Kármán line

Layers of Atmosphere.^[1] (not to scale)

The Kármán line, or Karman line, lies at an altitude of 100 kilometres (62 mi) above the Earth's sea level, and commonly represents the boundary between the Earth's atmosphere and outer space.^[2] This definition is accepted by the Fédération Aéronautique Internationale (FAI), which is an international standard-setting and record-keeping body for aeronautics and astronautics.

The line is named after Theodore von Kármán (1881–1963), a Hungarian-American engineer and physicist. He was active primarily in aeronautics and astronautics. He was the first to calculate that around this altitude, the atmosphere becomes too thin to support aeronautical flight, because a vehicle at this altitude would have to travel faster than orbital velocity to derive sufficient aerodynamic lift to support itself (neglecting centrifugal force).^[3] The line is approximately at the turbopause, above which atmospheric gasses are not well-mixed. The mesopause atmospheric temperature minimum has been measured variously at 85 km or 100 km, which puts the line at or near the bottom of the thermosphere.

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 Ivan Kincheloe in an X-2 rocket plane. Kincheloe flew 2000 mile per hour at 126,000 feet, or 24 miles up. At this altitude and speed aerodynamic lift still carries 98 per cent of the weight of the plane, and only two per cent is carried by centrifugal force, or Kepler Force, as the space scientists call it. But at 300,000 feet or 57 miles up this relationship is reversed because there is no longer any air to contribute lift. Only centrifugal force 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? Haley has kindly called it the Kármán Jurisdictional Line. Below this line space belongs to each country. Above this level there would be free space.^[4]

Definition

An atmosphere does not abruptly end at any given height, but becomes progressively thinner 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 to space to at least 10,000 km (6,200 mi) above sea level. The Kármán line thus is an arbitrary definition based on the following considerations:

An aircraft only stays aloft if it constantly travels forward relative to the air (airspeed is not dependent on speed relative to ground), so that the wings can generate lift. The thinner the air, the faster the plane must go to generate enough lift to stay up.

The amount of lift required at any given point can be calculated by the lift equation:^[5][6]

$L = \tfrac12\rho v^2 S C_L$

where

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.^[7]

Lift (L) generated is directly proportional to the air density (ρ). All other factors remaining unchanged, true airspeed (v) must increase to compensate for less air density (ρ) at higher altitudes.

An orbiting spacecraft only stays in the sky if the centrifugal component of its movement around the Earth is enough to balance the downward pull of gravity. If it goes slower, the pull of gravity gradually makes its altitude decrease. The required speed is called orbital velocity, and it varies with the height of the orbit. For the International Space Station, or a space shuttle in low Earth orbit, the orbital velocity is about 27,000 km per hour (17,000 miles per hour).

For an airplane flying higher and higher, the increasingly thin air provides less and less lift, requiring increasingly higher speed to create enough lift to hold the airplane up. It eventually reaches an altitude where it must fly so fast to generate lift that it reaches orbital velocity. The Kármán line is the altitude where the speed necessary to aerodynamically support the airplane's full weight equals orbital velocity (assuming wing loading of a typical airplane). In practice, supporting full weight wouldn't be necessary to maintain altitude because the curvature of the Earth adds centrifugal lift as the airplane reaches orbital speed. However, the Karman line definition ignores this effect because orbital velocity is implicitly sufficient to maintain any altitude regardless of atmospheric density. The Karman line is therefore the highest altitude at which orbital speed provides sufficient aerodynamic lift to fly in a straight line that doesn't follow the curvature of the Earth's surface.

Above 100 kilometers the air density is about 1/2200000 the density on the surface.^[8] At the Karman line, the air density ρ is such that

$L = \tfrac12\rho v_0^2 S C_L = mg$

where

v₀ is the speed of a circular orbit at the same altitude in vacuum

m is the mass of the aircraft

g is the acceleration due to gravity.

Although the calculated altitude was not exactly 100 km, Kármán proposed that 100 km be the designated boundary to space, because the round number is more memorable, and the calculated altitude varies minutely as certain parameters are varied. An international committee recommended the 100 km line to the FAI, and upon adoption, it became widely accepted as the boundary to space for many purposes.^[9] However, there is still no international legal definition of the demarcation between a country's air space and outer space.^[10]

Another hurdle to strictly defining the boundary to space is the dynamic nature of Earth's atmosphere. For example, at an altitude of 1,000 km (620 mi), the atmosphere's density can vary by a factor of five, depending on the time of day, time of year, AP magnetic index, and recent solar flux.

The FAI uses the Kármán line to define the boundary between aeronautics and astronautics:^[11]

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

Interpretations of the definition

Some people (including the FAI in some of their publications) also use the expression "edge of space" to refer to a region below the conventional 100 km boundary to 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.^[12][13]

Alternatives to the definition

The U.S. Air Force definition of an astronaut is a person who has flown more than 50 miles (~80 km) above mean sea level, approximately the line between the mesosphere and the thermosphere. NASA uses the FAI's 100-kilometer figure.^[12] The United States does not officially define a boundary of space. In 2005, 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 mi) and 108 km (67 mi) in the 1960s, but at the time had not been recognized as astronauts.^[12] The latter altitude exceeds the modern international definition of the boundary of space.

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. 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 (90 mi), whereas an object can maintain an elliptical orbit with perigee as low as about 130 km (80 mi) with propulsion. Above altitudes of approximately 160 km (100 mi) the sky is completely black.^[14]

Atmospheric gases 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.

See also

• Exosphere
• Atmosphere of Earth
  • Thermosphere
  • Mesophere
  • Stratosphere
  • Troposphere
• V-2 rocket – the first human-built object to cross the Kármán line

References

1. Layers of the Atmosphere, National Weather Service JetStream - Online School for Weather
2. Dr. S. Sanz Fernández de Córdoba (2004-06-24). "The 100 km Boundary for Astronautics". Fédération Aéronautique Internationale. Retrieved 2014-05-07.
3. O'Leary, Beth Laura (2009). Ann Garrison Darrin, eds. Handbook of space engineering, archaeology, and heritage. Advances in engineering. CRC Press. p. 84. ISBN 1-4200-8431-3.
4. Theodore von Kármán with Lee Edson (1967) The Wind and Beyond, page 343
5. "Lift Coefficient". Wolfram Alpha Computational Knowledge Engine. Wolfram Alpha LLC. Retrieved 2015-03-14.
6. Benson, Tom, ed. (2014-06-12). "The Lift Equation". Glenn Research Center. National Aeronautics and Space Administration. Retrieved 2015-03-14.
7. "The Lift Coefficient". Glenn Research Center. NASA. Retrieved May 1, 2015.
8. Squire, Tom (September 27, 2000), "U.S. Standard Atmosphere, 1976", Thermal Protection Systems Expert and Material Properties Database (NASA), retrieved 2011-10-23
9. "Schneider walks the Walk [A word about the definition of space]". NASA. 2005-10-21. Retrieved 2008-04-29.
10. 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 . . ."
11. PDF on the FAI website
12. "A long-overdue tribute". NASA. 2005-10-21. Retrieved 2006-10-30.
13. "World Book @ NASA". NASA. Archived from the original on May 31, 2009. Retrieved 2006-10-18.
14. "Space Environment and Orbital Mechanics". United States Army. Retrieved 24 April 2012.

External links

• Article on the Kármán line at the FAI website
• Layers of the Atmosphere – NOAA
• The Kármán Line music video featuring NASA footage
• Kármán line calculator