I want to record a long video with my phone but I will not be near a power source. Is there a way to turn off the screen while recording to save battery life?
There is an app that I've used that lets you record video with the screen off. It has tons of other goodies too, but this isn't the place for it. "Security Toolkit" has a motion sensor activated security recording feature. After some tweaking you probably can get it to do what you want it to.
This link will bring you to their app list. You can choose the entire toolkit or just get the motion camera portion (my favorite part).
You can not do this natively. However, I don't think there is any reason why an app couldn't be created to do so. It would be a bit tricky, but could be done.
That being said, I look through the marketplace and didn't see anything that would do that. If you have some developer friends, perhaps that can put something together for you.