In The Face of Battle, John Keegan runs through some thought experiments about cavalry and lances. For one thing, the vaunted “shock” effect of cavalry charges was largely moral, moreso than physical impact. Horses won’t intentionally run into solid objects nor armed men if they can help it. Apparently also a lot of “charges” were more like a steady advance, keeping the horses together and preserving their stamina as long as possible. It’s almost as dangerous to wind up among the enemy on a “blown” horse, unable to escape rapidly, as it is to pile into a line of pikes and get impaled.
So to fast forward a bit here, a typical “charge” seems to have involved the horsemen advancing steadily, but menacingly, on a line of foot.
If the footmen stay in formation and work together, they can repel almost any mounted force in hand-to-hand (horse archers like Mongols are another story) because you can fit a hell of a lot more spearmen/pikemen on a line than you can horsemen…I don’t recall precise numbers, but Keegan worked out something like 125-150 bayonets on one facing of a square, opposed by, at most, 35-36 riders. If the infantry doesn’t lose its nerve it vastly outnumbers the same frontage of cavalry. But mounted knights are scary as hell, and have a reputation their social “inferiors” have been taught from birth to fear. Sometimes one or more of the footmen has doubts, recoils at the last moment, breaks formation, or even runs.
In a memorable phrase, one soldier described a “visible shiver” running across a line of infantry standing to receive a charge. That moment of doubt is what the cavalry are looking for.
Disorganized footmen are wholly more vulnerable. If line is not solidly maintained by resolute fighters, openings or gaps appear as individuals shy away from impending contact. Horsemen can exploit these gaps, riding into the formation and fighting from their height advantage. Here the lance has another utility surprising to the modern mind – even from horseback, it’s easy to stick someone lying on the ground with your long spear, so there’s no escape by laying low. Keegan noted that written records from Waterloo, where a lot of lance-wielding cavalry fought, show a great deal of re-wounding of the wounded, who were presumably on the ground once wounded, and posits that the lances made it easy to inflict such injuries without the need to dismount and put oneself at risk.
The relevance here is that in real combat, there was apparently not a lot of running full tilt into something to add momentum to aid penetration. So the whole scenario many stem more from tournament fighting and/or fantasy than real war.