First there is no ambiguity as to how well a saddle distributes weight be that treed or not, the technology is available for us to see this in real time, even if it’s not cheap, when I looked at it a couple of years ago it was around £2000 iirc and that was the basic system not the one with twice the number of sensor or the software upgrade for extra functionality.
If you look at the three parts you split it into for a treed saddle, jumping, GP, Dressage.(Obviously there are other saddle designs)
First of all when you are talking about active forces created by the rider you can’t actively adapt the saddle in real time for the riders movement or riding style, so in the top layer of your three tier model you can’t really do much about the forces transferred into the next level be they active or static other than use a material that can absorbs some of the forces and this will only be for active forces.
The middle tier needs to be rigid enough to distribute the weight as evenly as possible across the surface area of the saddle in contact with the horse whilst also being flexible enough to assist the bottom layer (the part of the saddle that is in contact with the horse) with staying in contact with the horses moving back.
This type of saddle design has not changed much at all, other than change of tree material in recent times as far as i'm aware perhaps Wally could comment?
All the other things people are trying/making are to make the saddle easier to fit/adjust to more horses or simpler to change so it can be done at home.
None of these saddles distribute the pressure any better though with the exception of the wow system which is a completely different design although very similar in concept to the Universal Pattern saddle in concept.
If that makes any sense
I guess the point I disagree with you about is
“it's is not a simple problem, like for example, the problem of distributing weight across a flat, rigid surface, such as you might see in an O level physics class”
It’s exactly the same except it changes constantly (which can be monitored in real time 40-50 times a second) and instead of just having one value you have a number of values within a range and it’s the range that you are talking about not just one value as you would if the forces were static.
Haven’t got time or the inclination to go into the material properties in gel pads and some of the treeless saddles at the moment but the point is they can be proven how well they work or don’t.
But the bottom line is if you have materials with fantastic properties, if you add a well designed tree that complements the materials properties it makes an even better saddle for weight distribution than a treeless saddle using the same materials.
Those people who can tell what forces will be put into the exo-muscular system of the horse if it has a small child on it’s back while it goes for a little walk and say they are more than those going through the same exo-muscular system of a horse doing a 5 star event are pretty impressive, I guess compared to them everyone has half a brain cell.
As to it not being safe, I guess that means all the people who fall of horses or have them run off with them shouldn’t get on them either as it’s not safe for THEM.
I don’t think you can assume that every horse is dangerous and if we can’t trust people to have enough common sense to make a judgement call as to the risk involved, horse, location, task etc we may as well all give up now.
If it was not for children I would encourage anyone who is too stupid to make a risk assessment of anything they do to try it, get them out of the gene pool.