# Helicopter hovering

Question that was always bugging me.

Why doesn't a helicopter which could theoretically hover on the spot for hours doesn't end up in another part of the world. Since it's off from the ground doesn't it lose the velocity of earth's rotation? What keeps it in the same place/at same velocity all the time? I would assume that it's the atmosphere that's rotating along with the planet right?

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tiny-tim
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Welcome to PF!

Hi pr1de! Welcome to PF!
… Since it's off from the ground doesn't it lose the velocity of earth's rotation?
No … imagine a hovercraft on the Moon (obviously, a helicopter wouldn't work there … no air! ) …

it'll still hover!

The helicopter has horizontal momentum when it's on the ground.

When it lifts off, the only force is vertical, so it still has the same horizontal momentum: its horizontal speed still perfectly matches that of the Earth's surface.

If the 'copter was hovering at 100m above the Earth, to a rough approximation it would only need to move at about 0.01 mph to "keep up with" the rotation beneath it.

Hi pr1de! Welcome to PF!

No … imagine a hovercraft on the Moon (obviously, a helicopter wouldn't work there … no air! ) …

it'll still hover!

The helicopter has horizontal momentum when it's on the ground.

When it lifts off, the only force is vertical, so it still has the same horizontal momentum: its horizontal speed still perfectly matches that of the Earth's surface.
Increasing its distance from the centre means that its horizontal velocity (or angular velocity) must be less if its angular momentum remains the same.

I think Galileo tested that assumption by dropping balls from the mast of a ship and found they dropped straight down relative to the ship, not the earth. Newton explained it by saying that objects tend to remain as they are, either in motion or stationary. This he called inertia. The helicopter has the same velocity as the surface of the earth and will keep that velocity unless something causes that velocity to change.

DaveC426913
Gold Member
If the 'copter was hovering at 100m above the Earth, to a rough approximation it would only need to move at about 0.01 mph to "keep up with" the rotation beneath it.
Well, yes but first it would have to keep its rotation imparted to it from the Earth, which is 1000mph at the equator and ~707mph up near the the great Lakes.

The OP's question is a bit vague so it's hard to tell why he thinks the helicopter would not stay stationary wrt the ground.

Well, yes but first it would have to keep its rotation imparted to it from the Earth, which is 1000mph at the equator and ~707mph up near the the great Lakes.

The OP's question is a bit vague so it's hard to tell why he thinks the helicopter would not stay stationary wrt the ground.
Yes, 1000mph at the equator, and approx 1000.01 mph at a height of 100m would be necessary to keep up with the Earth below.
ie, to maintain the same angular velocity.

DaveC426913
Gold Member
1] While parked, the helicopter has momentum imparted to it from the ground. At the equator, this is 1000mph.
2] When it lifts off, it retains this momentum, and continues moving at 1000mph.
3] If the helicopter were to lift high enough off the ground that the curvature of the Earth became a factor, then the Earth would be able to move under the copter slightly faster and the copter would fall behind (just like a race car one curve in the outside lane will fall behind). The copter would have to move very slightly to "keep pace" with the Earth.
4] This assumes we ignore the effect of the atmosphere. The atmo is carried along with the Earth, even at altitude. Which means as the copter rises, the atmo will overwhelm this tiny force of angular momentum.

Thank you guys, it all makes sense to me now. It's always good to have someone confirm your thoughts :D

russ_watters
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