Hi daisy,
Welcome to the forum -- sounds like you have an idea that could evolve into a great project!
For measuring the number of times a football spirals, my first thought is that you could record the flight with a video camera, then replay it slowly and count the number of times the laces (or some other feature with good contrast -- you could add this if necessary) rotate through the side you're looking at. For that, you'd need a camera with pretty good resolution, since you would need to capture the entire length of the flight at once and have a detailed enough picture of the ball to see the laces even when the ball is far away. You would also want the frame rate to be high compared to the maximum rotation rate of the ball; this ensures that you don't miss any instances of the laces being visible (or not) on the camera side. You could search YouTube for something like "football spiral" to see if anyone has tried something like this and what your footage might look like -- sometimes people even post details about what cameras they have used. High-speed cameras (though you might or might not end up needing one) are being used more and more in science to understand physical phenomena, and there are a lot of interesting and entertaining videos out there!
With one camera, a good strategy might be to stand to the side of the middle of the football's path, with the camera initially pointed toward the person throwing it. Then, as the ball moves, smoothly rotate the camera to follow its path. Zooming in on the ball could compensate for low camera resolution, but would make it more difficult to track the ball. If you are able to automate the throwing with a machine so that it's the same every time, you might also be able to automate the camera's rotation -- this could make it easier to zoom in without losing track of the ball. If a person throws it, though, the trajectory will be a little different every time. If you have more than one camera, you could have multiple people filming spread out along the side of the ball's path, which could make it easier to capture a long flight. You'd have to be careful about piecing together the footage so that you don't double-count rotations, though.
Now, for a science project, you'll want to develop a hypothesis. This could be a guess regarding a variable that you think will affect the number of times a ball spirals, or a guess about the effect of the number of rotations on a variable like distance traveled or curvature of the path. You'd need to develop a method of measuring the other variable as well and to control all of the relevant constants. (When you start thinking about constants, the idea of an automatic throwing machine will become even more appealing. :) ) For lots more information about planning and conducting a good experiment, see our guide:
https://www.sciencebuddies.org/science- ... ndex.shtml
Here is a project idea related to yours -- note the citation for
The Physics of Football, which sounds like it could be a useful resource for you:
https://www.sciencebuddies.org/science- ... ?from=Home
Samples of that book and a similar one are online:
http://books.google.com/books?hl=en&lr= ... cM#PPP1,M1
http://books.google.com/books?hl=en&lr= ... ITk7aY_iTo
as well as some other background info:
http://www.howstuffworks.com/physics-of-football.htm
http://physicsworld.com/cws/article/print/1533
http://footballphysics.utk.edu/what_is_ ... hysics.htm
Hope that helps to get you started. Feel free to post more questions and thoughts in this thread as your project progresses!
Amanda