How Much Air Mass for a Hovering Helicopter?

[henry3369]

Homework Statement

During a rescue operation, a 5200-kg helicopter hovers above a fixed point. The helicopter blades send air downward with a speed of 70m/s .

What mass of air must pass through the blades every second to produce enough thrust for the helicopter to hover?

Homework Equations

ΣF = 0

The Attempt at a Solution

Since the helicopter is hovering, the magnitude of the downward forces have to be the same as the upward forces. The only downward force on the helicopter is the weight = mg. So this must equal the upward forces. I can't figure out what the upward force is. I tried using impulse and momentum to find force, but the change in momentum is zero, so impulse is zero so that doesn't help me find the force of the air on the helicopter. I know that the force the blades exert on the air, the air exerts on the helicopter, and all I have is the velocity of the air from the blades.

 

[lewando]

Looks like the air is changing momentum: vi=0, vf=70 m/s.

 

[henry3369]

Looks like the air is changing momentum: vi=0, vf=70 m/s.

Makes sense. I was thinking about the system as a whole. Thank you!

 

[henry3369]

Looks like the air is changing momentum: vi=0, vf=70 m/s.

Hmm. How did you conclude that the air was changing speed if it says that the blade sends air down at a speed of 70m/s.

 

[lewando]

A blade, not unlike a fan, accelerates air from a state of not moving to moving.

 

[mfb]

You can assume there is no wind down- or upwards, so initially the air is at rest.

 

[lewando]

Alright, in a wind tunnel, vin = vout, but in free air this is much less so. Even though there would seem to be some continuity of air flow near the blade, at some point far enough away, the air is not moving.