If you must go on the ride but would rather eat your own arm here is my suggestion. I used to close my eyes while on the ride and the smooth motion is actually quite peaceful. Once you get used to that you can open your eyes and it doen't seem so scary anymore.

Just remind yourself that the ride will be over really quickly, it will probably take longer to queue for the ride than to go on it, especially at the likes of Legoland, Disney et al.