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Theory of the Slat in a Two-Dimensional Flow
Published online by Cambridge University Press: 28 July 2016
Extract
The theory of the aerofoil has now been studied to such an extent that, from this province, it is hardly possible to expect further material improvement in its aerodynamical qualities : profiles differing but little from an inverse of a parabola (Joukovski profile) would appear to be the theoretical ideal. Subsequent important progress in that respect may be sought only in another direction, viz., in the application of a series of supplementary contrivances having a marked influence on the properties of the flow around the aerofoil. Here we are referring to such devices as the sucking away of the boundary layer (Absaugeflügel), or the insertion of appliances on the aerofoil itself. Nevertheless, up to the present, only one of the very earliest attempts in this direction, namely, the slotted wing, has developed sufficiently to be in any way widely adopted in contemporary aircraft construction.
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- Copyright © Royal Aeronautical Society 1936
References
1 The mathematical expressions in the present abridged version occasionally differ in points of detail from those in the original Russian text owing to the presence of algebraic errors in the latter.
2 “ Schematic Theory of the Slotted Wing of an Aeroplane.” (Nautchno-tekhnicheski Vestnik, Nos. 4–5, 1921).
3 “ Die Strömungsvorgänge an einem Profil mit Vorgelagertem Hilfsflügel.” (Z.F.M. Jahrgang 14, 1923).
4 “ Die Wirkungsweise von unterteilten Flugprofilen.” (Berichte und Abh. der Wissenschaften Gesellschaft für Luftfahrt, Jan., 1922).
5 “ On a Modification of Kirchoff's Method.” Collected Works. Vol. II, No. 2.
6 Villat. “ Aperçu Théorique sur la Résistance des Fluides.”
7 Bulletin of the Ivanovo-Voznesensk Polytechnic Institute, 1924.
8 Matematicheski Sbornik, 1928.
9 L. Prandtl. “ Vier Abhandlungen zur Hydro-und Aerodynamik,” 1927.
10 See §1. Reference (2).
11 ” On Lifting Planes of the Antoinette Type.” Trans. of the Physical Section of the Imperial Society of Friends of Natural Science, Vol. 15, No. 11, 1911 Google Scholar.
12 F. G. Schmidt. “The Theory of Drag in a Two-Dimensional Flow.” Bulletin of the State Hydrological Institute, No. 18, 1917. Michurine, S. N.. ” The Vortex Theory of the Drag of an Aeroplane.” Saratov, 1929 Google Scholar.
13 K. Polhausen. “ Zur näherungsweisen Integration der Difierentialgleichung der laminaren Grenzschicht.” Abh. aus dem Aerodyn. Inst, an der Technischen Hochschule zu Aachen. Heft 1, S.20.
14 Frequently in aerodynamic literature, the ratio of the radius of the larger circle C 1 to that of the smaller C is expressed as 1 + є1. The relationship between the thickness parameters є and є1, is obviously: 1+є1 = 1 / ( 1–є).
15 In the case where the point of breakaway is situated at the trailing edge, the author (pages 31–32 of the Russian Text), on substituting in Bernouilli's equation the expression §2(15) for the velocity, shows—under the assumption that є≤.3, α.≤20°, and θ≤15°—that the pressure varies linearly over the upper surface of the aerofoil throughout the interval between the point of minimum pressure and the point of breakaway.
16 See §1. Reference (13).
17 After correction for downwash, the mean value o£ the discrepancy amounts to about 5° on comparison with Göttingen experimental data.
18 This numerical example does not appear in the original Russian text.
19 This does not involve any serious restriction of the generality since the general formula for the circulation about the auxiliary aerofoil is:
4πRVα sin (β+α'/2)
where R is the radius of the circle in the z-plane corresponding to the profile in the ζ-plane, and 2α' the central angle of the skeleton.
Now, when α' is zero and є’ (thickness parameter of the slat) small, the chord b is equal approximately to 4R(1 – є'). The expression for the circulation may then be written:
π{b/(1 – є')}V a sin β
which reduces to that in the text on neglecting є'.