I don't really agree with the whole "knock-out" concept.
Modern bullets don't kill animals by knocking them down or out. They kill through: organ/system destruction and bleeding. When people refer to animals stumbling or falling down (temporarily or permanently) after a bullet strike, it's often due to the shock waves that bullets generate as they travel through the animal's body (this effect is especially likely if the bullet creates shock waves at or near the central nervous system).
Momentum, kinetic energy, sectional density and bullet construction are several factors which dictate the lethality of a particular bullet.
Kinetic energy indicates how hard the bullet hits the animal, and to some degree dictates penetration characteristics.
Momentum indicates how well the bullet will travel through the animal.
Bullet construction (expanding versus hard-cast versus monolithic, ect.) and sectional density also help to determine penetration characteristics.
If you want a basic guideline on determining the appropriate bullet weight/cartridge for various animal weights, check out Matuna's optimal game weight formula, which basically factors kinetic energy and momentum.
Generally speaking, a slow but heavy bullet is not optimal for killing large game. .44 magnum and .357 magnum are considered acceptable within the pistol world, but ultimately shotgun and centerfire rifle cartridges (6.5mm and bigger) are considered far more effective for such duties since they usually produce higher energy and momentum figures. People use pistols as backup's or in scenarios where carrying a rifle or shotgun is impractical, not because they think a magnum pistol cartridge is inherently better.
The contribution of hydrostatic shock to injury/death is controversial. If you've ever seen actual combat footage from the era before body armor, or been in actual combat, when people get shot even by massive rounds like a .50cal or high-velocity rounds like .338 Lapua, they don't go flying backward like in the movies. They just drop like cutting the strings on a puppet. On the other hand, those wearing body armor describe it like being hit with a sledgehammer - that's because the bullet
just stops, imparting all of its energy into the body/body armor system in an instant. Modern military ceramic body armor is designed to shatter locally to absorb that energy laterally (radially from the bullet vector) vs. transmitting it forward into the body where it will break ribs, bruise organs, and so on.
My feeling is less about "knocking out" the animal and more about slowing or stopping the charge, giving me space and time. Look at the posture of a large charging animal - most charge head down, straight at you from less than 25 yards away. If you've trained to quickly draw, aim center of mass, and squeeze, if you're accurate you're going to hit a vital area- head, neck vertebrae, heart. If you're a little off, you will hit something less vital, but something that will slow the animal down, and/or reduce the danger to you - shoulder joint/scapula, jaw, knees, hump - by
impairing mobility. A heavy,
fast round like a .454 carries more energy, and there's a time component to kinetic energy transfer. If that bullet only hits soft tissue, it imparts its energy into its target over a greater time/distance as it travels through. Deep penetration in soft tissue will make the animal bleed out, but that's not as good if you want to stop it quickly. When a heavy, fast bullet hits something solid like a heavy, dense animal bone (brown bear bone may be 10x as dense as human bone), much as with striking body armor, it imparts its energy in a shorter amount of time, simply by slowing down faster and/or fragmenting, and the bone and surrounding tissue have to absorb that energy. But that joint/skeletal member and the muscle that support it or organs it protects will be smashed.
In the unlikely event a large and dangerous animal charges, where you have maybe two seconds to get one shot off toward the center of mass, I want the highest probability that my first shot will impart the greatest amount of energy possible since the presented profile is mostly bone at center of mass. Therefore, I would opt for a heavy, fast caliber such as a .454 Casull. If it destroys a shoulder joint, or a jaw, or shatters neck vertebrae, that animal WILL slow down or stop, and not necessarily because of the energy transfer itself, but because of the musculoskeletal damage inflicted
via the energy transfer - maximizing the chance for me to move and compose an accurate follow up shot.
