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Actual figures of Penetration Impulse Per Bullet Frontal Area
As mentioned in the previous post, penetration is dependent on an impulse force, calculated by the equation: Force = Mass x Acceleration. Negative acceleration (slowing down) is used to calculate a rifle's recoil impulse, and similarly the bullet’s deceleration (negative acceleration) on impact is used to calculate penetration impulse. Below are some real figures to establish general Penetration Indices for hunting bullets, referenced to actual penetration on hundreds of animals I have observed over 55 years of big game hunting.
Unless the reader has repeatedly observed and tabulated a particular bullet's actual penetration distances on various animals under various field conditions over time the comparative figures arrived at below are just that: mere comparisons of relative penetration into the same media. First a few principles need to be considered.
Principles involved:
1. Bullet decelaration value: The time a bullet is acted upon by the average width of an animal’s shoulders is about 1/500th of a second whether the bullet passes through or is stopped by the resistance of the animal’s body, so all impulse calculations will be done using this figure.
2. Impact momentum: will be used as the pre-impact weight/velocity vector quantity, slowed down during 1/500th of a second to calculate the impulse force.
3. Bullet Frontal Area (Profile Drag): The raw impulse force is then applied to the full frontal area of the bullet to arrive at a force per square millimeter. This is the only way to compare relative penetration impulse forces between different calibres - and why the reader will see that the 9.3 x 62 with a 286 gr bullet has a higher penetration index than a .458 Win Mag and its 500 gr bullet - and the mathematical explanation why this has been observed since the inception - and subsequent termination of the .458 Win Mag in the field on Cape Buffalo and elephant.
Calculating Penetration Force (Impulse ÷ Frontal area) at 50 yards. All bullets are Peregrine VRG-2 monolithic solid for constant retained sectional density and frontal area.
(1). .458 Lott 480 gr [113 Newton per square mm frontal area]:
Bullet Mass: 480 gr (32,4g).
Retained Diameter: 11,6 mm.
Retained Frontal Area: 105,7 quare mm.
Impact Velocity: 680 m/sec.
Impact Momentum: 24 kg.m/sec (24 Newton/sec).
Time of change of Momentum (deceleration): 1/500th sec.
Impact Impulse (Impact Momentum ÷ Deceleration time): 12,036 Newton.
Penetration Force (Impulse ÷ Frontal Area): 113 Newton/ square mm.
(2). 6,5 x 57 mm Mauser 160 gr. [108 Newton per square mm frontal area]:
Bullet Mass: 160 gr (10,4g).
Retained Diameter: 6.7mm.
Retained Frontal Area: 35,26 square mm.
Impact Velocity: 730 m/sec
Impact Momentum: 7.6 kg.m/sec (7,6 Newton/sec).
Time of change of Momentum (deceleration): 1/500th sec.
Impact Impulse (Impact momentum ÷ Deceleration time): 3,800 Newton
Penetration Force (Impulse ÷ Frontal Area): 108 Newton/ square mm.
(3). .375 H&H 300 gr [104 Newton per square mm frontal area] (equals 7x57 with 175 gr bullet):
Bullet Mass: 300 gr (19,4g).
Retained Diameter: 9,5 mm.
Retained Frontal Area: 70,8 suare mm.
Impact Velocity: 760 m/sec.
Impact Momentum: 14,7 kg.m/sec (14,7 Newton/sec).
Time of change of Momentum (deceleration): 1/500th sec.
Impact Impulse (Impact momentum ÷ Deceleration time): 7,372 Newton.
Penetration Force (Impulse ÷ Frontal Area): 104 Newton/ square mm.
(4). 416 Rigby 400 gr [103 Newton per square mm frontal area] (equals 30-06 with 200 gr bullet):
Bullet Mass: 400 gr (25,9 g).
Retained Diameter: 10,6 mm.
Retained Frontal Area: 88 square mm.
Impact Velocity: 700 m/sec.
Impact Momentum: 18 kg.m/sec (18 Newton/sec).
Time of change of Momentum (deceleration): 1/500th sec.
Impact Impulse (Impact momentum ÷ Deceleration time): 9,080 Newton.
Penetration Force (Impulse ÷ Frontal Area): 103 Newton / square mm.
(5). 9,3 x 62, 286 gr [95 Newton per square mm frontal area]:
Bullet Mass: 286 gr (18,5 g).
Retained Diameter: 9,3 mm
Retained Frontal Area: 68 square mm.
Impact Velocity: 700 m/sec.
Impact Momentum: 12,95 kg.m/sec (12,95 Newton/sec).
Time of change of Momentum (deceleration): 1/500th sec.
Impact Impulse (Impact Momentum ÷ Deceleration time): 6,460 Newton.
Penetration Force (Impulse ÷ Frontal Area): 95 Newton/square mm.
(6). 458 Win Mag 500 gr [92 Newton per square mm frontal area]:
Bullet Mass: 500 gr (32,4g).
Retained Diameter: 11,6 mm.
Retained Frontal Area: 105,7 square mm .
Impact Velocity: 600 m/sec.
Impact Momentum: 19,4 kg.m/sec (19,5 Newton/sec).
Time of change of Momentum (deceleration): 1/500thsec.
Impact Impulse (impact momentum ÷ deceleration time): 9,720 Newton.
Penetration Force (Impulse ÷ Frontal Area): 92 Newton/ square mm.
(7). .45-70 Gov. 405 gr [47 Newton per square mm frontal area]:
Bullet Mass: 405 gr (26,2 g).
Retained Diameter: 11,6 mm.
Retained Frontal Area: 105,7 square mm.
Impact Velocity: 400 m/sec.
Impact Momentum: 10,4 kg.m/sec (10 Newton/sec):
Time of change of Momentum (deceleration): 1/500thsec.
Impact Impulse (Impact Momentum ÷ Deceleration time): 5,192 Newton.
Penetration Force (Impulse ÷ Frontal Area): 49 Newton/ square mm.
The folly of judging a bullet's momentum value before impact as an indication of its ability to penetrate is clearly demonstrated in the above calculations.
The Sectional Density Myth:
For consistent comparative impulse force per square mm bullet frontal area in the above calculatations Peregrine VRG-2 Flat Nose monolitic solids have been used. These bullets ensure calibre size entrance and exit holes, a 4x caliber inside permanent wound channel and zero meat damage - so they remove the need for expanding bullets. This is the only bullet I use for everyting I hunt with the .416 Rigby (400 gr), .303 Brit (168 gr) and 30-06 (168 gr).
The Peregrine VRG-3 has a constant expansion to about 1.8x calibre no matter the target or impact velocity exprienced in normal hunting, and this pre-known expanded frontal area can be used to calculate penetration impulse force per square mm for the new expanded frontal area.
It will be clear to the reader that the published sectional density figures of all "Ballistic Tip" style bullets, including all bullets that immediately shed their front part on impact like Nosler Partitions, and all other fast and uncontrolled expanding bullets are unusable figures. The moment they impact the animal that sectional density figure it had while lying in the box is in total tatters and had been nothing more than useless information.
About the lead photo of the elephant being shot:
A client (clearly a South African guy by the dress), novice elephant hunter with a .458 Win Mag was being guided for his first elephant hunt. He is seen in the centre, his rifle in full recoil (not very well contained by him), and his stance is also wrong. Understandable, as for the novice the moment would surely have been big, his first encounter with an elephant - and then the PH taking him to 10 yards.
At such close distance (20 yards and less) the PH (on the right in the photo) will always also aim because if the client misses the brain he will need to shoot immediately. There will be no time for him to raise his rifle, aim properly and fire in time as the elephant would have been full aware of them despite showing apparant ignorance in the photo.
As it is, the client's shot was perfectly into the brain, the dust of the bullet impact can be seen on the side of the bull's head which lifted a little from the shot. The clear indication for the PH that he did not need to shoot was the immediate folding of the rear legs of the elephant as can be seen in the photo.
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