r/theydidthemath • u/Fizzerolli • 3d ago

[request] Assuming fresh powdery snow, how deep would it have to be for the paratrooper to survive, if possible?

Post image

My son sent me this. My immediate thought based on nothing is that it’s unsurvivable regardless of the depth.

7.4k Upvotes

98% Upvoted

210 comments sorted by

View all comments

1.5k

u/SoylentRox 1✓ 3d ago

Note the skydiver doesn't have to be going terminal velocity. Potentially the drop could be from, say, 100 feet up, right at the stall speed of the 1940s Soviet transport aircraft used. At impact with the deep snow the skydiver will be traveling at ? m/s, or ? mph

Say it's 50-60 mph, for the Lisunov Li-2, a Soviet copy of the DC-3, which has a stall speed of 51 mph. Then at impact

v = sqrt[(v_0)^2 + 2gh]

Where:

  v₀ = initial speed (stall speed ≈ 27.7 m/s)
  g = 9.81 m/s² (gravitational acceleration)
  h = height (100 ft ≈ 30.5 m)

At impact, without drag, they will be traveling about 37 m/s or 83 mph.

I also tried a python script to model the speed vs time to take into account horizontal drag. I get

Impact results:

x: 61.19 m, y: -0.00 m

Horizontal speed: 18.97 m/s

Vertical speed: -21.59 m/s

Total speed: 28.74 m/s, which is ~64 mph

Then if the person, impacting at 64 mph, decelerates over 1m through the snow, they are subject to 42G of deceleration, which is on the edge of survivable.

About 5-10% of soldiers might survive this.

I am hoping the Soviets did experiments with dummies of the instrumented non living kind to test this before trying actual soldiers...

3

u/Gaboik 3d ago

I think it would be conceivable that they drop from even lower but going a little bit more above the stall speed. Say at 50 feet high but at 60 mph. Idk how much that would change the survivability