In this paper an analytic exact solution for two-dimensional potential flow past an arbitrary wing section is given and the effects of mean camber and thickness upon aerodynamic characteristics are discussed. Let the contour of an aerofoil be expressed by equation (1) with parameter ζ, the geometrical meaning of ζ being shown in fig. 1 and the x-axis being the line joining the farthest two points on the contour. If we take, as mean camber line, the locus of mid-points of ordinates of upper and lower surfaces, the coefficients of the cosine series in (1) are determined by the mean camber I ine only and the coefficients of the sine series by the thickness curve only. When a cylinder, the curve of the cross section being given by (4), translates, the complex potential (3) was given by Rosa M. Morris, where the function F(ζ) is a real function of and is determined from the facts that the potential function is nowhere infinite and vanishes at infinity. When the fluid flows past a fixed cylinder with velocity V in a direction making an angle α with the x-axis, the complex potential is given by (5), in which F is the circulation in clockwise direction. The function F(ζ) for the aerofoil section expressed by (1) is obtained as (6) and therefore the complex potential is given by (7) where F is determined as (8) so that the trailing edge may be a stagnation point.
No-lift-angle is given by (9) putting F=0 in (8). For NACA-4412 aerofoil, the nolift-angle is-4°01′, refering to NACA datum line, which is in very close agreement with experimental value. The curve in fig. 2 shows the variation of no-lift-angle against ∑nan, the one in fig. 3 against ∑nbn. These curves, then show respectively the effects of mean camber and thickness on no-lift-angle. We see that the effect of thickness is small. The forms of the aerofoils obtained by varying ∑nan or ∑nbn are not exactly the same as the NACA series, because the thickness is increased or decreased parallel to the y-axis, not noiraal to the mean camber line and the chord line does not coincide with that of NACA aerofoils. However the forms of the both series are in close resemblance, provided the mean camber is not large. In fig. 2 and 3, experimental values of NACA series are also inserted.
Lift coefficient is given by (10). The experimental values are smaller than the calculated ones due to damping action on circulation caused by viscosity. The effect of mean camber is again greater than that of thickness as illustrated in fig. 5 and 6.
Moment coefficient about the origin, regarding the nose down moment as positive, is given by (11) and that about any point (x, 0) on the chord by (12). In fig. 4 calculated and experimental moment coefficients about a point 1/4 chord aft from the leading edge are plotted against lift coefficient for NACA 4412 aerofoil. Frictional force exerts nose up moment and therefore the experimental values are less than the calculated. The difference between them is almost independent on the attack angle.
Pressure distribution is given by (14). The effect of thickness is considerable, especially near the leading edge, as shown in fig. 10.

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横の安定を支配する空力的因子及び慣性的因子を論じ,横の安定を推算する公式を与へた.そして,支配する各種因子とその結果として生する安定特性間に比較的簡単な関係を樹立した.かくて,安定特性を近似的に簡便に推算し得る線図を一揃ひ整へた.
次に,安定特性を支配する各種因子が安定特性に及ぼす影響を詳細に論じた.安定特性を巡航性,操縦性(riding,flying, and hanclling qualities)と関連させる為にも,又飛行機の安定特性を設計の途中で精確に推算するに要する資料を整備する為にも,尚多くの研究が必要であることを指摘して置いた.

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