Having a valid understanding of the problem, the solution is relatively basic.
The aforementioned issue of the “trapped air” scenario is readily rectified, if provision was made within the bullets base design that would allow the air to escape or otherwise be allowed to be replaced by the target mass.
The adding of “channels” along the base of the projectile, more or less laterally to intersect with the base of the inner cavity, will provide an evacuation path for the ambient gases.
This can be accomplished by adding “vents”, or “ports” in a radial pattern in such a way as to 1., not interfere with the designed aerodynamic flight characteristics of a given projectile, and 2., not weaken the overall expansion process.
Variations of the actual port designs will be relative to the multitude of bullets designs, weights, shapes, velocities and a host of other factors.
The results of this Ported Bullet design are significant;
By eliminating the “air factor”, the bullet reacts/opens much sooner on contact with the target, with a resultant exponential increase in reliability and performance.
Here is a graph showing the velocity of a bullet as it penetrates a block of standard ballistic gelatin. The bullet is a .357” (.38 special) 135 grain semi-wadcutter (aka the Speer Gold Dot JHP in the case of failure to expand). I did a numerical simulation with a dimensionless drag coefficient based on other weight SWC bullets tested in ballistic gelatin.
What this means is that if the bullet were to initiate expansion immediately upon entry to the ballistic gelatin, it would have 860 fps worth of energy (222 ft*lb of energy) to deform the cavity – but if expansion was delayed until the bullet had penetrated three inches into the gelatin (as is the case with current technology JHP bullets), the bullet only has 718 fps worth of energy (154 ft*lb of energy) to deform the cavity.
Energy Analysis of vented vs. standard hollowpoint bullet.
Air pressure in hollowpoint bullet cavity in flight at 850 fps:
Stagnation pressure in a compressible fluid (air) is:
Where:
p is the static pressure (atmospheric)
pt is the stagnation pressure (pressure in the cavity)
M is the mach number
Y is the ratio of specific heats (air = 1.4)
Therefore the stagnation pressure in air is:
This is the initial air pressure in the cavity of the hollowpoint as it flies through the air. The pressure at which the bullet expands can be assumed to be the 75% of the stagnation pressure in water, which is:
Where:
p is the density of the fluid (water = 995.6 kg/m3)
v is the velocity of the fluid (in relation to the bullet)
Then the stagnation pressure at 800 fps (243.84 m/s) is:
So the pressure at which the bullet expands (75% of the stagnation pressure) is then 25136.16 kPa, or 25.1 MPa.
If we assume the bullet is a Speer Gold Dot 135 grain low-velocity JHP with a measured cavity volume of 0.1 cm3, the work done to compress the air before expansion is (very simplified equation, approximate):
The change in volume is calculated by assuming it will be isentropic compression (no heat transfer in or out, aka instantaneous):
The trapped air in the cavity of the Gold Dot is wasting 0.83% of the kinetic energy.
Exterior (trajectory) Ballistics
First, regarding bullet mass change from hole drilling: a typical jacketed bullet has a density of about 10.7 gm/cc which equals 165 grains/cc. A 1/32” hole, about an eighth of an inch deep will have a volume of 0.00157 cc’s. 0.00157cc X 165 gr/cc = 0.259 grains. Three such holes will thus weigh less than a grain. That is within manufacturing weight tolerances for many bullets, and may therefore be ignored for trajectory purposes at all but long range benchrest accuracy levels.
In his book, Rifle Accuracy Facts (Precision Shooting Pub., 2nd Ed, 2000, pp 171-172), aerodynamicist Harold Vaughn drilled a larger hole in the side of 90 grain .277” rifle bullet to intentionally unbalance the mass. It resulted in the center of gravity being offset .00118” from the centerline. This opened the otherwise very accurate (1/4 moa) rifle’s groups up to about 2.5” at 100 yards. That spells disaster to a benchrest shooter, but a defensive load pistolero would be happy if about 2.5 moa were the only source of precision error he had?
Since your 1/32” hole, assuming it to be about an eighth of an inch deep, will only move the center of gravity of a 158 grain .357” diameter bullet by about two ten thousandths, it seems to me you are again doing something negligible to the trajectory for most purposes, even if you don’t drill more than one hole. Assuming wobble area were proportional to CG offset, you would be contributing an error area of about 0.4 moa by doing that. Of course, it won’t be that simple, rotation rate and stability factor at the velocity have to be considered, though they should make the effect on the 158 grain .357 at pistol velocities even less. But, of course, you are attempting to maintain balance anyway by drilling around the bullet. So, again, I don’t see how accuracy error significant to anyone but a benchrest or a long range varmint rifle shooter is likely to be introduced by adding your holes? It certainly won’t impact normal hunting accuracy.
This has the potential to change every hollowpoint in the world. It corrects a serious design flaw in every hollowpoint ever designed. Impressive.
-Isaiah Kellogg
Aerospace Engineering
MO. Univ. Science & Technology
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