# Problems Flying North/South due to the Earth's Rotation.

Q:
My question regards plane navigation with respect to the Earth's surface. The speed of rotation at the equator is roughly 1000mph relative to the (mostly) stationary poles. If a plane takes off at the pole and travels to the equator, does the path require and indirect path that intersects the destination as the Earth rotates? Or is a simple great circle path? If it's a direct/great-circle path, how does that work? The basis for this question is the old: 'if you jump on a train or plane, why do you land back in the same spot'... which we all know to be true if there's no change in velocity. I've read several discussions about this plane flight-path question, but all that I've read have asserted wind speed as the cause for flight time/path differential (and I have considered wind velocity to be negligible compared to the 1000mph), or that there is no need to consider Earth's rotation in the flight path since the plane starts off with the same (or close to) relative velocity as it's destination [not true in this case, by a long shot... or is it?]. Flights from Australia show great circle paths, so it's likely this question is already 'answered' in practice but I'd like to know how/why that is. Thanks for considering this! Thomas
- thomas (age 24)
oakland, ca USA
A:

Hi Thomas,

The effect you are talking about is very real.  It's called the Coriolis effect.  It was discovered in the 17th century by cannoneers  that if you shot a cannon ball in a north-south direction the ball didn't land where you thought it should.  Cannon balls shot in an east-west direction were not affected.    The basic problem is that the usual NSEW co-ordinates of the earth is not an inertial frame, it is a rotating frame.   In order to fix it up a fictitious force was invented called the Coriolis force.   This force is always perpendicular to a north-south line. It is given by Fc = --2m Ω x V   where  Ω is the rotational speed of the earth and V velocity of the moving object.

So that means that if you are in an airplane at the North Pole and the pilot flies due south headed toward Oakland without steering the plane a bit you will wind up somewhere in the Pacific Ocean.

Take a look at the Wikipedia article on Coriolis Force  for lots more detail.

LeeH

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(published on 04/15/2016)

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