A little off topic, but need help with science question:

[Dave]

Hello all,

I know this is a tad off topic, but the 'Aviation' groups
have few contributors, and it seems there a
lot of thoughtful science folks on this board.

My 9 year old asked a very hard-to-answer question,
at least for me, and I consider myself fairly scientific
and well-read.

Here it is:

Assuming unlimited gas and visibility:

a)You climb in your helicopter in your front yard,
say on the 45th Parallel, in Salem, Oregon.
You zoom straight up above your house to a
height of about 25,000 feet. We'll assume it's
a gloriously clear day and you can still see
Salem clearly at this point, far far below.

b) Assuming unlimited gas, will you look down
and see South Dakota 2 hours later, as the
Earth has turned on its axis? And then see
Bordeaux, France later that night, Turin Italy,
Siberia, and the vast Pacific at dawn, and finally at the
24th hour see Salem roll back under your chopper?
All of this assuming your copter is going 0 MPH
horizontally, while the earth chugs beneath you
at 1040+ MPH (The altitude of 25k feet assures
us there are no mountains racing towards us!)

c) I countered that the Earth turns at 1040 MPH or
so, so if you tilt your chopper the opposite way,
and gun it (we have a KILLER helicopter here!)
to go 1040 MPH, you'll still stay static. But this
cannot be right, or an airplane would have to travel
at LEAST 1040 when going E to W in order to gain
at all... so that cannot be true.

So how would this work? Would the earth simply
pass by while you watched? Or is there some speed
less than 1040 and greater than zero that will keep
your chopper 'in one place'? And if the earth DOES
just creep by, could you then stay low, and only go up
when you see mountains coming right at you?

Great question from a 9 year old, and our family and
friends have had fun over 2 weeks trying to solve it
to no avail. So I promised Jeremy I'd ask some folks
who might have the answer!

Thanks,

David & Jeremy
Tacoma, WA (above the 46th parallel, in a house that
moves exactly the same speed as the earth)

 

[Some Guy]

Because of friction, the air you are resting on moves with the surface of
the earth, with minor variations we call wind. Friction would keep you
motionless relative to the air. You would move relative to the earth at the
same speed, or slightly slower, than the wind. Think of a stick in a
stream. It doesn't just hover over one spot on the streambed. The water
pushes it in the direction the stream is flowing. Air is just a thinner
river. To have a situation like you describe, you would have to get above
the air, like in a spaceship. Even then, there would be magnetic effects,
space dust, etc... acting on the ship that would skew the rate of travel.
This is why we identified the Lagrange points in space. These are special
places where a spaceship could remain motionless relative to the earth,
where the magnetic and gravitational effects would not pull them somewhere
else. I am not sure, but I think there are two Lagrange points. One is in
front of earth in its orbit, the other follows earth.

In addition, you and your helicopter would already be moving at the same
speed as the earth when you take off. Inertia would tend to keep you moving
in the same direction, while gravity would keep you falling toward the
earth. Assume you used enough energy to keep yourself a specified distance
from the earth's surface. Now assume the air does not flow relative to the
surface -- no wind. The combination of inertia, gravity, the force you are
exerting to counter gravity, and friction with the air are all acting on
your helicopter, bending it's trajectory into a circle/ellipse that would
leave you hovering over one spot on the surface.

 

[Dana Raymond]

Uhmm... The problem is that as the copter rises its energy must rise to
track a given fixed spot on the earth. On the ground its angular momentum is
lower than if its a few miles up in geostationary orbit. It has to travel
faster to cover the increased circumference of its orbit to stay over a
fixed point on earth. Its angular velocity must increase, hence its energy
must increase.

Assuming 4,000 miles radius from earth center while on the surface, and
4,004.74 miles (25,000 feet up) while up in the air, the helicopter would be
traveling at 4000/4004.74 the angular velocity required for geostationary
orbit, assuming no other forces acting on it. That means that the helicopter
would travel West at a speed of 1.24 Mph relative to the earth.

Of course, the helicopter would pick up the required additional speed if it
maintained geostationary orbit while it rose above the earth, but the
problem stated "You zoom straight up above your house". If the path through
space was straight, then the angular velocity was constant. If the
helicopter tracked the spot on earth while is rose, then its actual path
would have been curved through space.

Dana Frank Raymond

 

[Charles Jean]

Uhmm... The problem is that as the copter rises its energy must rise to
track a given fixed spot on the earth. On the ground its angular momentum is
lower than if its a few miles up in geostationary orbit. It has to travel
faster to cover the increased circumference of its orbit to stay over a
fixed point on earth. Its angular velocity must increase, hence its energy
must increase.

Assuming 4,000 miles radius from earth center while on the surface, and
4,004.74 miles (25,000 feet up) while up in the air, the helicopter would be
traveling at 4000/4004.74 the angular velocity required for geostationary
orbit, assuming no other forces acting on it. That means that the helicopter
would travel West at a speed of 1.24 Mph relative to the earth.

Of course, the helicopter would pick up the required additional speed if it
maintained geostationary orbit while it rose above the earth, but the
problem stated "You zoom straight up above your house". If the path through
space was straight, then the angular velocity was constant. If the
helicopter tracked the spot on earth while is rose, then its actual path
would have been curved through space.

Dana Frank Raymond

Imagine you are in a airline terminal on one of those people walkway
gizmos, moving at about 2 feet per second. You jump straight up,
perpendicular to the surface of the walkway. You land in the same
place you started from, just like you thought you would. Jumping
higher doesn't help. Attaching springs to your feet doesn't help.
You always land in the same place you started from. While all this is
happening, you had a friend set up a video camera across the hall who
videotaped the whole session. He shoots the scene from your waist up.
What the videotape shows is you jumping up AND FORWARD, following a
parabolic curve! Forward velocity(from the mover, RELATIVE to the
wall). Vertical velocity(up, from your feet or springs; down,
increasing all the time from gravity; net velocity RELATIVE to the
wall). If the VCR had taped lower to show the people mover, you would
see the track moving under you while you were in the air, and position
itself under your feet just before you touched down. It's all
relativ(ity).
In reality, several planes can maintain a sustained speed greater than
the earth's rotational speed of about 1000 mph(at the equator). The
first was the B57 Hustler, back in the late 50's. They pointed it
west, throttled forward, and watched the sun rise from the WEST!

France launches its Arienne(sp?) rockets from some island(I forget
which) close to the equator, to get the highest "kick" from the
earth's rotation. Check the location of Cape Kennedy, too.

What happens when you're 20 feet south of the North Pole and start
running E to W around it? Remember the B57.

Getting into orbit is a whole 'nuther story. I'm tired and going to
bed.

If God hadn't intended us to eat animals,
He wouldn't have made them out of MEAT! - John Cleese

 

[Dana Raymond]

Yes, I understand what you are saying, but I think its a matter of degree.
Jumping a few feet off of a peoplemover is not the same thing as jumping
25000 feet. If you think of the copter on the earth as one orbit and at
25000 feet as another, you'll see that the circumference of the two orbits
are different. The additional energy required to travel faster in the higher
orbit has to come from somewhere, right?

Explain where that extra enegy comes from and you'll convince me. Anyway,
facinating topic for discussion!

Dana Frank Raymond

Imagine you are in a airline terminal on one of those people walkway
gizmos, moving at about 2 feet per second. You jump straight up,
perpendicular to the surface of the walkway. You land in the same
place you started from, just like you thought you would. Jumping
higher doesn't help. Attaching springs to your feet doesn't help.
You always land in the same place you started from. While all this is
happening, you had a friend set up a video camera across the hall who
videotaped the whole session. He shoots the scene from your waist up.
What the videotape shows is you jumping up AND FORWARD, following a
parabolic curve! Forward velocity(from the mover, RELATIVE to the
wall). Vertical velocity(up, from your feet or springs; down,
increasing all the time from gravity; net velocity RELATIVE to the
wall). If the VCR had taped lower to show the people mover, you would
see the track moving under you while you were in the air, and position
itself under your feet just before you touched down. It's all
relativ(ity).
In reality, several planes can maintain a sustained speed greater than
the earth's rotational speed of about 1000 mph(at the equator). The
first was the B57 Hustler, back in the late 50's. They pointed it
west, throttled forward, and watched the sun rise from the WEST!

France launches its Arienne(sp?) rockets from some island(I forget
which) close to the equator, to get the highest "kick" from the
earth's rotation. Check the location of Cape Kennedy, too.

What happens when you're 20 feet south of the North Pole and start
running E to W around it? Remember the B57.

Getting into orbit is a whole 'nuther story. I'm tired and going to
bed.

If God hadn't intended us to eat animals,
He wouldn't have made them out of MEAT! - John

Cleese

 

[Ghost Chip]

Science and electronics both deal with energy.
The extra energy that the helicopter gains to rise in altitude, (potential
energy), comes from all the fuel burned to get there. It gets most all of
it back as it comes down, (SPLAT). To not crash, it must spend additional
energy, fuel, to not let all that potential energy convert to kinetic
energy, velocity, going straight down. Essentially this is what allows a
glider to glide for a long distance against the air drag. The potential
energy converts to kinetic energy (speed) to make up for the speed lost due
to drag. The glide slope determines the gain/loss of speed. The only way a
glider can rise, is to steal energy from air movement or wind. This is why
windy days make for better gliding and why birds can soar for hours without
flapping. A form of solar energy use.

Wow, what questions will the child have when he's 18?

Ghost

 

[Dave]

You guys are ALL great in your answers! And funny thing, we STILL
don't really have 'the' answer!

I am going to print all the replies for Jeremy to read. And yes, I can
hardly wait for the questions when he turns 18. Of course, my answer
will be 'duh' most of the time....

Dave

ps - keep the hypotheses coming!

 

[Jibaro]

the answer today is YES. (he/she is 9)
in 9 years the question will be "where can I find girls?" for boys, or
"what's the shortest distance to the mall?" for girls.

 

[Ghost Chip]

Ans 1: No
Ans 2: No
Ans 3: It obeys the laws of physics.
Ans 4: No
Ans 5: No
Ans 6: Pilots choice