There are multiple layers to the subject:
1. What era we are talking
2. What specific country

Speaking from my country (Poland) perspective there are at least two "iterations" of heavy cavalry: the medieval knight and XVI-XVII-beginning of XVIII century hussar. While both are classified as heavy cavalry but there are major differences.

For Polish medieval heavy cavalry one major event is "Battle of Grunwald" (also known as first "battle of Tannenberg" or "battle of Stebark" in German sources, Žalgirio mūšis (Battle of Žalgiris) by Lithuanians), fought 15th of July, 1410. It was supposedly biggest horse army only battle in Europe. Written sources for this battle are: "Cronica conflictus Wladislai Regis Poloniae cum Cruciferis Anno Christi 1410"(Anonymus?) , Johann von Possilge: "Scriptores Rerum Prussicarum" (this two are supposedly written contemporaneously to the battle) , Jan Dlugosz (Joannes Longinus) : "Banderia Prutenorum" and "Annales" (written about 60 years after the battle), . I base following info on book by Andrzej Nadolski "Grunwald 1410" - seria "Historyczne Bitwy".
For long time it was assumed that this battle was fought with banners set in "picket fence" formations, where "lances" were just loose formations, roughly set in "line". This view is right now heavily contested, and polish historians think that battle was fought using banners in wedge-column formations, similar to ones desciribed in Branderburg chronicles from year 1477 (precise source is not stated). Generaly there are 3 "types" of banners described: Goncza (Rynnbanner), about 400 horses; sw. Jerzego (st. George), about 500 horses; Chorągiew Wielka (Hauptbanner, Great Banner), about 700 horses. Names from Branderburg chronicle correspond with ones known from the sources for Grunwald battle.
General setup is similar regardless of size: 5 ranks deep wedge formed by lancers following by collumn of shot troops flanked by additional lancers. It will probably be looking like in one in attachment (red- lancers, blue- crossbowmen, the exact lance/crossbow ratio is pure speculation on my part , based on 1+3 lance size)
The great banner can also be deployed with 7 horse wedge front, with longer column.
We do not know spacing of troops inside- if they rode "knee to knee" or maybe used spacing similar to later hussar formations. We do know that shot troops were expected to volley fire above the wedge. We do know that whole banners can be annihilated in single charge (as happened with one of Smolensk banners). We also know that knights sometimes detached from main body and fought one -on -one with single enemy, like in example of duel between Dypold von Kockritz and king Wladislaw Jagiello (though in some banners such behaviour was heavily fined). We do know that banners were able to pull out of contact and manoeuvre for whole duration of battle. Banners were rotated out of the field to resupply and rest before next attack, like in example of banners used in fatal raid by Ulrich von Jungingen near end of battle. As you see there are some facts, but they are "sketchy". There's no account on how precisely an attack of one banner on another was commenced. (at least- to my knowledge)

As for second instance, the Hussars, there are more "technical" details known from contemporary sources like "Memoirs" of Jan Chryzostom Pasek (thought one need to be careful with evaluating such sources) . Main armament was 5.5 m long lance (hollowed out on whole length, made from two pieces glued together), supplemented with tuck, sabre and at least pair of pistols. The banner is said to compromise from about 150-200 "horses" (but numbers varied in time). Primary manner of deployment was in 3-4 lines with 4 meter spacing between horses, to make a room to manoeuvre about obstacles and such , also this way it presented less "dense" target for infantry. First line was composed of "companions", having best armour and weapons. Against infantry the length of charge was in 375 meter range. During charge there was a technique to maximize shock - the far lines moved to canter faster than first line (last 30 meters mark for 1st line, 60 meters for deeper ranks), in a manner that made first and second line strike simultaneously . On those last meters the danger from shot infantry was lesser (as they usually were busy hiding behind pikemen at that point). Against infantry using countermarch technique there was expected causality rate of 3-5 hussars per charge; after changes in infantry tactics made by Gustavus Adolphus of Sweden (use of 4-6 ranks simultaneous fire) this rate grown to about 25 killed. As with medieval banners the hussars were expected of full manoeuvrability, and were rotated on the battlefield to resupply and rest. It is said that Hussars were expected to have at least "wagon of trees" for a campaign. (tree=colloquial for lance) .
For details about hussary there's an entry on the subject in "features" section.

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Possible layout of banner types for Battle of Grunwald, 15 July 1410

The biggest advantage for multiple lines in a formation of cavalry is to me pretty simple.

IF the cavalry does not balk and does get "into the opposing formation". and IF the infantry does not break, you have a "slogging match". The cavalry don't usually have the density of formation, and have an advantage here, but they do have their mounts as well as weapons, something the infantry do not.

In this situation you are probably looking at some interpenetration, i.e. the cavalry may wind up a few ranks deep in the infantry. Without any supporting cavalry (Or infantry for that matter), the cavalry will be outnumbered and if the infantry holds they will be in deep trouble. A second, third or how many depp line adds numbers to the cavalry, making it tougher for the infantry to "gang up" on the cavalry. My understanding is pulling the man from a saddle in this situation was a fairly common tactice - though stirrups make it a bit tougher than in ancient times.

BTW - IMO the entire infantry force does not "break", or nor would the entire cavalry force all "balk" in most situations. There will be some infantry standing their ground, maybe some flinching or trying to retreat through their own lines, which would cause a mess in the combat situation.

I would also think it was not nearly as perfect of a situation as one may think of by looking at a wargame - in other words, the first line of cavalry does not die neatly in fornt of the infantry formation. It would be much more chaotic, possibly infantry holding their ground with no interpenetration in some spots of the line, cavalry getting penetration in others.

A good example of the slogging match I mention above was at Ciavate (hopefully I spelled that right), where a group of dismounted Swabian knights hels their ground for a long time after much of the rest of the army had fled. They were eventually ridden down by cavalry, but this paricular part of the battle was costly in casualties to both sides. On an interesting note, they are sometimes mentioned as using 2-handed swords my some historians, but most think this is an incorrect interpretation of the translation.

Have you ever watched a steeple chase? It is not uncommon for a well trained horse to balk at a jump. I think this must be true of a charge. A horse is a herd animal, if the horse next to and behind you are running straight into a unit, as part of the herd you will too.

A heavy horse and man weigh near a ton running at near 35 miles an hour. Even if you kill the horse dead on the spot it will still crash threw your lines.

I have had a horse charge me, even when you know it is not going to run you down, or can't (because of a fence) it is hard to stand your ground and not to get your self clear. If you are hit with a wedge formation you have more directions to get away from the horse that will run you down, their by breaking the formation.

I have seen very major wounds not even slow a horse for more than enough time to complete a charge ( worst being disemboweled by a T-post).

I think you would attack what ever would work at the time. A riderless horse would not be much of a threat, a wounded horse could be

I have to agree with Bryan here. I've had horses charge me and having a half ton+ of meat come at you does make one think of their mortality, even knowing in my case that the horses were going to avoid running into me. I don't think one can really "get it" without having been around fast moving horses/other large animals. Maybe I'm just more used to cars passing me by the side of the road or something, but I don't get that same feeling from man-made vehicles as I did with horses. A sort of small and squashy feeling...

And as he says, simple physics isn't on your side. You may spear the horse, but that isn't going to stop him right off. Again, I have some experience here. One of my sister's horses was scared of a neighbor's mare and when she came into the barn he decided he was leaving by the shortest route possible: Through me. I bounced ten feet or so (better than going under the hooves I'm sure), but I don't think he even noticed me. Certainly didn't slow him down any. ;)

My other thought is that horse really shines when the foot does break and scatter. Then they can ride round in small groups attacking any easy targets. That could make a serious impression on the survivors and could lead to an unofficial PR campaign as they tell how the fearsome knights rode them down and slaughtered them en masse. Maybe what we hear is a slightly twisted story. Just a random thought.

Something that we read in books all the time nowadays is that "for every one we killed, there were two more to take his place". Now this is obviously impossible, but the best way to give this appearance is to ride in deep formations. You can have a relatively small front that seems numberless if you can always plug the gap in the line.

Also, as said before, Horses run as a herd, and the more they have running with them, the more likely they are to continue onward. Finally, remember that most infantry from the glory days of heavy cavalry were not wonderfully trained. The big downfalls of heavy cavalry come in battles where the enemy are well trained and effectively led, ie. Crecy, Poitiers and Agincourt.

It should be pointed out that there are very good examples of heavy cavalry charging into and defeating well disiplined formations of infantry. I think one can safely say that this is the exception over the rule most of the time and seems to come down to how many casualties both sides are willing to take. Some of the battles where this happens in the 16th century are just amazing how well the heavy cavalry did against pikes and shot.

I have said this before but I will say it once more. Having spoken to people all over the world that work in military and police work involving horses those animals are trained to run you down. I was talking to a police officer in England who worked in riot control and he made the comment that the horses, once they get trained for it, have no problem charging into thick mobs of people. When I lived in Chile and many of the police especially rural are still mounted, one carabinero told me that during a few years of contention in the country decades ago early on the protestors figured that the horses would not charge them if they were gathered in mass. He said after a few times of being run into by a group of mounted police the arrival of just a handful of horsemen would break up many crowds (not promoting one side of the conflict over the other just an example here). My guess is that these medieval horses were some of the best trained horses in the world and I have no doubt they would charge a wall of people if they were urged to.

RPM

I also have a modern example to add to the discussion of historical heavy cavalry. Take it for what it’s worth.

Any given weekend night in the downtown Minneapolis “Warehouse District” (bar district) provides a vivid snapshot of the importance of mounted police. Two mounted officers can control an unruly mob of 100 drunkards. The horses do not hesitate to push directly into the crowd, nor do they flinch when people get too close and wave their arms about.

Recently, there’s been an unfortunate increase in assaults on our police horses. Fortunately, the horses are very well trained haven’t spooked even after being assulted by a drunkard.

Moving a bit off-topic here, I'm surprised you don't really see any head/face armor on police horses. A horse's eyes aren't very well protected.

One might put some thought into other armor as well, perhaps put small spikes on the bridles to discourage people grabbing them. I heard that was sometimes done way back when.

Bah, who am I kidding. They'll never get funding for that. More likely to be disbanded because some group got together and whined to the government that horses are too dangerous and hard to control.

There are two movies that may be worth watching ( some scenes are somewhat brutal, but IMO they show the potential that calvary has vs infantry):

http://www.youtube.com/watch?v=rEUoqQrNspI

http://www.youtube.com/watch?v=dqm6Lg8XHSM

Modern horse armor

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