 ## How earth's rotation affects aircraft motion?

### What is the Coriolis effect?

Right from our school days, we have been studying about the fact that earth rotates about its axis from west to east direction i.e. in the counterclockwise direction and completes one rotation in 24 hours. Now according to simple physics, each and every particle on earth would follow the same rotational motion.

Let's understand this in a more simpler way, let's go to the nearby park an imagine the merry go round swing as the earth, come let us sit on the swing and one of our friends would move the swing for us. Wooah!! everything is rotating you are rotating I am rotating the air around us is rotating and even a piece of small stone on the floor of swing is rotating. Now let us make this game a bit more complicated you will move towards the center of rotation of the swing (the swing is stopped for a moment) as shown in the figure and I will stay at my place. The swing starts rotating again, both of us will stretch out our hands at exactly the same time and in the same direction. After five minutes of swing we stop the swing again, do our hands point in the same direction? Are they still aligned with each other?

Yes they are, this brings out a very interesting concept that you and I were at different radius of rotation at the swing but still our hands were aligned at every moment which brings out that the distance traveled by you and me was different as the circumference of circle followed by us can be given by 2*π*R (R-radius of rotation). The radius of circle followed by me is larger hence I have to cover a larger distance as compared to you in the same time now to do that my speed of rotation will be greater than yours.

Here A and B are are mine and your initial locations receptively, B' is your new location, the dotted circles show the path followed by us while rotation.

Hence it can be said that if a body A situated at a rotating body B moves towards the axis of rotation of body B then its speed of rotation will decrease given that its mass remains constant, i.e. the radius of rotation is directly proportional to the speed of rotation.

Now after learning about this fact lets move towards the main topic of our discussion the Coriolis effect. Let us now apply the principle learned for a merry go round to the earth. Consider you are at equator right now then your speed of rotation will be around 1647 km/h but once you will start moving towards the pole the radius of rotation will keep on decreasing and the speed of rotation will also decrease as discussed earlier. At some point between the equator and pole, your speed of rotation will be much less than that at the equator and at exactly at the pole your speed of rotation will be zero.

Ok, let's imagine one thing a hypothetical paper plane has to travel from Chennai which is near to the equator to New Delhi which is away from the equator in the north direction. If you would throw this paper plane in straight direction would it reach exactly at New Delhi? No, it won't, here come the Coriolis effect into play.

Before moving forward I need to explain a simple physics term called the angular momentum which is equal to Mass * Radius of rotation * Speed of rotation. This quantity always remains conserved in a rotational motion until and unless an external unbalanced torque is applied to the system.

Now as the plane leaves from Chennai its angular momentum is having some value A and when it reaches New Delhi, the value of angular momentum becomes B but as we know after traveling to New Delhi the value of angular momentum decreases as both the speed of rotation as well as the radius of rotation are decreasing. But according to the above said principle we need to have A= B, for that the path of motion of particle adjusts itself so that the angular momentum remains conserved i.e. A= B + C. Here C is the angular momentum generated due to the path change.

We can understand this in a more simpler way, Chennai is moving much faster as compared to Delhi hence a body leaving from Chennai won't be able to reach Delhi it would reach a point deviated in the anticlockwise point from Delhi. The solid line in the above image shows the desired that and the dotted line shows the actual path followed.

So to bring out the crux of Coriolis effect we can say that if a body is thrown in north direction from the rotating earth then its path of motion will be redirected or deflected in the right direction and vice versa for the southern direction i.e. body thrown towards south would get deflected towards the left direction. And if we would throw a ball from the north pole towards equator then it would get deflected the other way around.

Coriolis Effect on airplanes

As discussed earlier the effect of Coriolis effect on a hypothetical plane, the word hypothetical was used just to signify that the frame of reference for watching the plane was several lakhs kilometers away from the atmosphere of earth. If this frame of reference is taken on earth itself i.e. we are observing a plane flying over our head standing on the surface of earth then Coriolis effect won't play any role as we are also moving with the atmosphere of earth. So it is all about the frame of reference which we are talking about.

Coriolis effect would play an important role in case of Rocket Propulsion as rockets leave the atmosphere of earth.

Though the Coriolis effect does not affect the airplanes directly it has an indirect effect on the flight path by producing various phenomenon related to wind motion such as vortex winds, Jet streams etc.