r/theydidthemath 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.

7.3k Upvotes

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...

27

u/Fizzerolli 3d ago

Thanks for the answer! My son (15) was really curious whether or not it would be remotely feasible. I’m guessing flying an unarmored, unarmed transport at 100ft would be suicide, so I’m going with no

28

u/Xlaag 3d ago

Think about this too. Even if you had infinite loose snow to land in, and it was 100% survivable the biggest issue would be suffocation. You would basically be subjecting your soldiers to a personal self inflicted avalanche. Not even considering the broken bones it would be nearly impossible to dig yourself out of the snow.

5

u/Vegetable_Log_3837 3d ago

That’s my take as skier too. Fall damage is off in deep soft powder, which is pretty rare even where it snows all the time. If the snow is that deep and soft then if your head goes under you’re dead, better luck climbing out of quicksand.

So either it’s not the epic powder day and you die from the fall, or it is and you’re stuck in a tree well.

1

u/Finnegansadog 3d ago

I think you’ve got some bad info there, fellow skier. Deep and soft powder isn’t terribly rare, it’s just rare to find it in conjunction with skiable terrain.

Also, your head going under snow isn’t something immediately or even quickly deadly, especially if it’s light and soft powder. Part of a backcountry avvy course will include you getting buried in snow, so you know how to survive being buried by an avalanche. If the snow is so light and mobile that it fills in over your head like quicksand, it’s also so light that breathable air will move pretty easily around and through it.

1

u/Vegetable_Log_3837 2d ago

I’m talking like 3ft+ of blower where it’s safe to huck a 20ft cliff and land on your head. Only happens a few times a year in the PNW, and Colorado often goes years without a storm that big. I’ve taken the avy course and spend a lot of time in the backcountry, snow immersion deaths are more common than avy deaths around here. On the real deep days it’s pretty easy to get stuck in your own crater, but that only happens a few times a season.

2

u/CloseToMyActualName 2d ago

I'm less worried about the suffocation since I don't think the snow would be that deep outside of an avalanche or drifts in the mountains (that would be too hard to hit).

The realistic scenario would be a slow moving plane (close to 100 km/h?) within 10m of the ground over a farmer's field. Anything but a farmer's field and rocks and tree are taking folks out.

So the speed of impact is 50km/h and 100km/h horizontal. If you pad the hell out of them I think it's pretty survivable.

The trouble is that you need everything to go right for it to work in practice, plane can't be too high, can't have any tress/rocks/streams running through the field, can't have a spot with low snow cover.

And, since you're dropping behind enemy lines, you need to ensure those conditions without any scouting.

2

u/Photocracy 3d ago

Paratroopers are primarily used for rapid deployment to an area that's hard to access because of terrain between the front and your bases, rather than dropping behind or on enemy lines. The armour and the armament of the transport is not important, as the biggest danger in 100 ft of snow would be a surprise mountain or something.

Keep in mind that the Russians need to be able to project military power over the Siberian wasteland, an area famous for being big, hard to traverse, and having a lot of snow. The idea is stupid but probably seemed plausible enough to test, for a Russian design group.

1

u/Early_Bad8737 3d ago

If he is interested in this he should look up Vesna Vulovic. She fell more than 10km when the plane blew up and survived thanks to a mix of snow and trees.