Correcting for the Coriolis Effect

References:
Principles of Naval Weapon Systems by Craig M. Payne

For ranges up to 20,000 yards (18.2 km / 11.3 miles); the Coriolis force does not seriously affect fire control solutions. Beyond this however, the rotation of the earth has an increasing effect.

In the northern hemisphere, the displacement occurs to the right, while in the south it displaces to the left.

Computing Coriolis Acceleration on Earth

AccelerationCoriolis = 2 * Velocity * RateRotation

RateRotation = (2 * Pi / 86,400 Seconds) * Sin(Latitude)

Where:

AccelerationCoriolis = Coriolis Acceleration in m/sec.

Velocity: Speed of Projectile in m/sec.

Latitude: Latitude in Radians (e.g. if you had 40 Degrees North Latitude, it would be 0.7 Radians North).

86,400 Seconds: The Earth's rotational period is 24 hours, and each hour has 3,600 seconds; thus 86,400 seconds.

Computing Displaced Distance Due to the Coriolis Effect:

DistanceDisplaced = 0.5 * AccelerationCoriolis * TOF2

Where:

DistanceDisplaced: Distance displaced due to Coriolis Effect in Meters

AccelerationCoriolis: Acceleration due to Coriolis effect (previously calculated)

TOF: Time of Flight in seconds.

EXAMPLES: What is the displacement of artillery shells fired at 700 m/sec from a position at 20N Latitude (0.35 rad) with flight times of 35, 60, and 80 seconds respectively?

RateRotation = (2 * PI / 86,400 Sec) * Sin (0.35) = 0.0348 m/sec

Displaced Distance I: 0.5 * 0.0348 * 352 = 21.33 meters

Displaced Distance II: 0.5 * 0.0348 * 602 = 62.68 meters

Displaced Distance III: 0.5 * 0.0348 * 802 = 111.43 meters