Two identical planes leave Svalbard,Norway(80N,20E) at the same time.Both travel at a speed of 500 kph. Plane A travels along the 20 degree east meridian,till it arrives at the 35 degree south latitude. This is Capetown,South Africa(35S,20E). Plane B takes a great circle route as well, but travels southwest to the Falkland Islands(50S,60W).Which plane will arrive at its destination first?
The question of course is the relevance of starting from a low initial angular velocity due to the earths rotation and flying over a landscape that is moving in a transverse direction at a much greater speed than it was when you were initially in contact with it.
For $64,000 I’ll bet that Plane B makes it first. For $1,000,000, I’ll tell Regis I’m walking.
If I’m in the wrong place, Moderator, please move it. The question is related to the one David B. moved over here, called something like Weights on different parts of the earth. Effects of spin etc.
Ack, it’s late, but that was a blatant error on my part. I don’t think the effects of air currents should be ignored, as there are always wind currents flowing from west to east, making all flights going from east to west take longer, at least from experience. Anyways, the safest bet would be Plane A (taking air currents into account) on any pop quiz show. Perhaps some others who know better can help you find the time it takes for it to travel to both destinations without any air currents, I imagine it would be difficult as the velocity of the plane is constantly changing relative to the ground.
You need to take a look at an atlas, grienspace. The Falkland Islands are a lot farther away from Norway than South Africa. I don’t know where Svalbard is, but using Oslo as a starting point, trip A would cover 10,412 kilometers (6,470 miles), while trip B be would span 13,820 kilometers (8,588 miles). Even if you just looked at the lateral distance, the Falkland Islands are almost an extra 20 degrees south of Cape Town, and there’s nothing the Earth’s spin can do about that.
Zor, if I started at 80N and headed directly south on the 20E line I will continually have to compensate for the spin of the earth below me which accelerates to just over 1000 miles per hour at the equator before decelerating again. The total distance to Capetown will be the hypotenuse of the north south distance on the map and the distance traveled by Capetown towards the East minus the distance Svalbard traveled east. There are other geometric considerations of course and perhaps a questionable assumption, but it just may be that by keeping a true great circle course to true south one could intercept the Falklands as it passes by in shorter time.
** I would like to revise the airplane speed to 2730 kph**.If I’m correct, that could simplify the problem considerably. I think concordes can fly that fast.
If you’re talking just about speed relative to the ground, then the rotation of the Earth is irrelevant, and it’s just a matter of which destination is closer. However, it might be harder to maintain that course and speed on a rotating Earth, due to having to deal with the Coriolis effect. In this case, two identical planes with equivalent engines will not have the same effective maximum speed. I think that the plane which makes a greater change in latitude will suffer the most from this, but I’m too lazy to work the calculations right now, so I can’t be sure.
Thankyou, Chronos. I’ve the term Coriolis effect before but never tied to the question I had in mind. The first hit I got on google for coriolis effect explained every thing quite clearly so the essence of my question has been answered. Still if anyone cares to prove my proposition, it would make for an interesting bar or parlour bet.