unit91 said:
Furthermore, approximating the conical bullet as a spherical body indicates why large caliber bullets are so lethal. The mass of the displaced fluid (blood, organs) is m_fluid = (2/3)*pi*tissue_density*radius_of_bullet^3.
Take three typical hunting cartridges/bullets ... .223 Rem (55gr), .308 Win (165gr) and .338 Win Mag (225gr) and model them as you suggest as lead balls (spherical bodies) . You define the volume of the fluid displaced as being 1/2 of the volume of the lead sphere. If we assume that the fluid has a density similar to that of water i.e. 253gr/in^3 (1g/cm^3) and that lead has a density of 2906gr/in^3 (11.5g/cm^3) we then have the following:
.223 55gr, r = 0.165", mass of fluid displaced = 2.4gr
.308 165gr, r = 0.238", mass of fluid displaced = 7.2gr
.338 225gr, r = 0.264", mass of fluid displaced = 9.8gr
So the fact that a .338 Win Mag 225gr bullet displaces
9.8gr of fluid compared to a .223 Rem 55gr bullet that displaces
2.4gr of fluid explains why the .338 Win Mag cartridge is more lethal than the .223 Remington cartridge?
In all cases, the mass of the fluid displaced is only
4.4% of the mass of the bullet! Perhaps the difference in terminal performance has something to do with the fact that although both bullets at 200 yards are moving at around 2,500 fps, the .338 Win Mag 225gr bullet has
2964 ft-lb of energy compared to the .223 Rem 55gr bullet only has a measly
763 ft-lb of energy (Hornady factory ammunition).
I agree that larger bullets are generally more lethal but I'm just not convinced that it has anything to do with the mass of the fluid displaced since the mass of that fluid is negligible compared to the mass of the bullet (less than 5% of the bullet's mass). As has been mentioned, it's all about the energy of the bullet as it hits the target and the bullet's deceleration within the target which directly effects the amount of energy that is transferred to the target. A bullet's deceleration (dA/dt = IMPULSE) is greatly affected by bullet design and by what it hits ... this is obvious. More energy generally implies that the bullet can penetrate deeper into the target thereby increasing the chances of hitting a vital part of the target. Compare a .308 Win and .300 Win Mag using the same 165gr bullet. Both bullets will displace the same mass of fluid based on the model described above so they should have the same lethality right. However, common sense tells us that the .300 Win Mag with almost 700 ft-lb more energy at 200 yards will do more damage. In this case, given the same bullet, it's all about velocity.