By Hermann T. Schlichting, Erich A. Truckenbrodt (transl. by Heinrich J. Ramm)
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A) Total profile. (b) Profile teardrop (thickness distribution). (c) Mean camber (skeleton) line (camber height distribution). C (Fig. 2-1b) is another important quantity. From these designated quantities the following six geometric profile parameters may be formed: t/c hlc xtlc xh /c rN/c 2r relative thickness (thickness ratio)* relative camber (camber ratio)* relative thickness position relative camber position relative nose radius trailing edge angle For the complete description of a profile, the profile coordinates of the upper and lower surfaces, zu(x) and zl(x), must also be known.
A) Thin, symmetric profile with rounded nose, suction force present. (b) Flat plate with sharp nose, suction force missing. AIRFOIL OF INFINITE SPAN IN INCOMPRESSIBLE FLOW (PROFILE THEORY) 45 20 IO J 49 18 I i I 16 Thin profile.. 1 01 0 0,02 004 005 008 010 CD - 072 074 0° 016 1 2° 4° 6° B° 10° 12° CC -Figure 2-13 Aerodynamic coefficients of a sharp-edged flat plate and a thin symmetric profile for Re = 4 105, A = -, from Prandtl and Wieselsberger [47]. (a) Polar curves, CL vs. CD. (b) a b Glide angle, E = CD/CL- thin profiles; the resultant of the aerodynamic forces is inclined upstream relative to the direction normal to the profile chord.
The asymmetric force distribution along the span produces also a yawing moment, the so-called yawing moment due to roll rate. Introducing the dimensionless coefficients according to Eq. (1-21), the stability coefficients of sideslip acmz acMx and aS? asp are obtained. Q is the dimensionless angular velocity cw,. It is obtained from wX, the half-span s, and the flight velocity V: 5Q,; = E. -I, (1-30) V The rotary motion of an airplane about the vertical axis (yaw) produces additional longitudinal air velocities on the wing that have reversed signs on the two wing halves and that result in an asymmetric normal and tangential force distribution along the wing span, which in turn produces a rolling and a yawing moment.