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## Main Question or Discussion Point

This is not my homework this is just a random thought. Say you have a 1 kg helicopter hovering in midair. The question is, given perfect efficiency, how much power is it using to hover?

My approach is to think of the given information first. We know that g= 9.8. So you have a 1 kg mass that requires 9.8 N of thrust to remain hovering. Obviously there is no energy being added to the helicopter since it is standing still but there is some energy being used every second to move a certain volume of air. Let's assume that the blades are made so that they move 1 kg of air every second. So the next question is with what velocity must it blow that air to levitate? If the helicopter is in free fall then in 1 second it will attain a velocity of 9.8 m/s. It would have to blow 1 kg of air at 9.8 m/s to stop falling but it would have to blow it away at 19.6 m/s to get to the original spot. Using the equation for kinetic energy the helicopter uses 192 Joules of energy every second to hover. This of course is just 192 Watts of power. So in general 9.8 N of thrust in any situation is going to require 192 Watts. Is that correct? What is the equation that would generalize this calculation?

My approach is to think of the given information first. We know that g= 9.8. So you have a 1 kg mass that requires 9.8 N of thrust to remain hovering. Obviously there is no energy being added to the helicopter since it is standing still but there is some energy being used every second to move a certain volume of air. Let's assume that the blades are made so that they move 1 kg of air every second. So the next question is with what velocity must it blow that air to levitate? If the helicopter is in free fall then in 1 second it will attain a velocity of 9.8 m/s. It would have to blow 1 kg of air at 9.8 m/s to stop falling but it would have to blow it away at 19.6 m/s to get to the original spot. Using the equation for kinetic energy the helicopter uses 192 Joules of energy every second to hover. This of course is just 192 Watts of power. So in general 9.8 N of thrust in any situation is going to require 192 Watts. Is that correct? What is the equation that would generalize this calculation?