Penetration Index & Energy
See A.B.Alphin, Any Shot You Want, On Target Press 1996
About Penetration Index
The penetration index is calculated by dividing kinetic energy with the frontal area of the bullet and multiplying the result by the sectional density, as described by A. Alphin.
If you simplify the formula, you will find that the fundamental relation is proportional to the momentum divided by the area. The actual numerical value is squared, divided by 2 etc.to make the numbers better reading.
This number, called "momentum density" is a basic value calculating the penetration in solid materials of nondeforming projectiles etc. including HEAT warheads and the like.
This is an improvement on the older momentum theories, but for penetration in game you have to take into account the stability in aqueous media. For this read the chapter on the SuperPenetrator.
Penetration Index smaller than 85: doubtful, not recommended for head shots on elephant. PI between 85 and 100: just suitable. PI between 100 and 120: well suited for head shots. 120 to 130: very reliable. More than 130: absolute top values for big game cartridges, red highlighted.
The PI is a valuable figure to compare the relative penetration ability of non-deforming bullets for a given medium. It has nothing to do with killing power or knock down ability or other, most useless figures given in literature. It is a relative figure and not linearly correlated to the penetration depth in a target. That means a bullet with PI of 70 travels not half the way of one with a PI of 140. The real ratio depends on the energy dissipation on the way through the target. It is impossible to calculate the penetration depth in an animal by theoretical figures.
Some observations, which show how different the penetration depth on a head shot on an elephant bull can be:
All shots are with a .458, 500gr Woodleigh FMJ at 2400 f/s. PI = 132. Recovered bullets showed no sign of any deformation.
- Side brain shots
, with an angel up to 45° : the bullet excited on the opposite side. Penetration: more than 40".
- Frontal brain shot
, entered between the eyes, the bullet went through the brain, passes the Atlas joint, broke two ribs and travels another 40" through the flesh. Total Penetration around 80".
- Side head shot
, aimed at the ear hole, but the angle was slightly backwards, so I missed the brain and the shots were hitting exactly the Atlas joint. (The first vertebra, bearing the head). It must have an extraordinary tough structure. There was no bullet exit, they stuck under the hide on the opposite side. Penetration: about 30".
But the PI is a good means to judge the different big game cartridges (only solids) with respect to their suitability for elephant hunting and how much is the margin for difficult shots. It is shown, that the bigger the caliber the harder it is to get sufficient penetration and therefore less performance despite the tremendous figures of kinetic energy.
, Trusting on the myths around this caliber, a hunting party used reduced loads (less than 1900 f/s) to save their valuable double rifle. PI = 70. The could not drop any elephant with frontal head shots.
, Bell used a load with PI = 110 with success.
, 2400 f/s. PI = 132. Diagonal through an elephant bulls head: bullet exits.
, 2400 f/s. PI = 98. The same path as above from ear to opposite eye: the bullet sticks under the hide.
.600 NE and .700 NE
, It depends on the load, PI 70 to 90. No problems with side brain shots, but there are a lot of reports on failures with frontal brain shots. Sometimes the trunk can be a very hard to penetrate obstacle. But the old ivory hunters developed the technique to knock down the animal and gave it a final lung shot.
, PI = 130, very good reputation since its introduction as one of the best performers with respect to penetration.
4bore / 22Hornet
, Almost same penetration, with Selous shot behind the shoulder enough penetration, but the Hornet would have to little energy for a killing lung shot.
There is another simple rule for a dangerous game cartridge with a safety margin:
Use a .400 upwards diameter bullet with a sectional density of minimum .310 at a muzzle velocity of 2400 f/s.
The .458 500gr FMJ bullet in a belted H&H case (Lott, Watts, Ackley) are all loaded to 2400 f/s. That requires a little improvement to the Lott: Case 2.850, no tapered,but cylindrical neck, use of modern "High Energy" powder.
This chapter is not important for a hunter, but some people like formal expressions to judge their cartridges.
Because the listed data of a cartridge (weight, velocity, energy and caliber of the bullet) give not directly a measure of its efficacy, since decades authors tried to formulate numbers which reflect its quality. The basic data are only weight, velocity and diameter (or related figures like cross sectional area, radius etc). Physically meaningful calculated data then are the momentum and kinetic energy, which also lead not to sufficient information on its behavior in animals.
The authors now tried to get more significance of a physical property by adding (multiplication or division) some other values. This procedure normally gives not new physically meaningful numbers but is a kind of weighing energy or momentum with mass, cross section or the like. So authors were creating a lot of "indexes". But all these indices are overrated or misinterpreted, esp. when expressions are used like "killing power"or "knock out value". Some are useless, some are only meaningful if limited to a small range of caliber, weight etc. But than we can also judge from our experience. A bigger bore with near the same velocity is better than the small bore......and so on. Alphinīs PI is only used to have an impression on the penetration of solids. Nothing more. Not its interaction with the animal. Not the killing power of a bullet. Energy multiplied with diameter, radius or frontal area makes no sense. Energy distributed over a greater area results in less efficiency. ( A-Square Shock power, Arnolds Arms, Lott EEE2). The same applies to the momentum, evtl. multiplied with diameter etc. (Hatcher, Taylor, Keith, Ackley).
Energy or momentum divided by cross section or multiplied with the sectional density makes sense esp. for non deforming bullets. The more energy acting on a specific area the better the effect. (A-Square Penetration Index, Fuller, Lott EEE1, BSI). Also Matunas OGM, energy multiplied with momentum, results in a preferred weighing of the mass of the bullet. The BSI is equal to Lottīs EEE1 divided by the velocity. (Not taken into account some constants to make the numbers "looking better").The Penetration Index is proportional to the Momentum Density.
The validity of indices is often limited to neighboring calibers. If a .308 220 gr bullet at 2400 f/s shows the same BSI as a 12 gauge slug at 1400 f/s, it may be sufficient for a comparison on deer, but what about the result on an eland?
Because all the indices cited are developed from exterior ballistics data it is difficult to predict what is really happening when hitting an animal. What we need is a bullet performance index BPI, especially for soft points, evtl. for different target velocities. It should not calculated from bullet parameters, but derived from experiments on standard simulation targets. The main question would be: At what distance on its path through the animal does the bullet transfer most fo its kinetic energy to the animal. In the real world most of the energy is dissipated to early and not effective before reaching the vitals. A bullet leaving only a fraction of its energy (E in minus E out) in the body is often more effective than a bullet of the same energy transferring all its energy to the animal. In the first case there is a chance of transferring more energy to the vitals than in the second case, where all the energy can be dissipated in outer tissue. With conventional soft noses a high percentage of its energy is transferred without any effect on lethality to such outer tissue. That is what the BPI should give in the first instance: The amount of energy transfer as a function of the bullets path in different tissue and at different velocities. Next is the question: What kind of energy is the transferred one? We need work for crushing and cutting tissue and bone, not effective is displacement and heating of tissue.
Mechanism of penetration
Investigations of Fackler et.al. on military spitzer bullets confused some amateur ballisticians and generated some myths on tumbling and turning over of the bullets in the animal. Shoulder stabilisation may occur with mushrooming soft points, but is not the reason, why solids are going straight through the animal. The inertia of the bullet keeps it stabilized along the short path in the animal. The medium is not the dense tissue, but a bubble of water vapour of low pressure, generated at the nose which is jamming through the tissue and the hydrodynamic flow cuts off the bullets shank thus keeping it free from friction and other forces. "Supercavitation". Differences in the shape of the front area (disk, flat, small meplat, hemispherical RN) are important for the generation of the supercavitation bubble and therefore penetration, but have only a small effect on the difference in wounding, the main effect is caused by the hydraulic pressure. The reason for traversing straight through the tissue is that the gyroscopic stabilization, caused by the twist of the barrel for stabilization in air, is preserved in the tissue. There is no interaction like friction or other strong forces on the main part of the bullets body. The bullet behaves like a spinning top in a gaseous cavitation with a small point of support at the nose. Here we have the only damping mechanism of the angular momentum by friction, that means, we observe a relativ small decrease of the gyroscopic stabilization. When the bullet does`nt exit and the drag has stopped the travel of the bullet, it sticks nose in front or just turned about 90 degrees. If the bullet is well stabilized in air, there is no influence of the angle of impact over a wide range.
In general, it is very important to use bullets with a sufficient penetration. Many disappointing shots with the older big cartridges are caused by insufficient penetration. You may pump a lot of energy in one half of a buffalos body or a head of an elephant, if the bullet doesn't penetrate to the vitals of the animal, you loose it.
How amateur ballisticians are confusing their readers with useless tests you can see at numerous "tests" published in magazines and the internet. You can read that revolvers show the same penetration as a .500 rifle, or honestly: "The newspaper test was a total failure period. Wet paper was tried and dry paper was tried but whether I tried to put 9 shots or 3 shots into the 12 by 12 area we constantly lost bullets. After lining up the barrel for left/right and up/down a shot into the center of the 12 by 12 area exited the box within the first 28 inches." This author was very disappointed, as his tests in plywood showed far more penetration. My comment. 28 inches is a typical maximum length of a supercavitating RN bullet which is stabilized in aqueous media.
Discrepancies are observed, because the testers donīt know what they are doing with respect to the mechanics of penetration.
Penetration is a very complicated matter and test results are highly dependent on the methodology and and the test medium used. The only value of artificial target media such as plywood, wet paper, gelatin and others is to compare one bullet to another in that particular medium. Generally we can distinguish two different mechanisms of penetration in animals:
1. The penetration in aqueous tissue; limited by the stability of the bullet's travel in a supercavitation bubble;
2. The penetration in bone, hide and sinews; limited by the forces acting on the bullet, (jam pressure, friction, shear resistance, viscosity).
for 1.: Because the penetration in aqueous tissue is the most important, the best correlation an amateur can achieve, is with targets of high water content (80% like tissue) or thin-walled water containers. Penetration is not a question of friction, density or other forces decelerating the bullet, but how long the gyroscopic stabilization is preserved in a cavitation bubble, which is generated by the bullet. If this stabilization is lost, the bullet starts tumbling and changes its direction and penetration comes to an end. For more penetration = stabilization, the concept of the SuperPenetrator was created. (see the page on "SuperPenetrator")
for 2.: For hunting bullets, we also have to consider the stabilization in solid materials like bone, sinew and hide. Whereas long spitzer solids are prone to tumbling, conventional round nose solids are quite stable even in solid materials (including testing materials like plywood). Because in this case the center of movement is at the front end (nose), any disturbing force is compensated by forces acting on the shank and keeping the bullet in line. As this mechanism is very different from the penetration in aqueous tissue, which is dominant in animals, penetration test in plywood or other dense materials are of limited value in evaluating the properties of hunting bullets.
Further it is very important to look at the conditions of launching the bullet, esp. the distance to the target: Twist, length of the bullet, distribution of weight along its axis, barrel and muzzle properties causes a yaw at the muzzle. The bullet has not yet achieved proper gyroscopic stability shortly after it exited the muzzle. The bullet's nose still yaws in a diminutive circle around the line of flight (trajectory). This nose movement is called 'precession' If the angle of yaw (precession) is relatively high near the muzzle (3°-5°), the bullet tends to tumble at impact. It is unable to generate the stabilizing supercavitation bubble in aqueous tissue, because it tumbles immediately with so much yaw, that the yawing section exceeds the volume of the supercavitation bubble. This yawing decreases during travel and the bullets become "asleep". Full stabilization of big bores for a twist of 1:16 or 1:14 is established at about 20 yards. That is the reason why long rifle solids often fail at close distances (finishing shots) and at tests with the target within a few cm of the muzzle.
Handgun bullets are not affected by this phenomena, because their stability near the muzzle is much higher, their length is comparable to the diameter and they are not prone to tumble and if, there is not too much leverage to throw them out of line.
Testing straight line penetration of solids
When I were optimizing the design of the SuperPenetrator for hunting purposes, I used test media for the supercavitating effect and penetration in aqueous media and for penetration in hard materials separately. For the penetration in water I used plastic 1.32 gallon containers in a row, each 18.5 cm ( 7.3" ) width, up to 3 meters total. But I could not stop the bullets. For simulation of bone, hide, sinew etc. I used particle boards, 38 mm thick, in a row up to 20 boards which stopped the bullet after penetrating around 17 boards.
This experimental setup was not optimal for quick tests for a comparison of different bullet designs, especially for the numerous new FN designs. In the meantime the better penetration ability of FN bullets is common sense and many manufactures are offering such bullets. E.g. "Dzombo" in SA. When Barnes, as a major manufacturer, came with their new FN banded Solids, I repeated my tests for comparing the original SuperPenetrator with the new Barnes FN.
I now use for a quick characterization of different bullets a setup. which consist of an alternating row of 1.32 gallon water containers and 38 mm particle boards. I need maximum 10 containers/boards, so the resolution is not enormous, but sufficient for a quick impression.
The sequence is: container1, board 1, container 2, board 2, container 3, board 3, ............
By chance the Woodleigh RN, after leaving the setup, hit a paper target. Apparently it was flying nose down and turned over 90 °.
The procedure of the bullets travel through the setup is always resembling
It starts tumbling in a container number N. (It alwasy starts tumbling in the water, never in the particle board)
Then it penetrates board N more or less keyholing.
It veers off in the container N+1 and exits the setup
The board N+1 remains intact.
Bullets tested so far
1.) .458" 490 grs SuperPenetrator Vo= 2350 f/s N = 7
2.) .458" 450 grs Barnes FN Vo= 2445 f/s N = 5
3.) .458" 400 grs SuperPenetrator Vo= 2460 f/s N = 4
4.) .458" 500 grs Woodleigh FMJ Vo= 2300 f/s N = 3
Bullets recovered with exception Barnes FN
Tumbling and veering occurs only in water resp. aqueous media
Velocity doesnīt compensate for weight, see 2.) vs. 1.)
Higher SD performs better, see 2.) vs. 3.)
RN solids are absolutely obsolet, only reliable for broadside shots
For similar design the Penetration Index shows a good proportionality