Title: Influence of Acceleration on Aerodynamic Characteristics of Thin Airfoils in Supersonic and Transonic Flight
Abstract: An at tempt has been made to derive the aerodynamic characteristics, in the supersonic and transonic range, of a two-dimensional airfoil moving at uniformly accelerated speed; it is assumed that the airfoil is thin and the shocks resulting from its motion are extremely weak. Under these conditions, the airfoil motion may be treated as a time-dependent perturbation problem, which can be solved by means of Possio solutions. The solutions for lift, drag, and pressure on the airfoil surface turn out to be elliptic integral expressions, whose arguments depend on the Mach Number and on an acceleration parameter. The evaluation of these solutions is carried out in a different manner, depending on whether the transonic or the supersonic range is considered. In Section (A), the solution at supersonic speeds is expanded in positive powers of the acceleration parameter jS. The influence of acceleration turns out to be extremely small. In Section (B), the transonic range is treated, by expanding the expressions for lift and drag, at M = 1, into a series starting with the negative one-fourth power of /3. This elucidates why, a t M = 1, the theoretical expressions for the aerodynamic parameters remain finite in the case of accelerated motion but become infinite in the limit of stationary flight speed ((3 = 0). In Section (C), a physical discussion of the results for wedges and diamond profiles is given: The curves representing the aerodynamic parameters as a function of the Mach Number have a more or less pronounced maximum at M = 1, depending on the value of the flight acceleration #. The application of a validity criterion shows that for sufficiently large /3 the results can be taken quantitatively, while at small /? the results have only qualitative meaning.
Publication Year: 1950
Publication Date: 1950-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 5
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