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Gearing and Math Question ....
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Posted by Gyro Gearloose on November 13, 2005 at 05:20:50 from (64.42.242.10):
I was at a science exhibit yesterday and there was a large display of gears, gear ratios, etc. and how & why gearing systems work as they do. I think this question has been asked here before but it came to mind yesterday so here goes. Suppose you had two low-gear gearing systems, both with a 1:2 ratio of the drive gear to the driven gear. For simplicity sake (not practicality) lets say the two systems that were being compared were system A and B as follows: System A - the drive gear has 10 teeth and the driven gear has 20 teeth. Basic ratio is 1:2. System B - the drive gear has 15 teeth and the driven gear has 30 teeth. Basic ratio is 1:2. Now suppose that the materials from which the gearing systems were made were modified so that system A and system B had exactly the same overall weight so that wouldn't come into play (at least in our example it wouldn't). Nor would other factors such as dimensional size, friction, etc. between the two systems. We are just talking about the math comparison between the two setups. My question is this, if you (or an engine or whatever power source) were driving these systems against a load of some type (same load for both A and B), would you (or whatever power source you were using) be using or expending the same amount of force or power in both? For example, if you had two identical bicycles with these different gearing systems and were pedling up a hill, would you feel that both bicycle trips were as easy (or as difficult) as the other?
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