Where does the definition of the Kármán line on Wikipedia come from?

According to Wikipedia's article about the Kármán line:

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 ).

Edit: So the speed necessary to only aerodynamically support the airplane's full weight without the centrifugal force.

Is this the real definition ? Why does it not take the centrifugal force or Kepler force into account ?

The FAI (Fédération Aéronautique Internationale) doesn't mention the above definition in this article but instead the Kármán line being the 100 km altitude boundary.

So where does this so called "definition" in the Wikipedia article come from ?

It doesn't have any references that could lead to an authoritive source.

• I admit I'm intensely curious what your interest in the Karman line is - you've asked half the questions on the tag.
– Bear
Commented Dec 19, 2018 at 19:41
• @Bear I have to admit that i'm obsessed by the mysterious history of the calculations done by Von Kármán and colleages. Commented Dec 19, 2018 at 22:08
• it would help if you stopped editing your questions so much. Things went wrong the last time you did that: the question became a moving target and impossible to answer. Commented Dec 20, 2018 at 10:07
• @Hobbes I'm aware of that, but this edit is a crucial one about the Kepler force that isn't taken into account with the definition, and the answer does mention this force several times. Commented Dec 20, 2018 at 10:17

1 Answer

Immediately before the definition section, Wikipedia references Kármán's abstract concept from his autobiography:

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 per cent of the weight of the plane, and only two per cent is carried by centrifugal force, 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 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."

So Kármán presented his concept of the crossover point between aerodynamic lift and "Kepler force"; Andrew Haley referred to it as the Kármán Line. Since the exact crossover point will vary with the particular design of an aircraft, Kármán's 91.44 km figure is not actually definitional; FAI rounds it to 100km, which is the Kármán line for some purely notional aircraft.

Furthermore, section 2b of the FAI article you link does in fact refer to this same definition:

In Aeronautics, level flying higher and higher meant to deal with less and less dense atmosphere, thus to the need of greater and greater speeds to have the flying machine controllable by aerodynamic forces. A speed so big in fact, that, above a certain altitude, could be close or even bigger than the circular orbital speed at that altitude (i.e. lift was no longer needed, since centrifugal force took over; and consequently aerodynamic flight was meaningless).

So both the articles provide what you claim is lacking.

• So the Kármán line could be where lifting force equals Kepler force ? Commented Dec 19, 2018 at 22:05
• It's where the lifting force equals the Kepler force, for the speed at which the total force exactly balances gravity. Commented Dec 19, 2018 at 22:21
• In this question, space.stackexchange.com/questions/29721/… ,the lift force would be equal to the gravitational force, there is no Kepler force. Isn't that less realistic ? Commented Dec 19, 2018 at 23:53
• Very nice answer! nits follow: "autobiography" should be taken with a grain of salt as it was written several years after his death, with the help of a 2nd author. A scientist of this stature probably wouldn't write things like "there is no longer any air to contribute lift"; at least not verbatim. So I think this may be an interpretation or amateur reconstruction of what was done in the service of the well-paying space lawyers of the time.
– uhoh
Commented Dec 20, 2018 at 3:09
• Yes, well, when you significantly change the question two weeks later, the answer doesn't apply any more. I'm done here. Commented Jan 5, 2019 at 16:07