In my gym we do BHS with arms starting at the head and straight back. During shoot back drills my arms seems to swing correctly and even when I do it on the roller the speed of the arm swing seems ok. When I do it off a block or on the cheese mat I seem to slow down a lot. Might be a coordination problem since there are many things to think off, jumping, pushing the hips up, arching, swinging...
That's exactly where I was headed when I read your first post. It's very easy to get lost mentally while trying to go upside down as the first and most dominate thought is to "reach around". There's a couple of problems caused by reaching around.....
First, there's no way you can propel yourself through the air by reaching, and reaching severely limits your ability to push with your legs to get a good take-off into the skill.
Next, the reach is usually done by sticking out your chin while trying to get upside down and around, and that makes it harder to get a fast and complete arm swing.
Try to think of gymnastics as a study of things that don't make sense. Trying to go upside down.....just makes it harder to get upside down. If you concentrate on jumping back, extending your body with a very slight arch as a continuation of the of the jump back.....with or with-out the arm swing, you'll create actions that will cause you to go upside down. So concentrate on the start of the skill by jumping as hard and fast as you can, away from the wall you're facing when you start.....and follow through.
If you draw a stick figure of what a "jump back" away from the wall with an extended follow through would look like, you'll see that the jump and extension get you about 40% of the way upside down. That motion will continue after you leave your feet and you'll get the next 40% while airborne, and the last 20% is provided by your momentum after your hands hit the floor.
If you "buy into" the concept and work hard at it, your back handspring should improve quickly. Just a suggestion.......have your coach spot you on a bunch of them the first time you try it because it's probably going to feel a little weird at first.
