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?

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

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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...

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u/CaptainRex8669 3d ago

The Soviets did lots of parachuting with the AN-2, which is famously impossible to stall. The POH doesn't have a stall speed listed within.

The slowest speed the aircraft has been flown at is 26 knots, and the controls remain responsive at that speed. Keep in mind, this is airspeed, not groundspeed. If they fly in a strong enough headwind they could achieve a groundspeed of 0, or even fly backwards.

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u/SoylentRox 1✓ 3d ago

Ok so with a headwind, and I take it a white knuckle pilot to get the aircraft to a 50? foot altitude, so it's essentially hovering over the ground...still would be nice to have zip lines. But yes this seems survivable.

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u/CaptainRex8669 3d ago

I have some flight training (just over 20 hours, which is half of what you need for licence here in the UK).

In slow flight, with the ground that close to you, which you can use as a visual reference point, any pilot would be able to maintain altitude without deviating more than a foot, so flying at 20 feet, or even lower, would be achievable.

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u/SpoonNZ 2d ago

Tell me more about how the ground is a good visual reference point when it’s covered in a layer of snow thick enough for a man to jump into.

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u/CK2398 2d ago

During high winds as well. Sounds a lot like a snow storm

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u/CaptainRex8669 2d ago

I'm from England, so I've never seen snow deeper than 2 inches. You're probably right actually.

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u/SpoonNZ 2d ago

I’m from New Zealand. The Mt Erebus disaster happened long before I was born but it’s still something that comes up surprisingly often. If you can accidentally fly straight into a mountain because there’s no visual clues, maybe flying a few feet off the ground in the same conditions isn’t a good idea.

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u/CaptainRex8669 2d ago

There's something called VMC, which stands for Visual Meteorological Conditions. And there's IMC, which stands for Instrument Meteorological Conditions.

Whether an area is VMC or IMC is determined by visibility, not wind. Flying at night, for example, is IMC. Flying in clouds is also IMC.

Any pilot can fly in VMC, but you can only fly in IMC if you and your plane are rated for IFR, which stands for Instrument Flight Rules.

The Mount Erebus Disaster happened in IFR conditions, but the scenario we are talking about here would be VFR, so there should be no danger.

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u/Laffenor 1d ago

With 2 inches of snow to cushion the fall, I would prefer to be significantly lower than 20ft.

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u/EMDReloader 1d ago

20 feet off the ground at near zero velocity?

Sounds like target practice with extra steps.

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u/ZiLBeRTRoN 3d ago

That’s wild that you only need 40 hours for a flight license.

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u/CaptainRex8669 3d ago

Technically it's 45 hours. And it's only a PPL, which stands for Private Pilots Licence. To apply for a CPL, a Commercial Pilots Licence, the minimum is 200 hours. And you need a type-rating to fly specialised planes, like jets, which requires further specialised training. These are also just the minimum, most people go above the minimum before they do their check-ride.

Wanna know what's really wild?
You can start training at age 14.
You can fly solo, without a licence, from age 16.
You can take your check-ride from age 16.5.
You can get the licence from age 17.

If you pass your check-ride before you are 17, then you have to wait until you turn 17 before they actually give you the licence.

You have to be 25 to rent a car though.

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u/marxist_redneck 3d ago

Yep, it's wild. I thought it was crazy when I learned about it. I started flight training at 15 at the same time I got a driving learner's permit, and I got a PPL before I got my driver's license 😂

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u/basilect 3d ago

Same in the US as well, though a lot of people aren't ready by then (and wouldn't pass a checkride) so they won't go for it right at 40

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u/Nukethepandas 2d ago

At that point could you just land the plane on the spot? Like a vertical takeoff/landing plane but using the wind? 

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u/Mercury_Madulller 2d ago

Yes. That is why smart pilots tie down their planes when storing them outside at an airport, especially when windy conditions are expected.

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u/Relative_Ranger7640 1d ago

Existence of non smart pilots upset me

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u/Nukethepandas 2d ago

At that point could you just land the plane on the spot? Like a vertical takeoff/landing plane but using the wind? 

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u/CaptainRex8669 2d ago

It is possible technically, but probably not a good idea. I've seen videos of un-manned aircraft taking off by themselves in a strong headwind. It's why in some countries with extreme weather, pilots tie light-aircraft to the ground.

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u/Shamino79 2d ago edited 2d ago

If you’re considering paratroopers minus the para then pilots to do this isn’t a big stretch.