Falling from the friendly skies

How did Felix Baumgartner break the sound barrier by falling? I've always thought there was some kind of maximum velocity because of drag, even for someone trying to minimize it, in the vicinity of 200km/h.... Is this simply because the atmosphere is sparser up there? (Which would explain the bother about getting 42km off the ground when the max speed is reached after 40 sec.)

In the same vein, to what extent could an astronaut bail out of the ISS, Kursk-style?


(Everybody's seen the real video.)

The usually-quoted human terminal velocity - as you say, around 200 km/h for a skydiver in "star" pose, well over 300 km/h for a skydiver in a head-down pose with limbs tucked in - applies only to normal skydives, which don't start at such a high altitude that the divers even need supplementary oxygen, much less an actual pressure suit.

15,000 feet (about 4.6 kilometres) is a high jump altitude for a recreational skydiver. At that altitude atmospheric pressure is still above 50% of what it is at sea level. Unacclimated people won't be able to get much done at that pressure and will probably start feeling pretty miserable if they stay there for a long time, but if you're just sitting in a perfectly good aeroplane out of which you shortly intend to jump, it's not a huge problem.

5,000 feet (about 1.5 kilometres) is a much commoner skydiving altitude. At that altitude you've still got 80% of sea-level air pressure. The excitement of the impending jump will have much more effect on you, at that pressure, than the thinning of the air.

EDIT: As per ix's comment below, 13,000 feet is actually quite a common skydiving altitude for, as arkikol's comment explains, regulatory-loophole reasons.

(Katoomba, where I live, is about a kilometre above sea level, which is high for Australia; this country's pretty geologically inactive, so for a very long time erosion's been wearing the mountains down and nothing's been pushing them up. A thousand metres is still enough to drop atmospheric pressure to about 87% of that at sea level, though. I therefore get a very mild sort of altitude training any time I go to the shops, or take Alice the Wonder Dog, who needs more exercise than our friends who own her can quite manage to supply, for a walk.)

You need a pressure suit above the "Armstrong limit" (named for Harry George Armstrong, not Neil), which is the pressure where water boils at human body temperature. There is no way to survive for more than a minute or three above the Armstrong Limit, even if you've got pure oxygen to breathe.

The Armstrong limit is around 19.2 kilometres (about 63,000 feet above sea level, 2.2 Mount Everests), depending on the weather. Felix Baumgartner's Red Bull Stratos dive started from a little more than 39 kilometres above sea level.

At that altitude, the air pressure is about four thousandths of an atmosphere. That's 3.9 hectopascals, or 0.056 pounds per square inch. A home experimenter would be pretty pleased to own a mechanical vacuum pump able to pump down that low.

When the air is this tenuous, there is obviously not much air resistance to slow down a falling body. The terminal velocity of a skydiver (or a feather pillow, for that matter) will thus be far higher than it is for a human falling at normal skydiving altitudes.

The speed of sound in a gas, including air, depends on the gas's density, pressure and temperature. For the earth's atmosphere, this results in a rather odd variation of sound-speed with altitude, conveniently displayed in this graph I just ripped off from Wikipedia:

Speed of sound vs altitude

You can see that temperature is the major factor - the shape of the blue speed-of-sound line closely matches that of the red temperature line. This is because density and pressure decrease together with altitude, and cancel each other out.

You can also see, once again, that at 39 kilometres up where Baumgartner's dive started, there ain't much air left at all. The higher you go, the more perverse it therefore becomes to be concerned about the speed of sound at all, from the point of view of a skydiver.

Breaking the sound barrier at "normal" altitudes is a big deal. Even aircraft that only want to come vaguely close to the speed of sound, like jumbo jets, need special design features to prevent alarming things happening when they get above about Mach 0.75.

("Alarming things" include stuff like "the controls not working any more". Quite a lot of World War II airmen lost their lives when a power-dive pushed them fast enough that air was passing over certain parts of their aircraft at transonic speed. Some aircraft designs also helpfully went into a dive all by themselves if flown too fast.)

When the air's so thin that a paper plane would drop like a rock, though, all the same transonic shockwave stuff may be happening, but the forces involved are too feeble to worry about.

So yes, Baumgartner broke the speed of sound, but it wasn't that big a deal, because he was starting from so high up that he would probably have fallen at least a couple of hundred metres per second even if he'd opened his parachute the moment he jumped.

OK, on to bailing out from the International Space Station. This is problematic.

The ISS is in orbit, so if you jump out of it, you'll just be in orbit too. Whatever relative velocity you can give yourself with your legs will not be enough to make a significant difference. In order to actually fall into the atmosphere, you'll have to kill some of your orbital velocity with some sort of thruster - this is how spacecraft "de-orbit".

Let's presume you have a magical reactionless thruster doodad that lets you bring yourself to a halt relative to the surface of the earth directly beneath you, just as if you'd jumped out of a balloon that'd somehow made it to the ISS's altitude. Presumably you planned to further employ your reactionless lift belt or boots or whatever to float down majestically at whatever speed you wanted. But when you pressed the button to kill your orbital momentum, the device burned out, and now you're falling.

The ISS's low Earth orbit is about 400 kilometres above sea level. At that altitude, there's still enough of a trace of atmosphere to cause the ISS's orbit to decay by a couple of kilometres per month, so it requires frequent "reboosting" to stop it falling into the ocean ahead of schedule. From the point of view of someone who just told his fellow cosmonauts that he's just going outside and might be some time, though, it's a vacuum at 400 kilometres.

Low earth orbit is high enough that the Earth's gravity is somewhat attenuated, but only from about 9.8 metres per second squared to about 9.0.

So, starting at 400 kilometres and accelerating at nine metres per second per second, with both gravity and air density slowly rising as you fall. I don't know exactly how this'd work out, but I think that by the time you'd fallen 300 kilometres and passed the 100-kilometres arbitrary "start of space" altitude, you'd be falling at about 2.5 kilometres per second.

That's a pretty darn impressive speed, but it's much more manageable than actual orbital velocity. The ISS's orbital velocity is about seven kilometres per second; when the Shuttle Columbia broke up into flaming particles, it had managed to slow down to around six kilometres per second. Since energy increases with the square of the speed, an object travelling at seven kilometres per second that's trying to slow down has 7.8 times as much energy to get rid of as one travelling at 2.5 km/s.

2.5 km/s at a hundred kilometres altitude would probably be survivable, perhaps with some sort of ribbon parachute or similar drag device to bleed off speed steadily as the air got thicker.

But all of this is a bit silly, because it assumes that you've somehow managed to get rid of the several kilometres per second of your initial orbital velocity. That, there, is the big problem. If an orbiting spacecraft had enough reaction mass to kill its orbital velocity while it was still in space, it could then use wings or pop a gigantic parachute or three and sail down quite serenely, with no need for troublesome heat shields at all.

(This is why the Virgin SpaceShipOne and Two don't need heat shields. They're suborbital spaceplanes, not "real" spacecraft. They go very high by aircraft standards, then they fall back down again, never gaining or having to dispose of actual orbital velocity.)

Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

21 Responses to “Falling from the friendly skies”

  1. Reed Says:

    Back in the 60s, GE came up with a solution to the space station bailout problem. They called it MOOSE http://www.astronautix.com/craft/moose.htm ... For some quite unfathomable reason, no one seems to have wanted to try it.

    • Max Says:

      Even assuming that portable shield would have resisted reentry conditions, I have a sneaking suspicion that inducing a severe spin when firing the retro-burn rocket wold have been next to impossible to avoid.

      I assume you've seen what usually happens when the Mythbusters cheerfully strap bucket-o-rockets to anything and launch it: instead of straight flight, it spins wildly in the air. Unless they were extra careful that is, and made sure the thing is aerodynamically stable - you don't get that luxury in space. I guess the crew of Gemini 8 might have a few words regarding the matter...

      There, you either have to line up your center of gravity _perfectly_ with your thrust vector, or actively correct misalignment by maneuvering thrusters or a servo-gimballed main thruster. I saw no mention of either one...

      • Reed Says:

        Agree, guidance seems dicey at best.

        Some spacecraft do use solids without active guidance, but they are spin stabilized and carefully balanced. Having a human who needs to be conscious and not filling their helmet with puke puts limits on how much you can spin.

        De-orbit burns for crewed LEO craft are only around 100m/s, so the burn doesn't actually have to be violent. It's conceivable that the user could keep it pointed in the right general direction using the cold gas gun, but the description doesn't mention this.

  2. Tim Says:

    About SpaceShip One (and presumably Two) -- It does actually have some kind of painted-on thermal protection material on the nose and wing leading edges. After all, it's released from its carrier at an altitude where the air's fairly thick, and accelerates to Mach 3 during its rocket burn, enough to produce significant heating.

    Just not quite so much as that seen during a hypersonic reentry, of course.

  3. caerphoto Says:

    What would happen if you jumped out of the ISS directly "downwards" (i.e. towards Earth) ?

    Would you just end up in a slightly more elliptical orbit than before?

    • dan Says:

      Yeah, that's about it. Human muscle power can only be orbitally significant in VERY weak gravity - asteroids, moons of Mars, and so on.

      I can't honestly say I've an intuitive grasp of how this all works; The Integral Trees covers it pretty comprehensively, but I've always glazed over in those bits.

      I clearly need to play more Spacewar games.

      • caerphoto Says:

        I think part of my (and perhaps other people's) inability to really comprehend it is down to the huge distances involved – when you're high enough up that you can see almost half the planet at once (or imagine yourself to be so), your perception gets a bit... off.

        "It doesn't look that far away!"

        • Stark Says:

          As Dan said, your legs simply cannot produce the needed force to significantly alter your orbit.... but suppose they did.

          If you simply looked down while standing on the surface of the ISS and jumped towards the center of the Earth one of several possible deaths awaits you.

          First and most likely outcome: You end up not really going anywhere much at all and die in orbit, likely from lack of oxygen. You also have potentially inadvertently killed your fellow travelers on the ISS. This is because your attempt to push off from the ISS, with your rocket strong legs, simply results in a major breach of the hull of the ISS. Predictably this causes a bit of a stir amongst the other passengers of the ISS and potentially results in a sudden livability issue - namely explosive decompression and the resultant boiling and then freezing of all the bodily fluids of those inside the station. Luckily for the crew you were probably standing on the surface of the module with the airlock (seeing as how people are inherently lazy and why go further than you had to if you were just gonna jump off anyhow) so it's probable that the whole of the ISS remains relatively intact and livable since the airlock has a nice bulkhead between the newly remodeled (by your feet) airlock and the rest of the ship. Unluckily for you, you have just destroyed the only way you had back inside. Not that the rest of the crew is likely let you back in after after punching 2 holes the size of average space suit boots into the spacecraft (the boots look rather large though I couldn't quickly find the specific size). Jerk. The rest of the crew should be able to evacuate in the Soyuz docked as a trash container/emergency escape pod. Unless your kick to the station dislodged it of course.

          Second outcome: The station manages to magically have the materials strength to resist your jump. You succeed in jumping straight "down" at sufficient velocity as to ensure you will impact the earth somewhere in your field of view, though still quite a bit orbit-ward of your initial aiming point. (Remember, you are slinging around the planet at 7.8 Km/s, and you will still be going 7 Km/s sideways after your jump) This velocity, if my back o' the napkin calculations (ok, rough estimates would be more accurate) is somewhere north of 1500 Kph. So, within a few minutes of your jump you will hit a non-negligible portion of atmosphere while traveling somewhere in the realm of 7.8 Kps. The atmosphere, not being a pacifistic sort of gas, will hit back. Hard. You will end your days as a bit of charred carbon and ionized gas high in the atmosphere. Somebody might even see your end as a not particularly bright but possibly oddly coloured meteor.

          Third outcome : You jump from the ISS with not enough velocity to actually hit the planet within your field of view but instead only enough to graze the atmosphere....which you then bounce off of like a flat stone on a lake. You then proceed to assume a nicely elliptical orbit which occasionally skips you off the atmosphere slowing you down and tightening your orbit each time. You will eventually drop in and burn up, but it's gonna take awhile and in the meantime you asphyxiate. Whee.

          Now, lets assume you thought this out, realized the death waiting for you due to your orbital velocity and have the ability to jump at the 7.8 km/s acceleration that you'd need to cancel out your orbital velocity. You line up facing anti-orbitward and jump! Net orbital velocity is now 0! Then you're back in the realm that Dan already covered, and could potentially survive. Maybe. Except that normal space suits do not come equipped with any kind of parachute.

          Let's make one more assumption... you are massively drunk while doing all this. After all, jumping from a perfectly good space station going 7.8 km/s while you have a perfectly good Soyuz capsule you could ride down in instead doesn't sound like a choice made by somebody in full control of their faculties now does it? So, assuming you consumed a heroic quantity of alcohol, it is quite likely you could mistake which direction was retrograde to your orbit... and jump orbit-ward at 7.8 km/s instead. This results in a new personal velocity of 15.6 km/s. This is well above the paltry 11.2 km/s you need to escape the orbit of Earth. You have now become the first human to have their very own solar orbit! You also shatter the record for fastest man alive (briefly alive at least). Congratulations! Of course, you will die in the cold vacuum of space, likely after several hours of telling the universe around you "I love you man, no really, I do". You have also slowed the ISS down by about 1.1m/s with your jump - enough to cause anybody free floating inside to slam into whatever is orbit-ward of them at about 4Kph. This result in bumps and bruises and at least one bloody nose - nobody on board misses you much after this. Jerk.



  4. ix Says:

    I'm a skydiving newbie, but I find it hard to believe 5000 ft is the most common altitude to dive from. That doesn't leave you much time to actually skydive at all (consider you have to pull before 2000ft, some chutes 2500 at the latest). The local amateur club that I jumped with routinely do jumps from 13000 ft.

    • dan Says:

      Oh, fair enough; I have precisely zero direct knowledge of skydiving.

      About 13,000 feet was the ceiling according to Wikipedia, so I thought 15,000 would be a good example of a very high recreational dive. I suppose the distribution must be heavily weighted towards the high end, then?

      • Mayhem Says:

        Yep, tourist tandem skydiving back in NZ tends to be at 10k, 12k or 15k feet depending on how much you want to spend.
        Basically works out at 30/45/60 seconds of actual freefall followed by 5 min or so of dangling under a parachute madly spinning one way then the other to get down as quick as possible so they can cycle the next bunch of punters through.

        12k is pretty much the standard 'normal' height though.

      • ix Says:

        I guess it's hard to say what the normal height is if you include non-recreational skydiving. I reckon (military) air drops happen at lower altitudes. But when dong it recreationally I can't think of a reason not to go as high as you can (or are allowed). Unless you're base jumping of course.

  5. arikol Says:

    The reason for the 13000 foot limit on normal parachute jumping (and note that these 13000 feet should be above sea level, not above ground level. There might be some cheating going on in that, though...) is that aviation regulations state that no oxygen is needed below 10000 feet, and you may stay between 10000 and 13000 feet for 30 minutes without extra oxygen. Above 13000 feet requires oxygen, according to regulations.

    Of course, those who have flown a bit know that these regulations are aimed at old guys who have smoked their whole lives.. I have of course never taken a small aircraft up to almost 17000 feet without using oxygen without any problems (the aircraft can't get any higher. Its stated service ceiling is 14700 feet, and this would have been using an old engine/prop combination (if it had ever happened. Which it didn't!)

    So that's the reason for the 13000 foot limit. At 20000 feet you won't have much energy and will be extremely likely to get some oxygen uptake problems and become very sloppy relatively quickly. This does depend on physical shape, up to a point. A non-smoker in good shape will fare better than an overweight chainsmoker..

  6. Erik T Says:

    The speed of sound, in fact, is a function only of gas composition and temperature; unsurprising since it is, like temperature, a macroscopic manifestation of the speed of individual molecules.

    The pleasingly simple formula is a = sqrt((Cp/Cv)*R*T).

  7. TwoHedWlf Says:

    I always think with people talking about "Skipping" off the atmosphere, is it really skipping? Does your actual course change much?

    Assuming you don't have any airfoil or lifting body to produce lift it seems like you'd be more plowing through the atmosphere and popping out the other side. Like a secant cutting through a circle.

    It would only seem like skipping on a plot of your altitude, decreasing to your perigee(Some point within the atmosphere) and then increasing again.

    • Stark Says:

      You'd think so, because the atmosphere is rather tenuous at altitude... but objects do actually skip! This is due to the enormous velocities we're talking about here. Even a tenuous atmosphere gets quickly compressed under the velocity of a low angle planetary impact - enough so that it quickly equals a small positive force on the object impacting and you get a "skip".

      Admittedly this usually occurs with objects going a bit faster than 7.8km/s though. Typically it's a meteor moving along at anywhere up to about 70 km/s.

      So, upon reflection, the skip and asphyxiate death is probably not that likely, though not completely out of the realm of possibility. Much more likely is that you drop far enough into the atmo to induce enough drag to send you on a terminal trajectory and you end up, again, a bit of carbon and a wisp of gas... though the much more gradual atmospheric braking here might slow you enough for some actual carbonized chunks of you to fall to Earth.

      • caerphoto Says:

        Further question: since a human in a spacesuit is of significantly lower mass than a reentry vehicle, wouldn't the atmosphere slow the you down much quicker (possibly before you burned up) due to your much lower momentum? I have only dim memories of A-level maths/physics here, so I might be way off in my understanding of how these things work.

        • Stark Says:

          You might slow down quicker than a space shuttle size brick shaped object (AKA, a Space Shuttle) but... we are still talking about an incredible amount of kinetic energy here. 7.8Km/s is nothing to play about with!

          I've found that most folks think the heat in re-entry is from friction... it isn't. Its from compression. The amount of gas you compress per square centimeter across your body is going to determine how much heating you experience. When decelerating from 7.8Km/s down to a "normal" terminal velocity of ~200kph in the space of just a few minutes you are going to compress a lot of air. In fact, the per square centimeter loading, if my back of the napkin numbers here aren't too far off, really won't differ a whole lot whether you are the space shuttle or or a professional jockey. Physics says you gotta shed the energy of 7.8 km/s and doing so via an atmosphere is going to be a warm experience.

          In all likelihood the shuttle makes out a bit better than you do in your bulky and entirely not aerodynamic space suit. The shuttle was designed with the aerodynamic compression load taken into account and does it's very best to present a low compression aspect on the way down. That is to say, it tries hard to slice through the atmosphere instead of slap into it like a gangly sack of bones and water would, for example.

          Also, by way of comparison, very small rocks - grains of sand really - regularly impact the atmosphere in the 7-8km/s range and heat up enough to glow brightly and be visible from the ground! They only weigh a fraction of a gram. Your typical human weight object carries far more energy with it.

          I came up with an energy for your intrepid human cum asteroid of ~ 2.11 x 10^9 Joules. That would flash boil ~630 liters of water. Or, more entertainingly, it's the equivalent of about 480 kilo's of TNT. Boom!

  8. Jamesf1978 Says:

    I know the article is fairly serious and so are the comments but how come no-one seems to mention how awesome that video is!!!

    I mean how did they manage the film the Lego man going all the way up in that balloon?

  9. jwulsin Says:

    This article was also published in Marco Arment's iOS newsstand publication "The Magazine". Curious what kind of exclusive publishing rights you gave to Marco.

    • dan Says:

      Nothing exclusive at all; just rights to publish it there.

      I will be entirely delighted if Marco wishes to republish any other posts of mine. Anybody who gives you money for something you already did should be dear to your heart, no matter what they pay you.

Leave a Reply