A force that comes from Earth’s rotation
Earth turns once every 23 hours and 56 minutes (a sidereal day), at an angular speed Ω = 7.2921 × 10⁻⁵ radians per second. Seen from the ground, which turns with the planet, an object moving freely seems to curve sideways. Physicists account for this with an apparent force, named after the French engineer Gaspard-Gustave de Coriolis. It deflects moving objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
The formulas
For horizontal motion at latitude φ:
- Coriolis acceleration: a = 2 × Ω × v × sin φ
- Travel time: t = distance ÷ speed
- Sideways deflection: d = ½ × a × t²
- Inertial circle radius: r = v ÷ (2 Ω sin φ), the circle an object would follow with no other force
- Foucault pendulum: one full turn of its swing plane takes 23.93 h ÷ sin φ
Example: a long-range rifle shot
A bullet at 2,600 ft/s (792 m/s) travels 1,000 yards (914 m) at 40° north:
- Coriolis acceleration: 2 × 7.2921 × 10⁻⁵ × 792 × sin 40° = 0.0743 m/s²
- Travel time without drag: 1.15 s
- Deflection: ½ × 0.0743 × 1.15² = about 4.9 cm, or 1.9 inches to the right
A real bullet slows down because of air drag, so its flight lasts longer and the real deflection is noticeably larger. Long-range shooters and artillery crews correct for it.
Where it matters
- Weather: winds flowing toward a low-pressure area are deflected, which makes hurricanes spin counterclockwise in the Northern Hemisphere and clockwise in the Southern.
- Oceans: the Coriolis effect shapes the great gyres and coastal upwelling.
- Foucault pendulum: at 40° north the swing plane takes about 37 hours to turn once, about 34 hours at 45°, and 24 hours at the poles.
Where it does not
In a sink or toilet, the effect is far too weak, millions of times smaller than the influence of the basin shape and the way the water was poured. On a baseball pitch it shifts the ball by less than a millimeter. The effect is zero for horizontal motion at the equator, where sin φ = 0.