The Atmospheric Coriolis Force

The Coriolis force per unit mass acting on an air parcel is given by the expression

2 Ω v sin φ, 

where

    Ω = Earth's angular speed of rotation = 360°/(23^hr56^m) = 2π radians/86160 s = 0.000 0729 rad/s,

            v = the horizontal speed of the parcel in m/s,

             φ = the latitude of the parcel.

The Coriolis force direction always makes a right angle with the direction of the parcel's velocity and is directed to the right (left) of the velocity in the northern (southern) hemisphere.

Example:  an air parcel is moving from west to east at a speed of v = 100 mph (= 44.7 m/s), directly above Provo ( φ = 40.25°, sin φ = 0.646).  The Coriolis force per unit mass, directed due south, is

CF = 2 Ω v sin φ = 2 ´ 0.000 0729/s ´ 44.7 m/s ´ 0.646 = 0.004 21 N/kg.

Note that the Coriolis force is zero on the equator (φ = 0°, sin φ = 0), and greatest at the poles (φ = ± 90°, sin φ = ± 1).