# Hovering helicopter

1. Feb 15, 2015

### henry3369

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
ΣF = 0

3. 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.

2. Feb 15, 2015

### lewando

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

3. Feb 15, 2015

### henry3369

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

4. Feb 15, 2015

### henry3369

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.

5. Feb 15, 2015

### lewando

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

6. Feb 15, 2015

### Staff: Mentor

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

7. Feb 15, 2015

### 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.