Jim,
So I got thinking...If you should drill out the base of the bullet then the bullets moment of inertia will change and the bullet will resist being spun up compared to a solid copper. Inversely, it would resist being spun down.... Correct?
So, if this is true we would need a little less twist but trade off some of the BC due to having a lighter bullet. Of course, since it is lighter it will exit the barrel faster.
.....Trying to wrap my head around your new bullet designs and the external ballistics....Compromises, tradeoffs, etc...
Maybe you could use a hypothetical example using a 750 grain solid copper .50 BMG with a BC of 1.00 and an exit speed of 2800 fps. Of course we will use your recommended 10 twist.
1) To keep it simple we will use standard sea level and 2000 yards.
(a) Other than improved accuracy, what gains in velocity, at 2000 yards would be seen over a standard 15 twist?
2) If we drilled from the base and made the bullet 10% lighter or 675 grains and using a faster exit speed of 3000 fps...
(a) What would the BC of the bullet be now that it has less mass?
(b) How much less twist (slower) could we get away with compared to the 750 grain solid @10 twist?
(c) Would there be enough ballistic gains with the lighter, faster bullet. Such as a flatter, more efficient trajectory up to the transonic region?
3) If we filled the drilled base with aluminum ( 2/3 lighter than copper ) making it now essentially a solid again weighing 700 grains....
(a) Would there be any ballistic advantages to doing this design other than the added viability of that having a malleable aluminum core might make for a great hunting bullet?
Yes, I understand most of the physics in your hyper stabilized bullet ideas and see the benefits of you ''thinking out of the box''
BUT... I think for all of us that are math challenged, we would like to see some numbers that show it will be worth the cost and time to make the switch over. In other words " Old school vs New school "
Many Thanks
These are thoughtful and intelligent questions, MP, and I will attempt to answer them all, but it will require some thought and effort to do so properly.
First, I will explain the rationale for base-drilling certain of my copper ULD bullets. The cost in bullet performance of removing 6.9-percent of the solid monolithic bullet's mass is solely the 6.9-percent reduction in the Ballistic Coefficient (BC) of that base-drilled bullet. There are several advantages attributable to this base-drilling: 1) The 6.9-percent lighter bullet can be fired about 3.5-percent faster, for a wash in kinetic energy right from the muzzle. 2) Removal of this particularly troublesome mass near the spin-axis, but far from the CG of the bullet, makes the base-drilled bullet much easier to spin-stabilize in aerodynamic flight without directly affecting that bullet's ULD aerodynamic shape. 3) Ducting the base pressure inside the rear driving band allows that rifling-engraved rear driving band to expand elastically into the rifling grooves of the steel barrel--resulting in perfect sealing (obturation) of the hot powder gases at, or near, peak chamber pressure--just when it is most needed. [Smaller-caliber copper ULD bullets expand enough elastically for perfect obturation due to their higher inertial forces of acceleration. Larger-caliber copper bullets can use this additional help to expand enough for perfect obturation during firing. "Elastic" expansion of either type means that the bullets resume their "as manufactured" shape upon exiting the muzzle of the rifle barrel.], and 4) The effective combustion chamber volume of the parent cartridge case is increased slightly by this base-drilling, allowing a slightly larger powder charge to be loaded without increasing peak chamber pressure.
In the British Engineering System of units, which we use, BC is given in units of pounds of bullet weight divided by the square of the bullet diameter in inches-- that is, in pounds per square inch, or PSI. This is the "ballistic sectional density" portion of BC. If bullet weight is given in grains, it must be divided by 7000 to convert it into pounds. The BC of a rifle bullet is this "ballistic sectional density" divided by its "form factor" ratio of that bullet's aerodynamic drag coefficients (at each Mach-speed through the air) divided by the drag coefficients carefully measured for the reference projectile at each airspeed. The BC of any "Reference Projectile" is 1.0 PSI by definition. Each Gavre-standard reference projectile (G1, G7, etc.) weighs 1.0 pounds and is 1.0 inches in diameter. Its dimensionless "form-factor" ratio (i) is also 1.0 by definition, just because it is a "reference" projectile. If the drag curve for a rifle bullet (Cd versus Mach-speed) does not have the same shape as that of the selected reference projectile, its "form factor" ratio will vary with airspeed instead of being a nice constant ratio. That is why the BC(G1) of modern rifle bullets has to be given for various "velocity bands," and why ballisticians tend not to use BC very much if actual drag coefficient (Cd) data is available. Because the G7 reference projectile defines the basic shape of our "VLD" rifle bullets, their BC(G7) values are significantly less "velocity-dependent."
Base-drilling of modern monolithic copper bullets improves their mass properties in several important ways. Removal of bullet material near its spin-axis (its X-axis) very slightly decreases the "radius of gyration" about that X-axis, but it significantly decreases its cross-axis (Y-axis) radius of gyration because the material removed was far from the bullet's CG. The combination of these two effects directly increases the gyroscopic stability (Sg) of the spin-stabilized rifle bullet. For my copper ULD bullets, the Iy/Ix ratio for the solid (Mark I) bullet is 13.5, but it is only 12.0 after base-drilling; increasing the Sg at any spin-rate by 12.5-percent. By shifting the CG of the drilled bullet nearer to its aerodynamic Center-of-Pressure (CP), the lever-arm creating its aerodynamic overturning moment (M) is also significantly reduced. Since Sg is defined in aeroballistics as (P^2)/(4M), decreasing M also increases Sg. [The canonical variable P used by ballisticians is proportional to the spin-rate of the bullet; so increasing the spin-rate of the bullet by 41.4-percent (as proposed for "hyper-stability") will double the Sg of the bullet at any airspeed.]
I hope this clarifies my reasons for base-drilling the versions of my copper ULD bullets intended for "transitional" use in rifles having conventional twist-rate barrels. The Mark II ELR versions of my copper ULD bullets will not have base-drilling because they will be properly fired only from (approximately) 20 calibers per turn fast-twist rifle barrels, where retaining maximum bullet weight is the overriding design goal for achieving maximum supersonic range capability from very large "over-bore" cartridges. The Mk II ELR bullets will be 5.7-calibers in length versus 5.5-calibers for the "transitional" Mk I ULD bullets.
I will post more answers to MP's questions as I work them out.
