Updated: Sep 4, 2022
What Is Bullet Impulse?
Say a kid is bowling a 2.2 kg ball down an alley towards the end. Say there are no pins, and just before hitting the backstop the ball is travelling at (probably) 7 metres per second. Its momentum before hitting the obstruction of the backstop is (2.2 kg x 7 m/sec) = 15 kilogram.metres per second. In the International System of Units 1 kg.metre/sec momentum is also called 1 Newton-second. So the momentum value can also be called 15 Newton-second.
What makes this example relevant is that 15 Newton-second is exactly the momentum value of a 300 gr bullet from a .375 H&H hitting a Cape buffalo's shoulder from 50 metres at 747 metres per second on its way to cut open the heart's top chambers. Can a kid's bowling ball that has the same 15 Newton-sec momentum as a 300 gr .375 bullet kill a Cape buffalo? No, it can not. So how about without further debate, right here, right now we also bury the myth - like we did with kinetic energy – that momentum, even though it is a vector entity, can kill an animal.
So something other than a raw momentum value must therefore give a force to our imaginary, rather blunt "bullet-scalpel" in order to cut through all the resistance of skin and sinew and bone and flesh to reach the heart and cut off the oxygenated blood supply to the buffalo's brain and thereby killing it.
The answer can be found in examining two entities, 1) the frontal "cutting" radius of the imaginary “bullet-scalpel” which interacts directly with the material it is penetrating (creating a resistance to the cutting action - also called profile drag) and, 2) the time taken during which the interaction between the bullet and the obstruction changes the bullet's momentum (also called impulse). Furthermore, if there is any dynamic shape changing in the frontal area (nose radius) of the bullet during the penetrating process there will also be interaction between (1) and (2) which will affect the impulse force.
.375 calibre Peregrine VRG-2 monolithic copper solid bullets with total frontal area = 71 sq. mm. From 50 yards this bullet will penenetrate the thick skin and sinews and humerus-scapula joint of a Cape buffalo, cut through the overlapping 1" thick ribs, flare open the heart's top chambers, cut through the opposite overlapping ribs, punch through the opposite shoulder bones, cut through sinews and skin - and be lost in the dust some distance beyond the buffalo. An amazing amount of "energy being transferred" if you want to use the term - and work done inside the animal during its passage.
The profile drag value is a function of velocity times the total frontal area of the projectile in contact with the obstruction. The higher the profile drag figure as with the expanded 320 gr Rhino Solid Shank bullet from a .375 H&H on the left, the larger is the deceleration force on the projectile and the sooner will it experience a lowering of its velocity and its momentum and therefore have less penetration depth than a monolithic solid bullet of the same weight and impact velocity.
Because it slows down rapidly and comes to a complete stop, the average velocity during its interaction with the obstruction is lower than that of the solid, unexpanding VRG-2 bullet and therefore the time taken for this interaction is longer.
Momentum and Impulse
The momentum of an object is the product of its mass and velocity. Impulse is the change of momentum when a large external force is applied to an object for a short interval of time. In a collision with another body the impulse experienced by the impacted object is equal to the change in momentum of the impacting object over a set time. Let us say that in different words: When an object with a certain value of momentum impacts with another body with zero momentum the impacting body will decelerate. The difference between the start and end momentum values of the impacting body over the time of deceleration is the impulse of the impacting body on the impacted body.
A relevant example is the impulse of a 300 gr (20 gram) monolithic solid bullet from a .375 H&H on the shoulder of a Cape buffalo. At the moment of impact the bullet travels at 747 m/sec. After it has broken both shoulders it exits the buffalo at 305 m/sec. Its initial momentum was 15 kg.m/sec and its exit momentum was 6 kg.m/sec, so there was a 9 kg.m/sec change in its momentum value.
This change in momentum occured while the impacting bullet was in contact through the 1 metre wide body of the buffalo at an average velocity of (747m/sec + 305m/sec = 1052 ), and to get the average velocity through the buffalo we divide by 2 = 526 metres/sec. This relates to a time of deceleration of 0.502 sec inside the buffalo. So the bullet had an average momentum of (15kg.m/sec + 6 kg.m/sec = 21 divided by 2 = 9.5 kg.m/sec) impacting on the living fibres ahead of its frontal area. This 9.5 kg.m/sec interacted with the living fibres of the buffalo for 0.502 of a second, which is an impulse force of 19 Newton.seconds (N.s) exerted by its un-expanded frontal area that was in contact with the flesh and bone.
This in itself still does not tell us how well the bullet will overcome the resistance presented by the shoulder bones of the buffalo and penetrate to reach and cut open the heart and hopefully break the opposite shoulder as well, and penetrate all the way through. The total drag force executed by the living fibres on the bullet’s frontal area must be overcome by the impulse force to achieve the killing objective.
Even though the bullet will be slowing down all the time of its passage we want it to pass right through and do as much damaging work as possible along its way instead of losing all its momentum somewhere inside the animal. The bullet’s impulse force must be integrated with the size of the frontal area (the bullet’s profile) before we can form an idea of its penetration ability. This will give an index of penetrating ability compared to indices of bullets of other weights and / or frontal cross sections. Therefore the Impulse force per unit of frontal surface area (or in other words the work done on the flesh and bone in contact with the bullet's frontal area) must be determined.
The total frontal area of a bullet of .375” (9.5mm) diameter is phi x the square of the radius of the bullet and is about 71 square millimetres. The average impulse force per square millimetre frontal area of a monolithic solid .375 H&H bullet shot from 50 metres going through the shoulders of a Cape buffalo therefore is 19 Newton-metre divided by 71 square mm = 0.27 N.s per square millimetre. From experience we know that this impulse force value on that frontal area of our .375 H&H “bullet-scalpel” is enough to break through the inside shoulder of a Cape buffalo, break through overlapping ribs, cut open the heart, break through opposite overlapping ribs, break through the opposite shoulder bone and exit to fall into the dust some unknown distance beyond the animal. By passing all the way through the animal it has done the maximum possible amount of damaging work.
For maximun damaging work to be done must the bullet not rather stay inside "to transfer ALL its energy into the animal" as is often stated?
Let us start to unpack this often expressed opinion by agreeing on the following:
For a 300 gr monolithic solid to create the following damaging work: break the on-side shoulder joint, punch through 1” thick overlapping ribs, cut open the heart, punch through opposite overlapping ribs, break through the opposite shoulder joint and fly off into the wild blue yonder 0.27 Newton.seconds of force on every square millimetre frontal area was needed.
Assume the hunter shot his buffalo at 100 metres and not at 50 metres with the same rifle / bullet combination. Impact velocity will be 2 280 ft/sec (690 m/sec) and impact momentum will be 13.7 kg.m/sec and not 19 kg.m/sec..
Because of the lower impact momentum initial penetration will immediately be slower and the bullet will decelerate quicker. From experience let me state that the bullet will run out of momentum against the opposite shoulder joint and stop right there, only making a small white mark on the bone. The average velocity between 690 m/sec and zero m.sec during penetration will be (690 m/sec ÷ 2) = 345 m.sec. Average momentum between 13.7 kg/m/sec and zero kg.m/sec will be 7 kg.m/sec. and not 9.5 kg.m/sec as in a shot from 50 metres. The work done on the organic material in front of the bullet (bullet impulse) will be 7 N.m divided by 71 square mm = 0.1 N.sec per sq.mm and not 0.27 N.sec per sq.mm. LOSING all its momentum and staying inside the animal this bullet did only about 27% of the work done by the bullet that passed through the buffalo.
(As an aside observation this is exactly the average impact impulse of a 286 gr bullet from 9,3x62 on a Cape buffalo from 50 metres. It is still completrely adequate – and in the big five (lion excluded but hippo added) area where I live and operate it is a very popular cartridge).
What about “better energy transfer” if the shot at the buffalo is from the original 50 metres and a best quality expanding bullet like a 300 gr Barnes TSX is used instead of a monolithic solid and the bullet does not exit like a flat nose Peregrine VRG-3?
First off - clearly when a bullet's total momentum gets absorbed by the interacting flesh and bone of the Cape buffalo like these 500 gr Hornady DGX bullets from a .458 Win Mag because it broke up and lost 50% of its mass there can be no consideration of successful "transfer of energy", even if it is accepted that such a "transfer" in fact ever takes place - which is just a vulgar way of expressing impulse.
Indeed, all the momentum that these bullets had at the moment of impact was lost to the buffalo - but it was randomly distributed little packets of momentum by the seperated pieces and did no linear damaging work regarding reaching the heart and beyond and was useless sideways wastage. The immediately reduced weight and velocity of the intact blobs of lead and jacket did not retain sufficient momentum to have sufficient penetration.
Back to the question of so-called "energy transfer" (retained impulse): In case of this 300 gr Barnes TSX out of a .375 H&H from 50 yards that was stopped by a Cape buffalo's opposite shoulder the following physics are applicable:
There was an immediate 1.8x calibre expansion of the bullet which resulted in an immediate increase in the frontal drag force on the bullet. By doing forensic processes of reverse analysis the following becomes evident:
The bullet reached the same stopping point (against the opposite shoulder bone) as did the theoretical VRG-2 flat nose solid fired from 100 yards.
Because penetration is dependent on frontal drag it means that the impulse on the expanded bullet's frontal area was the same 0.1 Newton.seconds per square millimetre.
This means that the work done per square mm. frontal area by the expanded bullet fired from 50 yards was the same as the solid bullet fired from 100 yards.
The amount of damage (work done) by the expanding 300 gr bullet was in practice about 27-30% less than the solid bullet because it lost its penetrating momentum and impulse force.
In summary, what are the practical take aways from all the above?
When premium quality expanding monolithic bullets are used the Barnes TSX, Peregrine VRG-3, Rhino Solid Shank, Ballistix - and other South African made expanding monolithic designs - as well as he Hornady GMX - will perform adequately on Cape buffalo even though they will not penetrate all the way through (the same goes for lesser calibres on soft skinned game).
Modern real solid monolithic bullets like the flat nose Peregrine VRG-2, GS Custom Flat Nose and (as yet untested in South Africa - the new monolithic solids by Barnes and Hornady which really are Johnny-come-lately copies of the 30 years old SA designs) will always give full penetration even on the most difficult shots on Cape buffalo when the .375 H&H or .375 Ruger is used. The same goes for the .416 Rigby, the American .416s, the .458 Lott, the .458 3" Express and .458 Sabi. The 480 gr. Peregrine flat nose monolithic solid in a .458 Winchester Magnum will again bring this calibre with its too small case capacity back into the same class as at least the 9,3x62.
Significantly, the hackneyed adage that on Cape buffalo the hunter should use an expanding bullet for his first shot and thereafter use a solid is shown up as a myth in the foregoing discussion. Why would you not use your best bullet which was designed and proved to create the most damage and deepest penetration first? On Cape buffalo if you know you can break both shoulders then do that with the first shot.
In a following missive a very successful, novel concept in monolithic solid, light-weight / high velocity bullets will be discussed - the light weight Impala conical nose and conical flat nose designs are what it is about. It may just be my only bullet I shall use on soft skin game in future. The base line of the manufacturer's design philosophy can be summarised by the example of the 130 gr sharp conical nose bullet for the .303 Brit at 3,000 ft/sec from a 24" barrel. It already has shown its performance on all SA game from the springbok to the 2,000 eland. I already have some experience with is hybrid brother in the .303 Brit, namely a 150 gr shallow conical flat nose at 2,700 ft/sec from my 23" Lee Enfield.
In the final post of this series the penetration impulse figures of different calibres - each with different bullets - wil be calculated and presented for reference. Unless the reader has had repeated experience of these cartridges in the field – which by luck I have had – those figures will only be comparable indices for penetration potential and not forecasts of actual penetration depth. Field observations during my life of hunting big game allow me to say that these calculated figures are in effect accurate comparisons and I could accurately forcast the penetration depth for each shot on an animal.
Our American readers may find the following interesting: So far this season on this ranch of 6,000 acres, visiting SA hunters from other provinces have killed 14x kudu, 14 x warthog, 4x red hartebeest and 6 impala. The cartridges used were 8x .308W, 2x 30-06, 1x.303 Brit and 1x .300 Win Mag. Apart from the Win Mag there was no discernable difference in wound channels between the .308W / 30-06 / .303 Brit. No kudu went further than 20 metres. All were complete penetration pass through.
The entry wound and wound channel made by the 165 gr Winchester Fail Safe bullet at 3,200 ft/sec from the .300 Win Mag was huge in diameter, did not pass through and a lot of sideways damaged meat had to be cut away from the kudu. Only a small piece of the jacket was found. It is not my first experience with the missnomer "FailSafe" design - and in my opinion it must be the most useless bullet coming out of the Winchester stable ever.
There is nothing wrong with the .300 Win Mag cartridge if you are not opposed to having a belt AND a shoulder to do headspacing on – but it has a bad name in SA because of bad bullets used by most who own it. Using a properly designed and constructed 220 gr bonded core bullet will make it do the same neat work on kudu / wildebeest / sable / waterbuck / eland, etc. than the .308W / 30-06 / .303 Brit / 7x57 do with slower, premium bullets.
Shot placement on a roan antelope - the second heaviest antelope in Africa after the eland