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Mars winds push gently

Air and fluids · level 4, lesson 6 of 6

A question to start

NASA says the strongest winds in Mars dust storms reach about 60 miles per hour, about 27 metres each second. On Earth, that is a storm that knocks trees down. Would it knock you over on Mars?

The idea

How hard a wind pushes depends on two things:

  • the density of the air, and
  • the speed of the wind, squared.
\[\text{push} \propto \text{density} \times \text{speed}^2.\]

"Squared" means a wind twice as fast pushes four times as hard, and three times as fast pushes nine times as hard.

Mars air is about 75 times less dense than Earth's. So at the same speed, a Mars wind pushes about 75 times less hard.

Same push, from Mars Earth
A dust-storm wind 27 m/s (about 97 km/h) about 3 m/s, a light breeze
A usual wind 5 m/s about 0.6 m/s, almost still air
Mars: 27 m/sEarth: 3 m/sthe same push

Worked examples

1. The same speed. A 10 m/s wind on Mars pushes about 75 times less hard than a 10 m/s wind on Earth.

2. Finding the same push. To make the push 75 times smaller, divide the speed by about 8.7, because \(8.7 \times 8.7 \approx 75\). So a 27 m/s Mars wind pushes like \(27 \div 8.7 \approx 3\) m/s on Earth.

3. Twice as fast. A Mars wind that speeds up from 10 to 20 m/s pushes \(2 \times 2 = 4\) times as hard.

Try it

  1. A wind triples its speed. How many times harder does it push?
  2. Why does a Mars wind push less than an Earth wind at the same speed?
  3. A Mars wind blows at 17 m/s. About what Earth wind would push the same?
  4. Why might a light Mars wind still lift dust, even though its push is gentle?
Answers
  1. \(3 \times 3 = 9\) times.
  2. Mars air is about 75 times less dense.
  3. \(17 \div 8.7 \approx 2\) m/s.
  4. Mars dust is extremely fine and light, so even a gentle push can lift it.

Common mistake

"Faster wind, the same push." Doubling the speed does not double the push: it makes it four times bigger.

Where it leads