Warning - This post is full of boring physiology and physics stuff!I'm
fairly sure sure my level of knowledge is pretty good since I'm a teacher of historical fighting and do in-depth research on ancient warfare as part of writing RPGs and historical supplements. But I might just be a gifted amateur, who knows?
However, prompted by what you posted above I'll try to illustrate a few base concepts to help clear any misconceptions some people might have.
First off lets see how much Kinetic Energy is contained in some different types of weapons. I'll give the measurements in foot-pounds for the sake of American readers, but all you really need to worry about are the relative ratios.
Hunting rifle round - about 2,700
.357 Magnum handgun - about 580
Spear - 150ish (varies greatly depending on its weight)
Medieval War Arrow - roughly 100
Modern Arrow - about 60
The value for the historical arrow is an estimation since there are few intact finds of whole Medieval arrows, so the weight of the shaft is an approximation. Since warbows don't launch arrows any faster, merely allow heavier arrows to be shot, it is a fair extrapolation. Near double the weight of the arrow results in the same proportional increase in launch energy.
Now the first thing to notice is that modern projectiles from firearms have a far, far higher kinetic energy. As we can see a historical arrow (at point blank range) has about a fifth of the force of a powerful handgun bullet or nearly a thirtieth of a rifle round. Now Newton's third law in layman's terms says that every action has an equal an opposite reaction. So since firing a hunting rifle doesn't hurl you backwards, neither can its projectile do the same to the target. If a shooter stumbles its because they were firing from an unbalanced position. Likewise when the target is hit, they will likely not fall over unless they too were caught off-balance - in fact less so because the projectile would have lost a large proportion of its KE by the time it strikes. So if a rifle round cannot forcibly throw a human a single metre, there is little hope of a war arrow doing the same.
The second thing to be aware of is more technical in nature. The velocity of the projectile when it hits influences the impulse resistance of the material it strikes - i.e. the faster the projectile travels the greater the force the flesh will generate to initially slow it. Its the effect you experience when entering water; for example lowering yourself into a swimming pool is almost resistance-free, but diving into the same pool is harder because the fluid material has less time to flow out of the way. Animal tissue is the same. More interestingly the impulse resistance grows
exponentially with the velocity of the projectile. Thus being shot with a bullet means your body will act more like a solid wall than if you're shot by an arrow.
That last point is important because when you say above
Armour piercing arrows that punch through Plate armour would have had tremendous power its that 'punching through' bit which produces a tremendous
reduction in knock-back. Arrows have excellent penetration characteristics due to their tiny cross-section profile, (relatively) heavy weight and low velocity. In effect they go deeper because they decelerate
slower. Thus because energy is transferred over a longer period of time, they will inflict even
less of a knock-back.
Now I'm not saying a human can't be knocked over. Any significant force applied to an extremity can apply leverage to cause loss of balance, especially on a bipedal. Being shot in the head is a classic example because almost all the force of the projectile goes into rocking the head only, and where the head tips the rest of the body tends to follow - i.e. it overbalances and falls down. Another is to be shot from the side when running in mid-step. But they are not
thrown forcibly off their feet. That is a physical impossibility with the human powered weapons we are talking about.
For more visceral proof you could search the net for video clips of actual bow hunts against live deer and boars. You'll see arrows bed deep in the animal, which usually springs away in panic and pain, but is not knocked over by the impact. In fact hitting them with arrows from 160lb bows would be more likely to cause the arrow to punch completely through the body and transfer even less momentum to the animal.