Ferrell's Law

 

Ferrell's Law.

P.K.Ghatak, MD

No.44.

Modern warfare, to a large extent, depends on the precise computation of the target because the missiles are most effective when it hits the intended target and a miss means waste of several million dollars gone to manufacturing the missile.

In the earlier times when goods moved by boats utilizing the “trade wind” according to Ferrell's law was essential for safe navigation. It kind of lost its luster with the introduction of steam ships and transport planes. Nowadays, only the weatherman knows and uses Ferrell’s law, and the also the engineers engaged in planetary missions and electronic warfare.

Ferrell's law is modifications of Coriolis effect for much larger masses of air and sea currents.

Gustave Coriolis was a French mathematician and mechanical engineer in the eighteenth century, he solved the commonly observed phenomenon of objects, taking a curved path in reference to Earth rotatory motion.

Mr. William Ferrell was an American nineteenth century meteorologist and geophysicist. He stated in his law that when an object moving along the surface horizontally deflects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is due to the fact that the Earth is a sphere. It is wider at the equator than at the poles; and the Earth rotates east to west along its axis. The rate of rotation varies; at the equator it is rotating at 1000 miles per hour and at the pole it is only 2 inches per hour.  In the northern hemisphere when a mass of air or an ocean current moving from the north to the equator, when observed from the equator, will appear turning to the right and in the Southern Hemisphere it will appear turning to the left. In the equator no Coriolis effect is present, and no tornado or cyclone is seen for that reason.

 In the Northern Hemisphere tornadoes move anticlockwise and Cyclones in the Southern Hemisphere move clockwise for the reason mentioned above.

A few practical examples:

Long rage target shooting.

In a contest of hitting a target 5 football fields away with a high-power rifle and if the line of firing is north - south direction, the bullet by the time arrives at the target, the target has already moved a fraction of an inch due to difference in Earth’s rotational velocity from one zone to the other. To hit the target, Ferrell law has to be computed at the time of aiming at the target. 

If the line of firing is east - west direction the bullet takes an upward lift due to effects of initial velocity and gravitational pull on the bullet.

Flying.

A friend came to say goodbye to his friend at Atlanta airport. The plane leaves on time for Toronto, Canada. The airplane is flying in a straight line, however, his friend observes the plane moving in a parabolic trajectory because from the friend's perspective the ground is moving slower the land the plane crosses, so the path appears curved to the right to him.

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Footnote: Coriolis formula is - F = 2 mass (angular velocity vector of the rotatory frame times velocity vector of the object)

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