## Plane travelling

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Blacklilac
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### Plane travelling

Ok, so I was restless last night and posed myself a question I couldn't answer (mostly because I suck at physics). Here's my question, if you have a plane at point A on the equator. Then we have point B 500km directly east of point A, and point C 500km directly west of point A; now, if would the plane get to either point B or C faster because of the earths rotation? (I was thinking of a fly in moving vehicle as a starting point in trying to figure it out lol don't know how valid that is to this question).

niko7865
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### Re: Plane travelling

I don't think the rotation would have a direct effect on the plane speed. However the Jet stream would change the arrival time.
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Steve
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### Re: Plane travelling

If you assume that the atmosphere acts in solid body rotation with Earth, then no, neither point will be a quicker trip. In reality, the answer is yes (I cannot remember in which direction) due to Hadley cells that create an equatorial trade wind, aiding the plane in one direction and slowing it in the other (relative to ground of course).
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ST47
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### Re: Plane travelling

Equal times, if we disregard all atmospheric conditions. The airplane is on the ground moving at the same speed as the earth rotates. Taking off brings it to the same airspeed. It's still sort of geosynchronous, if you ignore the fact that it's a moving airplane. If that makes sense. It's still rotating around the earth, as is the ground, and the atmosphere.

Now if you want to be really technical, then there's this. Let's say the earth is rotating at 1kph. If you keep the same speed, and you double your distance from the center of earth, then the earth is now traveling .5kph faster than you. So, technically, you'd be moving backwards. So you'd get to the point 500km west of you faster. By a really tiny amount. I'm sure someone here can figure out how much faster. But remember that the atmospheric conditions, which are usually west to east winds, have a lot more influence on the plane's speed. Ground speed that is, not airspeed.

Charlie!
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### Re: Plane travelling

According to Multivac, trade winds at the equator run counter to the earth's rotation, speeding up westward travel and slowing down eastward travel. So in reality, point C wins. That's more meteorology than physics though.
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Herman
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### Re: Plane travelling

trade winds at the equator run counter to the earth's rotation, speeding up westward travel and slowing down eastward travel. So in reality, point C wins. That's more meteorology than physics though.

If you did this in a vacuum, with a rocket or something, a trip west would go faster because of the Coriolis force. So the effect of trade winds is very basically just a magnification of this effect.

According to Multivac,

Uh-oh...

Swordfish
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### Re: Plane travelling

If you completely discount the atmosphere, then it will take you the same amount of time to reach point B as it will point C. The Coriolis Force at the equator is zero, so it won't make a difference.

If we want to talk about the atmosphere, things get a little more complicated. First of all, there is no jet stream at the equator, the Jet Stream is the border between the Farrel Cells and the polar Hadley Cells, and, as such is found in the mid to polar latitudes. There is also a much weaker sub-tropical jet between the Tropical Hadley Cells and the Farrel Cells, but, again, it's not near the equator and it doesn't even exists everywhere all the time anyway.

It should also be noted that the equator and the meteorological equator are not the same thing, as the meteorology one is actually at about 5 N, which is the average position of the Inter-Tropical Convergence Zone.

... I'm probably going a little too deep here, so I'll just say that the prevailing wind flow in the tropics is out of the east, in which case you'd get to point C faster with help from the wind.
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Blacklilac
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### Re: Plane travelling

I like deep, all this stuff is new and intriguing to me Always love to learn stuff like this, similar to watching discovery channel lol So, from what i've read from you guys is that the only way you would get to one point faster is if there is a wind pushing you? Would it work differently on land or outside of the atmosphere?

Robin S
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### Re: Plane travelling

Why should it?
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Blacklilac
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### Re: Plane travelling

Robin S wrote:Why should it?

Why should what? >.<

Robin S
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### Re: Plane travelling

You wrote:Would it work differently on land or outside of the atmosphere?
I wrote:Why should it?
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cypherspace
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### Re: Plane travelling

Blacklilac wrote:I like deep, all this stuff is new and intriguing to me Always love to learn stuff like this, similar to watching discovery channel lol So, from what i've read from you guys is that the only way you would get to one point faster is if there is a wind pushing you? Would it work differently on land or outside of the atmosphere?

He means, no. You start off rotating at the same speed as the Earth, so any acceleration either way just adds to that speed. You'd travel the same distance in both directions in the same time, no matter whether you were on land, water, air, or orbit, provided there's no other forces acting on you that were related to the Earth's motion.

Analogy - pretend you're on a moving walkway. There's a point ten yards ahead of you marked on the walkway, and there's a point ten yards behind you marked on the walkway. You stand back to back with a friend and both walk forward at the same speed. Who gets to the ten yard point first? Neither of you, you arrive at the same time. It's the same as if you were on a piece of ground that wasn't moving (it is, of course, moving at the same speed as the Earth is rotating. You just don't notice it because you're moving at the same speed).
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Blacklilac
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### Re: Plane travelling

Oh ok, thank you cypher!

Charlie!
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### Re: Plane travelling

Herman wrote:
trade winds at the equator run counter to the earth's rotation, speeding up westward travel and slowing down eastward travel. So in reality, point C wins. That's more meteorology than physics though.

If you did this in a vacuum, with a rocket or something, a trip west would go faster because of the Coriolis force. So the effect of trade winds is very basically just a magnification of this effect.

According to Multivac,

Uh-oh...

Hmm, really? A plane isn't a weather system though. Some sort of vertical force (perhaps the http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_effect ? ) might keep the plane so if it maintained the same airspeed going west as it did going east, it would experience a drop in altitude going wet and a rise going east.

So the question is, would those changes in altitude balance the changes in equatorial position?
Last edited by Charlie! on Tue Mar 04, 2008 6:07 am UTC, edited 1 time in total.
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chrisshannon
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### Re: Plane travelling

A plane will gain westward velocity because it gains altitude (even neglecting all atmospheric effects). This is due to the conservation of angular momentum. This same phenomenon causes the space elevator cable to lean to the west when its payload rises. It is all explained by the Coriolis effect.

If the plane was a rocket that could only thrust directly away from the centre of the earth (had no horizontal thrust), it could still travel westwards by hovering.

The plane will therefore reach the westward point before the eastward point.

The conveyor belt analogy can't explain this phenomenon because it assumes a stationary, flat earth.

Swordfish
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### Re: Plane travelling

Charlie! wrote:Hmm, really? A plane isn't a weather system though. Some sort of vertical force (perhaps the http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_effect ? ) might keep the plane so if it maintained the same airspeed going west as it did going east, it would experience a drop in altitude going wet and a rise going east.

So the question is, would those changes in altitude balance the changes in equatorial position?

That's not quite going to affect the airplane's position. The Eotvos effect doesn't add net acceleration to the airplane. The downward acceleration on the airplane will be 9.8 m/sec2 due to gravity, while the upward acceleration will be .02 m/sec2 (which is what I calculated Eotvos to be for a plane traveling at 500 km/hr along the equator) plus 9.78 m/sec2 generated by the airplane's lift = 9.8 m/sec2.

If we want the thing to hover, then you'll probably only be applying enough acceleration to keep yourself at the same altitude, which means you're compensating for the Eotvos effect.

chrisshannon wrote:A plane will gain westward velocity because it gains altitude (even neglecting all atmospheric effects). This is due to the conservation of angular momentum. This same phenomenon causes the space elevator cable to lean to the west when its payload rises. It is all explained by the Coriolis effect.

If the plane was a rocket that could only thrust directly away from the centre of the earth (had no horizontal thrust), it could still travel westwards by hovering.

The plane will therefore reach the westward point before the eastward point.

If I have the plane travel to an altitude of 10 km at 10 meters per second, then by the time it's done climbing, it's gained about 1.46 m/sec of westward velocity or a little more than 5 km/hr. 505 km/hr will get you to point C in .99 hours while the 495 km/hr will get you to point B in 1.01 hours. That difference is a little bit more than a minute, which is probably gona be well less than the margin of error were you to actually try this.
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