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Homework Statement
A small dc motor has the following specifications and is being considered for powering the propeller of a model boat. The propeller has the intended capability of supplying 0.1Nm of torque at 200rpm.
Operating voltage = 4.5V
Stall torque = 6.6*10^-3 Nm
Stall current = 6.26 A
No load speed = 21 000 rpm
No load current = 0.29 A
Maximum load torque = 1.2*10^-3 rpm
Maximum load speed = 17 000 rpm
Show that this motor does have the power to meet this capability, and determine an approximate gear ratio with which it should be used in order to supply the required combination of torque and speed.
Homework Equations
Power = torque * angular speed
The Attempt at a Solution
Okay so the power required for the propeller is
=0.1 Nm * 200 rpm
=0.1 Nm * (200*2pi)/60 rad s^-1
=2.09W
The power produced by the motor at maximum load (low power point?) is
=1.2*10^-3 Nm * 17000 rpm
=1.2*10^-3 Nm * (17000 *2pi)/60 rad s^-1
=2.14W
Does this mean that since at its low power point the motor produces more than sufficient power to power the propeller that it is suitable?
As for the gear ratio:
17 000 rpm/ 200rpm = 85, so this would be the maximum gear ratio allowed
0.1 Nm/1.2*10^-3 Nm = 83.3, so this would be the minimum gear ratio allowed
Therefore a gear ratio of 85 would be suitable? (These margins seem rather close, especially because there will be power losses in any real system.)
Also: I've done all these calculations using the maximum load figures and ignored the rest. Is this correct? This is the only question for this data and I don't feel that the rest are likely be so superfluous.
