The principles relevant to the factors mentioned above are fully discussed here:

https://www.bullet-behavior.com/forum/totally-technical/relative-penetration-values-for-dangerous-game-cartridges

Momentum, Sectional Density And Penetration: Using The International System Of Units

About Penetration

A short visit needs to be made to the concepts that drive penetration, namely bullet mass and velocity. The force that drives a bullet (mass x acceleration) is its retained momentum over the very short time of its penetration into an animal exerted onto whatever tissue is in contact with its frontal area. It either passes through a buffalo’s shoulders or gets stuck somewhere along its path within about one 500th of a second.

A physics law states that to modify a body’s momentum there must be a force applied to that body. A car that weighs 1,000 kg (about a ton), travelling at 30 meters/second (about 65 mph) has a momentum force of 30,000 kilogram-metres per second. A force of one thousand kilogram-metres per second is called 1 Newton. To brake the car to a stop within ten seconds a counter-force supplied by the drag of the wheels on the road of 30 kilogram- metres must be applied for a time of ten seconds. The counter force needed is thus 30 Newton to be applied for that 10 seconds.

Now, if the car with its 30,000 Newton-metres per second momentum was stopped within one second by a big bus standing in its way, a counter-force of 30,000 Newton would have been applied to the car.

This also mean that the car applied a force of 30,000 Newton to the bus. What would the damage on the bus look like? The obvious answer is that the frontal shape and size of the car would show the imprinted damage onto the bus. The momentum of the car (30 000 kg-N/sec) and therefore a force of 30 000 Newton was imprinted onto the frontal area of the car during that second.

This imprinting force per a certain area of application is called impulse. This impulse of 30,000 Newton dented the bus on that specific area somewhat. At the same time the front end of the car was dented somewhat more due to its lesser mass and weaker construction onto which the counter force of 30,000 Newton worked. Had the car been made of solid steel the one second of its impulse would have dented the bus a bit deeper than the car’s normal construction - which is about equivalent to a Nosler Ballistic Tip bullet - did.

We can calculate the exact figure of that particular car’s impulse on the bus by dividing the Newton impact force by the area of impact. If the car had a frontal area of 2 metres wide x 1.8 metres high, then the frontal area would have been 3.6 square metres. The impulse during that single second onto the frontal area of the car was 30,000 Newton divided by 3.6 = 8,333 Newton.

Say the car was stopped not within one second but within 1/10th of a second? Then the force needed would have had to be ten times stronger, namely 83,333 Newton! When we come to calculating bullet impulse keep in mind that the time of the bullet’s force application is about one thousandth of a second.

(Next: To stop a .358" bullet with a momentum force of (284gr x 2,300 ft/sec) = 93 lb.ft/sec within one 500th of a second (time into a Cape buffalo body) a very large counter force or resistance is needed to be applied directly onto the frontal area of the bullet. We can therefor really accurately calculate " the bullet’s impulse onto the material in contact with its frontal area).

Bullet Behaviour: General Considerations

Kinetic Energy

Elsewhere in the forum as well as in the website I address the issue of what the effect of an excess of kinetic energy vs. bullet mass has on the carrier of that K.E. - namely the bullet. I shall not belabour this issue here save for summarising the baseline of this property of bullets because in the discussion to follow further on there will be brief references to K.E.

In summary: it was stated that as the bullet’s kineses becomes less during slow-down through the air and particularly at impact, K.E. - being latent heat energy due to kineses - is merely translated as heat into the bullet. Some of this acquired bullet heat may be conducted into the mass of meat or whatever component of the animal’s anatomy is in direct contact with the bullet.

As long as the bullet has some movement (kineses) the remaining kinetic energy will not be translated as heat but will be retained by the bullet as latent or potential heat. I also explained that kinetic energy, being potential heat and measured or calculated as joules on a scale from zero to a few thousand joules (where bullets are concerned) is just another form of the figures on a thermometer scale. That is why it is termed a scalar value.

A bullet can not forcefully eject (I think “dump” is the American term) a scalar value of potential heat. However, at rapid slow-down the potential heat of the bullet’s kinetic energy is indeed translated inside the bullet as raw heat which will be conducted by contact into its immediate surroundings. The blackly burned meat inside a wound channel where a fast bullet had suffered its most rapid slowing down is regularly observed evidence of this. Kinetic energy can not do any work despite the fact that it is religiously believed and propagated every moment of every day in US gun literature. Vector values like momentum and impulse can do work, but kinetic energy can not. There is no such thing as a bullet that has ”a ton of kinetic energy”. The property of weight can not be attached to the reading on a thermometer.

Besides, even if K.E. could be ejected from the bullet its value on the energy scale is so low that it would be totally useless as a working agent. A can of soda has more joules of energy in it than what is inside a 140gr bullet leaving the muzzle of a 7mm Remington Magnum at 3,100 ft/sec.

The Fallacies Of Momentum & Taylor’s Knock-out Values

Momentum. This is the working ability or force of a bullet’s mass multiplied by its velocity expressed as lb.ft/sec in American terms. A bullet’s momentum value at impact is the first quantity in the chain of vector based factors to begin expressing and quantifying the actual work it may be able to do. Momentum too, however, is a grossly misleading concept when seen on its own.

The relationship between a) the mass of the bullet, and b) its design and construction versus the mass of the obstruction it will meet must be considered and factored into the desired outcome calculation to form a judgement on how any one bullet will behave after impact despite its superficial momentum value. Just calculating any bullet’s momentum as is done in common literature without considering its design features and construction technique has no bearing on the actual performance it will have on an animal. The momentum figure calculated for a Winchester Ballistic Silvertip is not at all related to penetration - in fact it does not relate to anything, it is just a pointless exercise.

If the reason of such calculations of two different style bullets of the same calibre but of different design and weight, possessing the same momentum values at impact was to simply determine the theoretical quantum of meat damage that will be caused on an animal by either - no matter the appearance of that damage to the observer - then sure, bullets with the same momentum values will indeed create the same total amount of meat damage deep inside it or superficially. The quantum of work done will be the same but the width and depth of the damage may differ widely.

Specifics

Kinetic Energy, Momentum & Taylor's "knock-out" value

The table below shows two bullets of different designs having the same value of momentum:

7 mm Rem Mag 7x57 Mauser

Nosler Bal. Tip Peregrine VRG-2

Bullet Weight 130 g 175 gr

Bullet Velocity 3,400 ft/sec 2,450 ft/sec

Bullet Calibre 7mm 7mm

Kinetic Energy 4,523 joules 3,240 joules

Momentum 63 lb.ft/sec 63 lb.ft/sec

Taylor’s Knock Out Value 17 17

In our virtual test based on past empirical observations, to reach the heart both bullets will be shot through the low shoulder (humerus) bone of two similar big game. Study the typical front limb stance and structure of big game animals in the photo below:

Scapula. Often incorrectly called the "shoulder". Any shot “behind” or into this on Africa game is to probably lose the animal .

Shoulder Joint ("Shoulder"). Depending on the animal’s stance the bullet may need to break through this joint, or be placed into the triangle just “behind the shoulder”.

Humerus. The heart is mostly protected by this bone and will invariably be the first obstruction to face the bullet.

Elbow Joint. This often needs to be broken to reach the heart. The low shoulder “bulge” seen on all animals is formed by the tendons and muscles between the elbow joint and the shoulder joint. This muscle bulge is the first feature to be identified on the animal to finally decide where exactly to place the bullet.

There is no way a bullet of light weight or questionable construction can break these bones, then break through a rib, cut the heart, break through an opposite rib and break through the opposite low shoulder bones as well.

Please study and visualise the front limb bone structures protecting the hearts of the animals in the photos below (in the young gemsbok at the water the complete front limb bone structure including the scapula can be clearly seen). Then look at the opened anatomy in the rendering of an eland for understanding the useless value of momentum figures of just any bullet - as well as Taylor’s equally useless knockout figures with useless modern bullets when reading the table below that figure:

The perfect heart shot will be just above the visible humerus bone into the triangle formed by the scapula and humerus, 4" left of the shoulder joint - the original meaning of “behind the shoulder”.

In this particular stance even a standard cup and core bullet without a plastic tip of 170+gr will penetrate properly.

A very demanding shot through the elbow joint or humerus.

Same demanding shot as above: the heart is exactly behind the big elbow joint-humerus and thick ribs behind that.

The heart is exactly behind the juncture of the humerus where it articulates with the shoulder joint.

The heart is exactly behind the humerus bone.

Very demanding shot placement for the bullet- the shoulder joint must be broken to get to the heart.

Consider the bullet impact point for penetration through the heart in each of the above photos and relate that to the two 7 mm bullets with the same momentum value in the table:

7 mm Rem Mag 7x57 Mauser

Nosler Bal. Tip Peregrine VRG-2

Bullet Weight 130 g 175 gr

Kinetic Energy 4,523 joules 3,240 joules

Momentum 63 lb.ft/sec 63 lb.ft/sec

Taylor’s Knock Out Value 17 17

Nosler Ballistic Tip despite 63 lb.ft/sec momentum:

• On touching the eland’s resilient skin which is movably attached to the hard muscle and sinews covering the humerus, the plastic bullet tip will slam backwards, breaking open the fragile thin frontal jacket (it even happens on the skin of a little mule deer). The bullet’s thin frontal copper jacket will not be able to survive the Mach 3 impact, and together with the frontal narrow wire of unbonded lead inside will become brittle due to this massive force and become like gravel and even pulverised.

• Small pieces of brittle lead and copper (hundreds of them) are flung forward and sideways in a conical pattern up to a distance of about 10-12 inches into the shoulder (empirically observed by X-ray scanning of impala shoulder after Nosler Partition impact).

• The bullet’s rear end now tumbles, causing massive sideways meat damage as more brittle lead and copper slivers are flung off. As the mass is shed bullet speed rapidly decreases and the kinetic energy is translated into raw heat into the bullet softening the unbonded lead wire which now separates from the copper jacket. Sideways damage is massive.

• The rear jacket stays behind not much further than having passed the bone. The fragmenting rear end lead, where it meets a rib bone is now stopped, while individual slivers of lead gets flung in between the ribs, into the lungs and some of which may cut into the heart. The animal dies a slow death with a great many lead particles in the carcass.

Peregrine VRG-2 due to 63 lb.ft/sec momentum force:

• The solid flat nose of the bullet punches a calibre sized hole through the skin and bone, shattering it, and on reaching meat the front supersonic shock cone attached to the mephlat radial edge causes the start of the vapourising of the fluids in the tissue to initiate a larger than calibre vapour bubble (wound channel) around the bullet, lessening the rotational and linear drag.

• As the bullet entered the skin and flesh at about Mach 2 it sucks in behind it a rush of air, filling up and pressurising the wound channel from behind. The flat nose ensures that a large amount of bullet mass stays concentrated to absorb the raw heat as kinetic energy is translated during slow-down. No mass is lost so the bullet retains momentum.

• Any yaw is countered by what is arguably presently incorrectly termed “shoulder stabilisation” This is a correcting force exerted on the stagnation point on the flat nose surface of the mean isobaric tissue pressure from ahead. This stagnation point is momentarily displaced from the mephlat centre as soon as the slightest in-tissue yaw is experienced and auto-stabilises the front end. (More about this later).

• At the nose/shank junction the secondary shock cone enhances the vapourised “super cavitation” around the bullet which allows the bullet to retain it gyroscopic rigidity by preventing rotational drag on the shank.

• At the nose/shank junction the secondary shock cone enhances the vapourised “super cavitation” around the bullet which allows the bullet to retain it gyroscopic rigidity by preventing rotational drag on the shank.

• The solid flat nose of the bullet is not as easily deflected (yawed) by differing tissue densities including bone as round nose and standard radius ogive bullets suffer. Having no increase in expanding frontal area and therefore no sudden drag increase, the penetrating impulse is retained.

• The bullet will fly nose-on, punch a 4x calibre hole through a rib and rip a 10x calibre hole through the heart, assisted in this by the the hydraulic shock front it carries. If the atrium (top chamber) is hit the hydraulic shock wave and super cavitation will split the top of the heart open due to the hydraulic shock transmission through the amount of incompressible fluid under pressure in these contained chambers.

• The frontal increase to maybe 1.1x calibre on impact with bone will not in the least be affected by deceleration K.E. raw heat being released into it due to the amount of matter present. Experience shows that the bullet will break through an opposite rib and break the humerus bone and either gets stuck there or against the resilient opposite skin which acts like a shock absorbing spring.

Taylor’s Knock-out / Knock-down Value. John Taylor never proposed this relative figure as being at all related to killing an animal. He used it as a relative index for the momentary debilitating neurological shock the shot beast experiences when a wide and heavy projectile penetrates deeply into the chest part of the body body even though missing the heart.

Furthermore, this knocked-down or knocked-out condition referred to large animals like buffalo and elephant shot with big bore projectiles from very close in and allowing a momentary opportunity to ride up close to it for a quick brain shot. The same index figure of 17 for the two bullets in this discussion indicate that for modern lightweight, fragile ammunition it has no application value. Both the projectiles have the same index, only one can kill the animal outright, and none of the two has any “knock-down” ability.

The Sectional Density Fallacy

In one sentence: Unless it is a value related to a monolithic solid bullet that will have no frontal expansion, sectional density figures, like kinetic energy, hydrostatic shock and bullet momentum are falsely conceived and represented sales gimmicks by bullet manufacturers. It has zero value in our study of what happens to a bullet at impact on an animal’s shoulder and beyond.

Retained sectional density and its influence on sustained penetration after impact can be calculated for only one design of expanding bullets in existence - the Peregrine VRG-3/4 series. It will in each instance invariably expand in a rounded mushroom shape to about 1.5x calibre from impact velocities as low as 1,800 ft/sec to as high as 3,000 ft/sec. This bullet design is the only one that creates a perfect “mushroom” with no ragged petals that are either lost (Barnes, GSC at impact beyond 2,600 ft/sec), or which lowers the in-animal gyroscopic rigidity and straight line penetration by having ragged individual petals inhibiting rotation on big game and which may result in tumbling.

This design with its consistent 100% weight retention assists the hunter who likes to do calculations and pre-planning for the proper design and weight of the bullet to be used in each of his rifles dedicated to small, medium, big - or large game animals. Of course every premium bullet on the market is a quantum step upwards from the traditionally weak cup and core bullets. The above assertions do not take away the fine ability of the Swift A-Frame / GS Custom / Rhino / Barnes / Impala series of excellent performers.

There is no excuse however to put old style bullets like Remington CoreLokt, Nosler Ballistic Tips and others into an animal that have a known history to already at impact start shedding its mass, sectional density and momentum.

Impulse And Retained Penetration Index

Penetration impulse is the momentum force applied to a specific surface area-the frontal area of the bullet in contact with its obstruction. Into the same medium penetration depth will be relative to the expanded frontal surface reducing the sectional density, integrated with the retained momentum after the slowing influence of the higher drag force created by the larger frontal area. For the calculation purposes this drag coefficient is ignored.

My index of Relative Penetration Impulse figures has become an accurate reference for penetration estimation once the typical expansion of a bullet as well as its weight retention after impact is known. Presently only the South African designed and manufactured Peregrine afford this luxury, and to a lesser extent the Rhino, GS Custom, Swift A-Frame and Barnes series of bullets.​

The approach presented here can not with any accuracy review those bullets with proven unpredictable integrity on the shoulders of Africa big game. Unless used for brain shots when culling I have stopped loading the following types many years ago in any cartridge:

• Sierra Game King.

• All the Noslers.

• Speer Grand Slam.

• PMP "Red Kudu" (at least PMP responded to our complaints and re-tooled to produce the ProAmm series)

• Remington Corelokt.

Field experience indicate the Hornady Interbond as the present cup and core standard against which all else must be measured (after the most excellent Speer Deep Curl was suddenly removed from the shelves). Federal Fusion is on a par with the Interbond and the Federal bullet shows a remarkable similarity to the Deep Curl . The Barnes series perform as an almost-premium bullet, and field observations identify the Peregrine, GSC , Rhino and Impala series as the premium bullets to use - the latter on mostly non-dangerous game. The Hornady Interlock, PMP ProAmm, SAKO Hammerhead work fine at impact velocity below 2,400 ft/sec when they do not expand wider than 1.5x calibre. The moment impact velocity is such that expansion exceeds 2x calibre in any bullet penetration suffers markedly.

To set a base line for comparison, let us first consider a non expanding bullet using its calculated static sectional density to set the impulse reference value for a relative penetration index for Africa big game. Using the 30-06 as a known quantity and using a 180gr Peregrine VRG-5 monolithic solid - which experience shows will penetrate through both shoulders of a kudu, wildebeest, zebra (and therefor elk) at 200 yards. Consistent over-penetration, certainly, but setting a known baseline for understanding the following reasoning:

​

1. Using Peregrine VRG-2/5 or GS Custom bullets with no expansion:

1.a 30-06 180 gr solid copper Peregrine VRG-5:

Un-expanded sectional density: .271.

Impact velocity at 200 yards: 2,340 ft/sec

Impact momentum: 60 lb.ft/sec

Relative Penetration Impulse (RPI): 60x.271 = 16.

Knowing that this bullet with this RPI index of 16 penetrates completely through a kudu's shoulders at 200 yards we can use it as the 100% penetration standard. It will always penetrate all the way through.

Stepping up in weight to 220 gr, even though the impact velocity is decreased by more than 200 ft/sec, the 10% increase in impact momentum causes a 25% increase in the relative impulse force on the same bullet frontal area as shown below:

​

1.b 30-06 220 gr solid copper Peregrine VRG-5:

Un-expanded sectional density value: .331.

Impact velocity at 200 yards: 2,100 ft/sec

Impact momentum: 66 lb.ft/sec

Relative Penetration Impulse (RPI) = 60x .331 = 20.

As mentioned above that 22% increase in bullet weight causing a 10% increase in impact momentum amounts to a 25% increase in penetration impulse relative to the complete through ability of the 30-06 180gr non-expanding bullet at 200 yards. So, in the same calibre, increasing bullet weight by any percentage will, despite the lower impact velocity have a corresponding percentage increase in impact force and penetration will be increased if the bullet frontal area remains the same.

​

Should we use the same 180 gr bullet at original impact velocity but allow it to expand to 1.4x calibre and calculate the impulse force on the enlarged frontal area this is what we get:

​

1.c 30-06: 180 gr Peregrine VRG-4 bullet with 1.4x expansion:

Corrected sectional density value: .138

Impact velocity at 200 yards: 2,340 ft/sec

Impact momentum: 60 lb.ft/sec

Relative Penetration Impulse (RPI): 60x .138 = 8.

​

The moment we increase frontal impact surface area the Impulse force is immediately decreased despite experiencing exactly the same momentum value. In this case that impulse index per unit frontal area decreased almost by 50%.

When frontal area is doubled the drag force is also doubled, deceleration is quicker and retained momentum is less per distance penetrated. Penetration suffers even more.

Experience shows that this expanded bullet with a new RPI index of 8 will mostly stop against the opposite skin. We can use it as a new perfect penetration standard for an expanding bullet if it maintains 100% of the original weight like the Peregrine and Barnes bullets do.

2. Using Peregrine VRG-3/4 with known 1.4x calibre expansion for which we must now correct the decreased SD value:

2.a 30-06: 220gr Peregrine VRG-4 bullet with 1.4x expansion:

Corrected sectional density value: .170

Impact velocity at 200 yards: 2,100 ft/sec

Impact momentum: 66 lb.ft/sec

Relative Penetration Impulse (RPI): 66x .170 = 11.

The 22% weight increase causing a 10% increase in momentum causes a 38% penetration index increase relative to the reference 180gr bullet.

Using the above base lines of penetration ability one can calculate the worst case scenario for most premium bullets as well as for the top class bonded cup&core types.

So you shoot into the brain - like many hunters do in South Africa - and do not care about penetration? Choose the most accurate bullet for your particular rifle - the Hornady SST is a proven accuracy champion. For Cape buffalo and elephant brain shots? Stay with the flat nose solid premium bullets you use for heart shots.