Parameters
f = 2Ω sinφ Ω = 7.2921×10−5 rad/s
du/dt = f·v dv/dt = −f·u
x = (V/f) sin(ft), y = (V/f)[1−cos(ft)] (cross-track magnitude)
y ≈ ½ f V t² only when |ft| ≪ 1
inertial radius = V/f inertial period = 2π/f
Foucault rate = Ω sinφ period = 24 h / sinφ
Ro = V / (f L)
Ro compares inertia with rotation. Above about 1, rotation is a detail; below about 0.1 it governs the flow. A draining sink sits around 10³; a weather system around 0.2.
Live readout
What to watch for
Deflection grows with the square of time
Over a short flight the sideways offset is roughly ½fVt². Doubling the flight time quadruples the miss. That is why Coriolis can be negligible for a short rifle shot yet become an important correction for long-range trajectories.
The equator is genuinely exempt
Drag the latitude to zero and f goes to zero with it. Horizontal motion has no horizontal f-plane Coriolis deflection there. The weak Coriolis effect is also one reason tropical cyclones normally do not develop very close to the equator.
Speed does not change, only direction
The Coriolis force is always perpendicular to the velocity, so it does no work. Left alone, a body traces a closed inertial circle of radius V/f and returns to its starting speed exactly.
A pendulum measures your latitude
The plane of swing turns at Ω sinφ. Time one full rotation and you can solve for latitude — a laboratory experiment that detects the rotation of the Earth without looking outside.
One number settles the bathtub argument
On the Rossby tab, compare a sink with a weather system. The sink comes out near 10³ — rotation is thousands of times too weak to matter. The weather system comes out near 0.2, where it governs the flow.
Balanced flow runs along the isobars
When pressure gradient and Coriolis balance, the wind blows parallel to the contours rather than down the gradient. Above the friction-dominated boundary layer, this is why winds can run approximately along isobars, with low pressure on the left in the Northern Hemisphere.
Sources and technical basis
Rotating-frame dynamics on a constant-f plane, using the exact inertial-circle solution for the deflected-path tab and sidereal Earth rotation.