trying NOT to repeat what was just said...
This concept of matching rubber to rotor is a more advanced mathematical topic than generally dealt with in middle school, but lets see if we can give you a plan on how to go about doing it systematically.
First, as already noted, motor stick length isn't really critical (as long as its in a reasonable range, say 8-12 inches, and you hit the minimum weight and its stiff enough). So, build a nice, light, stiff one about 10 inches long and you will be fine for now.
OK, on the rubber. You have TWO control factors to play with to match the rotor for max time. Thickness and length. And they are not independant so you HAVE to test them together in an organized fashion (this is called a Designed Experiment), one at a time testing WILL NOT WORK.
- Starting assumption
-- Every test flight will be flown with a max wound motor, just short of breaking.
-- Every flight is in basically similar conditions. PREFERABLY no moving air, smooth ceiling, same height.
- Make a 3-d graph, rubber length on one horizontal axis, thickness on the other. Verticle axis gets the response, flight duration.
- Select a range of thicknesses and lengths you want to test. Divide those up into three. Minimum thickness, mid thickness & max thickness. Min lenght, mid length and max length.
- test every combination of those, that's 9 test points, at least twice each. Throw out and repeat test if flight gets caught in ceiling, or is otherwise bogus. But only if you really think its bogus.
- Graph all that data, preferably with a program that gives you nice output, maybe does some nice averaging.
- Interpret results.
-- IF you are lucky the average top time is the mid-point. Reduce the range you are testing and repeat.
-- More likely, one of the edge points is high point. Extend the range around that point and retest new points.
-- Repeat until your range collapses around the high point enough so there is little change in the max
Now, if you have someone who can interpret designed experiments for middle school students (its doable, I've done it as early as elementary school with my kids)you can make this more efficient, but only some. It will reduce some of the test points and make the data interpretation rigourous.
Hope that makes sense, never said it would be easy. Hey getting this test and data collection idea across is the whole point of the logs in the rules.
PS, after you've done this right once you'll be the expert and can 'guess where that optimum point is on the next rotor system more accurately and save a LOT of test time.