On a spinning planet, moving things veer sideways. The deflection is gentle — about 1×10-4 of gravity — but given a whole ocean and a day, it organizes every storm and current. It is a fictitious force: only the observer riding the rotating Earth sees it. The engine is the parameter f = 2Ωsinφ and the acceleration -2Ω×v. The blue team builds it; the red team tries to break it.
source Coriolis, Sur les équations du mouvement relatif des systèmes de corps (1835), J. École Polytech., Cahier XXIV, Tome XV, pp. 142–154 — gallica.bnf.fr · bpt6k29045h. Rendered, not quoted.
The whole effect is one number, the Coriolis parameter:
f = 2Ω sinφ
Ω = Earth's spin, 7.29×10-5 rad/s. φ = latitude. The horizontal deflection acceleration of a parcel moving with velocity (u east, v north) is (f·v, −f·u) — the velocity turned 90° and scaled by f.
Live values of f from the panel's current latitude:
| latitude φ | f (per second) | turns |
|---|
Coriolis 1835 derived -2Ω×v for rotating machines — waterwheels, not weather. The meteorologists borrowed it. From it falls f = 2Ωsinφ: zero at the equator, deflecting right in the north, doing no work.
Balance that steady veer against a pressure gradient and the wind stops crossing the isobars and runs along them — the twist behind the-geostrophic-balance. Each sphere is the next one's premise.
The blue team's live check: recompute f at the equator, at 45°, and at the poles, and confirm zero-at-equator, maximal-at-pole, right-in-north. If red tampers, this badge is where it shows.
Three inputs feed the engine: the planet's spin Ω (fixed), the latitude φ where the parcel moves, and the parcel's velocity v. Everything downstream is a consequence of the cross product -2Ω×v.
The sign of φ picks the hemisphere: + north (deflect right), − south (deflect left), 0 the equator (no horizontal deflection at all). Set the latitude below and watch the parcel veer.
Parcels launched in four directions. Under pure Coriolis each traces an inertial circle — clockwise in the north, counter-clockwise in the south, a straight line at the equator. AMBER the spin is exaggerated for visibility; the sign and geometry are the real physics.
Move the latitude — f, the turn direction, and the inertial period are computed from 2Ωsinφ on the spot, never looked up.
What the machine proves: f is zero at the equator (sin 0 = 0), maximal at the poles (2Ω ≈ 1.46×10-4/s), and ≈1.03×10-4/s at 45°. The deflection is to the right of motion in the north, left in the south, and does no work — -2Ω×v is exactly perpendicular to v.
The blue team's witness (left) confirms these live; the red team (right) tries to make them wrong.
It is a fictitious force AMBER — it exists only in the rotating frame. An inertial observer in space sees the parcel go straight; the "deflection" is the ground turning under it. Call it "real" and you have named a bookkeeping term for a bad choice of axes.
"Your toilet/sink drains the other way south of the equator." Cut. A myth. At sink scale Coriolis is swamped by geometry and initial swirl. It rules storms, not plugholes.
"The Coriolis force is a real force with a source." Cut. No agent pushes; it is an inertial (fictitious) term that appears only because the frame rotates. It vanishes when Ω = 0.
"Coriolis discovered it to explain weather." Kept, corrected. His 1835 paper is about energy in rotating machines — waterwheels. Ferrel and Buys Ballot carried it to the atmosphere decades later.
The red team's move: swap the law to f = 2Ωcosφ — making the deflection maximal at the equator and zero at the poles, exactly backwards. The blue team's witness (window 7) is watching.
Swap sin for cos and the equator becomes the strongest place for Coriolis — false. The witness recomputes f(0), finds it no longer zero, disagrees with the known law, and turns red. Nothing is faked; the attack is real and it is caught.