This is my area of expertise haha I am master at the the tight turns and I used to have the same problem with the bulging shoulder with my mare Lamia.
1. Make sure that your horse is engaged on his haunches so his stride is nice and round. When you have this type of stride it is much easier to condense when you are in your tight turn but still keeping it swift and tidy.
2. Try to land on the lead you need to make the turn that way you and your horse don't have to worry about the lead change. Also, if your horse has a sticky lead change you don't need to struggle and won't take away the tidiness or the momentum of your turn.
3. For the bulging shoulder half-halt with your outside rein while connecting with your outside leg. This will bring the shoulder back underneath you and your horse straight.
4. Make sure that you plan out the turns that you're going to take while going over the course with your trainer. This way you can decide which turns are best for your level of riding. And stay confident in the choices that you make!!!!
5. Make sure that while you are going over your fence you are keeping your eyes on the path that you want to take and make sure that all of your aids are following your eyes.
6. You can also slice a jump to make the turn even tighter and faster. This way you are also heading in the direction of the turn you are going planning on making. But it is also very handy if it is an extremely tight turn to slice away from the turn to give yourself some more room in the turn.
7. And last, but not least, practice makes perfect. At home and in the warm-up ring practice lots of circles. Practice tight turns, roll backs, and long galloping clear areas to make your jump-off as effective as possible when at a horse show. While at a horse show make sure that your horse is moving off of your outside leg. If he's being dull to your leg while making a small circle then you should maybe take a step back and avoid the tightest of turns to reduce the likelihood of a refusal. Also, practice your tight turns from jump to jump in the warm-up ring. What I like to do, if possible (assuming that there are three jumps in the warm-up ring and there are no others currently jumping over those jumps), is to serpentine over the three jumps. Also, I like to practice cantering in between the jumps because I get nervous going in between standards of jumps for a tight turn sometimes, so this opens up my mind to that idea.
And remember that in your power round the goal is to go clean. Just keep a steady pace, but don't worry about the tight turns. Then when you start the jump off get your horse moving and always look towards your next jump while in the air to see and plan those turns as early as possible.
Hope this helped!!!! Sorry it's long!!! And good luck!!!
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