East-to-West Flight Times

When we fly west over the Pacific Ocean (e.g. California to Bombay) it takes about 22 hours to reach the destination, but it only takes 17 hours back. Is this because when flying from California to India the direction of flight is the same as the direction of the Earth's rotation around its axis, so it takes longer because the destination is moving further away from the plane and the plane is trying to catch the destination? And when flying back the flight direction is opposite of the Earth's rotation and both the airplane and the destination are coming towards each other? Of course the head winds and the tail winds do play quite some role, but I'm guessing that the major factor is the Earth's rotation with respect to the flight direction. Is that correct?
- question from Raj
Speed can be a confusing topic when considered from an aerospace engineering standpoint. For this question, we need to consider two "concepts" of speed. The first is the speed of an object through space, which we will consider as the speed of the Earth's rotation about its axis. If we consider this concept, then you, sitting at your computer, are probably traveling somewhere around 735 mph (1,183 km/h) through space, depending on your location relative to the equator (are you wearing your safety helmet?).

The second concept of speed is an object's speed relative to the Earth's surface. In this case, you, sitting at your computer, are traveling at 0 mph relative to the Earth. Now let us consider what would happen if you suddenly stood up and started running (run Forrest, run). No matter which direction you run, your speed relative to the Earth would be 10 mph (16 km/h) or so (80 mph if you are a Cheetah). If you were running to the west, against the Earth's rotation, then your speed through space would be 725 mph (1,166 km/h). Of course, if you ran the opposite way, it would be 745 mph (1,199 km/h). Your speed relative to the Earth is the same no matter which way you run. It isn't affected by the rotation of the Earth.

Now stop running. If you were to jump straight up in the air, would the Earth rotate beneath you? (Those who do believe that the Earth rotates around them may want to stop reading right now.) No, because when you left the Earth's surface, you were traveling at the same speed as the surface, so, in essence, the Earth matched your speed through space while you were in the air! The same condition holds true for an airplane as it travels from Los Angeles to Bombay. If we were to ignore the winds, no matter which direction you flew from Los Angeles, the speed of the aircraft relative to the Earth would be the same. While the aircraft's speed through space would change, the effect of the Earth's rotation remains constant, and in effect is "cancelled out" no matter which direction you travel. In other words, the speed of the rotation of the Earth is already imparted to the aircraft, and the Earth matches that speed during the entire flight. (Of course, in the case of spacecraft, these speeds become very important.)

So, the end result of that long discussion is that the rotation of the Earth has no effect on the travel time of an aircraft. Actually, as you suggested, it is the headwinds and tailwinds that cause the change in travel times. Sometimes it is hard to believe that the winds can have that much effect, so let us consider the problem a bit more in depth. In the example given, the flight from Bombay to California (east) is 23% shorter than the trip from California to Bombay (west). This means that the speed of the trip east must be 23% faster. The prevailing winds pretty much anywhere that we are talking about blow from west to east, so when we are traveling east, we get a speed gain, and when we travel west, we get a speed penalty. Now, if we are to assume that the winds are identical on both days we fly, then the wind speed only needs to be equal to 11.5% of the aircraft's speed! This would cause a difference between the speed to the west and speed to the east of 23%! The cruise speed of the extended range Boeing 777 is about 550 mph (885 km/h) at 35,000 ft (10,675 m). This means that the winds only need a speed of about 65 mph (105 km/h) (good kite weather). Believe it or not, 65 mph is a very typical wind speed at such a high altitude. Speeds of over 100 mph (160 km/h) are not uncommon. If we wanted to make things more complicated, we could consider a region of high speed flow called the jet stream that flows eastward, and if an aircraft can take advantage of these winds, then the travel time can be reduced further. (We could get even more complicated and talk about El Nino and La Nina, but I think we have blamed them for enough already!)

So what is the bottom line? The rotation of the Earth does not effect the travel time of an aircraft, and, more importantly, a mere 65 mph wind is more than enough to cause a difference in travel time of five hours when you are traveling long distances!
- answer by Doug Jackson, 20 May 2001

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