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	<title>Monotonically normal space - Revision history</title>
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	<updated>2026-08-01T19:35:58Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<title>en&gt;ChrisGualtieri: Typo fixing, typos fixed: ,  → , using AWB</title>
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		<updated>2012-07-25T14:26:06Z</updated>

		<summary type="html">&lt;p&gt;&lt;a href=&quot;/w/index.php?title=WP:TSN&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;WP:TSN (page does not exist)&quot;&gt;Typo fixing&lt;/a&gt;, typos fixed: ,  → , using &lt;a href=&quot;/w/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{For|the sport of soaring in gliders (sailplanes)|Gliding}}&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Gliding flight&amp;#039;&amp;#039;&amp;#039; is heavier-than-air [[flight]] without the use of [[thrust]]; the term &amp;#039;&amp;#039;&amp;#039;volplaning&amp;#039;&amp;#039;&amp;#039; also refers to this mode of flight.&amp;lt;ref&amp;gt;[http://www.thefreedictionary.com/volplane volplane]. The Free Dictionary.&amp;lt;/ref&amp;gt;  It is employed by [[flying and gliding animals|gliding animal]]s and by aircraft such as [[glider (aircraft)|gliders]].&lt;br /&gt;
&lt;br /&gt;
Although the human application of gliding flight usually refers to aircraft designed for this purpose, most powered aircraft are capable of gliding without engine power. As with sustained flight, gliding generally requires the application of an [[airfoil]], such as the [[wing]]s on aircraft or birds, or the [[Patagium|gliding membrane]] on [[gliding possum]]. However, gliding can be achieved with a flat ([[Camber (aerodynamics)|uncambered]]) wing, as with a simple [[paper plane]],&amp;lt;ref&amp;gt;{{cite web|last=Blackburn|first=Ken|title=Paper Plane Aerodynamics|url=http://paperplane.org/paero.htm|publisher=Ken Blackburn&amp;#039;s Paper Airplanes|accessdate=8 October 2012|quote=Section 4.3}}&amp;lt;/ref&amp;gt; or even with [[card-throwing]].&lt;br /&gt;
 &lt;br /&gt;
==Instances of gliding flight==&lt;br /&gt;
===Aircraft (&amp;quot;gliders&amp;quot;)===&lt;br /&gt;
{{main|Glider aircraft}}&lt;br /&gt;
Most winged aircraft can glide to some extent, but there are several types of aircraft designed to glide:&lt;br /&gt;
*[[Glider (sailplane)|Glider]], also known as a sailplane&lt;br /&gt;
*[[Hang glider]] &lt;br /&gt;
*[[Paraglider]]&lt;br /&gt;
*[[Speed glider]]&lt;br /&gt;
*[[Ram-air parachute]]&lt;br /&gt;
*[[Rotor kite]], if untethered, known as a rotary glider, or gyroglider.&lt;br /&gt;
*[[Military glider]]&lt;br /&gt;
*[[Paper aeroplane]]&lt;br /&gt;
*[[Radio-controlled glider]]&lt;br /&gt;
*[[Rocket glider]]&lt;br /&gt;
&lt;br /&gt;
The main human application is currently recreational, though during the [[Second World War]] [[military glider]]s were used for carrying troops and equipment into battle. The types of aircraft that are used for sport and recreation are classified as [[glider (sailplane)|gliders (sailplanes)]], [[hang glider]]s and [[paraglider]]s. These two latter types are often foot-launched. The design of all three types enables them to repeatedly climb using rising air and then to glide before finding the next source of lift.  When done in gliders (sailplanes), the sport is known as [[gliding]] and sometimes as soaring. For foot-launched aircraft, it is known as [[hang gliding]] and [[paragliding]]. [[Radio-controlled glider]]s with fixed wings are also soared by enthusiasts. &lt;br /&gt;
&lt;br /&gt;
In addition to [[motor glider]]s, some powered aircraft are designed for routine glides during part of their flight; usually when landing after a period of a powered flight. These include:&lt;br /&gt;
*[[Experimental aircraft]] such as the [[North American X-15]], which glided back having used their fuel&lt;br /&gt;
*[[Spacecraft]] such as the [[Space Shuttle]]s, [[SpaceShipOne]] and the Russian [[Buran (spacecraft)|Buran]]&lt;br /&gt;
&lt;br /&gt;
Some aircraft are not primarily designed to glide except in an emergency, for example airliners that have run out of fuel.  See list [[List of airline flights that required gliding|List of airline flights that required gliding flight]].&lt;br /&gt;
&lt;br /&gt;
===Animals===&lt;br /&gt;
{{see|Flying and gliding animals|List of soaring birds}}&lt;br /&gt;
&lt;br /&gt;
A number of [[animal]]s have [[Convergent evolution|separately evolved]] gliding many times, without any single ancestor. Birds in particular use gliding flight to minimise their use of energy. Large birds are notably adept at gliding, including:&lt;br /&gt;
*[[Albatross]]&lt;br /&gt;
*[[Condor]]&lt;br /&gt;
*[[Vulture]]&lt;br /&gt;
*[[Eagle]]&lt;br /&gt;
*[[Stork]]&lt;br /&gt;
&lt;br /&gt;
Like recreational aircraft, they too can alternate periods of gliding with periods of soaring in [[lift (soaring)|rising air]], and so spend a considerable time airborne with a minimal expenditure of energy. For similar reasons to birds, [[bat]]s can glide efficiently. &lt;br /&gt;
&lt;br /&gt;
Other mammals such as [[gliding possum]]s and [[flying squirrel]]s also glide, but with much poorer efficiency than birds and cannot gain height. For these creatures, gliding has mainly evolved to get from tree to tree in [[rainforest]]s, most especially [[Borneo]], where the [[tree]]s are tall and widely spaced. This mode of flight involves flying a greater distance horizontally than vertically and is therefore can be distinguished from a simple descent like a parachute. Some reptiles, amphibians, [[flying squid]] and [[flying fish]] also glide.&lt;br /&gt;
&lt;br /&gt;
[[File:GliderForces.gif|thumb|right|Forces on a gliding animal or aircraft in flight]]&lt;br /&gt;
&lt;br /&gt;
==Forces==&lt;br /&gt;
Three principal forces act on aircraft and animals when gliding:&amp;lt;ref name=nasaforces&amp;gt;[http://www.grc.nasa.gov/WWW/K-12/airplane/glider.html NASA: Three forces on a glider or gliding animal]&amp;lt;/ref&amp;gt;&lt;br /&gt;
*weight – gravity acts in the downwards direction&lt;br /&gt;
*lift – acts perpendicularly to the [[Euclidean vector|vector]] representing airspeed&lt;br /&gt;
*drag – acts parallel to the vector representing the airspeed&lt;br /&gt;
&lt;br /&gt;
As the aircraft or animal descends, the air moving over the wings generates [[lift force|lift]]. The lift force acts slightly forward of vertical because it is created at right angles to the airflow which comes from slightly below as the glider descends, see [[angle of attack]]. This horizontal component of lift is enough to overcome [[Drag (physics)|drag]] and allows the glider to accelerate forward. Even though the weight causes the aircraft to descend, if the air is rising faster than the sink rate, there will be a gain of altitude.&lt;br /&gt;
&lt;br /&gt;
==Lift to drag ratio==&lt;br /&gt;
{{main|Lift to drag ratio}}&lt;br /&gt;
[[File:Polar Curve 2.jpg|thumb|right|Polar curve showing glide angle for best glide]]&lt;br /&gt;
The lift-to-drag ratio, or &amp;#039;&amp;#039;&amp;#039;L/D ratio&amp;#039;&amp;#039;&amp;#039;, is the amount of [[Lift (force)|lift]] generated by a [[wing]] or vehicle, divided by the [[drag (physics)|drag]] it creates by moving through the air. A higher or more favourable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft&amp;#039;s needed lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy and climb performance.&lt;br /&gt;
&lt;br /&gt;
The effect of [[airspeed]] on the rate of descent can be depicted by a [[polar curve (aviation)|polar curve]]. These curves show the airspeed where minimum sink can be achieved and the airspeed with the best L/D ratio. The curve is an inverted U-shape. As speeds reduce the amount of lift falls rapidly around the stalling speed. The peak of the &amp;#039;U&amp;#039; is at minimum drag.&lt;br /&gt;
&lt;br /&gt;
As lift and drag are both proportional to the coefficient or Lift and Drag respectively multiplied by the same factor (1/2mv&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;S), the L/D ratio can be simplified to  the Coefficient of lift divided by the coefficient of drag or Cl/Cd, and since both are proportional to the airspeed, the ratio of L/D or Cl/Cd is then typically plotted against angle of attack.&lt;br /&gt;
&lt;br /&gt;
==Drag==&lt;br /&gt;
&lt;br /&gt;
[[Induced drag]] is caused by the generation of lift by the wing. Lift generated by a wing is perpendicular to the wing, but since wings typically fly at some small [[angle of attack]], this means that a component of the force is directed to the rear. The rearward component of this force is seen as drag. At low speeds an aircraft has to generate lift with a higher angle of attack, thereby leading to greater induced drag. This term dominates the low-speed side of the drag graph, the left side of the U.&lt;br /&gt;
&lt;br /&gt;
[[Profile drag]] is caused by air hitting the wing, and other parts of the aircraft. This form of drag, also known as [[wind resistance]], varies with the square of speed (see [[drag equation]]). For this reason profile drag is more pronounced at higher speeds, forming the right side of the drag graph&amp;#039;s U shape. Profile drag is lowered primarily by reducing cross section and streamlining.&lt;br /&gt;
&lt;br /&gt;
[[File:Drag Curve 2.jpg|thumb|right|The drag curve]]&lt;br /&gt;
As lift increases steadily until the critical angle, it is normally the point where the combined drag is at its lowest, that the wing or aircraft is performing at its best L/D. &lt;br /&gt;
&lt;br /&gt;
Designers will typically select a wing design which produces an L/D peak at the chosen [[cruising speed]] for a powered fixed-wing aircraft, thereby maximizing economy. Like all things in [[aeronautical engineering]], the lift-to-drag ratio is not the only consideration for wing design. Performance at high [[angle of attack]] and a gentle [[Stall (flight)|stall]] are also important.&lt;br /&gt;
&lt;br /&gt;
Minimising drag is of particular interest in the design and operation of high performance [[glider (sailplane)]]s, the largest of which can have glide ratios approaching 60 to 1, though many others have a lower performance; 25:1 being considered adequate for training use.&lt;br /&gt;
&lt;br /&gt;
==Glide ratio==&lt;br /&gt;
When flown at a constant speed in still air a glider moves forwards a certain distance for a certain distance downwards. The ratio of the distance forwards to downwards is called the &amp;#039;&amp;#039;glide ratio&amp;#039;&amp;#039;. The glide ratio (E) is numerically equal to the [[Lift-to-drag ratio]] under these conditions; but is not necessarily equal during other manoeuvres, especially if speed is not constant. A glider&amp;#039;s glide ratio varies with airspeed, but there is a maximum value which is frequently quoted. Glide ratio usually varies little with vehicle loading however, a heavier vehicle glides faster, but maintains its glide ratio.&amp;lt;ref&amp;gt;&amp;#039;&amp;#039;Glider Flying Handbook&amp;#039;&amp;#039;, FAA Publication 8083-13, Page 3-2&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
[[File:Glide ratio.gif|300px|right]]&lt;br /&gt;
Glide ratio (or &amp;quot;finesse&amp;quot;) is the [[cotangent]] of the downward angle, the &amp;#039;&amp;#039;&amp;#039;glide angle&amp;#039;&amp;#039;&amp;#039; (γ).  Alternatively it is also the forward speed divided by sink speed (unpowered aircraft):  &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;{L \over D}={{\Delta s} \over {\Delta h}}={v_{\text{forward}} \over v_{\text{down}}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Glide number&amp;#039;&amp;#039;&amp;#039; (ε) is the reciprocal of glide ratio but sometime it&amp;#039;s confused.&lt;br /&gt;
&lt;br /&gt;
==Examples==&lt;br /&gt;
&lt;br /&gt;
{{Glide ratio examples}}&lt;br /&gt;
&lt;br /&gt;
==Importance of the glide ratio in gliding flight==&lt;br /&gt;
&lt;br /&gt;
Although the best glide ratio is important when measuring the performance of a gliding aircraft, its glide ratio at a range of speeds also determines its success (see article on [[gliding]]).&lt;br /&gt;
&lt;br /&gt;
Pilots sometimes fly at the aircraft&amp;#039;s best L/D by precisely controlling airspeed and smoothly operating the controls to reduce drag. However the strength of the likely next lift and the strength of the wind also affects the optimal [[speed to fly]]. To achieve higher speed across country, [[Glider (sailplane)|gliders (sailplanes)]] are often loaded with water [[Sailing ballast|ballast]] to increase the airspeed and so reach the next area of lift sooner. This has little effect on the glide angle but increases rate of sink (and airspeed in proportion) because the heavier aircraft achieves optimal L/D at a higher airspeed.&lt;br /&gt;
&lt;br /&gt;
If the air is rising faster than the rate of sink, the aircraft will climb. At lower speeds an aircraft may have a worse glide ratio but it will also have a lower rate of sink. A low airspeed also improves its ability to turn tightly in centre of the [[lift (soaring)|rising air]] where the rate of ascent is greatest. A sink rate of approximately 1.0 m/s is the most that a practical hang glider or paraglider could have before it would limit the occasions that a climb was possible to only when there was strongly rising air. Gliders (sailplanes) have minimum sink rates of between 0.4 and 0.6 m/s depending on the [[Glider Competition Classes|class]]. Aircraft such as airliners may have a better glide ratio than a hang glider, but would rarely be able to thermal because of their much higher forward speed and their much higher sink rate. (Note that the [[Boeing 767]] in the [[Gimli Glider]] incident achieved a glide ratio of only 12:1.)&lt;br /&gt;
&lt;br /&gt;
During landing, a high lift/drag ratio is desirable. Some aircraft therefore employ [[flap (aircraft)|flaps]], to increase their performance at lower speeds. Experiments with [[lifting bodies]] show that a lift/drag ratio below about 2 makes landing very difficult because of the high rate of descent.&lt;br /&gt;
&lt;br /&gt;
The loss of height can be measured at several speeds and plotted on a &amp;quot;[[polar curve (aviation)|polar curve]]&amp;quot; to calculate the best speed to fly in various conditions, such as when flying into wind or when in sinking air.   Other polar curves can be measured after loading the glider with water ballast.  As mass increases, the best glide ratio is achieved at higher speeds. (The glide ratio is not increased.)&lt;br /&gt;
&lt;br /&gt;
==Soaring==&lt;br /&gt;
{{main|Lift (soaring)}}&lt;br /&gt;
Soaring animals and aircraft may alternate glides with periods of soaring in [[lift (soaring)|rising air]]. Five principal types of lift are used:&amp;lt;ref name=Welch&amp;gt;{{cite book | last = Welch | first = John | title = Van Sickle&amp;#039;s Modern Airmanship | publisher = McGraw-Hill Professional | location = City | year = 1999 | pages = 856–858 | isbn = 0-07-069633-0 | quote = There are four main kinds of lift which the soaring pilot may use....}}&amp;lt;/ref&amp;gt; [[thermal]]s, [[ridge lift]], [[lee waves]], [[Convergence zone|convergences]] and [[dynamic soaring]]. Dynamic soaring is used predominately by birds, and some model aircraft, though it has also been achieved on rare occasions by piloted aircraft.&amp;lt;ref&amp;gt;&lt;br /&gt;
{{cite book |last= Reichmann |first= Helmut |title= Streckensegelflug |publisher= Motorbuch Verlag |year= 2005 |id = ISBN 3-613-02479-9 }}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Examples of soaring flight by birds are the use of:&lt;br /&gt;
*Thermals and convergences by [[bird of prey|raptor]]s such as [[vulture]]s&lt;br /&gt;
*Ridge lift by [[gull]]s near cliffs&lt;br /&gt;
*Wave lift by migrating birds&amp;lt;ref&amp;gt;[Report of use of wave lift by birds by Netherlands Institute for Ecology]&amp;lt;/ref&amp;gt; &lt;br /&gt;
*Dynamic effects near the surface of the sea by [[albatross]]es  &lt;br /&gt;
&lt;br /&gt;
For humans, soaring is the basis for three [[air sports]]: [[gliding]], [[hang gliding]] and [[paragliding]].&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
{{refbegin|3}}&lt;br /&gt;
*[[Approach slope]]&lt;br /&gt;
*[[Colditz Cock]] - a glider built to escape from [[Colditz]]&lt;br /&gt;
*[[Gimli Glider]] - a passenger jet aircraft that ran out of fuel&lt;br /&gt;
*[[Gliding]] (sport)&lt;br /&gt;
*[[Gliding competitions]]&lt;br /&gt;
*[[Gliding mammal]]&lt;br /&gt;
*[[Gravity drag]] [[rocket]]s can have an effective lift to drag ratio while maintaining altitude&lt;br /&gt;
*[[Gyroglider]]&lt;br /&gt;
*[[Hang Glider]]&lt;br /&gt;
*[[Inductrack]] [[Maglev (transport)|maglev]] has a higher lift/drag ratio than aircraft at sufficient speeds&lt;br /&gt;
*[[Military glider]]&lt;br /&gt;
*[[Paraglider]]&lt;br /&gt;
*[[Powered Hang Glider|Foot-Launched Powered Hang Glider]]&lt;br /&gt;
*[[Range (aircraft)]] range depends on the lift/drag ratio&lt;br /&gt;
*[[Sailplane]] - rigid wing soaring gliders&lt;br /&gt;
*[[Thrust specific fuel consumption|Specific fuel consumption]] the lift to drag determines the required thrust to maintain altitude (given the aircraft weight), and the SFC permits calculation of the fuel burn rate&lt;br /&gt;
*[[thrust to weight ratio]]&lt;br /&gt;
*[[Underwater gliders]]&lt;br /&gt;
{{refend}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Aircraft wing design]]&lt;br /&gt;
[[Category:Engineering ratios]]&lt;br /&gt;
[[Category:Wind power]]&lt;br /&gt;
[[Category:Gliding]]&lt;br /&gt;
[[Category:Unpowered flight]]&lt;br /&gt;
[[Category:Animal flight| ]]&lt;br /&gt;
[[Category:Gliding animals| ]]&lt;br /&gt;
&lt;br /&gt;
[[de:Gleitzahl]]&lt;br /&gt;
[[fr:Finesse (aérodynamique)]]&lt;br /&gt;
[[nl:Glijgetal]]&lt;br /&gt;
[[ru:Аэродинамическое качество]]&lt;/div&gt;</summary>
		<author><name>en&gt;ChrisGualtieri</name></author>
	</entry>
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