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For Christmas me and my brother got an AR Drone, the propellers are on a large gear, which is rotated by a small gear that is connected to the motor.

This means the small gear (and therefore the motor) must rotate many times in order to rotate the propeller just once.

Surely swapping the gears, so that the propellers are on a small gear, which is rotated by the large gear that is connected to the motor, would mean the propeller would spin faster (given that the motor is operating at the same speed as before), or that the motor could operate at a slower speed (and therefore use less energy) and maintain the same speed of the propeller as before?

Also what is the advantage of using any gears at all? Why not lose the gears, and get rid of the friction between the gears and between the gear and what holding them, and the added weight?

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An engineering question, really. I'd suggesting finding the datasheet for the motor and looking at its operational limits. In particular the torque it can generate with the supply's electrical properties, and it's range of operating speeds. –  dmckee Jan 6 '12 at 19:50
    
I was also thinking in terms of energy (given that battery life is quite short, every second counts) –  Jonathan. Jan 6 '12 at 20:03
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::shrug:: Physicists have the privilege of living in a land where we can order up the motor we want, people engineering things in the real world (which sometimes include us experimental types) have to read datasheets. Maybe there is a "better" solution, but if so could your brother still have afforded to buy it for you? That's why I see this as an engineering problem. –  dmckee Jan 6 '12 at 20:08
    
@dmckee, :) I'm not complaining just curious, seeing as I'd done similar stuff in Physics (half the as level is on mechanics at such)I figured it came under physics, if it's not I'll wait for a engineering SE site. Also I never said it had to realistic, I much prefer learning about things that cost too much, than are limited by money. –  Jonathan. Jan 6 '12 at 21:33
    
I see a couple of misconceptions in your question: 1. If the gears are swapped, the motor will not operate at the same speed (it will slow down because the propeller will create a larger load). 2. The motor will not necessarily use less energy by operating slower. –  user2963 Jan 6 '12 at 21:35
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Every motor has a torque vs. speed curve, and the product of those is power, and it has a speed at which it generates maximum power.

Every propeller generates thrust roughly proportional to its speed squared, or its power cubed. So for a given power, it has a particular speed at which it uses that much power.

What you want to do in an airplane is find the propeller speed that absorbs the best power output of the motor.

On a typical small airplane, each propeller blade, of length about 3 feet, can absorb about 100 horsepower and generate about 200 lb of thrust at about 2400 rpm.

On the F4U Corsair, a WW2 fighter plane, the propeller was about twice that radius, so it had to turn at about 1/2 that speed. It had 4 blades, and each blade absorbed about 500 horsepower. Since the engine turned at about 2400 rpm, it had to have a 2-1 reduction gear to drive the propeller.

So it's a matter of matching the engine to the propeller. Of course, you can throttle back the engine, in which case it uses less power by transmitting less power to the propeller, giving less thrust.

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Mmmm...rules of thumb! –  dmckee Jan 6 '12 at 21:35
    
"Since the engine turned at about 2400 rpm, it had to have a 2-1 reduction gear to drive the propeller." Why not just make it turn at half the speed (1200 rpm), and without gears? –  Jonathan. Jan 6 '12 at 21:36
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@Jonathan.: because at 1200 rpm the engine's product of torque and speed (power) was much less than optimal. It's like in your car, if you try to drive in a too-high gear. It "lugs". –  Mike Dunlavey Jan 6 '12 at 21:43
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