Empirical Earth · a measurement, checked

Baumgartner at 39 kilometers — the number, not the view.

On 14 October 2012, at 12:08 in the afternoon local time, Felix Baumgartner stepped off a capsule 38,969.4 meters above eastern New Mexico. Eight million people watched live. Afterwards he said that standing out there, the only thing he could hear was his own breathing, and that he could see the curvature of the Earth and a sky that was completely black.

That sentence is the weakest evidence he left behind. This page is about the rest of it.

What he did not see, in his own words. He was clear about the limit: he could not see the whole Earth, and said so plainly, adding that to see it as completely round you have to be much further out, or on another planet. He looked down and saw detail, including mountains. Anyone claiming Baumgartner photographed a globe is overstating it, and the overstatement is worth refusing before anyone else points it out. At 39 km you see a curved horizon. You do not see a ball. And as section 05 sets out, the lenses that recorded it were never published, so the photographs are the softest part of this case rather than the hardest.
On this page
  1. The ratified numbers
  2. The measurement that decides it
  3. Why a flat plane cannot produce it
  4. What was actually up there
  5. Which cameras can be trusted on geometry
  6. The evidence that is not a picture
  7. The speed record is a thermometer
  8. The fall time is a densitometer
  9. 1960, and what it does and does not prove
  10. Somebody did it again
  11. What would settle it

01The ratified numbers

These are not press figures. The Fédération Aéronautique Internationale verified them and issued three world records, and the final numbers came in slightly lower than the ones announced on the day, which is what independent verification looks like when it is working.

RecordValueFAI number
Exit altitude38,969.4 m (127,852.4 ft)16670
Vertical freefall distance36,402.6 m (119,431.1 ft)16671
Maximum vertical speed, no drogue1,357.6 km/h (843.6 mph), Mach 1.2516669

Freefall lasted 4 minutes 19 seconds. The whole descent took 9 minutes 3 seconds. The balloon was built by Raven Aerostar, the capsule by Sage Cheshire, the pressure suit by the David Clark Company. He reached the speed of sound about 34 seconds after stepping off, and the sonic boom was audible on the ground.

02The measurement that decides it

Forget the photographs for a moment. The quantity that separates the two models is not how curved the horizon looks. It is how far below level the horizon sits, an angle called the dip, and it is measured with an instrument rather than judged by eye.

dip = arccos( R / (R + h) )

Nothing in that formula is adjustable. Put in the Earth’s radius and an altitude and it returns an angle.

AltitudeDip, geometricDip, standard refractionDistance to horizon
eye level, 2 m0.045°0.04°5 km
100 m tower0.321°0.29°36 km
airliner, 35,000 ft3.318°3.02°369 km
Baumgartner, 38,969.4 m6.321°5.76°706 km
Eustace, 41,419 m6.516°5.94°728 km
what 6.3° meansThe Sun is about half a degree wide. So from that capsule the horizon sat roughly twelve solar diameters below level, all the way around. The visible circle was 1,411 km across, about 1.55 million square kilometers of ground, which is three tenths of one percent of the Earth’s surface.

03Why a flat plane cannot produce it

On a flat Earth the horizon is not a horizon at all. It is the limit of visibility, the point where haze and atmospheric extinction win, and it sits at eye level. That is not a detail of one flat model or another. It follows from the geometry of a plane: from any height above an infinite flat surface, the surface recedes to a vanishing line level with the observer.

So the flat prediction is zero dip, at every altitude, forever. Two meters up, zero. An airliner, zero. Thirty-nine kilometers, zero. There is no version of a flat Earth that produces 6.3°, because a plane has no curve to fall away from you.

The globe predicts a specific number that grows with height in a specific way, and it can be checked at any altitude anyone can reach. A sextant reads dip at sea level, where it is a couple of arcminutes, and navigators have corrected for it for centuries. An aircraft at cruise gives three degrees. The stratosphere gives six. The same formula fits all three.

04What was actually up there

The lens argument cannot be settled without knowing which lenses. The camera package was designed and built for the mission by Jay Nemeth of FlightLine Films, and the inventory was published in the trade press at the time, including a technical writeup in the Guild of Television Camera Professionals’ journal.

WhereWhatRecording to
CapsuleNine HD cameras (Lux Media Plan HD1200 miniature heads)Panasonic P2
Three 4K cinematography cameras, modified RED ONE512 GB RED RAM
Three high-resolution DSLRs, modified Canon 5Dinternal
Pressure suitFive HD cameras, modified GoPro Hero 2: two per thigh, one on the chest packSD cards, record only
HelicopterGyro-stabilized Cineflex HD, plus two interior HD
Ground × 2JLAIR long-range optical tracking: HD P2, RED Epic at 4K 120 fps, shortwave infrared, digital still, on high-power zooms and large telescopes

The electronics rode in a pressurized nitrogen-filled housing with more than 125 components and about two miles of wiring, because electrolytic capacitors fail in vacuum. Neutral-density filtration was fitted against the brightness of unfiltered sunlight at that altitude.

What is not published, and this page will not invent it. The exposure settings are not in the public record: no aperture, no shutter angle or speed, no ISO, and no specific lens focal lengths beyond the camera bodies. Anyone quoting those numbers is either working from a source this page has not found, or making them up. What is documented is the list above, and the list is enough.

05Which of those cameras can be trusted on geometry

The hardware list is the wrong list to reason from. A camera body tells you nothing about distortion. The lens does. A Canon 5D carrying a 50 mm lens renders a horizon essentially straight. The same body carrying a 15 mm fisheye bends it worse than an action camera. So the question is not which bodies flew but which glass was on them, and here the record runs out.

The lenses are not documented. The camera bodies, mounts and recording formats were published in detail. The focal lengths, apertures and lens models were not. That means no frame from this flight can be certified as geometrically trustworthy from the public record alone, and this page will not pretend otherwise. What follows is what can still be said.

One camera can be ruled out, and it is the famous one. The five suit cameras were modified GoPro Hero 2 bodies with a fixed ultra-wide lens taking in about 170 degrees diagonally. That lens bends straight lines hard, worst at the frame edge. A horizon shot on a Hero 2 curves whether the Earth is round or flat, so the thigh and chest-pack footage, which is the footage everyone screenshots, is the weakest evidence from the flight. Anyone building a case on it is building on sand, and that includes people arguing for a globe.

One camera can be ruled out for the opposite reason. The two ground-based JLAIR tracking systems used large telescopes and high-power zooms to follow the capsule from thirty miles away. Long focal lengths are the least distorting optics there are, but a lens that narrow sees a fraction of a degree of sky. It cannot contain a horizon. Those systems are superb evidence that a man was where the telemetry said he was, and no evidence at all about the shape of the horizon behind him.

Which leaves the capsule stills and the 4K footage, and an honest verdict on them: probably fine, not provably fine. Three modified Canon 5D bodies and three modified RED ONE cinema cameras shot the vista frames. Ordinary photographic and cine lenses are designed to be rectilinear, because a cinematographer whose verticals bow cannot use the shot. But "probably carried normal glass" is an inference about a production team’s habits, not a measurement.

The way to settle it, and anyone can do it. Two routes, both concrete. Read the EXIF. Released stills from a Canon 5D normally carry focal length, aperture and exposure in the file header. One published frame with its metadata intact converts "probably rectilinear" into a number. Or correct the GoPro frames properly. The Hero 2 lens is among the most thoroughly characterized optics in existence, because photogrammetry and drone mapping depend on knowing it; its distortion coefficients are published and every mapping package ships them. Apply them to the suit footage and whatever curve survives the correction is real. That is reproducible, needs no permission, and does not depend on trusting this page.
one documented data pointAt least some released Stratos imagery was lens-corrected before publication and said so. A frame from the March 2012 test flight, credited to Jay Nemeth and the Red Bull Content Pool, carries the caption note that lens profile correction was applied to the image. That establishes the practice on this project, though not that it was applied to any particular later frame, and it does not tell us which lens was corrected for.

Two further points hold regardless of any lens.

Barrel distortion is fixed to the frame, and a horizon is not. Lens curvature bends a line most near the picture edge and flattens it through the center, so the apparent bend rolls when the camera rolls. A real curved horizon stays put while the frame turns around it. That is checkable in raw footage with no software at all.

And the measurement in section 02 needs no camera. Dip is an angle against local vertical. An inertial reference reads it with no glass in the path, which is the reason this page leads with the angle and not the pictures.

06The evidence that is not a picture

The jump generated a data record, and the data agrees with the geometry in ways a photograph cannot be blamed for.

He went supersonic in air that barely exists. Mach 1.25 at that altitude required falling through a medium thin enough to permit it, and thickening fast enough to slow him down afterwards. He described the strangeness of it: no flapping suit, no sound, no sense of speed, because there was almost nothing there. Then, passing what he called the Armstrong line, the air grew thick enough for his skills to work again and he stabilized. That is a barometric profile being experienced by a human body, and it matches the exponential falloff a gravitationally bound atmosphere is required to have.

The balloon itself is a measurement. It launched limp and swelled as it climbed, because the pressure outside was dropping away underneath it in the same exponential fashion. A balloon that big at ground level would not have lifted; a balloon that small at altitude would have burst. The whole flight profile is only possible in an atmosphere that thins with height at a rate set by gravity and temperature.

The sonic boom reached the ground. Observers in the New Mexico desert heard it. Sound took time to arrive from a known height, through a known atmosphere, at a known temperature profile.

07The speed record is a thermometer

Here is a thing about that Mach number that is easy to walk past. Mach is not a speed. It is a ratio, the speed of the object divided by the local speed of sound, and the speed of sound in air depends on almost nothing except temperature:

a = √(γRT)

So the two ratified numbers, 1,357.6 km/h and Mach 1.25, are not independent. Divide one by the other and you get the local speed of sound: 301.7 m/s. Put that through the formula and it returns the air temperature where he was fastest:

the readinga = 301.7 m/s → T = 226.5 K, which is −46.7 °C. The US Standard Atmosphere gives 226.5 K at 30 km and 228.5 K at 32 km. He hit maximum speed about 34 seconds after stepping off, which in near-free fall is a drop of 5,670 m, putting him near 33 km. The speed record and the altitude record independently agree about the temperature of the stratosphere.

Nobody set out to measure that. It falls out of two records that were verified separately, by a body checking whether a man had gone fast enough, not whether the atmosphere is layered the way physics says. A stunt that was staged in a studio would have no reason to produce a Mach number that decodes to the right stratospheric temperature at the right height.

08The fall time is a densitometer

He fell 36,402.6 meters in 4 minutes 19 seconds. In vacuum, that same drop takes 86 seconds. Air stretched it to 259, a factor of three.

But the shape of the fall says more than the total. He accelerated hard at first, because at 39 km there was almost nothing to push against. He described it: no flapping suit, no rushing air, no noise, no sense of speed at all. Then he peaked at 377 m/s and began to slow down, because the air beneath him was thickening. Lower still, past what he called the Armstrong line, it grew dense enough for his limbs to bite and he stopped the spin.

A body that accelerates, peaks, and then decelerates while still falling is reading out the density profile of the medium it is in. A uniform atmosphere would give one terminal velocity all the way down. An atmosphere held to a planet by gravity gives exactly what happened: thin at the top, thickening exponentially, terminal speed falling as he descended into it.

That Armstrong line is worth naming, because it is a real threshold rather than a nickname. At about 21 km the pressure drops to roughly 6.3 kPa, and at that pressure water boils at body temperature. Above it an unprotected human does not suffocate slowly; their saliva and the water in their tissues boil. Both men crossed it going up and crossed it again coming down, which is the entire reason the pressure suits existed and the reason a suit failure would have been fatal rather than uncomfortable.

091960, and what it does and does not prove

On 16 August 1960, Captain Joseph Kittinger of the United States Air Force rode an open gondola to 102,800 feet, 31,333 meters, launching from Tularosa, New Mexico, on the third and final test of Project Excelsior. He fell for 4 minutes 36 seconds, reached about 614 mph, opened his main parachute at 17,500 feet and was down 13 minutes 45 seconds after stepping off. The gondola carried two placards: a plaque reading “This Is The Highest Step In The World,” and a paper license plate his five-year-old son had cut from a cereal box. During the ascent the pressure seal in his right glove failed and his hand swelled to nearly twice its size. He did not report it, in case they aborted the flight, and rode to altitude with one working hand.

The dip at his altitude computes to 5.67°, with the horizon 633 km away. His records stood for fifty-two years.

What this page will not claim. An earlier draft of this section said the Excelsior footage shows a curved horizon in the correct proportion for its altitude. That was written without checking, and it has been removed. The imagery that can be located from Excelsior III is Kittinger beside the gondola on the ground, the ground crew helping him out of his gear afterwards, a 1960 newsreel, and the well-known automatic-camera frame taken as he stepped off, which looks downward at a falling man rather than outward at a horizon. Several accounts state that the curvature was visible from that altitude, and the geometry says it would have been, but a general statement about what an altitude affords is not a photograph, and this page will not treat it as one.

So the honest weight of 1960 is not photographic. It is that the physics was replicated, independently, half a century earlier, by a different government for a different reason. The United States Air Force was not producing spectacle. Project Excelsior existed because jets were flying higher and dummies ejected at altitude tumbled into flat spins of 200 rpm or more, and the Air Force needed to know whether a pilot could survive a bailout from the stratosphere. The drogue system Kittinger proved is in ejection seats to this day.

Everything structural about the two flights agrees. A balloon that swells as it climbs. An atmosphere thin enough near the top to permit speeds no falling body reaches lower down, and thick enough beneath to slow a man to terminal velocity. A pressure suit required above the Armstrong line and fatal to be without. Two men, two eras, the same profile.

And then this. When Red Bull Stratos went up in 2012 to take his record, the voice in Baumgartner’s ear the whole way was Kittinger’s. He joined the team in 2008 as mentor and capsule communicator, and at 83 he talked the younger man through every step of taking the record away from him. Baumgartner fell farther and faster. He did not fall longer: his parachute opened a few seconds short, and Kittinger kept the freefall duration record. Joe Kittinger died on 9 December 2022, aged 94.

10Somebody did it again, higher

On 24 October 2014 Alan Eustace, then a senior Google executive, stepped off at about 41,419 m and fell 37,592 m under a drogue. Different team, different balloon, different suit, different sponsor, and almost no publicity: no livestream, no eight million viewers, no energy drink. He simply went higher and told people afterwards.

The dip at his altitude is 6.52°, a fifth of a degree more than Baumgartner’s, which is what the formula requires for 2.4 km of extra height.

Three men, three decades, one curve that grows the right amount each time. Kittinger 5.67° at 31 km in 1960 on film. Baumgartner 6.32° at 39 km in 2012 on video. Eustace 6.52° at 41 km in 2014, quietly. Different governments, sponsors, cameras and decades. A staged result is a claim about one event. Three results that scale correctly with altitude are a claim about the world, and each later team had every reason to find the earlier ones wrong.

11What would settle it

Measure the dip yourself, at any altitude you can get to. The prediction is stated in advance and it is a single number: arccos(R/(R+h)), reduced by about nine percent for standard refraction. At a seaside cliff it is a fraction of a degree and needs care. From a passenger window at cruise it is three degrees, which a phone with a level app can see. From a weather balloon it is five or six. A flat Earth says zero every time. One instrument, one angle, no lens, no trust required.

Baumgartner said he could see the curve, and he was telling the truth. But his eyes are the part of this that can be argued with, and the rest of it cannot. He fell 36,402.6 meters through an atmosphere that thinned exactly the way gravity requires, from a height where the horizon sits six degrees below level and 706 kilometers away, and the numbers were checked afterwards by a body whose job is to refuse records that do not hold up.

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