A question about a cavalry charge

[Ibrahim]

The lance piercing a target is one thing. Surely enough a rider's xyston or kontos will do the trick.

already explained, and you're right about that.

The solid mass of a heavy armored and disciplined cavalry element in tight formation should have another effect altogether. Even without the piercing, the impact will disrupt infantry formations and cause casualties, just like a car crash where no spears are involved. Just a lot of blunt hard surfaces and a significant amount of energy accumulated during the charge and discharged on impact. For the physics of it, what we should be looking at is the equation that defines momentum. And that is:
m*v=F*Δt (mass times velocity equals Force multiplied by the time interval during which the force is applied). Assuming that the time interval is more or less the same (the duration of the impact) for most charges, you can clearly see that the Force applied within the Cavalry-Infantry system increases as either Mass or Velocity increase.
Now this force can have two effects. It can increase the target's kinetic energy through acceleration (elastic impact) or it can have a more lasting effect on the target, i.e. part of the kinetic energy that was stored in the cavalry does not become the infantry's kinetic energy (in order to send them flying) but crashes bones, compresses air pockets in the human body, causes internal hemorrhage and all sorts of damage.

Does it really take equations to see how this would work? If it does then I've been posting on the wrong forum!

If I understand you right (please correct me if I didn't): that's another way of looking at the problem, and it is also valid--if you assume the horses are directly crashing into the line relying on mass of horse alone (so breast to face I guess ): they did not necessarily do that at full tilt (at a trot, maybe). you are certainly correct to say that in practice a good deal of any kinetic energy imparted would not go into force that pushes the target back: this applies both to the crushing angle, or to the lance itself (I've thus far been describing things in an idealized manner--for simplicity: mentioned it in my first post).

You do bring up a point (which I only incidentally mentioned): Momentum is important here--not just for the horse itself, but the lance.

to answer your question: It's good we bring this up. beats the hell out a boring lecture.


@Papewaio as to the first part of what you said: not really: remember, even factoring in friction, that's not why the horse is hardly affected: the horse and the rider are two separate entities, so the horseman is the one taking the hit at its worst, not the horse itself (if anything, the friction between the two will affect the displacement of the rider more than the horse, specifically by reducing the amount of displacement along the back of the horse).

secondly:

But you can count some of the mass of a horse in a charge.

well, not really. see above: I've been saying this repeatedly: the horse and the rider are separate in this case. even taking into account friction, the role of a horses' mass is negligible. To give you an idea of how dramatically unimportant the horses' mass itself is, here's an in-depth look at the matter--from a jouster:

http://www.classicalfencing.com/articles/shock.php

he treats the whole unit (horse, man, lance) slightly differently (and slightly inaccurately: he conflates the mass of the horse with that of the rider at times, and mass with weight, so his explanation seems contradictory: not the most precise language for sure), but his conclusions are generally the same--and best yet, based on years of observation: the size of rider himself is the main factor in determining the force and energy of impact of a lance, not that of the horse. Otherwise he wouldn't be worried about the Big guy on the little horse more than the Little guy on the big horse.

in fact, we can put what he observes into context pretty easily:

1-man's size: the force itself (as well as kE)
2-the man's strength/technique: efficiency of delivery, direction of delivery, etc.


finally:

A lance in line as much as possible with the center of mass of a charging horse is going to be more stable (pun intended) and more deadly then one further away.

if the horse were the one wielding the lance, sure (seriously though, you're not the first to figure this out: IIRC one Sassanid knight was described as lashing his lance to his mount directly). This would be extremely powerful, but lacks precision--for somewhat obvious reasons.

again, it must be emphasized that it's the rider who matters here in the end in most cases (since he's the one holding the lance). further, due to the way the lance is held (and the fact that he isn't standing up, but seated on his horse), his center of mass is going to be higher up than where it would normally be (where exactly depends on his posture). Not that any of this really matters when determining what the kE or F is (or p), but only on how efficiently it is transferred.

The stirrups can transfer energy and work as a fulcrum too... So if you stood up and held the lance at eye level you would pivot backwards on your rump on contact.

no, saddles and stirrups don't work the way you described in this context (and are not required--though they make life easier: I recommend the above link): And doing it the way you describe would make the man get knocked off his horse, not into his seat (the force affecting him pushes him directly back, or back and slight to one side: usually in context of jousting, it means the feet are removed from stirrups). Also, There's no practical way the stirrup can act as an effective fulcrum here: it even comes across as dangerous, even if we ignore the whole "knocked off your horse" problem.

Finally, No one did that historically: we have many depictions of European, Saracen, and Turkish riders--even Mongols and Mughals, and none use the method--quite the opposite: the soldier is firmly planted in the saddle, with the stirrup playing a support role (it really shines in melee, or in horse archery: the soldier can rear up on the stirrup to deliver a more powerful mace or sword strike from above, or deliver specific types of shot).