Gliding flight

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Gliding flight is heavier-than-air flight without the use of thrust; the term volplaning also refers to this mode of flight in animals. [1] It is employed by gliding animals and by aircraft such as gliders. This mode of flight involves flying a significant distance horizontally compared to its descent and therefore can be distinguished from a mostly straight downward descent like a round parachute.

Contents

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 wings on aircraft or birds, or the gliding membrane of a gliding possum. However, gliding can be achieved with a flat (uncambered) wing, as with a simple paper plane, [2] or even with card-throwing. However, some aircraft with lifting bodies and animals such as the flying snake can achieve gliding flight without any wings by creating a flattened surface underneath.

Aircraft ("gliders")

Most winged aircraft can glide to some extent, but there are several types of aircraft designed to glide:

The main human application is currently recreational, though during the Second World War military gliders were used for carrying troops and equipment into battle. The types of aircraft that are used for sport and recreation are classified as gliders (sailplanes), hang gliders and paragliders. 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 gliders with fixed wings are also soared by enthusiasts.

In addition to motor gliders, 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:

Aircraft which are not designed for glide may forced to perform gliding flight in an emergency, such as all engine failure or fuel exhaustion. See list of airline flights that required gliding flight. Gliding in a helicopter is called autorotation.

Gliding animals

Birds

A number of animals have 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:

Like recreational aircraft, birds can alternate periods of gliding with periods of soaring in rising air, and so spend a considerable time airborne with a minimal expenditure of energy. The great frigatebird in particular is capable of continuous flights up to several weeks. [3]

Mammals

Patagia on a flying squirrel Patagium-flying squirrel-psf.png
Patagia on a flying squirrel

To assist gliding, some mammals have evolved a structure called the patagium. This is a membranous structure found stretched between a range of body parts. It is most highly developed in bats. For similar reasons to birds, bats can glide efficiently. In bats, the skin forming the surface of the wing is an extension of the skin of the abdomen that runs to the tip of each digit, uniting the forelimb with the body. The patagium of a bat has four distinct parts:

  1. Propatagium: the patagium present from the neck to the first digit
  2. Dactylopatagium: the portion found within the digits
  3. Plagiopatagium: the portion found between the last digit and the hindlimbs
  4. Uropatagium: the posterior portion of the body between the two hindlimbs

Other mammals such as gliding possums and flying squirrels also glide using a patagium, but with much poorer efficiency than bats. They cannot gain height. The animal launches itself from a tree, spreading its limbs to expose the gliding membranes, usually to get from tree to tree in rainforests as an efficient means of both locating food and evading predators. This form of arboreal locomotion, is common in tropical regions such as Borneo and Australia, where the trees are tall and widely spaced.

In flying squirrels, the patagium stretches from the fore- to the hind-limbs along the length of each side of the torso. In the sugar glider, the patagia extend between the fifth finger of each hand to the first toe of each foot. This creates an aerofoil enabling them to glide 50 metres or more. [4] This gliding flight is regulated by changing the curvature of the membrane or moving the legs and tail. [5]

Fish, reptiles, amphibians and other gliding animals

In addition to mammals and birds, other animals notably flying fish, flying snakes, flying frogs and flying squid also glide.

Flying fish taking off Pink-wing flying fish.jpg
Flying fish taking off

The flights of flying fish are typically around 50 meters (160 ft), [6] though they can use updrafts at the leading edge of waves to cover distances of up to 400 m (1,300 ft). [6] [7] To glide upward out of the water, a flying fish moves its tail up to 70 times per second. [8] It then spreads its pectoral fins and tilts them slightly upward to provide lift. [9] At the end of a glide, it folds its pectoral fins to re-enter the sea, or drops its tail into the water to push against the water to lift itself for another glide, possibly changing direction. [8] [9] The curved profile of the "wing" is comparable to the aerodynamic shape of a bird wing. [10] The fish is able to increase its time in the air by flying straight into or at an angle to the direction of updrafts created by a combination of air and ocean currents. [8] [9]

Snakes of the genus Chrysopelea are also known by the common name "flying snake". Before launching from a branch, the snake makes a J-shape bend. After thrusting its body up and away from the tree, it sucks in its abdomen and flaring out its ribs to turn its body into a "pseudo concave wing", [11] all the while making a continual serpentine motion of lateral undulation [12] parallel to the ground [13] to stabilise its direction in mid-air in order to land safely. [14] Flying snakes are able to glide better than flying squirrels and other gliding animals, despite the lack of limbs, wings, or any other wing-like projections, gliding through the forest and jungle it inhabits with the distance being as great as 100 m. [13] [15] Their destination is mostly predicted by ballistics; however, they can exercise some in-flight attitude control by "slithering" in the air. [16]

Flying lizards of the genus Draco are capable of gliding flight via membranes that may be extended to create wings (patagia), formed by an enlarged set of ribs. [17]

Gliding flight has evolved independently among 3,400 species of frogs [18] from both New World (Hylidae) and Old World (Rhacophoridae) families. [19] This parallel evolution is seen as an adaptation to their life in trees, high above the ground. Characteristics of the Old World species include "enlarged hands and feet, full webbing between all fingers and toes, lateral skin flaps on the arms and legs

Forces

Forces on a gliding animal or aircraft in flight GliderForces.gif
Forces on a gliding animal or aircraft in flight

Three principal forces act on aircraft and animals when gliding: [20]

As the aircraft or animal descends, the air moving over the wings generates 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 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.

Lift to drag ratio

Drag vs Speed. L/DMAX occurs at minimum Total Drag (e.g. Parasite plus Induced) DragvsSpeed.jpg
Drag vs Speed. L/DMAX occurs at minimum Total Drag (e.g. Parasite plus Induced)
Coefficients of Drag and Lift vs Angle of Attack. Stall speed corresponds to the Angle of Attack at the Maximum Coefficient of Lift Coefficients of Drag and Lift vs AOA.jpg
Coefficients of Drag and Lift vs Angle of Attack. Stall speed corresponds to the Angle of Attack at the Maximum Coefficient of Lift

The lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the 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's needed lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy and climb performance.

The effect of airspeed on the rate of descent can be depicted by a 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 'U' is at minimum drag.

As lift and drag are both proportional to the coefficient of Lift and Drag respectively multiplied by the same factor (1/2 ρair v2S), 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.

Drag

Induced drag is caused by the generation of lift by the wing. Lift generated by a wing is perpendicular to the relative wind, 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 (parallel with the relative wind) 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.

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's U shape. Profile drag is lowered primarily by reducing cross section and streamlining.

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.

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 are also important.

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.

Glide ratio

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 glide ratio. 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's glide ratio varies with airspeed, but there is a maximum value which is frequently quoted. Glide ratio usually varies little with vehicle loading; a heavier vehicle glides faster, but nearly maintains its glide ratio. [21]

Glide ratio.gif

Glide ratio (or "finesse") is the cotangent of the downward angle, the glide angle (γ). Alternatively it is also the forward speed divided by sink speed (unpowered aircraft):

Glide number (ε) is the reciprocal of glide ratio but sometime it is confused.

Examples

Flight articleScenario L/D ratio/
glide ratio
Eta (glider) Gliding70 [22]
Great frigatebird Soaring over the ocean15–22 at typical speeds [23]
Hang glider Gliding15
Air Canada Flight 143 (Gimli Glider) Boeing 767–200 when all engines failed due to fuel exhaustion 12~
British Airways Flight 9 Boeing 747-200B when all engines failed due to volcanic ash 15~
Paraglider High performance model11
Helicopter in autorotation4
Powered parachute with a rectangular or elliptical parachute3.6/5.6
Space Shuttle unpowered approach from space after re-entry4.5 [24]
Wingsuit while gliding3
Hypersonic Technology Vehicle 2 Equilibrium hypersonic gliding estimate [25] 2.6
Northern flying squirrel Gliding1.98
Sugar glider (possum)Gliding1.82 [26]
Space Shuttle Supersonic2 (at Mach 2.5) [24]
Space Shuttle Hypersonic1.8 (at Mach 5), 1 (over Mach 9) [24]
Apollo CM Transonic0.50 (at Mach 1.13) [27]
Apollo CM Reentry and hypersonic0.368 avg (prior to 1st peak g), 0.41 (at Mach 6) [27]

Importance of the glide ratio in gliding flight

Polar curve showing glide angle for the best glide speed (best L/D). It is the flattest possible glide angle through calm air, which will maximize the distance flown. This airspeed (vertical line) corresponds to the tangent point of a line starting from the origin of the graph. A glider flying faster or slower than this airspeed will cover less distance before landing. Polar Curve 2.png
Polar curve showing glide angle for the best glide speed (best L/D). It is the flattest possible glide angle through calm air, which will maximize the distance flown. This airspeed (vertical line) corresponds to the tangent point of a line starting from the origin of the graph. A glider flying faster or slower than this airspeed will cover less distance before landing.

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).

Pilots sometimes fly at the aircraft's best L/D by precisely controlling airspeed and smoothly operating the controls to reduce drag. However the strength of the likely next lift, minimising the time spent in strongly sinking air and the strength of the wind also affects the optimal speed to fly. Pilots fly faster to get quickly through sinking air, and when heading into wind to optimise the glide angle relative to the ground. To achieve higher speed across country, gliders (sailplanes) are often loaded with water ballast to increase the airspeed and so reach the next area of lift sooner. This has little effect on the glide angle since the increases in the rate of sink and in the airspeed remain in proportion and thus the heavier aircraft achieves optimal L/D at a higher airspeed. If the areas of lift are strong on the day, the benefits of ballast outweigh the slower rate of climb.

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 the centre of the 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 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. (The Boeing 767 in the Gimli Glider incident achieved a glide ratio of only 12:1).

The loss of height can be measured at several speeds and plotted on a "polar curve" 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).

Soaring

Soaring animals and aircraft may alternate glides with periods of soaring in rising air. Five principal types of lift are used: [30] thermals, ridge lift, lee waves, 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. [31]

Examples of soaring flight by birds are the use of:

For humans, soaring is the basis for three air sports: gliding, hang gliding and paragliding.

See also

Related Research Articles

<span class="mw-page-title-main">Hang gliding</span> Unpowered glider air sport

Hang gliding is an air sport or recreational activity in which a pilot flies a light, non-motorised, heavier-than-air aircraft called a hang glider. Most modern hang gliders are made of an aluminium alloy or composite frame covered with synthetic sailcloth to form a wing. Typically the pilot is in a harness suspended from the airframe, and controls the aircraft by shifting body weight in opposition to a control frame.

<span class="mw-page-title-main">Unpowered aircraft</span> Aerial vehicle capable of sustaining flight without onboard propulsion

Unpowered aircraft can remain airborne for a significant period of time without onboard propulsion. They can be classified as gliders, lighter-than-air balloons and tethered kites. In the case of kites, lift is obtained by tethering to a fixed or moving object, perhaps another kite, to obtain a flow of wind over the lifting surfaces. In the case of balloons, lift is obtained through inherent buoyancy and the balloon may or may not be tethered. Free balloon flight has little directional control. Gliding aircraft include sailplanes, hang gliders, and paragliders that have full directional control in free flight.

<span class="mw-page-title-main">Fixed-wing aircraft</span> Heavier-than-air aircraft with fixed wings generating aerodynamic lift

A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using aerodynamic lift. Fixed-wing aircraft are distinct from rotary-wing aircraft, and ornithopters. The wings of a fixed-wing aircraft are not necessarily rigid; kites, hang gliders, variable-sweep wing aircraft, and airplanes that use wing morphing are all classified as fixed-wing aircraft.

<span class="mw-page-title-main">Paragliding</span> Soaring with a paraglider

Paragliding is the recreational and competitive adventure sport of flying paragliders: lightweight, free-flying, foot-launched glider aircraft with no rigid primary structure. The pilot sits in a harness or in a cocoon-like 'pod' suspended below a fabric wing. Wing shape is maintained by the suspension lines, the pressure of air entering vents in the front of the wing, and the aerodynamic forces of the air flowing over the outside.

<span class="mw-page-title-main">Flight</span> Process by which an object moves, through an atmosphere or beyond it

Flight or flying is the process by which an object moves through a space without contacting any planetary surface, either within an atmosphere or through the vacuum of outer space. This can be achieved by generating aerodynamic lift associated with gliding or propulsive thrust, aerostatically using buoyancy, or by ballistic movement.

<span class="mw-page-title-main">Variometer</span> Flight instrument which determines the aircrafts vertical velocity (rate of descent/climb)

In aviation, a variometer – also known as a rate of climb and descent indicator (RCDI), rate-of-climb indicator, vertical speed indicator (VSI), or vertical velocity indicator (VVI) – is one of the flight instruments in an aircraft used to inform the pilot of the rate of descent or climb. It can be calibrated in metres per second, feet per minute or knots, depending on country and type of aircraft. It is typically connected to the aircraft's external static pressure source.

<span class="mw-page-title-main">Lift-to-drag ratio</span> Measure of aerodynamic efficiency

In aerodynamics, the lift-to-drag ratio is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under given flight conditions. The L/D ratio for any given body will vary according to these flight conditions.

Aviation is the design, development, production, operation, and use of aircraft, especially heavier-than-air aircraft. Articles related to aviation include:

<span class="mw-page-title-main">Speed to fly</span>

Speed to fly is a principle used by soaring pilots when flying between sources of lift, usually thermals, ridge lift and wave. The aim is to maximize the average cross-country speed by optimizing the airspeed in both rising and sinking air. The optimal airspeed is independent of the wind speed, because the fastest average speed achievable through the airmass corresponds to the fastest achievable average groundspeed.

Dynamic soaring is a flying technique used to gain energy by repeatedly crossing the boundary between air masses of different velocity. Such zones of wind gradient are generally found close to obstacles and close to the surface, so the technique is mainly of use to birds and operators of radio-controlled gliders, but glider pilots are sometimes able to soar dynamically in meteorological wind shears at higher altitudes.

<span class="mw-page-title-main">Aériane Swift</span> Type of aircraft

The Aériane Swift is a lightweight (48 kg) foot-launched tailless sailplane whose rigid wings have a span of 40 feet. The Swift has been succeeded by the "Swift'Lite".

<span class="mw-page-title-main">Flying and gliding animals</span> Animals that have evolved aerial locomotion

A number of animals are capable of aerial locomotion, either by powered flight or by gliding. This trait has appeared by evolution many times, without any single common ancestor. Flight has evolved at least four times in separate animals: insects, pterosaurs, birds, and bats. Gliding has evolved on many more occasions. Usually the development is to aid canopy animals in getting from tree to tree, although there are other possibilities. Gliding, in particular, has evolved among rainforest animals, especially in the rainforests in Asia where the trees are tall and widely spaced. Several species of aquatic animals, and a few amphibians and reptiles have also evolved this gliding flight ability, typically as a means of evading predators.

<span class="mw-page-title-main">Glider (aircraft)</span> Aircraft designed for operation without an engine

A glider is a fixed-wing aircraft that is supported in flight by the dynamic reaction of the air against its lifting surfaces, and whose free flight does not depend on an engine. Most gliders do not have an engine, although motor-gliders have small engines for extending their flight when necessary by sustaining the altitude with some being powerful enough to take off by self-launch.

<span class="mw-page-title-main">Schweizer SGS 1-36 Sprite</span> Type of aircraft

The Schweizer SGS 1-36 Sprite is a United States, single-seat, mid-wing glider built by Schweizer Aircraft of Elmira, New York.

<span class="mw-page-title-main">Gliding</span> Recreational activity and competitive air sport

Gliding is a recreational activity and competitive air sport in which pilots fly unpowered aircraft known as gliders or sailplanes using naturally occurring currents of rising air in the atmosphere to remain airborne. The word soaring is also used for the sport.

<span class="mw-page-title-main">Glider (sailplane)</span> Type of aircraft used in the sport of gliding

A glider or sailplane is a type of glider aircraft used in the leisure activity and sport of gliding. This unpowered aircraft can use naturally occurring currents of rising air in the atmosphere to gain altitude. Sailplanes are aerodynamically streamlined and so can fly a significant distance forward for a small decrease in altitude.

<span class="mw-page-title-main">Hannover H 1 Vampyr</span> German single-seat glider, 1921

The Hannover H.1 Vampyr was a German glider designed by Georg Madelung for the 1921 Rhön gliding competition, which was held at the Wasserkuppe from 8 August to 25 August 1921. The Vampyr is believed to be the first heavier than air aircraft to use stressed skin. Several historical societies have argued that the aircraft is the precursor of all modern sailplanes.

Unpowered flight is the ability to stay airborne for a period of time without using any power source. There are several types of unpowered flight. Some have been exploited by nature, others by humankind, and some by both.

The drag curve or drag polar is the relationship between the drag on an aircraft and other variables, such as lift, the coefficient of lift, angle-of-attack or speed. It may be described by an equation or displayed as a graph. Drag may be expressed as actual drag or the coefficient of drag.

This is a glossary of acronyms, initialisms and terms used for gliding and soaring. This is a specialized subset of broader aviation, aerospace, and aeronautical terminology. Additional definitions can be found in the FAA Glider Flying Handbook.

References

  1. ↑ volplane. The Free Dictionary.
  2. ↑ Blackburn, Ken. "Paper Plane Aerodynamics". Ken Blackburn's Paper Airplanes. Archived from the original on 1 October 2012. Retrieved 8 October 2012. Section 4.3
  3. ↑ "Nonstop Flight: How The Frigatebird Can Soar For Weeks Without Stopping". NPR . Retrieved 2 July 2016.
  4. ↑ Strahan, the Australian Museum (1983). Ronald (ed.). Complete Book of Australian Mammals: The National Photographic Index of Australian Wildlife (1 ed.). Sydney: Angus & Robertson. ISBN   0207144540.
  5. ↑ "Sugar Glider Fun Facts". Drsfostersmith.com. Retrieved 22 June 2010.
  6. 1 2 Ross Piper (2007), Extraordinary Animals: An Encyclopedia of Curious and Unusual Animals, Greenwood Press.
  7. ↑ Flying Fish, Exocoetidae National Geographic. Retrieved 10 August 2014.
  8. 1 2 3 Kutschera, U. (2005). "Predator-driven macroevolution in flyingfishes inferred from behavioural studies: historical controversies and a hypothesis" (PDF). Annals of the History and Philosophy of Biology . 10: 59–77. Archived from the original (PDF) on 20 August 2007.
  9. 1 2 3 Fish, F. E. (1990). "Wing design and scaling of flying fish with regard to flight performance" (PDF). Journal of Zoology. 221 (3): 391–403. doi:10.1111/j.1469-7998.1990.tb04009.x. Archived from the original (PDF) on 20 October 2013.
  10. ↑ Fish, F. (1991). "On a fin and a prayer" (PDF). Scholars . 3 (1): 4–7. Archived from the original (PDF) on 2 November 2013.
  11. ↑ Garland, T Jr.; Losos, J.B. (1994). "10. Ecological morphology of locomotor performance in squamate reptiles". Ecological Morphology: Integrative Organismal Biology (PDF). Chicago: University of Chicago Press. pp. 240–302. Retrieved 14 July 2009.
  12. ↑ Jayne, B.C. (December 1986). "Kinematics of Terrestrial Snake Locomotion" (PDF). Copeia. 1986 (4): 915–927. doi:10.2307/1445288. JSTOR   1445288. Archived from the original (PDF) on 30 October 2006. Retrieved 15 July 2009.
  13. 1 2 Socha, J.J. (August 2002). "Kinematics – Gliding flight in the paradise tree snake" (PDF). Nature. 418 (6898): 603–604. Bibcode:2002Natur.418..603S. doi:10.1038/418603a. PMID   12167849. S2CID   4424131 . Retrieved 14 July 2009.[ dead link ]
  14. ↑ Wei, C. (May 2005). "Inside JEB – Snakes take flight". The Journal of Experimental Biology. 208 (10): i–ii. doi:10.1242/jeb.01644. S2CID   84133938.
  15. ↑ Ernst, C. H.; Zug, G. R. (1996). Snakes in Question: The Smithsonian Answer Book . Smithsonian Institution Press. pp.  14–15.
  16. ↑ "Researchers reveal secrets of snake flight". 12 May 2005. Retrieved 27 November 2007.
  17. ↑ "BBC Earth – Flying draco lizard" . Retrieved 5 October 2021.
  18. ↑ Emerson, S.B., & Koehl, M.A.R. (1990). "The interaction of behavioral and morphological change in the evolution of a novel locomotor type: 'Flying' frogs." Evolution, 44(8), 1931–1946.
  19. ↑ Emerson, S.B., Travis, J., & Koehl, M.A.R. (1990). "Functional complexes and additivity in performance: A test case with 'flying' frogs." Evolution, 44(8), 2153–2157.
  20. ↑ NASA: Three forces on a glider or gliding animal
  21. ↑ Glider Flying Handbook, FAA Publication 8083-13, Page 3-2
  22. ↑ Eta aircraft Archived 13 November 2017 at the Wayback Machine Eta aircraft performances plots – accessed 2004-04-11
  23. ↑ Flight performance of the largest volant bird
  24. 1 2 3 Space Shuttle Technical Conference pg 258
  25. ↑ Acton, James M. (2015). "Hypersonic Boost-Glide Weapons". Science & Global Security. 23 (3): 191–219. Bibcode:2015S&GS...23..191A. doi:10.1080/08929882.2015.1087242. S2CID   67827450.
  26. ↑ Jackson, Stephen M. (2000). "Glide angle in the genus Petaurus and a review of gliding in mammals". Mammal Review. 30 (1): 9–30. doi:10.1046/j.1365-2907.2000.00056.x. ISSN   1365-2907.
  27. 1 2 Hillje, Ernest R., "Entry Aerodynamics at Lunar Return Conditions Obtained from the Flight of Apollo 4 (AS-501)," NASA TN D-5399, (1969). p16
  28. ↑ Wander, Bob (2003). Glider Polars and Speed-To-Fly...Made Easy!. Minneapolis: Bob Wander's Soaring Books & Supplies. pp. 7–10.
  29. ↑ Glider Flying Handbook, FAA-H-8083-13. U.S. Department of Transportation, FAA. 2003. p. 5-6 to 5-9. ISBN   9780160514197.
  30. ↑ Welch, John (1999). Van Sickle's Modern Airmanship. City: McGraw-Hill Professional. pp. 856–858. ISBN   0-07-069633-0. There are four main kinds of lift which the soaring pilot may use....
  31. ↑ Reichmann, Helmut (2005). Streckensegelflug. Motorbuch Verlag. ISBN   3-613-02479-9.
  32. ↑ [Report of use of wave lift by birds by Netherlands Institute for Ecology]
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