Earth vs. airplane: Why jets don’t need to keep up with the planet’s rotation

Derek Wasylenko
19 September 2014

Above: Image © istockphoto.com/derrrek

At most latitudes, the Earth rotates eastward at a much higher speed than a typical jet airplane flies. So a passenger jet traveling in the same direction as the Earth’s rotation should never reach its destination, right? Yet somehow it is possible to fly east from Vancouver, British Columbia to Toronto, Ontario—a distance of over 3000 km—in just five hours! In fact, in the Northern Hemisphere, planes actually tend to fly faster when they’re travelling in the same direction as the Earth’s rotation. To understand why, you also need to understand how gravity and the jet stream come into play.

Spinning Earth

Did you know? The circumference of the Earth is slighter greater around the equator (40,075 km) than around the poles (39,941 km). This bulge at the equator is a result of centrifugal forces caused by the Earth’s rotation!

A typical passenger jet (such as a Boeing 737 or an Airbus A320) has a cruising speed of about 800 km/h. To calculate the Earth’s rotational speed, consider that the circumference of the Earth at the equator is about 40,000 km and it takes about 24 hours for the Earth to complete one rotation around its axis. This means that, at the equator, the surface of the Earth is spinning at around 1,700 km/h (40,000 km divided by 24 hours). This is called the Earth’s equatorial rotational speed, and it’s roughly twice the speed of a passenger jet.

However, the rotational speed at a particular point on the Earth’s surface varies depending on the latitude. For example, a single rotation covers much less distance near the poles that it does at the equator.

As a result, the Earth’s rotation has big implications for launching rockets into orbit. At lower latitudes, where the Earth is spinning faster, it actually takes less energy (and therefore less fuel) to get a rocket into orbit. This is one of the reasons that the United States launches rockets from Cape Canaveral, Florida. The other big reasons are favourable weather year-round and, since rockets travel east over the Atlantic Ocean, a low risk of crashing over a populated area.

To calculate the approximate rotational speed of the Earth at any point on the planet’s surface, multiply the cosine of the latitude by the equatorial rotational speed (1,700 km/h). So if you live near me in Calgary, Alberta (latitude 51° N), the Earth is spinning at only about 1,100 km/h.

1,700 km/h × cosine(51°) = 1,100 km/h

I feel dizzy! Also, the weather isn’t as nice as in Florida.

But even if the Earth’s rotational speed decreases as you move away from the equator, 1,100 km/h is still much faster than a typical passenger jet flies. And Calgary is pretty close to the route of that five-hour flight from Vancouver and Toronto.

Gravity

It turns out that the Earth’s rotation is not the only force at play. Gravity is also dragging down everything on or near the surface of the planet. This includes the atmosphere, which is mainly composed of nitrogen (78%) and oxygen (21%), but also contains traces of other gases such as argon, water, and carbon dioxide.

If gravity wasn’t pulling down on the atmosphere, the winds in Calgary would always be howling away at 1,100 km/h! That would be almost three times faster than the highest winds ever recorded on Earth—408 km/h, observed on an island off the north coast of Australia during Tropical Cyclone Olivia in 1996.

Furthermore, if you could escape the effects of gravity simply by being in the air, I would be able to travel about 150 m just by jumping and staying in the air for about half a second. That’s how far the Earth would travel beneath me in that time!

1100 km/h = 300 m/s; so 0.5 s × 300 m/s = 150 m

I’d land all the way down the block! Of course, if I could escape the effects of gravity, I might never land at all.

Since a jet airplane essentially works by pushing itself through the air, and the atmosphere is pulled by gravity towards the Earth’s surface, airplanes fly at speeds relative to the air around them (airspeed). At takeoff and landing, airspeed is usually about the same as the plane’s speed relative to the ground (ground speed). However, at cruising altitudes, a plane’s airspeed and ground speed can be very different.

Jet stream

Did you know? It actually takes 23 hours, 56 minutes, and 4 seconds for the Earth to complete one rotation relative to the background stars. This is called a sidereal day. Because the Earth also orbits around the Sun, it has to rotate another 3 minutes and 56 seconds to complete a solar day (from sunrise to sunrise).This is because of the jet stream, a fast wind that travels west to east at high altitudes and higher latitudes. Because of the direction of the jet stream in the Northern Hemisphere, it normally takes longer to fly west (with the Earth’s rotation) than east (against the Earth’s rotation)! For example, flying west from Toronto to Vancouver against jet stream tends to make a plane’s ground speed lower than its airspeed, making flights longer. And when flying east from Vancouver to Toronto, flying in the same direction as the jet stream often causes a plane’s ground speed to be faster than its airspeed.

Interestingly, the jet stream is partly caused by the Earth’s rotation, so technically the Earth’s rotation does affect flying times. Just not in the way you might have expected!

* * *

So even if most jets could never keep up with how fast the Earth spins, they don’t need to. Gravity conveniently pulls the atmosphere toward the Earth’s surface, allowing planes to fly all over the planet in any direction, with the jet stream causing only minor variations in flight times.

Learn more

A variety of general information about the Earth with links to additional resources.

An introduction to the jet stream and its effects on the weather.

Detailed statistics related to the circumference of the Earth.

A more detailed explanation of why Cape Canaveral is an ideal site for launching rockets.

Derek Wasylenko

Derek is currently a post-doctoral research associate at the University of Washington in Seattle. His current research interests are primarily involved with the design and study of catalytic materials for energy conversion applications. When not in the lab, Derek enjoys reading, hiking, biking, snowboarding, and spending time with family and friends.


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Comments

Avatar  mark

If "gravity" is strong enough to hold the trillions of tons of the great oceans of the earth from spinning off of it, then how could I ever raise my hand? How could birds fly? How could smoke rise?

Avatar  Enlightened

Was wonderful to read, thanks.