Q&A: Limits to the Growth of Mt. Everest

I recently discovered an article on BBC Future titled “How tall will Mount Everest get before it stops growing?”

https://www.bbc.com/future/article/20220407-how-tall-will-mount-everest-get-before-it-stops-growing

As you probably know, plate tectonics created Mt. Everest and those plates are still in motion. The Indian plate is moving northward at 5 cm/year and pushing against the Eurasian plate. This causes the plates to buckle and deform upward. Satellite measurements show Mt. Everest is growing taller at a rate of 4 mm/year, and other mountains in the Himalayas at up to 10 mm/year. This begs the question: Just how high could Mt. Everest grow before it reaches some kind of physical limit?

The article mentions a researcher at the Cavendish Laboratory in Cambridge, UK who had calculated a “rough estimate” of 45 km assuming the mountain’s base is granite (Everest transitions to limestone at higher altitudes). With a current height of 8.849 km that leaves a lot of room for growth, and plate tectonics are likely to continue for millennia.

But that 45 km surprised me so I decided to run the numbers and see for myself. The graphic shows how this calculation can be done:

One can only stack rock so high before the rocks on the bottom are crushed by the weight of the rock above. The same applies to bricks, which limited the heights of building to around four stories before the introduction of structural steel. I wrote about this physical limit back in 2016 in a post titled Why Mars Has Taller Mountains Than Earth but didn’t really do any calculations.

We know the relevant properties of granite:

  • density: ρ = 2.75 g/cm3 = 2.75 x 103 kg/m3
  • compressive strength: σ = 19000 psi = 13100 N/cm2 = 1.31 x 108 N/m2

The weight of a 1 m2 column of granite with height H would be:

F = ρ x V = ρ x 1 m2 × H

So we need to find the H at which F/A exceeds σ (at which point the bottom-most granite will be crushed). Since A = 1 m2 the equation can be simplified and solved for H as follows:

ρ × H = σ H = σ / ρ = (1.31 x 108 N/m2) / (2.75 x 103 kg/m3) = 47636 m = 48 km

That’s fairly close to the 45 km quoted in the article. Of course, my calculation assumes a uniform granite structure — unlike an actual mountain with varying mineral content and fractures and faults. But it was an enlightening calculation finding the theoretical height limit for (granite) mountains on Earth.

Of course, there are many forces working against Everest attaining that height, even if plate tectonics continues indefinitely. Opposing Everest’s growth are:

  • internal structural defects that weaken the rock
  • erosion, from glaciers and water and wind
  • fracturing caused by thermal expansion
  • fracturing caused by water freezing and expanding in crevices
  • landslides caused by earthquakes

Nobody knows if plate tectonics can stay ahead of these opposing forces. A recent study suggests that the plates will keep moving for at least another 1.45 billion years. By then, Earth’s interior will have cooled enough to shut down the plate tectonics engine. After that, Everest can only get shorter.

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Q&A: Earth's Tallest Mountain
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