# Kármán line

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

The Kármán line, or commonly simply Karman line, lies at an altitude of 100 kilometres (62 mi) above the Earth's sea level, and is commonly used to define 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 was named after Theodore von Kármán, (1881–1963) a Hungarian-American engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He first calculated that around this altitude the Earth's atmosphere becomes too thin for aeronautical purposes (because any vehicle at this altitude would have to travel faster than orbital velocity in order to derive sufficient aerodynamic lift from the atmosphere to support itself, neglecting centrifugal force).[3] There is an abrupt increase in atmospheric temperature and interaction with solar radiation just below the line, which places the line within the greater thermosphere.

## 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 to be 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 airplane only stays in the sky if it is constantly traveling 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 has to go to generate enough lift to stay up.

If the lift coefficient for a wing at a specified angle of attack is known (or estimated using a method such as thin-airfoil theory), then the lift produced for specific flow conditions can be determined using the following equation

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

where

L is lift force
ρ is air density
v is speed relative to the air
A is wing area,
CL is the lift coefficient at the desired angle of attack, Mach number, and Reynolds number.

Lift (L) generated is directly proportional to the air density (ρ). All other factors remaining unchanged, true airspeed (v) has to be increased 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 any more slowly, the pull of gravity will gradually cause its altitude to 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 that is trying to fly higher and higher, the thinning air gives less and less lift, requiring a higher speed to create enough lift to hold the airplane up. There comes an altitude where it needs to fly so fast to generate lift that it reaches orbital velocity. The concept of the Kármán line is the altitude where the flying speed necessary to aerodynamically support the full weight of the airplane would be equal to orbital velocity (assuming the wing loading of a typical airplane). In practice, supporting full weight wouldn't be necessary to maintain altitude because curvature of the Earth adds centrifugal lift as orbital speed is approached. However the Karman line definition neglects this effect because otherwise orbital velocity would be implicitly sufficient to maintain any altitude regardless of atmospheric density. The Karman line is therefore the highest altitude at which orbital speed can provide sufficient aerodynamic lift to keep flying in a straight line that doesn't follow the curvature of the Earth's surface.

When studying aeronautics and astronautics in the 1950s, Kármán calculated that above an altitude of roughly 100 km (62 mi), a vehicle would have to fly faster than orbital velocity in order to derive sufficient aerodynamic lift from the atmosphere to support itself.[citation needed] At this altitude, the air density is about 1/2200000 the density on the surface.[4] At the Karman line, the air density ρ is such that

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

where

v0 is orbital velocity
m is mass of the aircraft
g is acceleration due to gravity.

Although the calculated altitude was not exactly 100 km, Kármán proposed that 100 km be the designated boundary to space, since 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.[5] However, there is still no international legal definition of the demarcation between a country's air space and outer space.[6]

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.[citation needed]

The FAI uses the Kármán line to define the boundary between aeronautics and astronautics:[7]

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

## Interpretations of the definition

Some people (including the FAI[citation needed] 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.[8][9]

## Alternatives to the definition

Although the United States does not officially define a boundary of space, the U.S. definition of an astronaut, which is still held today, is a person who has flown more than 50 miles (~80 km) above mean sea level. (This is approximately the line between the mesosphere and the thermosphere.) This definition of an astronaut had been somewhat controversial, due to differing definitions between the United States military and NASA.[8]

In 2005, three veteran NASA X-15 pilots (John B. McKay, Bill Dana and Joseph Albert Walker) were retroactively (two posthumously) awarded their astronaut wings, as they had flown between 90 and 108 km in the 1960s, but at the time had not been recognized as astronauts.[8]

International law 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 (93 mi), while an object can maintain an elliptical orbit with perigee as low as 129 km (80 mi) with propulsion.[10]

Atmospheric gases scatter blue wavelengths of visible light more than other wavelengths, giving the Earth’s visible edge a blue 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.

• V-2 rocket - the first human-built object to cross the Kármán line

## References

1. ^ http://www.srh.noaa.gov/srh/jetstream/atmos/layers.htm
2. ^ "The 100 km Boundary for Astronautics" (DOC). Fédération Aéronautique Internationale Press Release. 2004-06-24. Retrieved 2006-10-30.
3. ^ O'Leary, Beth Laura (2009). Ann Garrison Darrin, ed. Handbook of space engineering, archaeology, and heritage. Advances in engineering. CRC Press. p. 84. ISBN 1-4200-8431-3.
4. ^ Squire, Tom (September 27, 2000), "U.S. Standard Atmosphere, 1976", Thermal Protection Systems Expert and Material Properties Database (NASA), retrieved 2011-10-23
5. ^ "Schneider walks the Walk [A word about the definition of space]". NASA. 2005-10-21. Retrieved 2008-04-29.
6. ^ 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 . . ."
7. ^ PDF on the FAI website
8. ^ a b c "A long-overdue tribute". NASA. 2005-10-21. Retrieved 2006-10-30.