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Communication Dans Un Congrès Année : 2022

A variant of the Kármán line theory facilitating the identification of a precise altitude boundary

Résumé

The concept of Kármán Line was first proposed by Andrew G. Haley in a 1957 IAC space law paper, following Kármán's idea to rely on flight mechanics considerations to identify a boundary between atmospheric flight and space flight. The physical phenomenon highlighted by Kármán, and illustrated by Masson & Gazley's diagram, is the fact that, starting from a certain altitude domain, a near-orbital velocity is required to meet equilibrium glide conditions, in which case weight compensation is nearly completely ensured by centrifugal force and lift becomes negligible. The Kármán line altitude was eventually set by FAI to 100 km in 1960, for the purpose separating aeronautics and astronautics records. Although we know that this altitude was set in accordance with Kármán's idea, it is at least partly an arbitrary choice, as Kármán's guidelines alone are insufficient to define a very precise altitude. Indeed, in a 1961 conference (i.e. one year after he contributed to FAI's choice), Kármán confirms that his proposal for the boundary of space is based on the Masson & Gazley diagram and the phenomenon of centrifugal force being "dominant" (consistently with Haley's and FAI's explanations) but he only points towards the approximate altitude range where this phenomenon is visible (300,000-400,000 ft, or 91-122 km) on the "lift barrier" part of the diagram, rather than a very precise altitude. In this paper, we propose a new solution to identify a unique altitude threshold while being consistent with Kármán's guidelines. The proposed solution is based on the fact, apparently never mentioned before in literature about the Kármán line, that the equilibrium velocity actually goes through a maximum when altitude increases. The corresponding altitude de facto separates two regions: an atmospheric flight region, where lifting flight behaviour prevails (equilibrium velocity increases with altitude), and a spaceflight region, where orbital flight behaviour prevails (equilibrium velocity decreases with altitude). We demonstrate, both numerically and theoretically, that this altitude boundary is relatively stable with regards to the vehicle's lift performance, and that it necessary yields near orbital velocity conditions (which fits Kármán's idea). Numerically, this variant of the Kármán line definition is 110 km, which is relatively close to FAI's setting, but with the advantage of being precisely set through flight mechanics considerations. Legal aspects of the boundary of space definition(s) are outside the scope of this paper, which focuses only on flight mechanics/astrodynamics aspects.
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Dates et versions

hal-03798830 , version 1 (05-10-2022)
hal-03798830 , version 2 (26-10-2022)

Identifiants

  • HAL Id : hal-03798830 , version 2

Citer

Nicolas Bérend. A variant of the Kármán line theory facilitating the identification of a precise altitude boundary. International Astronautical Congress 2022 ( IAC 2022 ), Sep 2022, Paris, France. ⟨hal-03798830v2⟩
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