Destructive testing in some way could be fun.

A cheaper one would be to test the effect of handlebar height on speed 
(aerodynamics). Find a big hill to coast down multiple times with the 
handlebar at different heights. Most cycle-computers have a max speed 
reading. To be consistent, put the hands in the same place in each test - 
I'm thinking resting on the hoods with the elbows bent in a normal, relaxed 
way, or on the hooks in a full aero tuck, or, heck, try both. Try also to 
conduct all tests at consistent air temperatures and pavement temperatures 
and no wind conditions and keep tire pressure consistent. Plot max speed vs 
handlebar height (stem protrusion or height from the ground?).

Then plot max speed vs handlebar height. Maybe max speed squared vs height. 
Try to find a relation that gives a straight line on the graph. The slope 
of that line would be a useful coefficient relating stem height to speed - 
i.e. for every cm higher the stem is raised, you lose x kph or kph. MS 
Excel is common software that does curve fitting and will give you a slope 
and intercept of your line.

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