I believe that I have stated this clearly enough elsewhere: but English "cavalry" is not the same as continental cavalry.

As Bachrach states: the warhorse was very expensive and the English and vikings had no use for them, seeing as how they were fighting each other and neither side employed warhorses in combat. Both sides, however, used horses extensively in war: for speed and rest in traveling, for scouting and most importantly for pursuit of a broken enemy. This last use is assumed rather than stated: but when the army rides to the battlefield, it would be stupid to let your enemy on foot get away because you tried to chase him down also on foot. A broken army will have difficulty getting quickly to horse if they are being driven from a lost field; and then the victors can get to horse and run the routed enemy down. That's the theory anyway, and it is apparently what Bachrach, et al (i.e. Glover), feel is all that Norman cavalry was really good for as well.

But the Bayeux Tapestry shows all three uses of the lance, not just over-hand: the couched position is used as well, and the underarm swinging thrust; the overarm could also indicate throwing lances/spears: and most probably does, since William of Poitiers states clearly that Normans threw spears from a distance; while the Bayeux Tapestry also shows spears in flight and quite a few of them sticking in shields and bodies.

The original sources make it very clear that the battle was primarily between mounted invaders (supported by archers) and English infantry in a dense "shieldwall". There was no slogging match with stalled out, motionless horsemen stabbing at the English: such a fight would have ended quickly enough in a Norman defeat. Rather, the cavalry of William's army advanced and withdrew repeatedly throughout the afternoon, taking breathers and reorganizing at their leisure. It was by a constant wearing down of the English through repeated cavalry charges up the hill (vitiated by the steepness and roughness to be sure), interspersed with missilefire, which caused the English to grow weary: and the chance to win that was apparently presented to them by precipitate Franco-Norman retreats caused sections of the English army to abandon the defensive and pursue their withdrawing enemies: which of course brought the advantage of the horse completely into its own, as William's "knights" turned and, using their speed of maneuver, cut in behind the advanced pockets of Englishmen and attacked them from all sides.

The speed of maneuver of cavalry has always been the greatest tactical advantage; this was limited at Hastings by the ground preventing outflanking of the English line. The winning strength of any cavalry capable of hand to hand combat is the weight of the moving horse: the rider needs hardly do more than defend his mount from enemy weapons, and can let the momentum of his steed do all the damage. A loosened formation of English pursuers would be easy meat to horsemen riding into them.

(The picture of Franco-Norman slaughter of the pursuing English must have looked very similar to the impressive graphics of the Rohirrim charge in the film "The Return of the King" - as long as the cavalry can keep moving forward, the weight of the horses crushes down all feeble resistence of a loosened infantry array.)


So I believe that the English seldom if ever used their horses on a battlefield: and if they did (according to Snorri Sturluson) it was in the nature of advance, throw-shoot, retreat, and there was no physical contacting the enemy shieldwall. While all the evidence indicates that the Franco-Norman cavalry was the main close combat arm. To assume that they did this at a walk is absurd. The horse would make a big target to defend if that is all it could do; and the horseman has much the harder task trying to strike an enemy on foot than a footman has trying to hit an exposed rider.