Air pushed by the pressure gradient force does not keep going straight on a map. In Earth Science you met the Coriolis effect turning the global winds; this lesson measures it, using the sine of the latitude.
Key idea
On the spinning Earth, anything moving across the surface is turned to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The turning is measured by the Coriolis parameter $$f = 2\Omega\sin\varphi, \qquad \Omega = 7.29 \times 10^{-5}\ \text{s}^{-1}$$ where $\varphi$ is the latitude. The sideways acceleration is $f \times$ speed. It is zero at the equator and strongest at the poles, and it changes only the direction of the wind, never its speed.
Why it works
Roll a ball straight across a spinning merry-go-round. Seen from the ground, the ball goes straight; but the merry-go-round turns underneath it, so to a rider the path curves. Earth is a slowly spinning platform. Looking down on the North Pole, Earth turns counterclockwise, and moving air seems to curve right; looking down on the South Pole it turns clockwise, and moving air curves left. How much the ground turns under you depends on latitude: at a pole the ground spins fully around once a day, at the equator it doesn't spin about the vertical at all. That is where the $\sin\varphi$ comes from.
Worked example: The Coriolis parameter at 45° N
Find $f$ at 45° latitude, and the sideways acceleration of a 10 m/s wind there.
- $\sin 45^\circ \approx 0.707$.
- $f = 2 \times 7.29 \times 10^{-5} \times 0.707 \approx 1.03 \times 10^{-4}$ s⁻¹.
- Acceleration: $f \times v = 1.03 \times 10^{-4} \times 10 \approx 1.0 \times 10^{-3}$ m/s², turning the wind to the right.
Answer: f ≈ 1.03 × 10⁻⁴ s⁻¹; about 0.001 m/s²
Worked example: Which way does it turn?
Air moves south (toward the equator) at 30° S. Which way does the Coriolis effect turn it?
- In the Southern Hemisphere, moving air is turned to its left.
- Facing south, your left is east.
- It is turned toward the east.
Answer: Toward the east
Common mistake
Thinking the Coriolis effect speeds the wind up, or that it is strongest at the equator. It always acts at right angles to the motion, so it changes direction only, and it grows with $\sin\varphi$: zero at the equator, largest at the poles. Hurricanes need it to spin up, which is why they almost never form within about 5° of the equator. Check: at 30° latitude, $\sin 30^\circ = 0.5$, so $f$ is half its polar value.
The Coriolis effect matters for winds and ocean currents that travel hundreds of kilometers over hours or days. It is far too weak to decide which way water swirls down a sink or toilet; the shape of the basin and how the water was poured matter much more.