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The '''drag divergence Mach number''' (not to be confused with [[critical Mach number]]) is the [[Mach number]] at which the [[Drag (physics)|aerodynamic drag]] on an [[airfoil]] or [[airframe]] begins to increase rapidly as the Mach number continues to increase.<ref>{{cite book|last=Anderson|first=John D.|title=Fundamentals of Aerodynamics|publisher=McGraw-Hill|year=2001|pages=613}}</ref> This increase can cause the [[drag coefficient]] to rise to more than ten times its [[aerodynamics#low-speed aerodynamics|low speed]] value. | |||
The value of the drag divergence Mach number is typically greater than 0.6; therefore it is a [[aerodynamics#transonic aerodynamics|transonic]] effect. The drag divergence Mach number is usually close to, and always greater than, the [[critical Mach]] number. Generally, the [[drag coefficient]] peaks at Mach 1.0 and begins to decrease again after the transition into the [[aerodynamics#supersonic aerodynamics|supersonic]] regime above approximately Mach 1.2. | |||
The large increase in drag is caused by the formation of a [[shock wave]] on the upper surface of the airfoil, which can induce [[flow separation]] and [[adverse pressure gradient]]s on the aft portion of the wing. This effect requires that [[aircraft]] intended to fly at [[supersonic]] speeds have a large amount of [[thrust]]. In early development of [[transonic]] and [[supersonic]] aircraft, a steep dive was often used to provide extra acceleration through the high drag region around Mach 1.0. | |||
This steep increase in [[drag (physics)|drag]] gave rise to the popular false notion of an unbreakable [[sound barrier]], because it seemed that no aircraft technology in the foreseeable future would have enough [[aircraft propulsion|propulsive]] force or [[Aircraft flight control systems|control]] authority to overcome it. Indeed, one of the popular analytical methods for calculating drag at high speeds, the [[Prandtl-Glauert rule]], predicts an [[infinity|infinite]] amount of drag at Mach 1.0. | |||
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the [[Whitcomb area rule]] and the [[supercritical airfoil]]. A [[supercritical airfoil]] is shaped specifically to make the drag divergence Mach number as high as possible, allowing aircraft to fly with relatively lower drag at high [[Subsonic flight|subsonic]] and low [[transonic]] speeds. These, along with other advancements including [[computational fluid dynamics]], have been able to reduce the factor of increase in drag to two or three for modern aircraft designs.<ref>{{cite book|last=Anderson|first=John D.|title=Fundamentals of Aerodynamics|publisher=McGraw-Hill|year=2001|pages=615}}</ref> | |||
Drag divergence Mach numbers for a given family of propeller airfoils can be approximated by Korn's relation:<ref>Boppe, C.W., "CFD Drag Prediction for Aerodynamic Design," Technical Status Review on Drag Prediction and Analysis from Computational Fluid Dynamics: State of the Art, AGARD AR 256, June 1989, pp. 8-1 – 8-27.</ref> | |||
:<math>M_{dd} + \frac{c_{l,design}}{10} + \frac{t}{c} = K</math> | |||
Where <math>c_{l,design}</math> is the coefficient of lift of a specific section of the airfoil, <math>t</math> is the airfoil thickness at a given section, and <math>c</math> is the chord length at a given section. <math>K</math> is a factor established through CFD analysis: | |||
K = 0.87 for conventional airfoils (6 series)<ref>Mason,W.H. [http://www.dept.aoe.vt.edu/~mason/Mason_f/TransonicAeroPres.pdf "Some Transonic Aerodynamics", p. 51.]</ref><br /> | |||
K = 0.95 for supercritical airfoils | |||
==See also== | |||
*[[wave drag]] | |||
*[[supercritical airfoil]] | |||
*[[critical mach]] | |||
*[[speed of sound]] | |||
*[[sound barrier]] | |||
== Notes == | |||
<references /> | |||
[[Category:Aerodynamics]] | |||
Latest revision as of 07:29, 19 January 2014
The drag divergence Mach number (not to be confused with critical Mach number) is the Mach number at which the aerodynamic drag on an airfoil or airframe begins to increase rapidly as the Mach number continues to increase.[1] This increase can cause the drag coefficient to rise to more than ten times its low speed value.
The value of the drag divergence Mach number is typically greater than 0.6; therefore it is a transonic effect. The drag divergence Mach number is usually close to, and always greater than, the critical Mach number. Generally, the drag coefficient peaks at Mach 1.0 and begins to decrease again after the transition into the supersonic regime above approximately Mach 1.2.
The large increase in drag is caused by the formation of a shock wave on the upper surface of the airfoil, which can induce flow separation and adverse pressure gradients on the aft portion of the wing. This effect requires that aircraft intended to fly at supersonic speeds have a large amount of thrust. In early development of transonic and supersonic aircraft, a steep dive was often used to provide extra acceleration through the high drag region around Mach 1.0. This steep increase in drag gave rise to the popular false notion of an unbreakable sound barrier, because it seemed that no aircraft technology in the foreseeable future would have enough propulsive force or control authority to overcome it. Indeed, one of the popular analytical methods for calculating drag at high speeds, the Prandtl-Glauert rule, predicts an infinite amount of drag at Mach 1.0.
Two of the important technological advancements that arose out of attempts to conquer the sound barrier were the Whitcomb area rule and the supercritical airfoil. A supercritical airfoil is shaped specifically to make the drag divergence Mach number as high as possible, allowing aircraft to fly with relatively lower drag at high subsonic and low transonic speeds. These, along with other advancements including computational fluid dynamics, have been able to reduce the factor of increase in drag to two or three for modern aircraft designs.[2]
Drag divergence Mach numbers for a given family of propeller airfoils can be approximated by Korn's relation:[3]
Where is the coefficient of lift of a specific section of the airfoil, is the airfoil thickness at a given section, and is the chord length at a given section. is a factor established through CFD analysis:
K = 0.87 for conventional airfoils (6 series)[4]
K = 0.95 for supercritical airfoils
See also
Notes
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Boppe, C.W., "CFD Drag Prediction for Aerodynamic Design," Technical Status Review on Drag Prediction and Analysis from Computational Fluid Dynamics: State of the Art, AGARD AR 256, June 1989, pp. 8-1 – 8-27.
- ↑ Mason,W.H. "Some Transonic Aerodynamics", p. 51.