Originally Posted by Danny
There are two forms of this one-armed freestyle, depending on which side you breath on. Supposedly each one highlights some aspect of balance and timing, but I won't try to get in to that, because I'm only familiar with the version I use, where I breath on the side of the stroking arm. I also like to swim this way with my hand closed in a fist. I can slow the stroke way down when I do this, which allows me to focus on my timing of hips and shoulders. The other thing this seems to help is precisely the bobbing that ZT was referring to. A slow one armed recovery means that your recovering arm is spending more time out of the water, which pushes your body down. This can help you to time your breathing with the natural bobbing of your body induced by the heavy arm outside the water. At more realistic swimming rates, this effect becomes smaller, so it is harder to teach yourself how to exploit it and coordinate it with your breathing.
The recovering arm should not push the body down, it should help stability. You are most likely over rotating and recovering the arm too high if that's happening. You should definitely not be "bobbing". That is not how to breathe efficiently when swimming freestyle.
This bobbing motion is more pronounced in the one arm drill because the opposing arm is down at your side and not extended. When the opposing arm is extended, it supports the weight of the recovering arm and damps the bobbing. If you look at the film of Terry doing the one armed drill you will also see a pronounced bobbing, as ZT has already pointed out.
In real freestyle, the opposing arm is extended and this effect is more subtle, but it is still there.