question for brian re least drag/max stability nose shape in transonic zone

[bruce moulds]

brian,
this question will not interest most, as it pertains to black powder shooting.
our bullets start their travel at 1300 to 1400 fps, top end transonic, and reach 1000 yds at roughly 800 fps.
from muzzle to say 600 yds they have roughly 3x wind deflection of a 308 palma load, and from there to 1000 yds roughly 2x
this would suggest that the bpcr bullet has higher drag at the closer ranges probably due to nose pressure.
because these bullets are not supported by jacket material, a practical maximum nose length is 1.5 to 1.7 calibres depending on the hardness of alloy used.
on firing, longer noses will either bump up to full barrel diameter, or bend and put the bullet off balance.
my understanding is that the elliptical shape is very efficient when subsonic, but I do not know about transonic.
there is another shape developed by metford of lee/metford fame where the actual nose is a sphere of 50 to 55% groove diameter of the barrel, going out to groove diameter in a secant ogive about 1.6 calibres long.
this bullet was used by the brits for many years.
it would seem that the transonic zone is very important in minimizing wind deflection and maximizing stability.
with your experience in both missiles and bullets, your comments would be of great interest.
keep safe,
bruce.

 

[Bryan Litz Ballistics]

Bruce,

Transonic is the messiest aerodynamic regime. There's almost never a simple answer when dealing with this condition.

The main attribute of the nose that will affect transonic aerodynamics is how far the center of pressure is pushed forward. This is mostly determined by the physical length of the nose, but is also affected by the shape.

Also very important to transonic stability is the ratio of transverse to axial moments of inertia. Think about twirling a broom-stick like a helicopter vs. spinning it like an axle. Same mass, but depending on what axis you spin it on can have much more or less inertia. This is a very important aspect of spin stability that's affected by physical shape. In general, longer bullets are more difficult to stabilize from an inertial perspective. The best tops are short and fat vs. long and skinny.

Don't forget about the complex boundary layer interaction with the grooves in the bullet surface. These features give rise to some very nasty effects which are as difficult to understand as they are to predict (Magnus force/moment, and dynamic derivatives).

There's very few basic guidelines that can be given. Those things that would improve your stability (shorter bullets) are the very things that decrease the BC and add to wind deflection. So you're in a trade-off between the two.

If I were to explore radical design changes for BPCR bullets to maximize BC in the trans/subsonic zone, I would first go to a faster twist rifle barrel. Then see how long a nose could be stabilized. If a long lead nose can't hold it's shape, I would look to install a plastic or aluminum tip, like a nose-cone to reduce drag. I'd also try and reduce the number and depth of the grooves. Maybe with a fast enough twist you could do a boat tail.

Keep things in perspective; at those speeds, your groups can get a lot of vertical from even a slight inconsistency in MV. Wind stretches out the group for sure, but if your vertical spread is very big then wind performance may not be the driving factor to design when hitting targets is the objective.

Good luck,
-Bryan

 

[XTR]

Bryan, I don't know how much you've looked into BPCR shapes. What seems to be about the best thing out there today is the Paul Jones design known as the Money Bullet. It has an elliptical nose shape. I believe I've seen them used in both grease groove and in paper patched bullets. (I have a mold for a grooved 525 Money Bullet)

The difference in the old Postell design and the PJ Money Bullet nose is about 225MOA to 1000 vs 175MOA to 1000 (pretty big)

With out looking back at the rules I think BPCR/BPTR bullets have to be cast lead with out the inserts or nose you mention.



In practice BPCR bullets are typically chambered at bore diameter and when hit from behind by the shockwave from the black powder obdurate (bump up) to groove diameter, examination of recovered bullets indicates that this happens before they move (no sliding or slipping of the rifling). This process has been found to be one of the keys to accuracy with BPCR (or at least believed to be so). BP fouling can also make this a very useful trait as you may not be able to chamber a groove diameter bullet if you have a bunch of fouling. (I've read that while smokeless powder is about 95+% converted to gas BP is closer to 35% so there is a ton of fouling.

Lead alloys are necessarily soft to get this to happen. I think most of the target shooters out there aren't shooting anything harder than about a 16:1, and I read a lot of 20:1 references, which is really soft to nose deformation on firing is quite probable on a longish nose shape.

In BPCR there is an obvious (at least to me) advantage to PP bullets in that they don't have grooves, but I'm not sure it's being borne out on the range. There are disciples of both.

Not sure if this is helpful or interesting. I too have often wondered just how much we could improve on the shapes that are out there today. Boat tails are pretty definitely out. In my time dabbling with BPCR there is certainly nobody with your understanding of ballistics that has looked at the question of ideal bullet shape. Most of what I've read looks like a lot of trial and error and inspiration.

 

[bruce moulds]

brian,
thank you for the reply.
yes smooth sided bullets show less wind deflection and require less comeup than grooved ones, suggesting reduced drag.
the easiest way to shoot smooth sided bullets is to paper patch.
interestingly grease grooves are referred to as "speed humps".
the drag produced by speed humps could however be an aid to stability, as they are on the back half of the bullet.
using jbm ballistics, I have established an average g1 b.c. out to 1000 yds, of around 0.530 for a pp elliptical I use.
the bullet is 1.5" long and comes out of a 13" twist at 1330 fps, so the stability factor is fairly high.
long range bp target rifles tend to run stability factors of 1.8 to 2.0.
this could be quite useful, as 3 seconds flight time could allow for an amount of spin decay.
my main concern regarding stability is to find an optimum nose shape to minimize hammering of shockwaves.
even more desired is knowledge of nose shapes that have the least drag in transonic speeds in order to retain velocity as much as possible.
I have heard of von karmen shapes, and power series shapes, but do not understand about that, and do not know if it is relevant.
if you were to design a bullet for a mach range of 1.2 to 0.8, what shape would you make the nose given that it cannot be over 1.7 calibres long?
keep safe,
bruce.