Re-Thinking Transonic Zone effects

[LRRPF52]

This discussion is starting to get into some of the more advanced aspects of aerodynamics and will be relevant for the long range shooter if they are looking at controlling the types of bullets they use for 800yds and farther.

If you've ever watched the mach wave form on a supersonic object, whether it be an aircraft or bullet, there are certain behaviors that are very interesting. Aircraft meant for high supersonic speeds around or over Mach 2 (Think F-111, SR-71, MiG-25, F-22) will have different shaping compared to aircraft designed for subsonic or low-mid supersonic speeds (F/A-18).

Ogive shaping science dates back to artillery projectiles, rifle bullets, and really took off with the supersonic jet age and the Sears-Haack body theory. With early supersonic jet testing, they learned the hard way that aerodynamic shapes that work well in subsonic flight become useless or dangerous in supersonic flight, elevators being one example.



Relevant to bullets, if you look at fighter aircraft radome shapes, those aren't some designer just sitting there drawing what he thinks would be cool-looking. They are very math-heavy and are derived from a series of calculations which usually begin with what size the fighter's radar antenna needs to be in order to meet the detection and tracking range requirements set forth in the program specs. Once they determine the antenna size and gimbal limits (for mechanically-steered arrays, now being phased-out by electronically-steered arrays that don't physically move), they know the diameter of the radome seam with the forward fuselage and then can start playing with frontal Sears-Haack equations to determine the radome shape for the max speed requirements.



This will eventually lead to driving the aircraft weight, center of gravity (C of G), and center of aerodynamic pressure. With an aircraft, these aerodynamic centers can be shifted and are frequently in flight, especially with considerable changes in speed and fuel management.

With a bullet, one of the main differences is that it is gyroscopically stabilized to the tune of usually over 200,000rpm from centerfire rifles.

So now we have a spinning aerodynamic gryo that rapidly decelerates due to atmospheric drag and gravity negatively affecting its trajectory.

When it leaves the muzzle at its maximum velocity, there is a certain supersonic waveform being pushed by the bullet in the thick atmosphere, which provides significant drag on that bullet.



If the bullet would stay at the same speed through a uniform atmospheric density, the drag waveform would remain at a constant cone angle, but it of course doesn't due to deceleration.

As it rapidly decelerates, that mach cone waveform goes from being more elongated, to more flat, which affects the bullet's center of pressure.

If you can keep a VLD-shaped bullet (one with a long, secant ogive and long Sears-Haack-like boat tail) pointed optimally throughout the flight profile, it will retain energy better than if the nose deteriorates into an out-of-alignment gyroscopic wobble that bites into the radius of the mach cone, instead of staying oriented to the point of the mach cone.

Designing a bullet that will nose-over after the maximum ordinate rather than staying oriented to its original angle of attack (the difference in where the nose is pointed vs where the bullet is actually traveling) is one of the things Litz and Berger have been chasing, although much of this was pioneered by Swedes and Germans way back in the day for artillery.

At some of the Sniper Competitions I've RO'd or competed in, I had the opportunity to go pull TGTs that were well over 1100m, made from aluminum plates. We could see several projectile impacts that were still going supersonic at that range, but the bullets hadn't nosed-over, so you could see keyhole-shaped impacts that were all nose-up, as opposed to erratic. These were from either 7mm or .338LM or both, and the shooters were getting consistent and predictable hits at those ranges with the bullets coming down after the maximum ordinate. My guess is that due to the sheer mass of those projectiles, they were able to maintain enough inertia to stay supersonic, even with the additional drag from an AOA that appeared to be at least 25˚ or more, but they certainly were decelerating more than they would have had they been able to nose-over.

With the traditional rifles that start to peter-out at around 800yds using more tangent ogive bullets and token boat tails that don't do much for Sears-Haack Effect, my guess is that the increased frontal area of those bullets in a shorter amount of length, without the benefit of a long secant ogive cutting through the air ahead of the shank, causes them to deviate from their intended flight path more rapidly.

This is just a guess. Combine that with looser twists that don't maximize gyro stability, and I think this is why I have seen the beaten zone expand dramatically past 800yds, even up at 6600ft elevation. This effect has been noticeable with rifles that had no problem making consistent and predictable hits out to 800yds, then not even be able to get more than maybe 1/10 hits at 850yds, with the 1 being more luck, and impacts 3-4 mils left and right of the TGT.