Coriolis Effect Calculator

The Coriolis effect is an inertial force that acts on objects in motion relative to a rotating system. To calculate the magnitude of the Coriolis force (F_c), the calculator utilizes the fundamental cross-product equation: F_c = 2 * m * ω * v * sin(φ), where m represents the mass of the moving object, ω is the angular velocity of the rotating reference frame (such as Earth's rotation rate of approximately 7.2921 × 10^-5 rad/s), v is the velocity of the object, and φ is the latitude. Additionally, the resulting Coriolis acceleration (a_c) is derived by isolating acceleration from Newton's second law, yielding a_c = F_c / m, which simplifies to a_c = 2 * ω * v * sin(φ). The sign of the force depends on the hemisphere, as the effect deflects objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

Imagine an aircraft with a mass (m) of 50,000 kg traveling eastward at a velocity (v) of 250 m/s at a latitude (φ) of 45 degrees North. The angular velocity of the Earth (ω) is 7.2921 × 10^-5 rad/s. First, calculate the sine of the latitude: sin(45°) ≈ 0.7071. Next, substitute these values into the Coriolis force formula: F_c = 2 * 50,000 * (7.2921 × 10^-5) * 250 * 0.7071. Multiplying these values together gives a Coriolis force of approximately 1,292.4 Newtons. To find the Coriolis acceleration, divide this force by the mass: a_c = 1,292.4 / 50,000, resulting in an acceleration of 0.0258 m/s² directed to the right of the aircraft's motion.

When working with Coriolis calculations, always ensure your units are consistent: use kilograms for mass, meters per second for velocity, and radians per second for angular velocity. Remember that latitude must be converted to radians if you are programming custom scripts, though standard calculators handle degree inputs directly. Finally, keep in mind that the Coriolis effect is negligible at the equator where sin(0°) equals zero, and reaches its maximum intensity at the North and South Poles where sin(90°) equals one.