That third seat is also called a Half Seat. Butt in the saddle but the amount of weight in it varies and is controlled by hip angle, shoulders stay above the hips and don’t move indepently, only via changes in hip angle.
Sounds confusing and it’s very, very hard to master but mastering it allows a rider to advance to a very sophisticated level where it looks like they are doing nothing.
If you go back to Deweys post, #13, the riders in the upper right and lower left pics are using the half seat. Note the upper right rider’s fanny lightly in the seat
with a slightly closed hip angle, straight back and shoulders only slightly forward as she sends her horse straight forward.
The lower left rider is also in a half seat but has opened the hip angle, bringing shoulder slightly back very close to full seat but still not all the way there as she executes a corner. Note both these horses are ahead of the leg and both rider appear to be very correct Eq riders.
Then we go to the real world Jumper riders driving their horses up into the bridle well ahead of the leg. First rider, upper left, looks like he’s on a short corner to a big fence. Obviously he’s out of the saddle here but compare his leg and shoulders to the two Eq riders. It’s almost identical . You could drop him on the ground and he’d be standing straight on his feet. That’s one strong and very correct position. Weight out of the seat but legs are exactly where they’d be if he was in it and he has not closed the hip angle, he’s got horse precisely where he wants him.
The rider on the lower right appears to be having a bit of discussion with this horse about coming forward so has dropped well behind to drive him up and forward. Hes in a driving seat and has opened his hip angle to bring shoulder back and seat deeper in the saddle. The remarkable thing about all four of these different riders working different pace and control questions is if you compare ALL four of their leg and back positions, they are almost the same. Everything is generated from controlling the hip angle. No shoulder throwing, no loose below the knee leg. And no hint of a perch.
Try to watch these videos over and over looking at just between waist and knees and how that controls everything. Hopefully you will have an “ Edison moment” and the light bulb will go off and you’ll get it. It’s all about that hip angle. Also suggest you watch MacLaine Ward, who, IMO, does this better then anybody… And watch the Maclay Medal Finals. Once you learn to see and understand it, it all makes sense. Won’t make learning it any easier but at least you’ll know where you are going.
One hint on full seat. Drop your irons, sit up straight, try to touch your belly button to your spine and pretend you’ve got a hundred dollar bill in your back pocket, sort of roll your hips under and sit on your pockets. Suggest you start at the walk, then sitting trot, then canter. You have to loosen up your core and retrain those muscles and your brain because it won’t feel right. And you will be sore, mostly abs, glutes and upper hammies right under your butt. That’s where your seat security and true control of the horses body really comes from. Surprises me the number of trainers out there who don’t teach this despite the numerous upoer level clinicians and authors who stress it.
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Finally, your saddle may not be helping you at all. It might not put you in a proper spot to let your legs, hips and shoulders align properly or allow you to control them. It could also have you slipping and unable to stay in a correct, strong and balanced position. I had one like that, mid price range. My ( Medal Finals winning) Pro rider could not even stay with it. You need to right tools ti be successful. Might include a different saddle…maybe trainer too.