Alina wrote:I can hit a human head-sized target on foot at about sixty yards now, provided it's not moving.
Then I believe we're in agreement that horse archers were
moving (unless there's no return fire, in which case we also agree that there's no compelling reason to move)
Alina wrote:I've watched competitions of horseback archery, and the targets are uniformly close - ~10 yards away, while people ride by at high speed to shoot. If this is really how they were intended to be employed...
In fact, I doubt strongly that this is how they were intended to be employed. To me, the competition setup merely reflects the reality that in many areas, finding 100m of land to gallop down is difficult enough without asking for depth downrange, that 25# bows are in general kinder to the neighbors' health and property than war bows, and that almost no one these days does mounted archery as anything more than a hobby.
Furthermore, shotgun events are not rifle events, and mounted archery isn't pedestrian archery, the crux (at least for beginners) is not sniping accuracy as much as it is the ability to nock, lead a target, and shoot in a 3-4 second rhythm.
My best guess as to how they were actually used is an extrapolation from the turkish sport of cirit; I know very little about it (not having any turkish, either), but the general idea seems to be to run into no-man's land towards the other team, throw a stick at one of your opponents, and then try to run back to your side before they manage to hit you with a thrown stick. In other words, "do unto others, then run", which is the classical light cavalry skirmishing role.
Given that arrows fly a bit farther than wooden sticks, I'd expect a mounted archer's skirmish to look similar, but on a scale at least 3 or 4 times as large (simulation would require 4-8 ha, or 10-20 acres, for the playing field, not to mention the problem of blunts), with many more people in motion (these one-at-a-time throws being for the benefit of the scorekeepers)
Alina wrote:So are there any examples of mounted archers charging around at breakneck speed shooting?
Other than the artwork? Looking through the books here, there's only one example of someone shooting from anything other than a gallop, and it depicts a pause during a hunt: the archer is plinking at a bird while his horses nibbles some grass. It may be counterintuitive, but if you try it, I think you'll find it's actually easier
to shoot at speed; the trot and canter impart much more extraneous motion than a good gallop. (as the difference between a jockey seat and a jumping seat will quickly attest!)
 my wife and I recently competed with well under 20 hours of practice and our horses never having seen a competition course before (getting a horse to the range is a little more involved than putting bow and arrows in the car); given the logistics of day jobs, I think the hard-core competitors at our national level count themselves lucky if they manage 50-ish hours of practice a year. to put that into context, I'm a poor fencer (250 hours) and a middling amateur in the disciplines I take seriously (10'000 hours); by comparison any 14 year old steppe dweller would already have had far, far, more saddle and bow time.
 the archer's equivalent of the "assault rifle" principle? (this calculation also illustrates that competition archers are not moving at "high speed", but only at half speed. high speed would leave under 2 seconds per target)
 cf http://www.youtube.com/watch?v=d4FS9remb7U
How long does it take these guys to close 80-100 yards?
 Xenophon talks about iberian horse somewhere in his account of spartan wars, who, like the turks above, are effective at running in, throwing javelins, and getting back out (probably much more effective; cf ). He does mention that they dismount occasionally, but not to improve their firing platform: it's simply a ruse to lure opposing units in, getting them out of position.