Physics question... maybe? Air Travel, Earth Rotation...

Maybe Im crazy and missing something, so help me out friends.

A friend of mine said he took a 20 hour flight from NY to South Africa. Well it got me thinking about air travel and the Earths rotation. If you could float above the Earth and remain stationary, the Earth would begin to fly beneath you and you could travel in theory all the way around the world in 24 hours, right?? By that ration how the hell could a flight take 20 hours assuming the plane is moving? Unless of course you are flying against the earth’s rotation, but why would an airline do that?

So whats up, clear me up on this please. And if anyone knows do airlines send planes in the directions that may be a longer route mile-wise but faster because of the rotation of Earth???

Thanks…

Well, yeah, you could get to any new location at your latitude IF you could hover above the earth’s surface and let it spin beneath you. But that would be extremely hard to do.
Airplanes move through the air more or less like boats move through the water - what they are basically doing is pushing fluid around. So the challenge on an airplane is to push your way through thousands of miles of air, and do it fast enough that you support your weight in the process. Whether the planet you’re doing it on is also spinning doesn’t change this.
If you really want it easy, why fool with an airplane? Just pull your feet up and let the ground spin under you…

…unless the aircraft has entered outer space and left the earth’s atmosphere. If it just sat there suspended in air, it would merely move along with the jet stream.

That’s my theory, anyway… I could be wrong.

You couldn’t just pull your feet up and have the planet move under you. As long as you’re on Earth, you’re moving at a speed equal to that of the earth’s rotation (not sure of the speed, but pretty d*mn fast). Jumping in the air (according to physics) means you go up a certain height (based on the strength of your jump) but you’re also moving the same direction the Earth is at the same speed the earth is (frame of reference).
Picture yourself in a car, going 100 km/h on the expressway (60+ mph) and throwing a tennis ball in the air. If there was an absence of wind, the ball would stay above the car, only moving up and down. You are the tennis ball.

Also note that when you jump up, because of your inertial velocity (you are moving at the speed of Earth’s rotation), you will continue moving at that velocity regardless if your feet are firmly planted on the ground. IIRC, the equation for velocity depending on your latitude is: 2PiRCos(PiL/180)/86400 where R is the Earth’s radius (~6.3710^6 m), L is your latitude, and the answer is in m/s.

The earth also has a tendancy to pull at objects, I believe, and thus the velocity differential between something in the air in a rotating system and a non-rotating system isn’t that great, relative to the reference frame that is.

Momentum.

The airplane has the momentum of the earth’s rotation. When you jump off the ground, you continue at the speed the Earth was moving at when you jumped off. Relative to the ground, you aren’t moving, relative to some arbitrary fixed point, you’re whirling away right above the earth.

The air also has this momentum, which is why the situation is different from throwing a tennis ball out a car window. Try riding a bike (so that air friction is minimal) past a friend. When you get to the friend, throw the ball straight up. To you, the ball goes straight up and down. To the friend, it travels in a parabola.

The plane is like the ball. Air friction isn’t necessarilly minimal, but it has the same speed as the earth’s rotation (discounting wind).

So, there you have it. When travelling around the surface of the earth, you ignore the actual velocity of the earth, because YOU have that velocity, too. They cancel out (technically not the case, but good enough for high school physics).

There’s a good answer. I get it now. Thanks Surgoshan…

I don’t have any references, but I do believe that on north/south flights, some degree of compensation for the Earth’s rotation is necessary, or you’ll end up a little west of your destination.

AWB writes, “I don’t have any references, but I do believe that on north/south flights, some degree of compensation for the Earth’s rotation is necessary, or you’ll end up a little west of your destination.”

I’m not aware of any such compensation. We do, however, compensate for such things as the earth being a sphere (and most flight planning (in the Navy, anyway) is done on a flat map), and magnetic variation. If you can find any references, AWB, let me know, cause I’d love to take a look!

As for the OP, 20 hours does seem a bit long for such a flight. South Africa is +2 from GMT; someone taking off at 10am EST from NY would land (assuming this is actually closer to a 10 hr flight… I’m too lazy to actually spread a chart out, measure the distance, and get a more accurate time) in SA at 8pm EST, or 3am local time, which may make it seem more like 20 hrs vs. only 10. And were there any stops/layovers along the way? This would add a couple hours to the total.

I don’t have any references either, but I would imagine that the effect of flying perpendicular to the Jet Stream would be far greater than any effect caused by the rotation of the earth.

You may also be talking about compensating for TRUE NORTH instead of MAGNETIC NORTH (or vice versus). The Magnetic North Pole (the point where the compass is pointing to) is not actually over the North Pole (The northern point where the axis of the earths rotations intersects the Earth)

Not crazy my friend, just misinformed.

If they do send planes on longer routes, its more likely to take advantage of the jet stream than the earths rotation.

If you look at a planes flight path on a flat map, it takes usually takes the form of a parabola. This is because planes fly along a “great circle”. Essentially, this is a circle drawn around the diameter of the globe so it intersects the start and end locations. When you transcribe that path from a 3d globe to a 2d map, you get some distortion.
The Earth dosn’t move underneath an airplane for the same reason you don’t fly to the back of the plane if you jump up in the air.

I can relate at least one experience in the use of the jet stream for air travel.

Recently I took a flight from San Francisco to Tokyo (and back). On the way there, we flew roughly a great circle route over Alaska. On the way back, though, we flew almost directly (on a 2-d map) across the Pacific with some slight curve north, but well south of the Aleutians. We had a 120 mph tailwind most of the way, with a fair amount of turbulence, but ended up two hours ahead of schedule.

And if you want to look at at funny, it took us 29 hours to get to Tokyo, and -7 to get back.

The answers up to this point are correct and right on. Just for kicks I include the following:

The earth rotates roughly 1,000 mph at the equator (the earth is roughly 25,000 miles in circumference at the equator and there are [nearly] 24 hours in a day). Our continued motion with the earth, as others have mentioned, is a good thing or else you’d be pulverized against nearby walls at 1,000 mph anytime you jumped.

Of course, if you’re standing at the North Pole (or South Pole) then you are moving hardly at all (the circumference of your body once per day…maybe 2-3 feet per day). If you’re really curious as to the speed you’re moving where you are now then multiply the speed at the equator by the cosine of the latitude where you are at.

Our actual motion while standing on our planet is much more complex if you consider the rotation of the earth, earth’s orbit around the sun, the suns orbit around the Milky Way Galaxy and the Milky Way Galaxy’s motion. All told, to an observer sitting outside of it all, you trace a very squiggly line through space.

Slight hijack… Why is flying in the “great circles” preferable to a more direct route? Is it for the wind? Specifically, crossing from the Midwest to England. We took a VERY circuitous route up past Newfoundland.

A great circle is the shortest distance between two points on a sphere (if you are prevented from tunneling through the sphere). The route only looks less “direct” when you look at it projected on a flat map. Go look at your route on a globe!

No. The “great circle” is the direct route. We have gotten used to thinking of things in terms of straight lines. We think of latitude as the “straight line” going east and west and longitude as the “straight line” going north and south and we imagine that they are on a square grid like the Mercatur Projection maps that hung on our classroom walls.

However, the Earth is a sphere and the latitude and longitude lines are simply imaginary marks to aid us find places on the globe. If you got hold of a globe map of the world and put one end of a string on Chicago then pulled the string across to London, you would see that the string did not follow the latitude lines from 40° at Chicago angling up to 50° at London, but would actually ignore the latitude and curve up near the Arctic Circle and back down.

If you do not have a globe, try this with a grapefruit or a basketball or something. Draw a line around the middle of the object to be the “equator.” Then draw another line parallel to the “equator” halfway between the equator and the top of the sphere. Hold a piece of string on either of the two “latitude” lines, then move the other end of the string to any other point on the same line. Note that unless you are exactly following the “equator” line, the string will always appear to “bulge” up toward the top (or “pole”) in the middle.

The eye is fooled by our desire to see lines joining at right angles into thinking that the sphere is laid out like a grid. But grids are flat and globes (such as the Earth) are not flat.

One other thing to note on the error imposed by a flat map compared to a globe is to look at Greenland. On a flat map Greenland looks HUGE (bigger than the US). In reality it’s much smaller (about the size of the US from the Mississippi to the Atlantic coast IIRC).

Notice on a globe how all of the longitude lines converge at the poles? On a flat map they stay equidistant. The extra space between the lines as you approach the poles distort what is actually there.

Yes, compensation is required for for objects travelling longitudinally due to the coriolis effect. As I stated earlier, the way Newton was able to explain why it is possible for the Earth to rotate three hundred years ago was through his first law of motion, and this doesn’t change. But, what does change as an object travels longitudinally, is that their speed relative to the ground beneath them changes. As a plane travels from north to south the earth appears as though it has started to move faster westward (depending on the hemisphere). If the coriolis effect isn’t taken into account an object will appear as though it has been deflected west (in the northern hemisphere) and east (in the southern hemisphere) even though it’s latitudinal (is that the correct word?) velocity hasn’t changed. This simply has to do with the fact that when the Earth rotates, and with any sphere for that matter, it rotates faster at the equator than near the poles.

You can find information on the coriolis effect anywhere, but for our purposes, it’s basic physics.

Maybe I should clarify that. As a plane travels from north to south in the northern hemisphere the earth moves faster eastward. As it travels from north to south in the southern hemisphere the earth’s speed slows down, therefor resulting in a apparant deflection east (or, that the earth has started moving west relative to the plane).