Coriolis Effect - Formula

Formula

In non-vector terms: at a given rate of rotation of the observer, the magnitude of the Coriolis acceleration of the object is proportional to the velocity of the object and also to the sine of the angle between the direction of movement of the object and the axis of rotation.

The vector formula for the magnitude and direction of the Coriolis acceleration is

where (here and below) is the acceleration of the particle in the rotating system, is the velocity of the particle in the rotating system, and Ω is the angular velocity vector which has magnitude equal to the rotation rate ω and is directed along the axis of rotation of the rotating reference frame, and the × symbol represents the cross product operator.

The equation may be multiplied by the mass of the relevant object to produce the Coriolis force:

.

See fictitious force for a derivation.

The Coriolis effect is the behavior added by the Coriolis acceleration. The formula implies that the Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the frame's rotation axis. So in particular:

• if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero.
• if the velocity is straight inward to the axis, the acceleration is in the direction of local rotation.
• if the velocity is straight outward from the axis, the acceleration is against the direction of local rotation.
• if the velocity is in the direction of local rotation, the acceleration is outward from the axis.
• if the velocity is against the direction of local rotation, the acceleration is inward to the axis.

The vector cross product can be evaluated as the determinant of a matrix:

where the vectors i, j, k are unit vectors in the x, y and z directions.