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{{Refimprove|date=July 2009}}
A '''catch-22''' is a [[paradoxical]] situation from which an individual cannot escape because of contradictory rules.<ref>{{cite journal | title=Catch-22 | journal=Random House
Dictionary | publisher=Random House | year=2012 | url=http://dictionary.reference.com/browse/catch-22}}</ref><ref name=OALD>"[http://oald8.oxfordlearnersdictionaries.com/dictionary/catch-22 Catch 22]", ''Oxford Advanced Learners' Dictionary'', accessed 16 August 2013.</ref> Catch-22s often result from rules, regulations, or procedures that an individual is subject to but has no control over. One connotation of the term is that the creators of the "Catch-22" have created arbitrary rules in order to justify and conceal their own abuse of power.
== Origin and meaning ==


[[File:Lift-induced vortices behind aircraft (DLR demonstration).ogv|thumb|Lift-induced vortices behind a jet aircraft are evidenced by smoke on a runway]]
[[Joseph Heller]] coined the term in his 1961 novel ''[[Catch-22]]'', which describes absurd bureaucratic constraints on soldiers in World War II. The term is introduced by the character Doc Daneeka, an army psychiatrist who invokes "Catch 22" to explain why any pilot requesting mental evaluation for insanity—hoping to be found not sane enough to fly and thereby escape dangerous missions—demonstrates his own sanity in making the request and thus cannot be declared insane.<ref>Scriptures for a Generation: What We Were Reading in the '60s - Page 162 Philip D. Beidler - 1995 "It is Catch-22: Doc Daneeka explains how anybody who is crazy has a right to ask to be removed from combat status but how anybody who asks is"</ref>
[[File:2011-06-05 19-32 Berlin TXL Airplane Flyover plus Wingtip Vortex.ogg|thumb|An audio recording of lift-induced vortices heard shortly after an airliner overfly]]
{{quotation|"You mean there's a catch?"
<p>
"Sure there's a catch", Doc Daneeka replied. "Catch-22. Anyone who wants to get out of combat duty isn't really crazy."
<p>
There was only one catch and that was Catch-22, which specified that a concern for one's own safety in the face of dangers that were real and immediate was the process of a rational mind. [[Orr (Catch-22)|Orr]] was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane, he had to fly them. If he flew them, he was crazy and didn't have to; but if he didn't want to, he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.|4 = }}


'''Wingtip vortices''' are circular patterns of rotating air left behind a [[wing]] as it generates [[Lift (force)|lift]].<ref name=Clancy5.14>Clancy, L.J., ''Aerodynamics'', section 5.14</ref>  One wingtip [[vortex]] trails from the [[Wing tip|tip]] of each wing. Wingtip vortices are sometimes named ''trailing'' or ''lift-induced vortices'' because they also occur at points other than at the wing tips.<ref name=Clancy5.14/> Indeed, vorticity is trailed at any point on the wing where the lift varies span-wise (a fact described and quantified by the [[lifting-line theory]]); it eventually rolls up into large vortices near the wingtip, at the edge of [[Flap (aircraft)|flap devices]], or at other abrupt changes in [[planform|wing planform]].
Different formulations of "Catch-22" appear throughout the novel. The term is applied to various loopholes and quirks of the military system, always with the implication that rules are inaccessible to and slanted against those lower in the hierarchy. In chapter 6, Yossarian is told that Catch-22 requires him to do anything his [[commanding officer]] tells him to do, regardless of whether these orders contradict orders from the officer's superiors.<ref name=Henriksen>Margot A. Henriksen, ''Dr. Strangelove's America: Society and Culture in the Atomic Age''; University of California Press, 1997; ISBN 0-520-08310-5; p. [http://books.google.com/books?id=KGrsQOIQgeYC&lpg=PP1&pg=PA250#v=onepage&q&f=false 250].</ref>


Wingtip vortices are associated with [[induced drag]], the imparting of [[downwash]], and are a fundamental consequence of three-dimensional lift generation.<ref>Clancy, L.J., ''Aerodynamics'', sections 5.17 and 8.9</ref> Careful selection of wing geometry (in particular, [[Aspect ratio (wing)|aspect ratio]]), as well as of cruise conditions, are design and operational methods to minimize induced drag.
In a final episode, Catch-22 is described to Yossarian by an old woman recounting an act of violence by soldiers:<ref>"[http://www.answers.com/topic/joseph-heller Joseph Heller]", ''Gale Encyclopedia of Biography'', accessed via Answers.com, 16 August 2013.</ref><ref name=CombsNimmo />


Wingtip vortices form the primary component of [[wake turbulence]]. Depending on ambient atmospheric humidity as well as the geometry and wing loading of aircraft, water may condense or freeze in the core of the vortices, making the vortices visible.
{{quotation|"Catch-22 says they have a right to do anything we can't stop them from doing." <p> "What the hell are you talking about?" Yossarian shouted at her in bewildered, furious protest. "How did you know it was Catch-22? Who the hell told you it was Catch-22?" <p> "The soldiers with the hard white hats and clubs. The girls were crying. 'Did we do anything wrong?' they said. The men said no and pushed them away out the door with the ends of their clubs. 'Then why are you chasing us out?' the girls said. 'Catch 22,' the men said. All they kept saying was 'Catch-22, Catch-22. What does it mean, Catch 22? What is Catch-22?" <p> "Didn't they show it to you?" Yossarian demanded, stamping about in anger and distress. "Didn't you even make them read it?" <p> "They don't have to show us Catch-22," the old woman answered. "The law says they don't have to." <p> "What law says they don't have to?" <p> "Catch-22".}}


== Generation of trailing vortices ==
According to literature professor Ian Gregson, the old woman's narrative defines "Catch-22" more directly as the "brutal operation of power", stripping away the "bogus sophistication" of the earlier scenarios.<ref>Ian Gregson, ''Character and Satire in Post War Fiction''; London: Continuum, 2006; ISBN 9781441130006; p. [http://books.google.com/books?id=e0qqaRTVt_sC&lpg=PP1&pg=PA38#v=onepage&q&f=false 38].</ref>
[[Image:Tip vortex rollup.png|thumb|Euler computation of a tip vortex rolling up from the trailed vorticity sheet.]]
When a wing generates [[lift (force)|aerodynamic lift]] the air on the top surface has lower pressure relative to the bottom surface. Air flows from below the wing and out around the tip to the top of the wing in a circular fashion. An emergent circulatory flow pattern named [[vortex]] is observed, featuring a low-pressure core.


Three-dimensional lift and the occurrence of wingtip vortices can be approached with the concept of [[horseshoe vortex]] and described accurately with the [[Lifting-line theory|Lanchester–Prandtl theory]]. In this view, the trailing vortex is a continuation of the ''wing-bound vortex'' inherent to the lift generation.
=== Other appearances in the novel ===
Besides referring to an unsolvable logical [[dilemma]], Catch-22 is invoked to explain or justify the military bureaucracy. For example, in the first chapter it requires Yossarian to sign his name to letters that he censors while he is confined to a hospital bed. One clause mentioned in chapter 10 closes a loophole in promotions, which one private had been exploiting to reattain the attractive rank of [[Private First Class]] after any promotion. Through [[courts-martial]] for going [[AWOL]], he would be busted in rank back to private, but Catch-22 limited the number of times he could do this before being sent to the stockade.


If viewed from the tail of the airplane, looking forward in the direction of flight, there is one wingtip vortex trailing from the left-hand wing and circulating clockwise, and another one trailing from the right-hand wing and circulating anti-clockwise. The result is a region of downwash behind the aircraft, between the two vortices.
At another point in the book, a prostitute explains to Yossarian that she cannot marry him because he is crazy, and she will never marry a crazy man. She considers any man crazy who would marry a woman who is not a virgin. This closed logic loop clearly illustrated Catch-22 because by her logic, all men who refuse to marry her are sane and thus she would consider marriage; but as soon as a man agrees to marry her, he becomes crazy for wanting to marry a non-virgin, and is instantly rejected.


The two wingtip vortices do not merge because they are circulating in opposite directions. They dissipate slowly and linger in the atmosphere long after the airplane has passed. They are a hazard to other aircraft, known as [[wake turbulence]].
At one point, Captain Black attempts to pressure Milo into depriving Major Major of food as a consequence of not signing a loyalty oath that Major Major was never given an opportunity to sign in the first place. Captain Black asks Milo, "You're not against Catch-22, are you?"


== Effects and mitigation ==
In chapter 40, Catch-22 forces Colonels Korn and Cathcart to promote Yossarian to Major and ground him rather than simply sending him home. They fear that if they do not, others will refuse to fly, just as Yossarian did.


[[File:Air France Boeing 777-300ER planform view.jpg|thumb|Modern airliners often feature [[Aspect ratio (wing)|slender wings]] and [[wingtip device]]s]]
=== Significance of the number 22 ===
{{main|Catch-22#Explanation of the novel's title|Catch-22}}
Heller originally wanted to call the phrase, and hence the book, by other numbers, but he and his publishers eventually settled on 22. The number has no particular significance; it was chosen more or less for [[euphony]]. The title was originally ''Catch-18'', but Heller changed it after the popular ''[[Mila 18]]'' was published a short time beforehand.<ref name="Aldridge1986" /><ref name=Telegraph />


Wingtip vortices are associated with [[induced drag]], an unavoidable consequence of three-dimensional lift generation. The rotary motion of the air within the shed wingtip vortices (sometimes described as a "leakage") reduces the effective [[angle of attack]] of the air on the wing.
== Usage ==


The [[lifting-line theory]] describes the shedding of trailing vortices as span-wise changes in lift distribution. For a given wing span and surface, minimal induced drag is obtained with an [[Elliptical wing|elliptical lift distribution]]. For a given lift distribution and surface, induced drag is reduced with increasing [[Aspect ratio (wing)|aspect ratio]].
The term "catch-22" has filtered into common usage in the English language.<ref name=OALD /> In a 1975 interview, Heller said the term would not translate well into other languages.<ref name=Telegraph>"[http://www.telegraph.co.uk/culture/3669372/A-classic-by-any-other-name.html A classic by any other name]", ''The Telegraph'', 18 November 2007.</ref>


As a consequence, aircraft for which a high [[lift-to-drag ratio]] is desirable, such as [[Glider aircraft|gliders]] or long-range [[airliner]]s, typically have high aspect ratio wings. Such wings however have disadvantages with respect to structural constraints and manoeuvrability, as evidenced by [[Fighter aircraft|combat]] and [[Aerobatics|aerobatic]] planes which usually feature short, stubby wings despite the efficiency losses.
James E. Combs and Dan D. Nimmo suggest that the idea of a "catch-22" has gained popular currency because so many people in modern society are exposed to frustrating bureaucratic logic. They write:


Another method of reducing induced drag is the use of [[Wingtip device|winglets]], as seen on most modern airliners. Winglets increase the effective aspect ratio of the wing, changing the pattern and magnitude of the [[vorticity]] in the vortex pattern. A reduction is achieved in the kinetic energy in the circular air flow, which reduces the amount of fuel expended to perform work upon the spinning air.
<blockquote>Everyone, then, who deals with organizations understands the bureaucratic logic of Catch-22. In high school or college, for example, students can participate in student government, a form of self-government and democracy that allows them to decide whatever they want, just so long as the principal or dean of students approves. This bogus democracy that can be overruled by arbitrary fiat is perhaps a citizen's first encounter with organizations that may profess 'open' and libertarian values, but in fact are closed and hierarchical systems. Catch-22 is an organizational assumption, an unwritten law of informal power that excepts the organization from responsibility and accountability, and puts the individual in the absurd position of being excepted for the convenience or unknown purposes of the organization. <ref name=CombsNimmo>James E. Combs & Dan D. Nimmo, ''The Comedy of Democracy''; Westport, CT: Praeger (Greenwood Publishing Group), 1996; ISBN 0-275-94979-6; p. [http://books.google.com/books?id=VJw9OdBFgmgC&lpg=PP1&pg=PA152#v=onepage&q&f=false 152].</ref></blockquote>


== Visibility of vortices ==
Along with George Orwell's "[[doublethink]]", "Catch-22" has become one of the best-recognized ways to describe the predicament of being trapped by contradictory rules.<ref>Richard King, "[http://thesmartset.com/article/article07181101.aspx 22 Going on 50: Half a century later, the world is full of Catch-22s]"; ''The Smart Set'', 20 July 2011.</ref>


[[File:FA-18C vapor LEX and wingtip 1.jpg|thumb|Vortices shed at the tips and from the [[leading-edge extension]]s of an F/A-18]]
== Logic ==


The cores of the vortices are sometimes visible because water present in them [[condensation|condenses]] from [[gas]] ([[vapor]]) to [[liquid]], and sometimes even freezes, forming ice particles.
The [[Archetype|archetypal]] ''catch-22'', as formulated by [[Joseph Heller|Heller]], involves the case of [[John Yossarian]], a [[United States Army Air Corps|U.S. Army Air Forces]] [[Bombardier (air force)|bombardier]], who wishes to be grounded from combat flight. This will only happen if he is evaluated by the squadron's [[flight surgeon]] and found "unfit to fly". "Unfit" would be any pilot who is willing to fly such dangerous missions, as one would have to be [[Insanity|mad]] to volunteer for possible death. However, to be evaluated, he must ''request'' the evaluation, an act that is considered sufficient proof for being declared sane. These conditions make it impossible to be declared "unfit".


Condensation of water vapor in wing tip vortices is most common on aircraft flying at high [[angle of attack|angles of attack]], such as fighter aircraft in high [[g-force|''g'']] maneuvers, or [[airliner]]s taking off and landing on humid days.
The "Catch-22" is that "anyone who wants to get out of combat duty isn't really crazy".<ref name="Heller1999" /> Hence, pilots who request a mental fitness evaluation ''are'' sane, and therefore must fly in combat. At the same time, if an evaluation is not requested by the pilot, he will never receive one and thus can never be found insane, meaning he must also fly in combat.


=== Aerodynamic condensation and freezing ===
Therefore, Catch-22 ensures that no pilot can ever be grounded for being insane even if he is.
{{Anchor|Discussion of the physics of aerodynamic condensation and freezing}}


The cores of vortices spin at very high speed and are regions of very low pressure. To [[Orders of approximation|first approximation]], these low-pressure regions form with little exchange of heat with the neighboring regions (i.e., [[Adiabatic process|adiabatically]]), so the local temperature in the low-pressure regions drops, too.<ref name="Green Fluid Vortices">Green, S. I. [http://books.google.com/books?id=j6qE7YAwwCoC&pg=PA427&lpg=PA427&dq=condensation+in+wingtip+vortices&source=bl&ots=S8a5ApDgog&sig=wMqbujbSVVVVGJ9yNq9CnQyW368&hl=en&ei=E6BLSpj2FZqytwfT0PibDQ&sa=X&oi=book_result&ct=result&resnum=8 “Wing tip vortices”] in ''Fuid vortices,'' S. I. Green, ed. ([[Kluwer]], Amsterdam, 1995) pp. 427-470. ISBN 978-0-7923-3376-0</ref>  If it drops below the local [[dew point]], there results a condensation of water vapor present in the cores of wingtip vortices, making them visible.<ref name="Green Fluid Vortices"/> The temperature may even drop below the local [[freezing point]], in which case ice crystals will form inside the cores.<ref name="Green Fluid Vortices" />
A logical formulation of this situation is:


The [[Phase (matter)|phase]] of water (i.e., whether it assumes the form of a solid, liquid, or gas) is determined by its [[temperature]] and [[pressure]]. For example, in the case of liquid-gas transition, at each pressure there is a special “transition temperature” <math>T_{c}</math> such that if the sample temperature is even a little above <math>T_{c}</math>, the sample will be a gas, but, if the sample temperature is even a little below <math>T_{c}</math>, the sample will be a liquid; see [[phase transition]]. For example, at the [[standard conditions|standard atmospheric pressure]], <math>T_{c}</math> is 100&nbsp;°C&nbsp;=&nbsp;212&nbsp;°F. The transition temperature <math>T_{c}</math> decreases with decreasing pressure (which explains why water boils at lower temperatures at higher altitudes and at higher temperatures in a [[pressure cooker]]; see [[Vapor pressure#Water vapor pressure|here]] for more information). In the case of water vapor in air, the <math>T_{c}</math> corresponding to the [[partial pressure]] of water vapor is called the [[dew point]]. (The solid–liquid transition also happens around a specific transition temperature called the [[melting point]]. For most substances, the melting point also decreases with decreasing pressure, although water ice in particular - in its [[Ice Ih|I<sub>h</sub> form]], which is [[Phases of ice|the most familiar one]] - is a prominent [[Water (properties)|exception to this rule]].)
# <math>(E \rightarrow (I \land R))</math> ([[Premise]]: If a person is excused from flying (E) because of mental illness, that must be because he is both insane (I), and requests an evaluation (R));
# <math>(I \rightarrow \neg R)</math> ([[Premise]]: If a person is insane (I), he should not realize that he is, and would have no reason to request an evaluation)
# <math>(\neg I \or \neg R)</math> (2, [[Material implication (rule of inference)|Definition of implication]]: since an insane person would not request an evaluation, it follows that all people must either not be insane, or not request an evaluation)
# <math>(\neg (I \land R))</math> (3, [[De Morgan's laws|De Morgan]]: since all people must either not be insane, or not request an evaluation, it follows that no person is both insane and requests an evaluation)
# <math>(\neg E)</math> (4, 1, [[Modus Tollens]]: since a person may be excused from flying only if he is both insane and requests an evaluation, but no person ''can'' be both insane and request an evaluation, it follows that no person can be excused from flying for reasons of insanity)


Vortex cores are regions of low pressure. As a vortex core begins to form, the water in the air (in the region that is about to become the core) is in vapor phase, which means that the local temperature is above the local dew point. After the vortex core forms, the pressure inside it has decreased from the ambient value, and so the local dew point (<math>T_{c}</math>) has dropped from the ambient value. Thus, ''in and of itself'', a drop in pressure would tend to keep water in vapor form: The initial dew point was already below the ambient air temperature, and the formation of the vortex has made the local dew point even lower. However, as the vortex core forms, its pressure (and so its dew point) is not the only property that is dropping: The vortex-core temperature is dropping also, and in fact it can drop by much more than the dew point does, as we now explain.
Philosophy professor Laurence Goldstein argues that the 'airman's dilemma' is logically not even a condition that is true under no circumstances; it is a "vacuous biconditional" that is ultimately meaningless. Goldstein writes:<ref>Laurence Goldstein, "[http://philpapers.org/rec/GOLTBR The Barber, Russell's paradox, catch-22, God, contradiction and more: A defence of a Wittgensteinian conception of contradiction]"; in ''The law of non-contradiction: new philosophical essays'', ed. Graham Priest, Jc Beall & Bradley Armour-Garb; Oxford University Press, 2004.</ref>


Here we follow the discussion in Ref.<ref name="Green Fluid Vortices" /> To [[Orders of approximation|first approximation]], the formation of vortex cores is [[thermodynamics|thermodynamically]] an [[adiabatic process]], i.e., one with no exchange of heat. In such a process, the drop in pressure is accompanied by a drop in temperature, according to the equation
{{quotation|The catch is this: what looks like a statement of the conditions under which an airman can be excused flying dangerous missions reduces not to the statement


:<math>\frac{T_{\text{f}}}{T_{\text{i}}}=\left(\frac{p_{\text{f}}}{p_{\text{i}}}\right)^{\frac{\gamma -1}{\gamma}}.</math>
:(i) `An airman can be excused flying dangerous missions if and only if Cont’ (where `Cont’ is a contradiction) 
(which could be a mean way of disguising an unpleasant truth), but to the worthlessly empty announcement
:(ii) `An airman can be excused flying dangerous missions if and only if it is not the case that an airman can be excused flying dangerous missions’
If the catch were (i), that would not be so bad – an airman would at least be able to discover that under no circumstances could he avoid combat duty. But Catch-22 is worse – a welter of words that amounts to nothing; it is without content, it conveys no information at all.}}


Here <math>T_{\text{i}}</math> and <math>p_{\text{i}}</math> are the [[Thermodynamic temperature|absolute temperature]] and pressure at the beginning of the process (here equal to the ambient air temperature and pressure), <math>T_{\text{f}}</math> and <math>p_{\text{f}}</math> are the absolute temperature and pressure in the vortex core (which is the end result of the process), and the constant <math>\gamma</math> is about 7/5&nbsp;=&nbsp;1.4 for air (see [[Adiabatic process#Ideal gas (reversible case only)|here]]).
== See also ==
 
{{portal|Novels}}
Thus, even though the local dew point inside the vortex cores is even lower than in the ambient air, the water vapor may nevertheless condense — if the formation of the vortex brings the local temperature below the new local dew point. Let's verify that this can indeed happen under realistic conditions.
* [[Begging the question]]
 
* [[Cornelian dilemma]]  
For a typical transport aircraft landing at an airport, these conditions are as follows: We may take <math>T_{\text{i}}</math> and <math>p_{\text{i}}</math> to have values corresponding to the so-called [[standard conditions]], i.e., <math>p_{\text{i}}</math>&nbsp;=&nbsp;1&nbsp;[[Atmosphere (unit)|atm]]&nbsp;=&nbsp;1013.25&nbsp;[[Bar (unit)|mb]]&nbsp;=&nbsp;101<math>\,</math>325&nbsp;[[Pascal (unit)|Pa]] and <math>T_{\text{i}}</math>&nbsp;=&nbsp;293.15&nbsp;[[Kelvin (unit)|K]] (which is 20&nbsp;°C&nbsp;=&nbsp;68&nbsp;°F). We will take the [[relative humidity]] to be a [[dew point#Human reaction to high dew points|comfortable]] 35% (dew point of 4.1&nbsp;°C&nbsp;=&nbsp;39.4&nbsp;°F). This corresponds to a [[partial pressure]] of water vapor of 820&nbsp;Pa&nbsp;=&nbsp;8.2&nbsp;mb. We will assume that in a vortex core, the pressure (<math>p_{\text{f}}</math>) drops to about 80% of the ambient pressure, i.e., to about 80&nbsp;000&nbsp;Pa.<ref name="Green Fluid Vortices" />
* [[Deadlock]]
* [[Double bind]]
* [[False dilemma]]
* [[Ironic process theory]]
* [[No-win situation]]
* [[List of paradoxes]]
* [[Mu_(negative)#.22Unasking.22_the_question|Mu]]  
* [[Pyrrhic victory]]
* [[Social trap]]
* [[Vicious circle]]


Let's <!--"Let us" does not mean "let's."-->first determine the temperature in the vortex core. It is given by the equation above as <math>T_{\text{f}}=\left(\frac{\scriptstyle 80\,000}{\scriptstyle 101\,325}\right)^{\scriptscriptstyle 0.4/1.4}\,T_{\text{i}}= 0.935\,\times\,293.15=274\;\text{K},</math> or 0.86&nbsp;°C&nbsp;=&nbsp;33.5&nbsp;°F.
===Related stories and logic problems===
* [[Hobson's choice]] – Choice between taking what is offered and taking nothing; named after James Hobson, owner of a livery stable who required his customers to take the horse nearest the door
* [[Kobayashi Maru]] – A scenario involving a choice presented to a cadet in ''[[Star Trek]]'' where they either violate military regulations concerning the rendering of aid to a freighter crippled by a mine and in imminent threat of destruction, or violate the terms of a peace treaty by crossing into enemy territory (where the freighter lies in distress), risking one's company and crew to attempt to save the crippled freighter, and committing an act of war in the process of violating that treaty
* [[The Lady, or the Tiger?]] – A short story involving a princess who must make a decision in a no-win situation
* [[Morton's Fork]]
* [[Zugzwang]]


Next, we determine the dew point in the vortex core. The partial pressure of water in the vortex core drops in proportion to the drop in the total pressure (i.e., by the same percentage), to about 650&nbsp;Pa&nbsp;=&nbsp;6.5&nbsp;mb. According to a dew point calculator at [http://antoine.frostburg.edu/chem/senese/javascript/water-properties.html this site] (as an alternative, one may use the [[Antoine equation]] to obtain an approximate value), that partial pressure results in the local dew point of about 0.86&nbsp;°C; in other words, the new local dew point is about equal to the new local temperature.
== References ==
 
Therefore, the case we have been considering is a marginal case; if the relative humidity of the ambient air were even a bit higher (with the total pressure and temperature remaining as above), then the local dew point inside the vortices would rise, while the local temperature would remain the same as what we have just found. Thus, the local temperature would now be ''lower'' than the local dew point, and so the water vapor inside the vortices would indeed condense. Under right conditions, the local temperature in vortex cores may drop below the local [[freezing point]], in which case ice particles will form inside the vortex cores.
 
We have just seen that the water-vapor condensation mechanism in wingtip vortices is driven by local changes in air pressure and temperature. This is to be contrasted to what happens in another well-known case of water condensation related to airplanes: the [[contrail]]s from airplane engine exhausts. In the case of contrails, the local air pressure and temperature do not change significantly; what matters instead is that the exhaust contains both water vapor (which increases the local water-vapor [[concentration]] and so its partial pressure, resulting in elevated dew point and freezing point) as well as [[aerosol]]s (which provide [[Nucleation|nucleation centers]] for the [[Condensation (aerosol dynamics)|condensation]] and freezing).<ref>[http://asd-www.larc.nasa.gov/GLOBE/science.html NASA, Contrail Science]{{dead link|date=May 2014}}</ref>
 
== Formation flight ==
[[File:CanadianGeeseFlyingInVFormation.jpg|thumb|[[Canada goose|Canada geese]] in [[V formation]] make use of each bird's wingtip vortices]]
 
Migratory birds take advantage of each other's wingtip vortices by flying in a [[V formation]] so that all but the leader are flying in the [[downwash|upwash]] from the wing of the bird ahead. This upwash makes it easier for the bird to support its own weight, reducing fatigue on migration flights.<ref>{{cite conference |author=Thien, H.P. |author2=Moelyadi, M.A |author3=Muhammad, H.  |url=http://arxiv.org/abs/0804.3879 |title=Effects of Leader’s Position and Shape on Aerodynamic Performances of V Flight Formation, Paper No. ICIUS2007-A008 |booktitle=Proceedings of the International Conference on Intelligent Unmanned System (ICIUS 2007) | pages=1–7| date=October 24–25, 2007 |location=Bali, Indonesia |publisher=Aeronautics and Astronautics Department Bandung Institute of Technology (via Arxiv.org) |accessdate=29 May 2014}} <br/>([http://arxiv.org/pdf/0804.3879v1 Download paper]. {{PDF|336 Kb}})</ref>
 
== Hazards ==
[[Image:Airplane vortex edit.jpg|thumb|right|A [[NASA]] study on wingtip vortices produced illustrating the size of the vortices produced.]]
 
Wingtip vortices can pose a hazard to aircraft, especially during the [[landing]] and [[takeoff]] phases of flight. The intensity or strength of the vortex is a function of aircraft size, speed, and configuration (flap setting, etc.). The strongest vortices are produced by heavy aircraft, flying slowly, {{Citation needed span|text=with [[Flap (aircraft)|wing flaps]] and landing gear retracted ("heavy, slow, and clean")|date=July 2012}}.  Large [[jet aircraft]] can generate vortices that can persist for many minutes, drifting with the wind.
 
The hazardous aspects of wingtip vortices are most often discussed in the context of [[wake turbulence]].  If a light aircraft is immediately preceded by a heavy aircraft, wake turbulence from the heavy aircraft can roll the light aircraft faster than can be resisted by use of ailerons. At low altitudes, in particular during takeoff and landing, this can lead to an upset from which recovery is not possible.  [[Air traffic controller]]s attempt to ensure an adequate separation between departing and arriving aircraft by issuing wake turbulence warnings to pilots.
 
== Gallery ==
<gallery>
Image:EA-6B Prowler from VAQ-138.jpg|An [[EA-6 Prowler]] with condensation in the cores of its wingtip vortices and also on the top of its wings.
Image:Wingtip condensation.jpg|The core of the vortex trailing from the tip of the [[Flap (aircraft)|flap]] of a commercial airplane with landing flap extended.
Image:Cessna 182 model-wingtip-vortex.jpg|Wingtip vortices from a Cessna 182 [[wind tunnel]] model.
Image:C17-Vortex.JPG|Wingtip vortices shown in [[Flare (countermeasure)|flare]] smoke left behind a [[C-17 Globemaster III]].  Also known as smoke angels.
file:DN-SD-06-03008.JPG|The [[MV-22 Osprey]] [[tiltrotor]] has a high [[disk loading]], producing visible blade tip vorticies.
File:Euler tip vortex.png|Euler computation of a steady tip vortex. Contour colours and isosurface reveal vorticity.
File:Model in Vortex Facility - GPN-2000-001288.jpg|A [[Boeing 747]] model has just passed through a stationary sheet of smoke, which is showing its trailing vortices, at the Vortex Facility at the [[Langley Research Center]].
</gallery>
 
== See also ==
* [[Aspect ratio (wing)]]
* [[Contrail]]
* [[Helmholtz's theorems]]
* [[Horseshoe vortex]]
* [[Lift-induced drag]]
* [[V formation]]
* [[Vortex]]
* [[Wake turbulence]]


==References==
{{reflist
*Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London ISBN 0-273-01120-0
| refs =


===Notes===
<ref name="Heller1999">
{{reflist}}
{{cite book
| last = Heller
| first = Joseph
| authorlink = Joseph Heller
| title = Catch-22: A Novel
| page = 52
| publisher = Simon and Schuster
| year = 1999
| isbn = 978-0-684-86513-3
| url = http://books.google.com/books?id=Xfze51E7TEoC&lpg=PP1&dq=isbn%3A9780684865133&pg=PA52
| accessdate = 2011-01-09
}}
</ref>


==External links==
<ref name="Aldridge1986">
{{Commons|Wingtip vortices}}
{{cite news
*Video from [[NASA]]'s [[Dryden Flight Research Center]] tests on wingtip vortices:
| last = Aldridge
**[[C-5 Galaxy]]: [http://www1.dfrc.nasa.gov/Gallery/Movie/C-5A/HTML/EM-0085-01.html]
| first = John W.
**[[Lockheed L-1011]]: [http://www1.dfrc.nasa.gov/Gallery/Movie/L-1011/index.html]
| authorlink = John W. Aldridge
*[http://www.ll.mit.edu/AviationWeather/WW-11077_WindPrediction.pdf Wind prediction for analysis of vortex drift]
| title = The Loony Horror of it All&nbsp;– 'Catch-22' Turns 25
*[http://antwrp.gsfc.nasa.gov/apod/ap060822.html Flares released by an air force jet form a "smoke angel"]
| newspaper = The New York Times
*[http://www.youtube.com/watch?v=PpUftG_mxg8 Wingtip Vortices during a landing - Video at Youtube]
| date = 1986-10-26
| page = Section 7, Page 3, Column 1
| url = http://www.nytimes.com/books/98/02/15/home/heller-loony.html
| accessdate = 2011-01-09
}}
</ref>


{{Aviation lists}}
}}


{{DEFAULTSORT:Wingtip Vortices}}
{{DEFAULTSORT:Catch-22 (Logic)}}
[[Category:Aviation risks]]
[[Category:English idioms]]
[[Category:Aerodynamics]]
[[Category:Paradoxes]]
[[Category:Vortices]]
[[Category:Catch-22]]
[[Category:Aircraft wing design]]
[[Category:Metaphors referring to war and violence]]
[[Category:Dilemmas]]


[[ja:ウェーク・タービュランス]]
[[ru:Уловка 22]]
[[sv:Moment 22]]

Revision as of 09:10, 13 August 2014

A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules.[1][2] Catch-22s often result from rules, regulations, or procedures that an individual is subject to but has no control over. One connotation of the term is that the creators of the "Catch-22" have created arbitrary rules in order to justify and conceal their own abuse of power.

Origin and meaning

Joseph Heller coined the term in his 1961 novel Catch-22, which describes absurd bureaucratic constraints on soldiers in World War II. The term is introduced by the character Doc Daneeka, an army psychiatrist who invokes "Catch 22" to explain why any pilot requesting mental evaluation for insanity—hoping to be found not sane enough to fly and thereby escape dangerous missions—demonstrates his own sanity in making the request and thus cannot be declared insane.[3] 36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

Different formulations of "Catch-22" appear throughout the novel. The term is applied to various loopholes and quirks of the military system, always with the implication that rules are inaccessible to and slanted against those lower in the hierarchy. In chapter 6, Yossarian is told that Catch-22 requires him to do anything his commanding officer tells him to do, regardless of whether these orders contradict orders from the officer's superiors.[4]

In a final episode, Catch-22 is described to Yossarian by an old woman recounting an act of violence by soldiers:[5][6]

36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

According to literature professor Ian Gregson, the old woman's narrative defines "Catch-22" more directly as the "brutal operation of power", stripping away the "bogus sophistication" of the earlier scenarios.[7]

Other appearances in the novel

Besides referring to an unsolvable logical dilemma, Catch-22 is invoked to explain or justify the military bureaucracy. For example, in the first chapter it requires Yossarian to sign his name to letters that he censors while he is confined to a hospital bed. One clause mentioned in chapter 10 closes a loophole in promotions, which one private had been exploiting to reattain the attractive rank of Private First Class after any promotion. Through courts-martial for going AWOL, he would be busted in rank back to private, but Catch-22 limited the number of times he could do this before being sent to the stockade.

At another point in the book, a prostitute explains to Yossarian that she cannot marry him because he is crazy, and she will never marry a crazy man. She considers any man crazy who would marry a woman who is not a virgin. This closed logic loop clearly illustrated Catch-22 because by her logic, all men who refuse to marry her are sane and thus she would consider marriage; but as soon as a man agrees to marry her, he becomes crazy for wanting to marry a non-virgin, and is instantly rejected.

At one point, Captain Black attempts to pressure Milo into depriving Major Major of food as a consequence of not signing a loyalty oath that Major Major was never given an opportunity to sign in the first place. Captain Black asks Milo, "You're not against Catch-22, are you?"

In chapter 40, Catch-22 forces Colonels Korn and Cathcart to promote Yossarian to Major and ground him rather than simply sending him home. They fear that if they do not, others will refuse to fly, just as Yossarian did.

Significance of the number 22

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Heller originally wanted to call the phrase, and hence the book, by other numbers, but he and his publishers eventually settled on 22. The number has no particular significance; it was chosen more or less for euphony. The title was originally Catch-18, but Heller changed it after the popular Mila 18 was published a short time beforehand.[8][9]

Usage

The term "catch-22" has filtered into common usage in the English language.[2] In a 1975 interview, Heller said the term would not translate well into other languages.[9]

James E. Combs and Dan D. Nimmo suggest that the idea of a "catch-22" has gained popular currency because so many people in modern society are exposed to frustrating bureaucratic logic. They write:

Everyone, then, who deals with organizations understands the bureaucratic logic of Catch-22. In high school or college, for example, students can participate in student government, a form of self-government and democracy that allows them to decide whatever they want, just so long as the principal or dean of students approves. This bogus democracy that can be overruled by arbitrary fiat is perhaps a citizen's first encounter with organizations that may profess 'open' and libertarian values, but in fact are closed and hierarchical systems. Catch-22 is an organizational assumption, an unwritten law of informal power that excepts the organization from responsibility and accountability, and puts the individual in the absurd position of being excepted for the convenience or unknown purposes of the organization. [6]

Along with George Orwell's "doublethink", "Catch-22" has become one of the best-recognized ways to describe the predicament of being trapped by contradictory rules.[10]

Logic

The archetypal catch-22, as formulated by Heller, involves the case of John Yossarian, a U.S. Army Air Forces bombardier, who wishes to be grounded from combat flight. This will only happen if he is evaluated by the squadron's flight surgeon and found "unfit to fly". "Unfit" would be any pilot who is willing to fly such dangerous missions, as one would have to be mad to volunteer for possible death. However, to be evaluated, he must request the evaluation, an act that is considered sufficient proof for being declared sane. These conditions make it impossible to be declared "unfit".

The "Catch-22" is that "anyone who wants to get out of combat duty isn't really crazy".[11] Hence, pilots who request a mental fitness evaluation are sane, and therefore must fly in combat. At the same time, if an evaluation is not requested by the pilot, he will never receive one and thus can never be found insane, meaning he must also fly in combat.

Therefore, Catch-22 ensures that no pilot can ever be grounded for being insane even if he is.

A logical formulation of this situation is:

  1. (Premise: If a person is excused from flying (E) because of mental illness, that must be because he is both insane (I), and requests an evaluation (R));
  2. (Premise: If a person is insane (I), he should not realize that he is, and would have no reason to request an evaluation)
  3. (2, Definition of implication: since an insane person would not request an evaluation, it follows that all people must either not be insane, or not request an evaluation)
  4. (3, De Morgan: since all people must either not be insane, or not request an evaluation, it follows that no person is both insane and requests an evaluation)
  5. (4, 1, Modus Tollens: since a person may be excused from flying only if he is both insane and requests an evaluation, but no person can be both insane and request an evaluation, it follows that no person can be excused from flying for reasons of insanity)

Philosophy professor Laurence Goldstein argues that the 'airman's dilemma' is logically not even a condition that is true under no circumstances; it is a "vacuous biconditional" that is ultimately meaningless. Goldstein writes:[12]

36 year-old Diving Instructor (Open water ) Vancamp from Kuujjuaq, spends time with pursuits for instance gardening, public listed property developers in singapore developers in singapore and cigar smoking. Of late took some time to go China Danxia.

See also

Sportspersons Hyslop from Nicolet, usually spends time with pastimes for example martial arts, property developers condominium in singapore singapore and hot rods. Maintains a trip site and has lots to write about after touring Gulf of Porto: Calanche of Piana.

Related stories and logic problems

  • Hobson's choice – Choice between taking what is offered and taking nothing; named after James Hobson, owner of a livery stable who required his customers to take the horse nearest the door
  • Kobayashi Maru – A scenario involving a choice presented to a cadet in Star Trek where they either violate military regulations concerning the rendering of aid to a freighter crippled by a mine and in imminent threat of destruction, or violate the terms of a peace treaty by crossing into enemy territory (where the freighter lies in distress), risking one's company and crew to attempt to save the crippled freighter, and committing an act of war in the process of violating that treaty
  • The Lady, or the Tiger? – A short story involving a princess who must make a decision in a no-win situation
  • Morton's Fork
  • Zugzwang

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

ru:Уловка 22 sv:Moment 22

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  2. ↑ 2.0 2.1 "Catch 22", Oxford Advanced Learners' Dictionary, accessed 16 August 2013.
  3. ↑ Scriptures for a Generation: What We Were Reading in the '60s - Page 162 Philip D. Beidler - 1995 "It is Catch-22: Doc Daneeka explains how anybody who is crazy has a right to ask to be removed from combat status but how anybody who asks is"
  4. ↑ Margot A. Henriksen, Dr. Strangelove's America: Society and Culture in the Atomic Age; University of California Press, 1997; ISBN 0-520-08310-5; p. 250.
  5. ↑ "Joseph Heller", Gale Encyclopedia of Biography, accessed via Answers.com, 16 August 2013.
  6. ↑ 6.0 6.1 James E. Combs & Dan D. Nimmo, The Comedy of Democracy; Westport, CT: Praeger (Greenwood Publishing Group), 1996; ISBN 0-275-94979-6; p. 152.
  7. ↑ Ian Gregson, Character and Satire in Post War Fiction; London: Continuum, 2006; ISBN 9781441130006; p. 38.
  8. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Aldridge1986
  9. ↑ 9.0 9.1 "A classic by any other name", The Telegraph, 18 November 2007.
  10. ↑ Richard King, "22 Going on 50: Half a century later, the world is full of Catch-22s"; The Smart Set, 20 July 2011.
  11. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Heller1999
  12. ↑ Laurence Goldstein, "The Barber, Russell's paradox, catch-22, God, contradiction and more: A defence of a Wittgensteinian conception of contradiction"; in The law of non-contradiction: new philosophical essays, ed. Graham Priest, Jc Beall & Bradley Armour-Garb; Oxford University Press, 2004.
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