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PROFILE THEORY BY THE METHOD OF SINGULARITIES
2- 4-1 Singularities
The method of conformal mapping was applied in Sec. 2-3 to the computation of velocity distributions about a given wing profile. Another means of computing the aerodynamic properties of wing profiles is the method of singularities (see Keune and Burg [33]). This consists of arranging sources, sinks, and vortices within the profile. Through superposition of their flow fields with a translational flow, a suitable body contour (profile) is produced. The flow field within the contour has no physical meaning. For the creation of a symmetric profile in a symmetric incident flow field (teardrop profile), only sources and sinks are required, whereas for the creation of camber, vortices must be added within the profile. This procedure is shown schematically in Fig. 2-19.
These sources, sinks, and vortices are termed singularities of the flow. In most cases it is necessary to distribute the singularities continuously over the profile chord rather than discretely.
It is expedient to treat the very thin profile (skeleton profile) first. For such profiles the skeleton theory (Sec. 24-2) produces all essential results for their lift. For representation of the skeleton profile, only a vortex distribution is needed. The symmetric profile of finite thickness (teardrop profile) in symmetric flow (angle of attack zero) is produced by source-sink distributions (teardrop theory). In this case the displacement flow about the profile is obtained (Sec. 24-3). The cambered
Figure 2-19 The singularities method. (a) Cambered profile of finite thickness with angle of attack а. (&) Symmetric profile of finite thickness in symmetric flow, a = 0. (c) Very thin profile with angle of attack.
Figure 2-20 The skeleton theory. (a) Arrangement of the vortex distribution on the skeleton line, (b) Arrangement of the vortex distribution on the chord (slightly cambered profile), (c) Circulation distribution along the chord (schematic).
profile of finite thickness is essentially the product of superposition of a mean camber line (skeleton line) with a teardrop profile (Sec. 24-4).
