What is Horizontal Axis Spin, and how does it happen?
The greatest single advantage in using a curved approach is that it allows you to generate the spin you need about the bar without sacrificing anything else.
Your angular momentum about the bar is set at the moment you leave the ground. Your rate of spin will vary slightly during your flight because you arch your back as you cross the bar, but there is little you can do to adjust it in flight. You MUST have the right rate of spin at takeoff.
Of course, if your hips are clearing the bar by a foot (0.30 M), then you may have some room to play with. You can make up for a bit of poor technique with extra height. However, as you attempt greater heights, you will eventually run out of room for error. You will eventually be limited by your rate of spin about the bar, and that is a product of your approach and takeoff technique.
So, what is the right amount of spin about the bar? Although a detailed analysis would be quite complex, the bottom line is this: your spin about the bar is right if your shoulders, back, hips, thighs, calves, and feet all clear the bar by about the same amount. The most common problem is not spinning fast enough. Without enough spin, you will knock the bar off with your legs or feet. On the other hand, it is very rare to spin too fast and knock the bar off with your upper body on the way up. To see why this is so, we will need to look at the source of your spin about the bar: your takeoff.
There are two methods by which you can create spin about the bar. Both of them occur during your takeoff stroke. The method I recommend is to remain in your curve at the same bank angle until you plant your takeoff foot. Plant your takeoff foot slightly inside the point that would allow you to continue running in your curve. This will cause a rapid reduction in your bank angle as you "come out of your curve". If done correctly, your bank angle will reach zero degrees (your body will be vertical) at the moment you leave the ground.
Of course, there are a great many variables in the takeoff that affect your rate of spin. Your brain handles them automatically with just a little practice. Except one - the main one - starting your takeoff while still banked in a turn away from the bar. Your brain will fight this with all it's power because it is completely outside all of your past experience.
Your natural reaction to approaching your takeoff point in a curve is to come out of the curve early, plant your takeoff foot with your body fully upright, and then dive over the bar. If your body is already vertical at the moment you plant your takeoff foot, then all the effort you put into running a curved approach is wasted. You might as well have run a straight approach. Three bad things happen when you come out of your curve early or run a straight approach. All of them are related to the fact that you will be leaving the ground with your body leaned toward the bar.
First, your center of mass is lower than it would be if you left the ground vertically. This means you have to raise your mass farther to clear the same height.
Second, your vertical velocity is less than it would be if you left the ground vertically. Part of the power you put into your jump is going to move you sideways across the ground. A cannon ball fired straight up in the air will go higher than one fired at an angle. This means you will not raise your mass as high as you might.
The combined effects of lowering your center of mass and reducing your vertical velocity can reduce your jump by several centimeters. The farther your takeoff angle is from vertical, the more height you loose. At only 5 degrees from vertical you loose almost 1 cm ; at 10 degrees more than 3 cm; and at 15 degrees over 7 cm.
Third, Leaving the ground leaned toward the bar places your shoulders too close to the bar at takeoff. This causes you to unconsciously adjust the rate of spin you generate during your takeoff to keep from hitting the bar on the way up. Even if your shoulders barely skim past the bar, the rate of spin will not be enough for your legs and feet to clear on the way down. This means that you may clear the bar by a good margin with your upper body, only to drag it off with your legs.
This kind of takeoff is a losing proposition in every respect. The only cure is to plan your approach so you can leave the ground as near vertically as possible. The only way to do that is to stay in your curve until you plant your takeoff foot.