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From Issue #2 October 25, 2012

Falling From The Friendly Skies

How did Felix Baumgartner break the sound barrier by falling?

By Daniel Rutter Twitter icon 

On October 14, Felix Baumgartner completed a record-breaking skydive. A reader of my blog asked:

How did 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 200 km/h. […]

In the same vein, to what extent could an astronaut jump out of the International Space Station?


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 kilometers) 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 airplane out of which you shortly intend to jump, it’s not a huge problem.

At a mere 5,000 feet (about 1.5 kilometers), you’ve still got 80% of sea-level air pressure. The excitement of the impending jump — which at this altitude won’t give you a lot of free-fall time — will have much more of an effect on you than the thinning of the air.1

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 kilometers (about 63,000 feet above sea level, or 2.2 Mount Everests), depending on the weather. Felix Baumgartner’s Red Bull Stratos dive started from a little more than 39 kilometers 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.

Speed of sound

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 on Wikipedia. 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 kilometers up where Baumgartner’s dive started, there isn’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 things2 happening when they get above about Mach 0.75.

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.

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

Jumping from the ISS

Bailing out from the International Space Station 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 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 kilometers 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 kilometers per month, so it requires frequent “reboosting” to stop it from 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 kilometers.

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

Starting at 400 kilometers and accelerating at 9 meters per second squared, both gravity and air density slowly rise as you fall. I don’t know exactly how this’d work out, but I think that by the time you’d fallen 300 kilometers and passed the 100-kilometers arbitrary “start of space” altitude, you’d be falling at about 2.5 kilometers per second.

That’s an impressive speed, but it’s much more manageable than actual orbital velocity. The ISS’s orbital velocity is about 7 km/s; when the Shuttle Columbia broke up into flaming particles, it had managed to slow down to around 6 km/s. Since energy increases with the square of the speed, an object traveling at 7 km/s 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 an altitude of 100 kilometers 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 kilometers 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 and sail down quite serenely, with no need for troublesome heat shields at all.3

Adapted from the author’s Falling from the friendly skies, originally published on his blog, How to Spot a Psychopath, on October 18, 2012.4

  1. Katoomba, where I live, is about a kilometer 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 meters 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 our friends’ energetic dog for a walk. 

  2. “Alarming things” include stuff like “the controls not working anymore”. 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. 

  3. This is why the Virgin SpaceShipOne and SpaceShipTwo 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. 

  4. Editor’s note: In the Foreword, I wrote that I’d like to occasionally feature articles originally published elsewhere to bring new authors to The Magazine’s audience and add value to their prior work. This is the first such article. 

Dan Rutter is an Australian journalist who writes about science, technology, video games, computer hardware, gadgets, strange tales, and anything else that catches his attention. His websites are Dan's Data and How To Spot A Psychopath.

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