This NASA report (PDF!) lists a range of supercritical airfoils with different thicknesses and design lift coefficients. Supercritical airfoils have negative camber over most of their forward part and strong positive camber only in the rearmost 20 - 30% of their chord. The added lift at the forward part also lowers the pitching moment of supercritical airfoils. On the most recent designs another small lift contribution results from a slower pressure drop on the forward edge of the lower side pressure distribution (the forward lower-surface undercutting of Phase 3 airfoils).Įffect of forward lower surface undercutting, from NASA Technical Paper 2969. Supersonic flow on the upper side allows to create more lift over the full chord. In oder to produce the most lift at a given Mach number, the pressure difference between upper and lower side can be maximized where thickness is low, i.e. Practical designs aim for a weak shock over a range of lift coefficients. Key is the low curvature on the suction side which makes a shock-free pressure rise possible. When transsonic research started, inverted airfoils paradoxically turned out to perform better at moderate lift coefficients and high Mach numbers than regular airfoils. It should be obvious which one is to prefer. While the NACA 6-digit series was among the first set of airfoils computed from a design pressure distribution, they will suffer from shocks when operated above their critical Mach number just as any other airfoil.Ĭomparison of drag rise over Mach for 6-series and early supercritical airfoils from NASA Technical Paper 2969. How do airliners tackle the problem? I think I read that they allow mach numbers a little bit higher until the drag divergence velocity? So the only way to have less sweep angle: find another airfoil (I think 64006 is already one of the best free available airfoils) or I accept higher values of drag coefficient ? So normal commerical aircraft have angles between 30 to max. I am wondering now, if this is normal that I need such a high sweep angle? Or did I choose the wrong airfoil. In order to prevent Mach=1 on the airfoil, I would need a swept wing with an angle of more than 50° to reach Ma_crit=0.88. So actually, this is my first demand for the airfoil. So when I think of which airfoil to choose, I have to consider aspects likeīut what comes first in my mind is, that I have to prevent shock waves forming on my airfoil, because drag will dramatically increase. The mathematical theory is developed in some detail and supported by more physical arguments, and the paper is concluded by a section where some relevant experimental evidence is discussed.I am desigining an aircraft, which shall fly up to Mach=0.9 in cruise flight in an altitude of 10 km. The limiting high-speed form of the convection augmentation factor is |M cos θ| -5 which combines with the basic eighth power velocity law to yield the result that radiation intensity increases only as the cube of velocity at high supersonic speed. When quadrupoles approach the observer with supersonic speed sound is heard in reverse time, but is once again of a quadrupole nature and the general low-speed result is again applicable. This simple-source radiation is likened to a type of eddy Mach wave whose strength increases with the cube of a typical flow velocity. At that condition a quadrupole degenerates into its constituent simple sources, for each quadrupole element moves with the acoustic wave front it generates and cancelling contributions from opposing sources, so essential in determining quadrupole behaviour, cannot combine but are heard independently. At supersonic speeds the augmentation factor becomes singular whenever the eddy approaches the observation point at sonic velocity, M cos θ = 1. At low subsonic speeds the radiated intensity increases with the eighth power of velocity although quadrupole convection augments this basic dependence by a factor |1 - M cos θ| -5, where M is the eddy convection Mach number and θ the angular position of an observation point measured from the direction of eddy motion. The sound is that which would be produced by a distribution of convected acoustic quadrupoles whose instantaneous strength per unit volume is given by a turbulence stress tensor, T ij. The theory initiated by Lighthill (1952) for the purpose of estimating the sound radiated from a turbulent fluid flow is extended to deal with both the transonic and supersonic ranges of eddy convection speed.
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