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to the cube of its length, whereas for a given lift coefficient, the area of the lifting surfaces should be increased as a square of the ship's length. Therefore, to provide dynamic support of large hydrofoil ship one needs either to disproportionally increase the area of hydrofoils, or to increase the magnitude of the lift coefficient. The former measure results in heavy and “clumsy” hydrofoils whereas the latter measure normally requires an augmentation of the adjusted angle of attack and, consequently, leads to reduction of the speed range of noncavitating flow regime. Utilization of the jet flap, as follows from the article of Kaplan [3], allows to gain the same increment of lift as for the incidence induced lift case with diminution of the leading edge suction due to transition to the “saddle-backed” loading distribution. Kaplan and Goodman explored possibilities of utilization of jet flapped wings as anti- pitching devices, [4]. The same authors carried out experiments in water tunnel on symmetric hydrofoils with measurement of the lift and drag, estimation of required power and measurement of velocity distribution across the jet, [ 4]. In addition, Kaplan and Lehman conducted measurements of unsteady forces acting upon a wing due to unsteady variation of the jet deflection angle, in view of possible application to control surfaces of a submarine, [5].

One of the features of the flow problem for a lifting surface with a jet flap consists in a necessity to fulfil kinematic and dynamic boundary conditions upon the jet, the form of which is not known in advance. The important step in development of mathematical model of a jet flapped wing had been made by Spence in his research work [6], where the jet behind the wing was treated as a surface of tangential discontinuity, possessing a finite momentum and capable of withstanding pressure jump. In this and following publications [7], [8] ,[9] and [10]. Spence gave detailed analysis of the two-dimensional flow problem. Using linear theory, he replaced the wing and the jet by an equivalent vortex layer, distributed along the semi-infinite cut and subject to tangency condition on the foil as well as to kinematic and dynamic conditions upon the jet. The latter has been written as the requirement of proportionality of the pressure difference across the jet to its longitudinal curvature. The resulting mixed boundary problem had been solved by Spence, at first with use of Fourier expansions [ 6] and later on by means of the Mellin transform, [10]. Theoretical results of Spence are in fair agreement with experimental data up to sufficienly large magnitudes of the jet deflection angle of the order of 60°, which confirms the adequacy of the mathematical model of infinitely thin jet. Kuchemann [11] extended the approach of Spence to the case of the foil of small thickness and was able to calculate not only the lift, but also pressure distributions on the upper and lower surfaces of the winng with jet flap. His calculated results confirmed that a typical loading distribution along the wing with a jet flap has a “saddle-backed” character with maxima both near the leading edge and the jet flap. The said loading distribution is essentually different from that for the foil without jet flap at an angle of attack. For the latter case there is only one peak of hydrodynamic loading near the leading edge. Comparing loading distributions for a wing with and without jet flap, one can easily conclude that for the same magnitude of the lift coefficient the maximum suction at the leading edge is lower for the jet flapped wing. With use of Fourier method Spence had calculated 9 terms of the series decsribing the strength of the vortex layer with a square root singularity at he leading edge and logarithmic singularity at the trailing edge. In a work [10] with use of the method of integral transforms an asymptotic expansion of the flow problem solution had been constructed for the case of small magnitude of the jet momentum coefficient. As a result the lift coefficient was found in the form

where

To determine characteristics of a jet flapped wing Stratford [12] used an analogy between the wing with a jet flap and a wing with a mechanical flap. This approach resulted in an expression for the lift coefficient which for small values of the jet momentum coefficient was similar to that obtained by Spence in [6]. The work of Maskell and Spence [13] was the first where an attempt had been made to extend the approach of [6] to three-dimensional case. In [13] the flow problem for a wing of finite aspect ratio with a jet flap was formulated within linear theory of the lifting surface. Due to complexity of the problem the authors developed only approximate solution, based upon two-dimensional theory of Spence and assumption of uniform spanwise distribution of downwash which corresponds to elliptic loading along the span. As a matter of fact, the authors assumed that both local chord and momentum distribution along the span were elliptic for constant magnitudes of the incidence α and



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