Coriolis - apparent?

[D120A]

Coriolis simply (I hope) explained

Coriolis acceleration is the acceleration experienced by an object moving in a straight line on a rotating frame of reference. Let me use a simple example. An old-style gramophone record rotates (at 33 and a third rpm, if it is an old LP player). A fly, trying to walk in a straight line at a constant speed across the rotating record, would experience a Coriolis acceleration. The fly would have to dig his heels in to ensure that he developed the necessary force to be able to accelerate that way, where the force required equals his mass times the required acceleration. If he couldn’t, he wouldn’t be able to hold the straight line and he would wander off!

(To digress a moment, a similar situation exists when you consider centripetal acceleration and force; if you whirl a mass around your head on a piece of string, the tension in the string provides the ‘centripetal’ force that makes the mass seek (Latin, ‘peto’ – to seek) the centre of the circle. Cut the string and the mass would whirl away in a straight line like a slingshot because, then, no force is causing it to change its ‘state of uniform motion’ - which is to travel at constant speed in a straight line - Newton’s Law. Be careful not to use the term ‘centrifugal’ force in such analysis, because it doesn’t exist. ‘Fugo’ is Latin for ‘to flee’. There may be a centrifugal reaction of the string on your fingers as you whirl the mass round, but what makes the mass accelerate towards the centre is centripetal force. End of rant!)

Back to Coriolis. The value of the Coriolis acceleration is 2 times the angular velocity of the rotating frame of reference (in radians per second) times the speed of the object travelling across it. The direction of it is a vector product of the two, and that is fiendishly difficult to explain without waving hands in the air because it has both magnitude and direction, but I will have a go. Magnitude is easy, it is the product of 2 and the two values. For direction, however, we have to consider the vector directions of the two values and how they multiply – which will give us a vector in a third direction. Consider the turntable. If you look down upon it, suppose it rotates clockwise. Curl the fingers of your right hand in the direction of rotation; where is your thumb? Pointing downwards. That is the direction of the angular velocity vector of the record turntable.

Now the fly. If it is struggling to walk from the rim of the record to the centre, that direction is that of its velocity vector on the rotating frame of reference - the record. The vector product of two vectors, one down the spindle into the record player and the other at right angles to it, is again given by the right-hand-rule. Use the fingers to align the rotation vector with the velocity vector and where is the thumb? Out to the right as you look down on the turntable and that’s the direction of the Coriolis acceleration.

So, I reckon an aircraft tracking over the North Pole in a straight line at 500 mph (733 feet/sec), where the earth is rotating at 2-pi (6.283) radians per day with a vector vertically upwards, experiences a Coriolis acceleration of 0.1066 feet per sec per sec, out towards the port wing tip. Check my calculation, and remember a day has 24x60x60 seconds! So there, it will be ‘left wing down a bit’ (I think) to counter it, and that is the maximum value of Coriolis you will experience over the earth at 500 mph – it is only 0.33% of a ‘g’. But, in contrast, an aircraft travelling northwards at the Equator experiences zero Coriolis, because the angular velocity and aircraft velocity vectors are in the same direction and so their vector product is zero. The brave souls who first developed INS (the late Charles Stark Draper and his team, at MIT) had to work out the Coriolis equations to allow for all latitudes, speeds and three-dimensional flight paths. 0.33% of a ‘g’ is a big number in an inertial navigation system.