from what i could find it's a 9yo arabian endurance stallion in all the videosFantastic video. Depth of sink of the fetlock appears to correlate with the shoe, assuming it's the same horse, taken after a similar amount of warm up. Strongly suggests that no shoe and then plastic shoe stop forces being transferred up to the fetlock.
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Hard to really see the difference tbh... the metal shoe distributes force that would otherwise be absorbed in the heel bulbs forward in the form of a shunt but that was the only thing I thought to be interesting.
I don't like seeing things out of context - which is the control?

The "control" absolutely must be left in any experiment it cannot be left out. That group is what any experimental/active groups are measured against. It would usually be the accepted standard - in this case - which is it? The shod hoof? The unshod hoof? A wild hoof? A pathological hoof? And which part of the hoof?What do either of you mean by "control".
Control usually means a group left out of an experiment, I don't understand what you are asking for.
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A metal shoe absolutely can distribute force/energy - or else bells would not exist, nor would electricity.
In the case of hooves - the metal will transfer its energy which is why I observed how the force of landing was distributed throughout the whole hoof, not in the heels as the barefoot hoof.