the CG to hide from the wind.
But if CG
isn't ahead of CP, it will tend to have
negative longitudinal stability. The CP will tend to win that wrestling match, in which case it turns the whole contraption around so it can be in its preferred orientation, with the CG between it and the wind. Imagine shooting an arrow fletchings-first. It will swap ends so fast, all you will see is a blur. If that.
What's true of bullets is equally true of rockets
Both of the projectiles I've been talking about have tremendous positive longitudinal stability, but their ballistic coefficients suck. Which isn't really a handicap at their typical working velocities.
Which brings me back to high speed bullets. For centerfire rifle bullets, this whole CP-CG wrestling match thing causes two distinct problems.
The first problem is that the CP is always going to be very near the nose of the bullet. That's the part that's doing the lion's share of the aerodynamic labor, boring a hole in the wind for the remainder of the bullet to pass through. And the faster an object is moving, the harder it has to work, and the more pronounced this tendency becomes. And we
want out bullets to be
very, very fast. So there's no getting around that, we've just got to deal with it.
The second problem is what you have to do to a bullet in order to streamline it. Remember me writing that we're deliberately fucking up out bullets? This is it.
We've already established two key points. #1, it blows you projectile's longitudinal stability to hell and gone if it doesn't fly CG-first. And #2, the nature of driving a bullet at supersonic velocity necessarily and unavoidably means that the CP will be manifested
real damn close to the nose.
And now we're going to really screw things up by
deliberately moving the bullet's CG further aft, further away from the meplat. Because that's an unavoidable side-effect to tapering the nose of the bullet down to a point. That leaves less material on the pointy end, so the CG
has to go the other way.
Image from "Applied Ballistics for Long Range Shooting," by Bryan Litz
This is what comes from tapering the nose. CP is ahead of CG,
way ahead, exactly the opposite configuration of the diabolo pellet and the badminton birdie. And we know CP-before-CG
is not going to have positive longitudinal stability. CP was always going to be ahead of CP anyway, because even if the bullet was a blunt-ended cylinder, CP was always going to be manifested in the upwind end, and CG always was going to be slap in the middle. The tapering just made the problem worse.
Long story short,
that is what's wrong with bullets, why we have to spin them to make them stable. CP-before-CG means it needs an external force applied to overcome the tendency of the CP to run back behind the CG and hide from the wind. And the shooter's external force of choice is angular momentum, AKA gyroscopic force.
Notice the arrow on that last diagram, the one pointing out the distance between the two centers of pressure? That's called a "moment arm." CP can use that moment arm like a lever to win its wrestling match against CG. And as we all know, the longer the lever, the greater the lever-age, and the more force that can be applied. As a bullet of the same shape gets longer (and heavier), the longer this moment arm gets. And the more leverage the CG has. And the more un-stable the bullet becomes.
So that's why a bullet is unstable to begin with,
and why the instability increases as the bullet gets longer. It's got nothing to do with bearing surface length, and nothing directly to do with bullet weight, but everything to do with weight distribution.
High velocity bullets are statically unstable because we build them so they'll fly CP-before-CG.
And whenever CP flies before CG, the longer CP-CG moment arm is, the worse the instability becomes.
And as we've touched on in other threads, if you shoot the same bullet as in the diagram backwards, ass-end first, the CG won't move but the CP
will change ends. So CP probably still will be in the lead, but the moment arm will be much shorter because the designer moved the CG nearer to the bullet's base when we created the ogive. And the shorter the moment arm, the less un-stable the bullet is. So at any given rate of twist, the bullet will be
more stable if fired backwards. A handy trick if you're into loading subsonic.
