Editing Atmospheric entry (section)

==Entry vehicle shapes==
{{Main|Aeroshell}}
{{see also|Nose cone design}}
There are several basic shapes used in designing entry vehicles:

===Sphere or spherical section===
[[File:Apollo cm.jpg|thumb|[[Apollo command module]] flying with the blunt end of the [[heat shield]] at a non-zero [[angle of attack]] in order to establish a lifting entry and control the landing site (artistic rendition)]]
The simplest axisymmetric shape is the sphere or spherical section.<ref>{{cite web|last1=Przadka|first1=W.|last2=Miedzik|first2=J.|last3=Goujon-Durand|first3=S.|last4=Wesfreid|first4=J.E.|title=The wake behind the sphere; analysis of vortices during transition from steadiness to unsteadiness.|url=http://sphere.meil.pw.edu.pl/publi/AoM_60_2008_6.pdf|website=Polish french cooperation in fluid research.|publisher=Archive of Mechanics., 60, 6, pp. 467–474, Warszawa 2008. Received May 29, 2008; revised version November 13, 2008.|access-date=3 April 2015|archive-date=December 21, 2016|archive-url=https://web.archive.org/web/20161221044217/http://sphere.meil.pw.edu.pl/publi/AoM_60_2008_6.pdf|url-status=live}}</ref> This can either be a complete sphere or a spherical section forebody with a converging conical afterbody. The aerodynamics of a sphere or spherical section are easy to model analytically using Newtonian impact theory. Likewise, the spherical section's heat flux can be accurately modeled with the [[Fay-Riddell equation|Fay–Riddell equation]].<ref name="Fay-Riddell">{{cite journal|last1=Fay |first1=J. A. |last2=Riddell |first2=F. R. |title=Theory of Stagnation Point Heat Transfer in Dissociated Air |journal=Journal of the Aeronautical Sciences |volume=25 |pages=73–85 |date=February 1958 |url=http://pdf.aiaa.org/downloads/TOCPDFs/36_373-386.pdf |format=PDF Reprint |access-date=2009-06-29 |issue=2 |doi=10.2514/8.7517 |url-status=dead |archive-url=https://web.archive.org/web/20050107202757/http://pdf.aiaa.org/downloads/TOCPDFs/36_373-386.pdf |archive-date=2005-01-07 }}</ref> The static stability of a spherical section is assured if the vehicle's center of mass is upstream from the center of curvature (dynamic stability is more problematic). Pure spheres have no lift. However, by flying at an [[angle of attack]], a spherical section has modest aerodynamic lift thus providing some cross-range capability and widening its entry corridor. In the late 1950s and early 1960s, high-speed computers were not yet available and [[computational fluid dynamics]] was still embryonic. Because the spherical section was amenable to closed-form analysis, that geometry became the default for conservative design. Consequently, crewed capsules of that era were based upon the spherical section.

Pure spherical entry vehicles were used in the early Soviet [[Vostok programme|Vostok]] and [[Voskhod programme|Voskhod]] [[space capsule|capsule]]s and in Soviet Mars and [[Venera]] descent vehicles. The [[Apollo command module]] used a spherical section forebody heat shield with a converging conical afterbody. It flew a lifting entry with a hypersonic trim angle of attack of −27° (0° is blunt-end first) to yield an average L/D (lift-to-drag ratio) of 0.368.<ref>{{Cite web |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690029435_1969029435.pdf |title=Hillje, Ernest R., "Entry Aerodynamics at Lunar Return Conditions Obtained from the Flight of Apollo 4 (AS-501)," NASA TN D-5399, (1969). |access-date=July 7, 2017 |archive-date=September 16, 2020 |archive-url=https://web.archive.org/web/20200916020329/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690029435_1969029435.pdf |url-status=live }}</ref> The resultant lift achieved a measure of cross-range control by offsetting the vehicle's center of mass from its axis of symmetry, allowing the lift force to be directed left or right by rolling the capsule on its [[Flight control surfaces#Longitudinal axis|longitudinal axis]]. Other examples of the spherical section geometry in crewed capsules are [[Soyuz programme|Soyuz]]/[[Zond program|Zond]], [[Project Gemini|Gemini]], and [[Project Mercury|Mercury]]. Even these small amounts of lift allow trajectories that have very significant effects on peak [[g-force]], reducing it from 8–9&nbsp;g for a purely ballistic (slowed only by drag) trajectory to 4–5&nbsp;g, as well as greatly reducing the peak reentry heat.<ref>{{cite report|last1=Whittington|first1=Kurt Thomas|title=A Tool to Extrapolate Thermal Reentry Atmosphere Parameters Along a Body in Trajectory Space|url=http://repository.lib.ncsu.edu/ir/bitstream/1840.16/6817/1/etd.pdf|website=NCSU Libraries Technical Reports Repository|date=April 11, 2011|publisher=A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Master of Science Aerospace Engineering Raleigh, North Carolina 2011, pp.5|access-date=5 April 2015|archive-date=April 11, 2015|archive-url=https://web.archive.org/web/20150411064311/http://repository.lib.ncsu.edu/ir/bitstream/1840.16/6817/1/etd.pdf|url-status=live}}</ref>

===Sphere-cone===
The sphere-cone is a spherical section with a [[frustum]] or blunted cone attached. The sphere-cone's dynamic stability is typically better than that of a spherical section. The vehicle enters sphere-first. With a sufficiently small half-angle and properly placed center of mass, a sphere-cone can provide aerodynamic stability from Keplerian entry to surface impact. (The ''half-angle'' is the angle between the cone's axis of rotational symmetry and its outer surface, and thus half the angle made by the cone's surface edges.)

[[File:Mk 2.jpg|thumb|left|Prototype of the Mk-2 Reentry Vehicle (RV), based on blunt body theory]]
The original American sphere-cone aeroshell was the Mk-2 RV (reentry vehicle), which was developed in 1955 by the [[General Electric]] Corp. The Mk-2's design was derived from blunt-body theory and used a radiatively cooled thermal protection system (TPS) based upon a metallic heat shield (the different TPS types are later described in this article). The Mk-2 had significant defects as a weapon delivery system, i.e., it loitered too long in the upper atmosphere due to its lower [[ballistic coefficient]] and also trailed a stream of vaporized metal making it very visible to [[radar]]. These defects made the Mk-2 overly susceptible to anti-ballistic missile (ABM) systems. Consequently, an alternative sphere-cone RV to the Mk-2 was developed by General Electric.{{citation needed|date=November 2013}}

[[File:Mk 6 reentry vehicle on display at National Atomic Museum.jpg|thumb|upright|right|[[LGM-25C Titan II#Development|Mk-6]] RV, [[Cold War]] weapon and ancestor to most of the U.S. missile entry vehicles]]
This new RV was the Mk-6 which used a non-metallic ablative TPS, a nylon phenolic. This new TPS was so effective as a reentry heat shield that significantly reduced bluntness was possible.{{citation needed|date=November 2013}} However, the Mk-6 was a huge RV with an entry mass of 3,360&nbsp;kg, a length of 3.1 m and a half-angle of 12.5°. Subsequent advances in nuclear weapon and ablative TPS design allowed RVs to become significantly smaller with a further reduced bluntness ratio compared to the Mk-6. Since the 1960s, the sphere-cone has become the preferred geometry for modern ICBM RVs with typical half-angles being between 10° and 11°.{{citation needed|date=November 2013}}

[[File:Rv film pod.jpg|thumb|upright|left|"Discoverer" type reconnaissance satellite film Recovery Vehicle (RV)]]
[[File:Galileo probe.jpg|thumb|right|[[Galileo Probe]] during final assembly]]
[[Reconnaissance satellite]] RVs (recovery vehicles) also used a sphere-cone shape and were the first American example of a non-munition entry vehicle ([[Corona (satellite)|Discoverer-I]], launched on 28 February 1959). The sphere-cone was later used for space exploration missions to other celestial bodies or for return from open space; e.g., [[Stardust (spacecraft)|''Stardust'']] probe. Unlike with military RVs, the advantage of the blunt body's lower TPS mass remained with space exploration entry vehicles like the [[Galileo Probe]] with a half-angle of 45° or the [[Viking program|Viking aeroshell]] with a half-angle of 70°. Space exploration sphere-cone entry vehicles have landed on the surface or entered the atmospheres of [[Mars]], [[Venus]], [[Jupiter]], and [[Titan (moon)|Titan]].
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===Biconic===
[[File:Delta Clipper DC-X first flight.jpg|thumb|right|upright|The [[McDonnell Douglas DC-X|DC-X]], shown during its first flight, was a prototype [[single-stage-to-orbit]] vehicle, and used a biconic shape similar to AMaRV.]]
The [[biconic]] is a sphere-cone with an additional frustum attached. The biconic offers a significantly improved L/D ratio. A biconic designed for Mars aerocapture typically has an L/D of approximately 1.0 compared to an L/D of 0.368 for the Apollo-CM. The higher L/D makes a biconic shape better suited for transporting people to Mars due to the lower peak deceleration. Arguably, the most significant biconic ever flown was the ''Advanced [[Maneuverable reentry vehicle|Maneuverable Reentry Vehicle]]'' (AMaRV). Four AMaRVs were made by the [[McDonnell Douglas]] Corp. and represented a significant leap in RV sophistication. Three AMaRVs were launched by [[LGM-30 Minuteman|Minuteman-1 ICBMs]] on 20 December 1979, 8 October 1980 and 4 October 1981. AMaRV had an entry mass of approximately 470&nbsp;kg, a nose radius of 2.34&nbsp;cm, a forward-frustum half-angle of 10.4°, an inter-frustum radius of 14.6&nbsp;cm, aft-frustum half-angle of 6°, and an axial length of 2.079 meters. No accurate diagram or picture of AMaRV has ever appeared in the open literature. However, a schematic sketch of an AMaRV-like vehicle along with trajectory plots showing hairpin turns has been published.<ref>Regan, Frank J. and Anadakrishnan, Satya M., "Dynamics of Atmospheric Re-Entry", AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., New York, {{ISBN|1-56347-048-9}}, {{doi|10.2514/4.861741}}, (1993).<!-- I think this refers to diagrams of simulations on pg. 268 & 269. Is there a way to note that? ([https://books.google.com/books?as_isbn=1563470489 Google Books]) --></ref>

AMaRV's attitude was controlled through a split body flap (also called a ''split-windward flap'') along with two yaw flaps mounted on the vehicle's sides. [[Hydraulic machinery|Hydraulic actuation]] was used for controlling the flaps. AMaRV was guided by a fully autonomous navigation system designed for evading [[anti-ballistic missile]] (ABM) interception. The [[McDonnell Douglas DC-X]] (also a biconic) was essentially a scaled-up version of AMaRV. AMaRV and the DC-X also served as the basis for an unsuccessful proposal for what eventually became the [[Lockheed Martin X-33]].

===Non-axisymmetric shapes===
Non-[[axisymmetric]] shapes have been used for crewed entry vehicles. One example is the winged orbit vehicle that uses a [[delta wing]] for maneuvering during descent much like a conventional glider. This approach has been used by the American [[Space Shuttle]], the Soviet [[Buran (spacecraft)|Buran]] and the in-development [[SpaceX_Starship|Starship]]. The [[lifting body]] is another entry vehicle geometry and was used with the [[X-23 PRIME]] (Precision Recovery Including Maneuvering Entry) vehicle.{{citation needed|date=November 2013}}