Establishment of Lift on an Aerofoil with a Jet Flap: A Theoretical Note Relating to a Wing with Trailing Edge Jet with Extension to Cover Wings of Finite Span

The circulation which is established around an aerofoil section which has i trailing edge jet, and thus also the lift, is directly dependent on a trailing edge condition similar to the Joukowski condition in conventional steady and unsteady flow. There is a downwash made up of elementary vortices but in this case the vortex density is not zero when the sheet extends to infinity. The problem is govcrnec by an equation similar to the Wagner equation, into which is introduced the curvature of the downwash at the trailing edge. Certain precautions have to be taker when calculating this. The law governing the movement of the elementary vortices in the downwash plays a very important part. It is directly dependent on the viscous damping of the vorticity. This effect has also had to be taken into consideration, and the drag law of the jet behind the nozzle established. Other results follow concerning the solution of the transient case, and the determination of the circulation up to the moment of reaching its steady limit value, which is achieved in finite time. The velocity distribution on the aerofoil can be found at any instant, and thus also all the properties concerning the aerodynamic forces. The method has been applied to two cases, and a comparison is made with experimental results. An extension to the case of a conventional aerofoil (without jet) is possible; in this case the circulation must have a slightly lower value than in the Joukowski case, the difference depending on the Reynolds number. There is a potential drag resulting from the existence of the downwash and its loss of momentum. In Part II the finite span case is considered. The basic equations are established, and an approximate solution of the steady How case found, where the distribution of circulation is elliptical. A wing interrupted by a fuselage is also considered, and comparison with experimental results given.