Kármán line

The Kármán line (or von Kármán line /vɒn ˈkɑːrmɑːn/)^[1] is an attempt to define a boundary between Earth's atmosphere and outer space, and offers a specific definition set by the Fédération aéronautique internationale (FAI), an international record-keeping body for aeronautics. Defining the edge of space is important for legal and regulatory purposes since aircraft and spacecraft are subject to different jurisdictions and are subject to different treaties. International law does not define the edge of space, or the limit of national airspace.^[2][3]

Earth's atmosphere as it appears from space, as bands of different colours at the horizon. From the bottom, afterglow illuminates the troposphere in orange with silhouettes of clouds, and the stratosphere in white and blue. Next the mesosphere (pink area) extends to just below the Kármán line at one hundred kilometers and the pink line of airglow of the lower thermosphere (dark), which hosts green and red aurorae over several hundred kilometers.

The FAI defines the Kármán line as space beginning 100 kilometres (54 nautical miles; 62 miles; 330,000 feet) above Earth's mean sea level. This number is well above the altitude reachable by a conventional airplane and is approximately where satellites, even on very eccentric trajectories, will decay before completing a single orbit.

While experts disagree on exactly where the atmosphere ends and space begins, most regulatory agencies (including the United Nations) accept the FAI Kármán line definition or something close to it.^[4] As defined by the FAI, the Kármán line was established in the 1960s.^[5] Various countries and entities define space's boundary differently for various purposes.^[6][2][7]

The Kármán line is named for Theodore von Kármán (1881–1963), a Hungarian-American engineer and physicist who was active in aeronautics and astronautics. In 1957, he was the first person to attempt to calculate a theoretical limit of altitude for airplane flight.

Definition

 

The Kármán line lies within the lower thermosphere (not to scale).^[8]

The FAI uses the term Kármán line to define the boundary between aeronautics and astronautics:^[5]

• Aeronautics: For FAI purposes, aerial activity, including all air sports, within 100 km of Earth's surface.
• Astronautics: For FAI purposes, activity more than 100 km above Earth's surface.

Interpretations of the definition

The expressions "edge of space" or ″near space″ are often used (by, for instance, the FAI in some of their publications)^[9] to refer to a region below the boundary of Outer Space, which is often meant to include substantially lower regions as well. Thus, certain balloon or airplane flights might be described as "reaching the edge of space". In such statements, "reaching the edge of space" merely refers to going higher than average aeronautical vehicles commonly would.^[10][11]

There is still no international legal definition of the demarcation between a country's air space and outer space.^[12] In 1963, Andrew G. Haley discussed the Kármán line in his book Space Law and Government.^[13] In a chapter on the limits of national sovereignty, he made a survey of major writers' opinions.^{[13]: 82–96} He indicated the inherent imprecision of the Line:

The line represents a mean or median measurement. It is comparable to such measures used in the law as mean sea level, meander line, tide line; but it is more complex than these. In arriving at the von Kármán jurisdictional line, myriad factors must be considered – other than the factor of aerodynamic lift. These factors have been discussed in a very large body of literature and by a score or more of commentators. They include the physical constitution of the air; the biological and physiological viability; and still other factors which logically join to establish a point at which air no longer exists and at which airspace ends.^{[13]: 78, 9}

Kármán's comments

In the final chapter of his autobiography, Kármán addresses the issue of the edge of outer space:

Where space begins ... can actually be determined by the speed of the space vehicle and its altitude above the Earth. Consider, for instance, the record flight of Captain Iven Carl Kincheloe Jr. in an X-2 rocket plane. Kincheloe flew 2000 miles per hour (3,200 km/h) at 126,000 feet (38,500 m), or 24 miles up. At this altitude and speed, aerodynamic lift still carries 98 percent of the weight of the plane, and only two percent is carried by inertia, or Kepler force, as space scientists call it. But at 300,000 feet (91,440 m) or 57 miles up, this relationship is reversed because there is no longer any air to contribute lift: only inertia prevails. This is certainly a physical boundary, where aerodynamics stops and astronautics begins, and so I thought why should it not also be a jurisdictional boundary? Andrew G. Haley has termed it the Kármán Jurisdictional Line. Below this line, space belongs to each country. Above this level there would be free space.^[14]

Technical considerations

An atmosphere does not abruptly end at any given height but becomes progressively less dense with altitude. Also, depending on how the various layers that make up the space around the Earth are defined (and depending on whether these layers are considered part of the actual atmosphere), the definition of the edge of space could vary considerably: If one were to consider the thermosphere and exosphere part of the atmosphere and not of space, one might have to extend the boundary of space to at least 10,000 km (6,200 miles) above sea level. The Kármán line thus is a largely arbitrary definition based on some technical considerations.

An aircraft can stay aloft only by constantly traveling forward relative to the air (rather than the ground), so that the wings can generate aerodynamic lift. The thinner the air, the faster the plane must go to generate enough lift to stay up. The amount of lift provided (which must equal the vehicle's weight in order to maintain level flight) is calculated by the lift equation:^[15][16]

${\displaystyle L={\tfrac {1}{2}}\rho v^{2}SC_{L},}$ 

such that

L is the lift force,

ρ is the air density,

v is the aircraft's speed relative to the air,

S is the aircraft's wing area,

C_L is the lift coefficient.^[17]

Lift (L) generated is directly proportional to the air density (ρ). An aircraft maintains altitude if the lift force equals the aircraft weight such that

${\displaystyle L=mg}$ 

where ${\displaystyle m}$  is the aircraft mass, ${\displaystyle g}$  is the acceleration due to gravity, and ${\displaystyle mg}$  is the downward force due to gravity (weight). All other factors remaining unchanged, true airspeed (v) must increase to compensate for lower air density at higher altitudes.

At very high speeds, centrifugal force (Kepler force) given by ${\displaystyle mv^{2}/R}$ , where ${\displaystyle R}$  is the distance to the center of the Earth, contributes to maintaining altitude. This is the virtual force that keeps satellites in circular orbit without any aerodynamic lift. An aircraft can maintain altitude at the outer reaches of the atmosphere if the sum of the aerodynamic lift force and centrifugal force equals the aircraft weight.

${\displaystyle L+{\frac {mv^{2}}{R}}=mg}$ 

As altitude increases and air density decreases, the speed to generate enough aerodynamic lift to support the aircraft weight increases until the speed becomes so high that the centrifugal force contribution becomes significant. At a high enough altitude, the centrifugal force will dominate over the lift force and the aircraft would become effectively an orbiting spacecraft instead an aircraft supported by aerodynamic lift.

In 1956, von Kármán presented a paper in which he discussed aerothermal limits to flight. The faster aircraft fly, the more heat they would generate due to aerodynamic heating from friction with the atmosphere and adiabatic processes. Based on the current state of the art, he calculated the speeds and altitudes at which continuous flight was possible – fast enough that enough lift would be generated and slow enough that the vehicle would not overheat.^[18] The chart included an inflection point at around 275,000 feet (52.08 mi; 83.82 km), above which the minimum speed would place the vehicle into orbit.^[19][20]

The term "Kármán line" was invented by Andrew G. Haley in a 1959 paper,^[21] based on von Kármán's 1956 paper, but Haley acknowledged that the 275,000 feet (52.08 mi; 83.82 km) limit was theoretical and would change as technology improved, as the minimum speed in von Kármán's calculations was based on the speed-to-weight ratio of current aircraft, namely the Bell X-2, and the maximum speed based on current cooling technologies and heat-resistant materials.^[19] Haley also cited other technical considerations for that altitude, as it was approximately the altitude limit for an airbreathing jet engine based on current technology. In the same 1959 paper, Haley also referred to 295,000 feet (55.9 mi; 90 km) as the "von Kármán Line", which was the lowest altitude at which free-radical atomic oxygen occurred.^[19]

Alternatives to the FAI definition

 

Atmospheric gasses scatter blue wavelengths of visible light more than other wavelengths, giving the Earth's visible edge a blue halo. The Moon is seen behind the halo. At higher and higher altitudes, the atmosphere becomes so thin that it essentially ceases to exist. Gradually, the atmospheric halo fades into the blackness of space.

The U.S. Armed Forces definition of an astronaut is a person who has flown higher than 50 miles (80 km) above mean sea level, approximately the line between the mesosphere and the thermosphere. NASA formerly used the FAI's 100-kilometre (62-mile) figure, though this was changed in 2005, to eliminate any inconsistency between military personnel and civilians flying in the same vehicle,^[22] when three veteran NASA X-15 pilots (John B. McKay, William H. Dana and Joseph Albert Walker) were retroactively (two posthumously) awarded their astronaut wings, as they had flown between 90 km (56 miles) and 108 km (67 miles) during the 1960s, but at the time had not been recognized as astronauts.^[10] The latter altitude, achieved twice by Walker, exceeds the modern international definition of the boundary of space.

The United States Federal Aviation Administration also recognizes this line as a space boundary:^[23]

Suborbital Flight: Suborbital spaceflight occurs when a spacecraft reaches space but its velocity is such that it cannot achieve orbit. Many people believe that in order to achieve spaceflight, a spacecraft must reach an altitude higher than 100 kilometers (62 miles) above sea level.

Works by Jonathan McDowell (Harvard-Smithsonian Center for Astrophysics)^[24] and Thomas Gangale (University of Nebraska-Lincoln) in 2018^[19][25] advocate that the demarcation of space should be at 80 km (50 miles; 260,000 feet), citing as evidence von Kármán's original notes and calculations (which concluded the boundary should be 270,000 ft), confirmation that orbiting objects can survive multiple perigees at altitudes around 80 to 90 km, plus functional, cultural, physical, technological, mathematical, and historical factors.^[2][26] More precisely, the paper summarizes:

To summarize, the lowest possible sustained circular orbits are at of order 125 km altitude, but elliptical orbits with perigees at 100 km can survive for long periods. In contrast, Earth satellites with perigees below 80 km are highly unlikely to complete their next orbit. It is noteworthy that meteors (travelling much more quickly) usually disintegrate in the 70–100 km altitude range, adding to the evidence that this is the region where the atmosphere becomes important.

These findings prompted the FAI to propose holding a joint conference with the International Astronautical Federation (IAF) in 2019 to "fully explore" the issue.^[9]

Another definition proposed in international law discussions defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle, but does not specify an altitude.^[27] This is the definition adopted by the U.S. military.^[28]: 13 Due to atmospheric drag, the lowest altitude at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately 150 km (93 miles), whereas an object can maintain an elliptical orbit with perigee as low as about 130 km (81 miles) without propulsion.^{[citation needed]} The U.S. government is resisting efforts to specify a precise regulatory boundary.^[29][30]

For other planets

While the Kármán line is defined for Earth only, if calculated for Mars and Venus it would be about 80 km (50 miles) and 250 km (160 miles) high respectively.^[31]

See also

• Armstrong limit – Altitude above which water boils at human body temperature
• Atmosphere of Earth – Gas layer surrounding Earth
  • Thermosphere – Layer of the Earth's atmosphere above the mesosphere and below the exosphere
  • Mesosphere – Layer of the atmosphere directly above the stratosphere and below the thermosphere
  • Stratosphere – Layer of the atmosphere above the troposphere
  • Troposphere – Lowest layer of Earth's atmosphere
• Exosphere – The outermost layer of an atmosphere
• Free molecular flow – Gas flow with a large mean free molecular path
• MW 18014 – 1944 German V-2 rocket test launch

References

1. "Von Kármán". Dictionary.com Unabridged (Online). n.d.
2. Voosen, Paul (2018-07-24). "Outer space may have just gotten a bit closer". Science. doi:10.1126/science.aau8822. S2CID 126154837. Retrieved April 1, 2019.
3. Harwood, William; "Richard Branson and Virgin Galactic complete successful space flight", CBS News, 2021-07-12
4. "The Kármán Line: Where does space begin?".
5. Sanz Fernández de Córdoba, Dr. S. (2004-06-24). "The 100 km Boundary for Astronautics". Fédération aéronautique internationale. Retrieved 28 December 2020.
6. Drake, Nadia (2018-12-20). "Where, exactly, is the edge of space? It depends on who you ask". National Geographic. Retrieved 2021-07-14.
7. "Air Force Guidance Memorandum to AFMAN 11-402" (PDF). Department of the Air Force. 2021-05-27. Retrieved July 13, 2021.
8. Layers of the Atmosphere, National Weather Service JetStream – Online School for Weather
9. "Statement about the Karman Line". Fédération aéronautique internationale (World Air Sports Federation). 2018-11-30. Retrieved April 1, 2019.
10. Levine, Jay (2005-10-21). "A long-overdue tribute". NASA. Retrieved 2006-10-30.
11. "World Book @ NASA". NASA. Archived from the original on May 4, 2009. Retrieved 2006-10-18.
12. International Law: A Dictionary, by Boleslaw Adam Boczek; Scarecrow Press, 2005; page 239: "The issue whether it is possible or useful to establish a legal boundary between airspace and outer space has been debated in the doctrine for quite a long time. … no agreement exists on a fixed airspace – outer space boundary …"
13. Haley, Andrew G.; (1963) Space Law and Government, Appleton-Century-Crofts
14. von Kármán, Theodore; Edson, Lee (1967). The Wind and Beyond, page 343
15. "Lift Coefficient". Wolfram Alpha Computational Knowledge Engine. Wolfram Alpha LLC. Retrieved 2015-03-14.
16. Benson, Tom, ed. (2014-06-12). . Glenn Research Center. National Aeronautics and Space Administration. Archived from the original on 2015-03-17. Retrieved 2015-03-14.
17. "The Lift Coefficient". 2016-10-26 at the Wayback Machine. Glenn Research Center. NASA. Retrieved May 1, 2015.
18. Theodore von Kármán, Aerodynamic Heating – The Temperature Barrier in Aeronautics, PROC. HIGH-TEMPERATURE SYMPOSIUM, BERKELEY, CALIFORNIA (1956).
19. Gangale, Thomas (2017). (PDF). Journal of Space Law. 41 (2): 155. Archived from the original (PDF) on 24 May 2021.
20. Grush, Loren (2018-12-13). "Why defining the boundary of space may be crucial for the future of spaceflight". The Verge. Retrieved April 1, 2019.
21. Andrew G. Haley, Space Exploration: The Problems of Today, Tomorrow and in the Future, 2 PROC. ON THE L. OF OUTER SPACE 49 (1959).
22. Jenkins, Dennis R. (2005-10-21). "NASA – Schneider walks the Walk [A word about the definition of space]". www.nasa.gov. NASA. Retrieved 19 October 2018.
23. "Space: Commercial Space Transportation Licenses: Human Spaceflight (also referred to as crewed spaceflight)", [US] Federal Aviation Administration, 2021-03-16
24. McDowell, Jonathan C. (2018). "The edge of space: Revisiting the Karman Line". Acta Astronautica. 151: 668–677. arXiv:1807.07894. Bibcode:2018AcAau.151..668M. doi:10.1016/j.actaastro.2018.07.003.
25. Gangale, Thomas (2018). How High the Sky? The Definition and Delimitation of Outer Space and Territorial Airspace in International Law. Studies in Space Law. Vol. 13. Leiden, The Netherlands: Koninklijke Brill NV. doi:10.1163/9789004366022. ISBN 978-90-04-36602-2. S2CID 135092905.
26. Specktor, Brandon (2018-07-25). "The Edge of Space Just Crept 12 Miles Closer to Earth". Live Science. Retrieved April 1, 2019.
27. . Army Space Reference Text. United States Army. 2000. Archived from the original on April 18, 2012. Retrieved April 24, 2012. Where Space Begins: There is no formal definition of where space begins. International law, based on a review of current treaties, conventions, agreements and tradition, defines the lower boundary of space as the lowest perigee attainable by an orbiting space vehicle. A specific altitude is not mentioned. By international law standards aircraft, missiles and rockets flying over a country are considered to be in its national airspace, regardless of altitude. Orbiting spacecraft are considered to be in space, regardless of altitude.
    U.S. definition: The U.S. government defines space in the same terms as international law.
28. National Security Space Institute in conjunction with U.S. Army Command and General Staff College (2006). U.S. Military Space Reference Text. National Security Space Institute. Retrieved April 1, 2019 – via Homeland Security Digital Library.
29. King, Matthew T. (2016). "Sovereignty's Gray Area: The Delimitation of Air and Space in the Context of Aerospace Vehicles and the Use of Force". Journal of Air Law and Commerce. 81 (3): 377–497 [p. 432].
30. "Delegation of the U.S., Statement on the Definition and Delimitation of Outer Space and the Character and Utilization of the Geostationary Orbit, to the Comm. on the Peaceful Uses of Outer Space, Legal Subcomm. of Its Fortieth Session (Apr. 2–13, 2001)". from the original on 2020-03-28. Retrieved 2019-11-21. With respect to the question of the definition and delimitation of outer space, we have examined this issue carefully and have listened to the various statements delivered at this session. Our position continues to be that defining or delimiting outer space is not necessary. No legal or practical problems have arisen in the absence of such a definition. On the contrary, the differing legal regimes applicable in respect of airspace and outer space have operated well in their respective spheres. The lack of a definition or delimitation of outer space has not impeded the development of activities in either sphere.
31. Martínez, Isidoro; Space Environment, 2021

External links

• at the FAI website
• Layers of the Atmosphere – NOAA 2005-12-19 at the Wayback Machine
• "The Kármán Line" music video featuring NASA footage
• Kármán line calculator