The following was inspired by a recent discussion I had about analyzing a vacuum ball magnet:
The power required to drive a certain vacuum impeller is given by the equation
The impeller is being driven by two motors: a CIM and an FP, each through a separate gearbox.
The motors are each being driven at 12 volts.
Find the theoretical gear ratios of the two gearboxes which produce the fastest impeller speed.
[edit 11:56am] Note: for purposes of this analysis, ignore gearbox losses. [/edit]
[edit 4:54pm] Note: For this hypothetical problem, ignore the 40amp breaker and allow each motor to draw whatever current it needs (with 12V applied) in order to maximize the impeller speed. Pretend the impeller is only operated momentarily. [/edit]