How to Derive Power for a Drone Hovering Using a Capacitor?

[Chris Johns]

A 1 F capacitor is charged at 10 Volt and powers a small copter drone of m=20 grams.
The copter generates a vertical lift to balance gravity. It does this with a
propeller than pushes air downward at a velocity v. Show that the power required
is mgv/2. At an air flow velocity of 2 m/s , calculate how long the copter stays up
(assuming 100% energy efficiency and controlling the power distribution to be
steady).

 

[Ray Vickson]

A 1 F capacitor is charged at 10 Volt and powers a small copter drone of m=20 grams.
The copter generates a vertical lift to balance gravity. It does this with a
propeller than pushes air downward at a velocity v. Show that the power required
is mgv/2. At an air flow velocity of 2 m/s , calculate how long the copter stays up
(assuming 100% energy efficiency and controlling the power distribution to be
steady).

PF rules require some effort on your part. Try solving the problem for yourself, and if you are stuck on some issue, come back here and explain the difficulty. Maybe then you can be receive help.

 

[Chris Johns]

I've been trying for a week now! I know that
Power = rateOfDoingWork

Work = Force * Distance = mass * g * Distance

Power = d/dt (Work) = d/dt (Force * Distance) = d/dt (Force)* Distance + d/dt (Distance) * Force

also d/dt(Force) goes to zero because mass (m) is constant and gravitational acceleration (g) is constant.

Thus Power = m * g * v

But I can't go any further than this. I would greatly appreciate any help.

 

[CWatters]

For the blades to generate a force what must they do to the air?