Elliptic Loading Research Articles

Steady oscillations of a rectangular plate due to the rotation of an elliptic loading area

Steady oscillations of a rectangular plate due to the rotation of an elliptic loading area

Axial flow in laminar trailing vortices

The structure of laminar trailing vortices behind a lifting wing is considered. The inviscid roll up of the trailing vortex sheet is examined, and the nature of the singularity at the centre of the spiral is determined. It is shown that viscosity removes the singularity and the structure of the viscous core is obtained. The pressure in the viscous core is found and used to calculate the axial velocities produced by streamwise pressure gradients. It is found that the per­turbation of axial velocity can be either away from the wing or towards the wing depending on the distribution of tip loading on the wing. For elliptic loading, the perturbation is towards the wing. The axial flow deficit in the core due to the boundary layers on the wing is also estimated. A comparison with experiment is made and reasonable agreement is found.

On the Rolling Up of a Trailing Vortex Sheet

One of the best known results in finite wing theory, which is quoted in aerodynamic text books, states that the distance between two rolled up vortices behind a wing with an elliptic spanwise load distribution is sπ/2, where s is the wing semi-span. Within the framework of linear wing theory this result is correct. But it is of interest to enquire how this result is affected when the standard linear model becomes less valid, for example, at higher wing lift coefficients.In this note, it is assumed that a continuous trailing vortex sheet rolls up into two discrete vortices. These two discrete vortices are assumed to have cores of finite radius; inside the cores the flow is taken to be solid body rotation, while the flow outside the cores is the standard irrotational vortex field. It is assumed that this rolling up process takes place far downstream of the finite wing which generates the trailing vorticity.

The Application of Lifting Line Theory to an Upright Bermudan Mainsail

SummaryUsing Glauert's analysis and taking into account the restraint due to the surface of the sea, lifting line theory is applied to calculate the distribution of loading, downwash velocity and vortex drag of a “Finn” dinghy's sail when upright. It appears that the loading can probably be represented with sufficient accuracy byI=I0(sin θ+sin 2θ)where k is largely dependent on the apparent twist in the sail and has a value generally of the order of 0-5, that the apparent twist may not be twist at all in the aerodynamic sense, and that the vortex drag is considerably greater than it would be if it were possible to make a sail to give elliptic loading.

Comments on "Limiting Circulatory Lift of a Wing of Finite Aspect Ratio"

The second point questions the direct application of Eq. (1) to the finite jet-flapped wing. In the derivation of Eq. (1), it is assumed tha t the wing has an elliptic spanwise loading distribution and tha t the trailing vorticity lies in a plane inclined to the free stream at the induced down wash angle calculated at the wing lifting line. But, the ultimate downwash angle far behind the wing will be twice the inclination at the wing. Thus, the effects of the curvature of the trailing vorticity in the stream direction are neglected. However, it is possible to include these effects by considering the forces on a control surface at infinit}^ in the usual manner. A wing, which has an elliptic load distribution given by r = r0(i v A) (2)

On the Accuracy of the Representation of a Lifting Line by a Finite Set of Horseshoe Vortices

Summary The paper examines the error involved when the continuous distribution of lift on an unswept lifting surface is represented by a finite number of horseshoe vortices, the strengths of which are determined by a prescribed downwash. Attention is directed mainly to the case of elliptic loading, but an anti-symmetrical case is also studied to ensure that the conclusions are not peculiar to the elliptic case.

Approximate Solution of Voith-Sohneider Propeller

Assuming the uniform longitudinal induced velocity on the propeller stream and the elliptical loading on the blades, the Voith-Schneider-propeller is solved approximately. And the characteristic curves are calculated, with which man can roughly select and design the propeller.

Aerodynamics for Engineers

(1) Theoretical consideration of aerofoils of limited span led, in Article III, to a need for some assumption as to lift‐grading along the span, to give the span‐grading of circulation. Fig. 1 shows at (a) the experimental distribution of lift along a rectangular aerofoil of 7·6 per cent camber and aspect ratio 6, at an angle of incidence of 6 deg. At (b) elliptic loading is shown, which, from several points of view, may be regarded as ideal for the same lift coefficient. Assumption of the latter form permits of greatly simplified treatment. Even compared with rectangular aerofoil distribution, the assumption gives differences of little importance in many practical calculations, while these are still less with aeroplane wings, owing to the wash‐out usually introduced at their rounded wing‐tips. The following is, therefore, restricted to elliptic loading, but sufficient generality of presentation is preserved to allow, if desired, other forms to be substituted.