42:
73:
298:, discovered Tricomi's work in the process of applying the hodograph method to transonic flow near the end of World War II. He focused on the nonlinear thin-airfoil compressible flow equations, the same as what Tricomi derived, though his goal of using these equations to solve flow over an airfoil presented unique challenges. Guderley and Hideo Yoshihara, along with some input from Busemann, later used a singular solution of Tricomi's equations to analytically solve the behavior of transonic flow over a
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272:(3D flow paths) to contract enough around the object to minimize the disturbance, and thus the disturbance propagates. Aerodynamicists struggled during the earlier studies of transonic flow because the then-current theory implied that these disturbances– and thus drag– approached infinity as local Mach number approached 1, an obviously unrealistic result which could not be remedied using known methods.
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blades of helicopters and aircraft. This puts severe, unequal stresses on the rotor blade and may lead to accidents if it occurs. It is one of the limiting factors of the size of rotors and the forward speeds of helicopters (as this speed is added to the forward-sweeping side of the rotor, possibly
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of the plane wings, and one solution to prevent transonic waves was swept wings. Since the airflow would hit the wings at an angle, this would decrease the wing thickness and chord ratio. Airfoils wing shapes were designed flatter at the top to prevent shock waves and reduce the distance of airflow
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powered aircraft are engineered to operate at transonic air speeds. Transonic airspeeds see a rapid increase in drag from about Mach 0.8, and it is the fuel costs of the drag that typically limits the airspeed. Attempts to reduce wave drag can be seen on all high-speed aircraft. Most notable is the
184:
era in 1941. Ralph Virden, a test pilot, crashed in a fatal plane accident. He lost control of the plane when a shock wave caused by supersonic airflow developed over the wing, causing it to stall. Virden flew well below the speed of sound at Mach 0.675, which brought forth the idea of different
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designed "dive flaps" to help stabilize the plane when reaching transonic flight. This small flap on the underside of the plane slowed the plane to prevent shock waves, but this design only delayed finding a solution to aircraft flying at supersonic speed. Newer wind tunnels were designed, so
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speeds for these clouds to form. Typically, the tail of the aircraft will reach supersonic flight while the nose of the aircraft is still in subsonic flight. A bubble of supersonic expansion fans terminating by a wake shockwave surround the tail. As the aircraft continues to accelerate, the
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The outflows or jets from young stellar objects or disks around black holes can also be transonic since they start subsonically and at a far distance they are invariably supersonic. Supernovae explosions are accompanied by supersonic flows and shock waves. Bow shocks formed in
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for either wholly subsonic or supersonic flows. This assumption is fundamentally untrue for transonic flows because the disturbance caused by an object is much larger than in subsonic or supersonic flows; a flow speed close to or at Mach 1 does not allow the
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as well as
Tricomi's original equations to complete a set of four numerical solutions for the drag over a double wedge airfoil in transonic flow above Mach 1. The gap between subsonic and Mach 1 flow was later covered by both
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did not have the capability to create wind speeds close to Mach 1 to test the effects of transonic speeds. Not long after, the term "transonic" was defined to mean "across the speed of sound" and was invented by NACA director
313:, aimed to supplement Guderley's Mach 1 work with numerical solutions that would cover the range of transonic speeds between Mach 1 and wholly supersonic flow. Vincenti and his assistants drew upon the work of
126:
The issue of transonic speed (or transonic region) first appeared during World War II. Pilots found as they approached the sound barrier the airflow caused aircraft to become unsteady. Experts found that
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are a direct result of transonic winds from a star. It had been long thought that a bow shock was present around the heliosphere of our solar system, but this was found not to be the case according to
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researchers could test newer wing designs without risking test pilots' lives. The slotted-wall transonic tunnel was designed by NASA and allowed researchers to test wings and different
359:
In astrophysics, wherever there is evidence of shocks (standing, propagating or oscillating), the flow close by must be transonic, as only supersonic flows form shocks. All black hole
226:, major changes in aircraft design were seen to improve transonic flight. The main way to stabilize an aircraft was to reduce the speed of the airflow around the wings by changing the
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downstream, increasing drag, adding asymmetry and unsteadiness to the flow around the vehicle. Research has been done into weakening shock waves in transonic flight through the use of
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supersonic expansion fans will intensify and the wake shockwave will grow in size until infinity is reached, at which point the bow shockwave forms. This is Mach 1 and the
283:, who used the transformation to simplify the compressible flow equations and prove that they were solvable. The hodograph transformation itself was also explored by both
259:. A common assumption used to circumvent this nonlinearity is that disturbances within the flow are relatively small, which allows mathematicians and engineers to
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Although successful, Guderley's work was still focused on the theoretical, and only resulted in a single solution for a double wedge airfoil at Mach 1.
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a visible cloud will form. These clouds remain with the aircraft as it travels. It is not necessary for the aircraft as a whole to reach
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form intense low-pressure, low-temperature areas at various points around an aircraft. If the temperature drops below the
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700:"From Engineering Science to Big Science: The NACA and NASA Collier Trophy Research Project Winners. Pamela E. Mack"
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became one of the first engineers to investigate the effect of compressibility on aircraft. However, contemporary
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Hicks, Raymond M.; Vanderplaats, Garret N.; Murman, Earll M.; King, Rosa R. (1 February 1976).
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transformation. This concept was originally explored in 1923 by an
Italian mathematician named
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One of the first methods used to circumvent the nonlinearity of transonic flow models was the
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Flight condition in which airflow speeds are concurrently above and below the speed of sound
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Streamlines for three airflow regimes (black lines) around a nondescript blunt body (blue).
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Engineering theory in the making: Aerodynamic calculation "breaks the sound barrier."
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are transonic. Many such flows also have shocks very close to the black holes.
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airflow around that object. The exact range of speeds depends on the object's
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in 1937, though neither applied this method specifically to transonic flow.
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Prior to the advent of powerful computers, even the simplest forms of the
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the compressible flow equations into a relatively easily solvable set of
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Shock waves may appear as weak optical disturbances above airliners with
850:"NASA – IBEX Reveals a Missing Boundary At the Edge of the Solar System"
326:, completing the transonic behavior of the airfoil by the early 1950s.
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Issues with aircraft flight relating to speed first appeared during the
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in transonic airflow to find the best wingtip shape for sonic speeds.
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Aircraft performance and sizing. fundamentals of aircraft performance
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591:. New York City: Momentum Press Engineering. pp. 10–11.
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over the wing. Later on, Richard
Whitcomb designed the first
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Gottfried
Guderley, a German mathematician and engineer at
115:, but transonic flow is seen at flight speeds close to the
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presents a cross-sectional area variation that minimises
436:(Sixth ed.). New York, NY. pp. 756–758.
502:Vincenti, Walter G.; Bloor, David (August 2003).
185:airflows forming around the plane. In the 40s,
162:Transonic speeds can also occur at the tips of
119:(343 m/s at sea level), typically between
792:Fluid dynamics for the study of transonic flow
355:Transonic flows in astronomy and astrophysics
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287:and O.G. Tietjen's textbooks in 1929 and by
202:of the California Institute of Technology.
464:: CS1 maint: location missing publisher (
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589:Aircraft Performance and Sizing, Volume I
826:Theory of Transonic Astrophysical Flows
552:Takahashi, Timothy (15 December 2017).
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45:Aerodynamic condensation evidences of
795:. New York: Oxford University Press.
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628:"Mach 1: Assaulting the Barrier"
828:. Singapore: World Scientific.
558:. Momentum Press. p. 107.
167:causing localized transonics).
430:Anderson, John D. Jr. (2017).
87:Transonic flow patterns on an
32:For the American company, see
1:
176:Discovering transonic airflow
824:Chakrabarti, Sandip (1990).
669:Vincenti, Walter G. (1997).
433:Fundamentals of aerodynamics
587:Takahashi, Timothy (2016).
349:Prandtl–Glauert singularity
253:compressible flow equations
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789:Ramm, Heinrich J. (1990).
743:SAE Technical Paper Series
309:, an American engineer at
235:using similar principles.
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710:(2): 417–418. 2000–2006.
508:Social Studies of Science
408:Supersonic expansion fans
336:supersonic expansion fans
47:supersonic expansion fans
632:Air & Space Magazine
520:10.1177/0306312703334001
375:data published in 2012.
265:differential equations
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141:supercritical airfoils
131:can cause large-scale
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239:Mathematical analysis
233:supercritical airfoil
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300:double wedge airfoil
113:critical Mach number
93:critical Mach number
34:Transonic Combustion
330:Condensation clouds
206:Changes in aircraft
200:Theodore von Kármán
78:supercritical wings
49:around a transonic
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157:Whitcomb area rule
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598:978-1-60650-683-7
565:978-1-60650-684-4
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281:Francesco Tricomi
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369:solar winds
320:Julian Cole
270:streamtubes
210:Initially,
196:Hugh Dryden
153:swept wings
129:shock waves
869:Categories
681:1027014606
574:1162468861
414:References
402:Hypersonic
396:Supersonic
361:accretions
344:supersonic
182:supersonic
133:separation
109:supersonic
105:transsonic
18:Transsonic
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724:0021-1753
528:0306-3127
460:cite book
452:927104254
340:dew point
277:hodograph
261:linearize
101:Transonic
66:wave drag
880:Airspeed
637:14 March
536:13011496
390:Subsonic
379:See also
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171:History
151:use of
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228:chord
164:rotor
830:ISBN
807:OCLC
797:ISBN
720:ISSN
704:Isis
677:OCLC
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570:OCLC
560:ISBN
524:ISSN
466:link
448:OCLC
438:ISBN
373:IBEX
322:and
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