Flying from Auckland to Santiago takes about eleven hours. Coming home takes closer to thirteen. The explanation everyone reaches for is that the Earth spins eastward, so on the way east the destination comes to meet you, and on the way back you have to chase it.

This is wrong, and it is wrong in a way I find genuinely satisfying, because the thing people are blaming turns out to be responsible after all. Just not for the reason they think.

Why the obvious answer fails

Before your plane leaves the ground it is already travelling east at about 1,670 kilometres per hour, assuming you took off near the equator. So is the runway. So is the terminal, the air traffic controller, your checked bag, and every molecule of air the aircraft is about to fly through.

The atmosphere is not a stationary thing that the planet rotates underneath. It is bolted to the planet by gravity and friction and it comes along for the ride. When the wheels leave the tarmac, nothing lets go.

If the popular explanation were right, a helicopter could hover over Auckland for a few hours and wait for Santiago to arrive. Helicopter pilots have not noticed this working.

But eastbound flights really are faster

The asymmetry is real. The cause is wind.

Jet streams, according to the National Weather Service, are “relatively narrow bands of strong wind in the upper levels of the atmosphere, typically occurring around 30,000 feet (9,100 meters) in elevation.” They “vary in height of four to eight miles and can reach speeds of more than 275 mph (239 kts / 442 km/h).”

And the direction matters: “Within jet streams, the winds blow from west to east.”

That is your eleven hours. An aircraft cruising at 900 kilometres per hour with a 200 kilometre per hour tailwind is doing 1,100 over the ground. Turn around and you are doing 700. Nothing about the planet’s rotation enters the arithmetic. You are swimming with a current, or against it.

The part that redeems the myth

Here is where the popular explanation gets a partial pardon. Why does the wind blow west to east in the first place?

The same NOAA page answers it. Air moving toward the poles keeps the eastward speed it had when it started, but the ground beneath it is rotating more slowly, because the circles of latitude get smaller as you go north. So the air outruns the surface and drifts east relative to it. That is the Coriolis effect, and it is a consequence of the Earth’s rotation.

So the rotation does not push your aeroplane. It carves the river of air that pushes your aeroplane. The people confidently explaining tailwinds to their seatmates have the right suspect and the wrong crime.

I like corrections that end this way. The claim was false, the instinct behind it was sound, and the truth needed one more step.

Where the rotation shows up on a scale you can measure

Shoot a rifle far enough and the Earth turns under the bullet while it is in the air. This is not folklore. It is in the ballistics tables.

Bryan Litz of Applied Ballistics breaks it into two components. The horizontal part depends on your latitude, is strongest at the poles, vanishes at the equator, and does not care which way you are facing. At 45 degrees north it pushes a small-arms bullet “about 2.5 to 3.0 inches to the right at 1000 yards.”

The vertical part is stranger. It depends entirely on which way you shoot. “Firing due North or South results in zero vertical deflection, firing East causes you to hit high, West causes you to hit low.” It peaks at the equator and disappears at the poles, and at 45 degrees it is worth another two and a half to three inches, up or down.

Snipers really do dial this in before taking a long shot.

What I did not expect is that it is not the biggest effect on the list. A bullet from a right-twist barrel also drifts right by 8 or 9 inches at 1000 yards, purely from its own spin, with no help from the Earth at all. Litz notes the two add up: about 9 inches of gyroscopic drift plus 2.5 inches of Coriolis gives 11.5 inches of rightward drift in dead calm air. Put a left-twist barrel on the same rifle in the northern hemisphere and they partly cancel, leaving 6.5 inches.

Coriolis is the effect with the famous name and the physics-lecture pedigree. Gyroscopic drift is three times larger and gets a fraction of the attention. Long-range shooters spend a lot of energy on the smaller of the two forces bending their bullet.

Why an eastbound bullet flies high

That vertical component has a name and a nice origin story.

Around the turn of the last century a German team from the Geodetic Institute of Potsdam took gravity measurements from ships crossing the Atlantic, the Indian and the Pacific. When Loránd Eötvös went through their numbers he spotted something odd. The readings came out low when the ship was steaming east and high when it was steaming west. In 1908 he settled it by sending two ships out onto the Black Sea, one heading each way, and watching the gravimeters disagree.

The reason is almost embarrassingly simple. You are already going around the Earth’s axis once a day. Move east and you add to that rotation, which increases the centrifugal effect flinging you outward, which cancels a little more of your weight. Move west and you subtract from it, and you get heavier.

The size of it, for anything human, is comic. Take a 10 kilogram mass to the equator and run it east at 10 metres per second, then run it west at the same speed. The difference in what the scale reads is about 3 grams.

An eastbound bullet, then, hits high because it weighs slightly less on the way to the target.

Which means your aeroplane is lighter going east

I could not resist working this one out.

The leading term of the Eötvös effect is 2Ωu cos φ, where Ω is the Earth’s rotation rate, u is your eastward speed and φ is your latitude. Put a 300 tonne airliner at 45 degrees latitude, cruising at 250 metres per second, and that comes to 0.0258 metres per second squared, or about 0.26 percent of gravity.

That is 790 kilograms of apparent weight. Fly the same aircraft west instead and the sign flips, so the gap between an eastbound and a westbound aircraft is around 1.6 tonnes.

I checked the method against the two worked examples on Wikipedia’s page and got 2.97 grams where they say about 3, and 3.72 grams where they say about 4, so I believe the airliner number.

So the Earth’s rotation does affect your flight, just not in any way you will feel. It shaves a tonne and a half off the lift the wings have to generate, an effect thoroughly buried under a 200 kilometre per hour jet stream and the weight of the drinks trolley. The myth was closer to the truth than the people repeating it realised, and still not close enough to be worth saying.

The sink, briefly, because you were going to ask

No, the Coriolis effect does not decide which way your bath drains. At that scale it is roughly three ten-millionths of gravity, which loses comfortably to the shape of the basin, the residual swirl from the tap and somebody walking past.

It is not zero, though, and two teams proved it. In 1962 Ascher Shapiro filled a two-metre dish with a nine-millimetre hole in the middle, covered it with plastic to keep the air still, held the room at a steady temperature, and let it settle for a full day before pulling the plug. The water took twenty minutes to drain. For the first twelve to fifteen there was no rotation at all. Then it began turning anticlockwise, working up to a full turn every four seconds. In 1965 Trefethen and his colleagues did it again in Sydney with an eighteen-hour settle and watched it go clockwise.

So the effect is real, and detecting it requires you to remove every other thing that could possibly move the water. Your toilet, which fires water through angled jets, is not a controlled experiment. Litz, in among the ballistics tables, has the best line about this. He suggests it may not be worth “carrying around the flushing toilet that’s required to measure the strength of the Coriolis effect that day.”

The train

All of this started because I asked a stupid question and got a good answer.

If a heavy freight train, say 10,000 tonnes, is rolling east at 100 miles per hour and slams to a stop, what does that do to the rotation of the Earth?

Angular momentum is conserved, so the train’s share has to go somewhere, and the only thing to give it to is the planet. Multiply the mass by the speed by the distance to the Earth’s axis, divide by the Earth’s moment of inertia, and the spin rate changes by about five parts in ten quintillion. Spread across a day, that is 42 femtoseconds.

I put this to ChatGPT at the time and it produced exactly that, with the working shown. I rechecked every step and the arithmetic holds, give or take its rounding of 42 femtoseconds down to 40.

What it did not mention is the thing that makes the answer interesting.

The train was not born at 100 miles per hour. To get moving east it had to shove backwards against the rails, and the rails are attached to the Earth. Accelerating that train slowed the planet’s rotation and made the day 42 femtoseconds longer. When it brakes, it hands all of that back.

The day does not get shorter when the train stops. It returns to exactly the length it was before the train pulled out of the yard. Over any journey that starts and ends at rest, the net effect on the Earth’s rotation is zero, and the correct answer to my question is not 42 femtoseconds but nothing at all.

This is the same shape as the router dimensions I went looking for, where the AI’s confident tables of numbers disagreed with each other. Here it was worse in a quieter way. Every number was right. The physics was half a step short, and a correct calculation of the wrong quantity looks exactly like a correct answer.

The length of the day does genuinely wander, by a millisecond or so, pushed around by tides and the atmosphere and the churn of the Earth’s core. Trains are not on the list.

The short version

Eastbound flights are faster because of the jet stream, not because the planet is rotating out from under the aircraft. The atmosphere rotates too. But the jet stream itself blows west to east because of the Coriolis effect, which exists because the planet rotates, so the rotation is guilty of everything except the mechanism it gets accused of.

The rotation will move a bullet three inches sideways at 1000 yards, and three inches up if you fire east, though the bullet’s own spin moves it three times further. It makes an eastbound airliner about 790 kilograms lighter than it would be sitting still. It will not empty your bath in a preferred direction unless you seal the room and wait a day.

And it does not care about your train.

Sources

  • The Jet Stream, NOAA National Weather Service. Altitude, speeds above 275 mph, west-to-east flow, and the Coriolis explanation for why.
  • Litz, B. (2021). Gyroscopic (spin) Drift and Coriolis Effect (PDF), Applied Ballistics. Horizontal and vertical Coriolis components, and the 8 to 9 inches of gyroscopic drift that dwarfs both.
  • Eötvös effect. Wikipedia. The Potsdam ship measurements, the 1908 Black Sea experiment, the 2Ωu cos φ term and the worked examples I checked my arithmetic against.
  • Shapiro, A. H. (1962). Bath-Tub Vortex. Nature 196, 1080 to 1081.
  • Trefethen, L. M., Bilger, R. W., Fink, P. T., Luxton, R. E. and Tanner, R. I. (1965). The Bath-Tub Vortex in the Southern Hemisphere. Nature 207, 1084 to 1085.