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Sand piles and dunes

Forces and motion · level 6, lesson 6 of 6

A question to start

Pour dry sand from your hand on to a table. It makes a cone, and however much you pour, the sides never get steeper than a certain angle. Mars has huge fields of dunes. Are their slopes steeper, in the weak gravity?

The idea

Each grain on the surface of a sand pile is like a tiny block on a slope. Friction between grains, and the way they lock together, holds it there. When the slope gets too steep, grains slide and roll down in a small avalanche, until the slope is back at a steady angle.

That steepest steady angle is called the angle of repose. For dry sand it is usually about 30° to 35°. By the last lesson's reasoning, it depends on the grains and their friction, \(\tan\theta \approx \mu\), and not on \(g\).

wind side: gentleslip faceabout 30° wind

A dune moving in the wind has a gentle side facing the wind and a steep slip face on the other side, where blown sand piles up and avalanches down. Slip faces sit at the angle of repose.

Images of active dunes on Mars, taken by the HiRISE camera in orbit, show slip faces at about the same angle as on Earth, as the simple reasoning predicts. What gravity does change is speed: an avalanche of sand flows down more slowly on Mars, and the wind must blow harder to lift grains in the thin air.

A dry sand slope Mars Earth
Angle of repose about 30° about 30° to 35°
Pull along the slope on a 1 g grain at 30° 1.9 mN 4.9 mN

Worked examples

1. Measuring \(\mu\) with a pile. Sand makes a cone at 33°. Then \(\mu \approx \tan 33° = 0.65\) for those grains.

2. Building with regolith. A berm of loose Mars soil piled against a habitat wall can be no steeper than about 30°. A berm 3 m high then needs a base at least \(3 / \tan 30° = 5.2\) m wide on its open side.

Try it

  1. What is the angle of repose?
  2. Why does it barely depend on gravity?
  3. A pile of gravel has an angle of repose of 38°. Estimate \(\mu\).
  4. A mound of soil 2 m high, at 30°: how far does its slope reach out from the top's edge?
Answers
  1. The steepest angle a pile of loose grains can hold without sliding.
  2. The pull down the slope and the friction both scale with \(g\), so \(g\) cancels, as for a block.
  3. \(\tan 38° = 0.78\).
  4. \(2 / \tan 30° = 3.5\) m.

Common mistake

"Low gravity would let sand stand up in tall steep piles." Steepness is set by friction between the grains. Low gravity changes how fast sand slides, and how easily wind lifts it, not how steep it can stand.

Where it leads