Jumping from an airplane without a parachute

[Mr Skeptic]

My Dad told me long ago about Soviet soldiers jumping off an airplane without a parachute onto snow. Now I wonder whether it is true or not. This website collected some accounts of the supposed jumps, and concludes they are probably propaganda or exaggerations. It also examines some physics, but I don't think it's a very good analysis. They seem to be calculating using the maximum velocity but calculating as though the fall angle were straight down.

 

So here is my proposed scenario: an airplane with a stall speed of either 40 mph or 100 mph. Snow 1 m deep, no more, with a reasonable density and compressibility. Suitable but reasonably possible terrain. Can the jump be done with greater than 50% chance of coming out unhurt (or alternately, alive)?

 

My analysis: let the airplane speed be V, and the minimum fly height h. Then the total velocity of the fall (assuming negligible air resistance) is [math]v = \sqrt{2 g h + V^2}[/math], of which the vertical component is [math]v_{vert} = \sqrt{2 g h}[/math] and the horizontal component V. So long as the plane's speed is high and the height low, even a small slope could match the angle of the fall. So, find a slope matching the angle of the fall (same as the ratio of the appropriate velocities). Ideally you want a gentle slope: it will be harder to miss that way, but on the other hand it means that you're moving faster. By matching the angle of the fall with the angle of the slope, you get effectively infinite "depth" of snow, and furthermore that is on the surface. My thinking is that if you can match the angle of fall and slope you get an effect similar to skipping a rock on water, so that our soldier never hits hard ground nor is even buried in snow, and furthermore is only about half-way into the snow and so afforded a gentler deceleration. As for position I would suggest a position feet-first and face up, with the feet tilted so that they form a nice angle, so that your feet end up above the snow and therefore the rest of the body ends up at an angle, preventing the body from sinking into the snow.

 

However, I'm not really sure how to calculate this, since I've never done a "moving through a solid material" physics problem, and more so since this would be at the surface.

[alpha2cen]

One possibility is like this. It is the plane path. First plane lowers the hight as possible as it can be. And suddenly makes it's hight high. At this moment the soldiers jump off the plane. The plane clime angle is very important. Then, soldiers body reduce gravity effect and horizontal direction velocity is reduced by air fraction loss. This is an assumption, but it is not easy.

Edited February 8, 2011 by alpha2cen

[ajb]

My thought is to calculate the force viz

 

[math]\mathbf{F} \cdot d\mathbf{x} = m \mathbf{v} \cdot d\mathbf{v}[/math].

 

You could assume a linear deacceleration from a specified velocity (terminal?) over a distance dx. I have no idea what this should be, maybe just a few meters.

 

I think you could get a good handle on the magnitude of the forces involved. Then you would have to see if such forces are likely to cause serious injury.

[alpha2cen]

The thought is that we can reduce the gravity acceleration . Before we obtain the high gravity velocity, we land down on the ground. Because of this, the plane climb angle is very important. The angle can reduce linear direction velocity. And the soldier's motion is also important, too, as possible as he can, he try to wide his body to increase drag fraction by the wind. And remaining kinetic energy can be reduced by thick snow cushion. This possibility is based on the phenomena during the Hurricane human body is flied by the strong wind. I think this is dangerous and very high skill training.

Edited February 8, 2011 by alpha2cen

[ajb]

The thought is that we can reduce the gravity acceleration .

 

No, but as you suggest you can maximise your air resistance so that your terminal velocity due to falling is reduced.

[alpha2cen]

The air resistance is horizontal direction resistance and very small gravity direction resistance. We can not reduce gravity direction acceleration. So, before we obtain gravity direction speed, we have to land down on the ground.

Edited February 8, 2011 by alpha2cen

[TonyMcC]

There are several recorded instances of people forced to leave aircraft in flight who have survived.

http://www.greenharbor.com/fffolder/ffallers.html

Additionally if you could somehow convert downward speed into horizontal speed just above a forgiving surface you would have a fair chance of survival. Racing motorcyclists often "come off" their bikes at this sort of speed and sometimes even get up and walk away. If an aircraft such as a Hercules flew at minimum speed a few feet above a smooth surface, perhaps carpeted in snow or wet to reduce friction, and you jumped out of the back you would have a fair chance of survival.

I don't recommend it though and even in my younger days I certainly would not have volunteered!

By the way, the case of Sgt. Nicholas Alkemade is particularly well documented as he was denied membership of the "Caterpillar Club" because he did not use a parachute.

Edited February 8, 2011 by TonyMcC

[ajb]

Lets do a "back of the envelope calculation" here.

 

Work done = change in Kinetic energy = Force times distance.

 

Lets assume we come to rest in a distance d starting from speed v. So

 

[math]|F| d= \frac{1}{2}m v^{2}[/math],

 

where we take the mass of the person to be m.

 

Let us assume that the human body can withstand up to 50g before there is a risk of death or serious injury. (I took this from Wikipedia). Then we can calculate the required stopping distance.

 

[math]d = \frac{v^{2}}{2 \: 50g}[/math].

 

So now lets say the speed is the terminal velocity of 55m/s. Say g = 10 m/s/s, So

 

[math]d = \frac{55^{2}}{2 \times 50 \times 10} \approx 3 [/math] meters.

 

So, I think the "parachutist" would have to decelerate to stationary in no less that 3 meters.

 

You could now fiddle the numbers a bit with the speed and the maximum g's. But as a "guesstimate" you get an idea of the distances required.

[Mr Skeptic]

Sure, but the important thing to remember is that the velocity component could be largely horizontal right from the start, so a shallow angle. For example if you can get a plane traveling at 100 mph (44.7 m/s) and 5 m altitude, the downwards component of velocity would only be 9.9 m/s. That would be 12 degrees from horizontal, which is a fairly reasonable slope to be able to find. On such a slope, the stopping distance could be very long... so long as they don't sink into the snow. Even without a slope, falling at that angle would mean that 1 m of snow depth would be 4.6 m at the 12 degree angle.

[Cap'n Refsmmat]

Air resistance will very shortly lower your horizontal velocity component, since gravity isn't helping that out any. Vertical terminal velocity relies on gravity to oppose the air resistance, but that doesn't happen horizontally. Your horizontal component should decrease to 0 rapidly.

[ajb]

In my calculation I have just looked at the total magnitude of the forces involved. Just to get an idea of what stopping distances would be reasonable. Three meters to me sounds shorter that I initially thought. So, like you say Mr Skeptic you could arrange the angles etc so that 1m of snow give you an "effective depth" of greater than 3 meters.

 

It is starting to sound more and more possible. Though I am not sure if my 50g is too high or if we would still expect minor injuries. Either way, I would not want to try it.

 

Also, we would need to know more about the physics of the snow. I expect that the "parachutist" would compress the snow and not travel that far though it. Thus, accelerations >50g are likely. More injuries that we might expect from my calculation. Then like you have suggested, it may be possible to just skim the snow and decelerate that way. I just think it is all too tricky to pull off regularly with a lot of men.

Edited February 9, 2011 by ajb

[moth]

Anybody can jump from an airplane with no parachute at least one time.

Have you seen the

? Most people do use a parachute to land, but a couple of years ago this guy had a plan to land on a mountainside or skijump type of ramp. Some people combine the wing suit with a strap-on jet pack for even more fun(but they use a parachute to land). Edited February 9, 2011 by moth

[John Cuthber]

I suspect that one of the best things to land on would be the top of a water slide, but if your luck is that good, you won't ever need to fall out of a plane.

 

Aiming for the steepest part of a snow covered hill is probably the best bet- that way you can be brought to a halt over a longer distance- sacrificing vertical speed for horizontal speed, then dissipating that by sliding along.

[Doc. Josh]

Ive never jumped from an airplane but have a similar event happen to me. I was a teenager and had built a big rope swing in the mountins of blue ridge (where im from) And it was over a cliff with a atleast 80ft drop below when you swung out but had a slope. So i was being a stupid kid and climbed up higer and the swung out the impact of the rope snapping threw me off and i fell straight down in a slant and it was full of snow at the bottom. It hurt from the ice packing under me and scraped me up pretty good but fortunatly WALKED away with nothing broken. so as to my discovery yes it's very possible. Now being an airplane is quite diffrent than my measly 80ft rope swing but with the right pitch and angle yes i believe its very fesible.

[Moontanman]

Evidently it has happened...

 

http://209.157.64.200/focus/f-news/1071076/posts

 

A B-17 ball turret gunner, Magee had no choice but to jump out of a disabled, spinning-out-of-control bomber from about 22,000 feet.

 

A drop of more than four miles. Without a parachute. And Magee miraculously lived.

 

His incredible story was featured in a 1981 Smithsonian Magazine on the 10 most amazing survivals during World War II.

[lemur]

I think this question should be simplified to what is the lowest possible speed that people can land on a ski-slope from an aircraft without a parachute. Then the question should go to a skiier, snowboarder, or someone with experience in wintersports to ask how dangerous it would be to ski/sled/slide at that speed. Then the operative question would become how dangerous it would be to JUMP at that speed, as jumping requires landing. Sorry for circumventing the physics here but I think this question would be more effectively answered in terms of practical approximations/comparisons based on comparable vectors/speeds of landing.

[Mr Skeptic]

In my calculation I have just looked at the total magnitude of the forces involved. Just to get an idea of what stopping distances would be reasonable. Three meters to me sounds shorter that I initially thought. So, like you say Mr Skeptic you could arrange the angles etc so that 1m of snow give you an "effective depth" of greater than 3 meters.

 

It is starting to sound more and more possible. Though I am not sure if my 50g is too high or if we would still expect minor injuries. Either way, I would not want to try it.

 

I think that a deceleration of 10 g would be a more appropriate target. We'd want to leave the getting hurt to when something goes wrong, and given a lack of a pressure suit and likeliness of uneven stresses and variable deceleration, we'd have to stay well away from injury-level g forces.

 

Also, we would need to know more about the physics of the snow. I expect that the "parachutist" would compress the snow and not travel that far though it. Thus, accelerations >50g are likely. More injuries that we might expect from my calculation. Then like you have suggested, it may be possible to just skim the snow and decelerate that way. I just think it is all too tricky to pull off regularly with a lot of men.

 

Per the russian stories, there was a reasonable number of both injured and uninjured men after the jump. Something about necessity combined with a lack of parachutes. So I'm not looking for something you could reliably do, only that you have decent odds of surviving uninjured enough to fight.