Is air travel time the same whether or not the plane is flying with or against the rotation of the Earth?
If you were to ask the boy, he would tell you no, silly, the ball went straight up and down, and it landed at the exact same spot from where he threw it. If you were to ask a farmer standing in her field beside the train tracks, she would tell you she saw the boy and the ball travel together at 80 kph, and the ball went in the path of an arc while the seated boy traveled in the path of a straight line, and while the ball landed in the boy's hand, both the boy and the ball had travelled 20 meters (66 feet) down the tracks during the time the ball was airborne.
From the boy's perspective, neither he nor the ball moved sideways, and the ball simply when up and down. From the farmer's perspective, both the boy and the ball travelled much farther sideways (20 meters) than the ball travelled up and down (1 meter). It is important to accept that both accounts, while radically different, are correct.
Now imagine the boy had a friend, and they tossed the ball back and forth along the aisle of the train car. Again, from their perspective, nothing unusual would happen - the boys would toss the ball back and forth exactly as expected. More importantly, from the boys' perspective the ball would not go faster in one direction than the other because of the speed of the train. That is because the ball, the boys, the train, the seats, and the other annoyed passengers are all travelling at the same base velocity. From the stationary farmer's perspective, the ball does travel faster when thrown in one direction compared to when thrown in the other direction, but the ball still takes the same amount of time when thrown in both directions, owing to the fact that the train (and the boys and the ball on the train) are all traveling at the same constant base velocity.
For purposes of this discussion, it is more useful to consider the boy's frame of reference, however we will ultimately get exactly the same answers from the farmer's point of view. Both the boy and the farmer will tell you the ball took the same time to go from one boy to the other, regardless of which direction it was thrown. In the remainder of this discussion, we will consider the situation from the moving frame of reference.
Now instead of talking about boys on a moving train, lets talk about airplanes on a rotating earth. All the principles discussed above still apply. The earth, the mountains, people, animals, plants, the atmosphere, clouds - everything - travels at the same speed, just like the boys on the train. That is assuming the winds are calm - more about that in a moment. And since airplanes travel through air (that is what airspeed means) in calm winds it does not matter if you travel in the same direction as the earth's rotation, or in the opposite direction. Just like the boys tossing the ball back and forth on the train, the airplane takes the same time regardless of which direction it travels. Put simply, the earth's rotation does not affect the time it takes for an airplane to fly, regardless of whether it is flying East or West.
If that is so, you ask, then why does it take longer to fly from Paris to New York than from New York to Paris. The answer is the prevailing trade winds. The winds and jet streams at that latitude travel from West to East, giving an eastbound plane a tailwind, and thus a higher groundspeed, compared to a headwind on the return trip, which has a lower groundspeed.
Does the aiming process for long range artillery, and especially naval gunfire, have to adjust calculations to allow for the earth's rotation? Also, when aircraft fly north/south, do compass headings have to be adjusted for rotational effects? Are the jet streams themselves partially a consequence of the earth's rotation? I think the answer to all of the above may be 'yes', bringing the image of aircraft moving in synchronicity with the earth's rotation into some doubt.- Agilis
It is true that when a plane takes off, it is moving with the earth's rotational velocity as well as its own, but the tangential velocity of the earth is not the same everywhere. At the equator, the speed the earth is traveling is much greater than the speed at, say, the 43rd parallel because the 43rd parallel is a lot closer to the axis of the earth's rotation. This phenomenon was brought to light during World War II when the Allies attempted to fire long-range artillery into central Europe from North Africa. They projectiles flew off course because their tangential velocity at North Africa was greater than that of the earth in Europe. This is known as the Coriolis Effect.
Actually, long range artillery adjustments to compensate for the earth's rotation have almost nothing to do with the coriolanus effect. No artillery travels far enough to come close to a transit of the Mediterranian Sea. North Africa to Central Europe is possible only with modern ballistic missles. Under 30 miles is the absolute range limitation for most artillery, naval or ground, except for some gigantic multitube experimental monsters. Some of the longest range highly specialized artillery was developed in WW1, when the Germans shelled Paris from a remarkable distance. In any case, aiming adjustments to compensate for the Earth's rotation began in the first decade of the 20th century, and reached an apogee :) during and after WW1, when vessels began shelling each other at ranges that could extend to 20 miles, with huge projectiles that entered the stratosphere before dropping with an impressive multicolor pyrotechnic display as two tons of steel reached white hot temperatures. Computer(primitive) assisted naval gun aiming systems were developed before WW2, and could adjust for the target moving left or right when firing in a north or south direction, farther or closer when firing east or west, and (usually) some combination of two of the earth's rotational elements, along with all the usual range, atmospheric density, and other variables. High altitude experiments in the US immediately after WW2 were conducted with specially modified 16 inch naval guns, until the Army got Von Braun and his colleagues settled properly and V2 rockets operational again. Anything moving with sufficient mass and velocity will be unaffected by atmospheric phenomena. Only gravity becomes a factor, until its limits are escaped.