A quadrilateral vortex method applied to configurations with high circulation

A quadrilateral vortex-lattice method is briefly described for calculating the potential flow aerodynamic characteristics of high-lift configurations. It incorporates an iterative scheme for calculating the deformation of forcefree wakes, including wakes from side edges. The method is applicable to multiple lifting surfaces with part-span flaps deflected, and can include ground effect and wind-tunnel interference. Numerical results, presented for a number of high-lift configurations, demonstrate rapid convergence of the iterative technique. The results are in good agreement with available experimental data

A subvortex technique for the close approach to a discretized vortex sheet

The close-approach problem associated with vortex-lattice methods was examined numerically with the objective of calculating velocities at arbitrary points, not just at midpoints, between the vortices. The objective was achieved using a subvortex technique in which a vortex splits into an increasing number of subvortices as it is approached. The technique, incorporated in a two-dimensional potential flow method using "submerged" vortices and sources, was evaluated for a cambered Joukowski airfoil. The method could be extended to three dimensions, and should improve non-linear methods, which calculate interference effects between multiple wings and vortex wakes, and which include procedures for force-free wakes

Application of the AMI C sub l sub max prediction method to a number of airfoils

A method for calculating the flow about airfoils up to and beyond the stall is described. It is an iterative procedure between potential flow and boundary layer solutions. The separated region is modeled in the potential flow analysis using free vortex sheets which require an inner iteration to establish their shapes. The free vortex sheet length is an important parameter in the potential flow calculation. Results so far indicate a possible correlation between wake length and airfoil thickness/chord ratio. Calculated and experimental results are compared for a series of airfoils

Study for prediction of rotor/wake/fuselage interference, part 1

A method was developed which allows the fully coupled calculation of fuselage and rotor airloads for typical helicopter configurations in forward flight. To do this, an iterative solution is carried out based on a conventional panel representation of the fuselage and a blade element representation of the rotor where fuselage and rotor singularity strengths are determined simultaneously at each step and the rotor wake is allowed to relax (deform) in response to changes in rotor wake loading and fuselage presence. On completion of the iteration, rotor loading and inflow, fuselage singularity strength (and, hence, pressure and velocity distributions) and rotor wake are all consistent. The results of a fully coupled calculation of the flow around representative helicopter configurations are presented. The effect of fuselage components on the rotor flow field and the overall wake structure is detailed and the aerodynamic interference between the different parts of the aircraft is discussed

Study for prediction of rotor/wake/fuselage interference. Part 2: Program users guide

A method was developed which permits the fully coupled calculation of fuselage and rotor airloads for typical helicopter configurations in forward flight. To do this, an iterative solution is carried out based on a conventional panel representation of the fuselage and a blade element representation of the rotor where fuselage and rotor singularity strengths are determined simultaneously at each step and the rotor wake is allowed to relax (deform) in response to changes in rotor wake loading and fuselage presence. On completion of the iteration, rotor loading and inflow, fuselage singularity strength (and, hence, pressure and velocity distributions) and rotor wake are all consistent. The results of a fully coupled calculation of the flow around representative helicopter configurations are presented. The effect of fuselage components on the rotor flow field and the overall wake structure is discussed as well as the aerodynamic interference between the different parts of the aircraft. Details of the computer program are given

An analysis method for multi-component airfoils in separated flow

The multi-component airfoil program (Langley-MCARF) for attached flow is modified to accept the free vortex sheet separation-flow model program (Analytical Methods, Inc.-CLMAX). The viscous effects are incorporated into the calculation by representing the boundary layer displacement thickness with an appropriate source distribution. The separation flow model incorporated into MCARF was applied to single component airfoils. Calculated pressure distributions for angles of attack up to the stall are in close agreement with experimental measurements. Even at higher angles of attack beyond the stall, correct trends of separation, decrease in lift coefficients, and increase in pitching moment coefficients are predicted

Formation flying benefits based on vortex lattice calculations

A quadrilateral vortex-lattice method was applied to a formation of three wings to calculate force and moment data for use in estimating potential benefits of flying aircraft in formation on extended range missions, and of anticipating the control problems which may exist. The investigation led to two types of formation having virtually the same overall benefits for the formation as a whole, i.e., a V or echelon formation and a double row formation (with two staggered rows of aircraft). These formations have unequal savings on aircraft within the formation, but this allows large longitudinal spacings between aircraft which is preferable to the small spacing required in formations having equal benefits for all aircraft. A reasonable trade-off between a practical formation size and range benefit seems to lie at about three to five aircraft with corresponding maximum potential range increases of about 46 percent to 67 percent. At this time it is not known what fraction of this potential range increase is achievable in practice

Shakespeare and the Earl of Warwick: the kingmaker in the Henry VI trilogy

This thesis is an appraisal of Shakespeare’s characterisation of Richard Neville, the Earl of Warwick, colloquially known by his soubriquet ‘kingmaker’. Shakespeare’s reification of the reputations of characters from the regal history of late medieval England substantially maintains our interest in historical figures such as Warwick. By a process of dramatic and literary osmosis, Shakespeare infiltrates the national consciousness with such figures, refreshing individual and collective memory. The majority of the thesis is taken up with an examination of key scenes which I consider most successfully explore the roots of Warwick’s reputation. Finally, I will consider Warwick’s role in performance, though a discourse with three actors who have previously been assigned the role. I will examine their various approaches to the characterisation of the part. In the course of distilling Warwick’s clearly defined characteristics, Shakespeare examines fundamental questions of the delegation of right to rule and the accepted qualities required for effective leadership. In this context, the dramatist follows the course of events by which the Kingmaker achieved the agnomen which continues to define him as a symbol of medieval potency

A submerged singularity method for calculating potential flow velocities at arbitrary near-field points

A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices)

Program VSAERO theory document: A computer program for calculating nonlinear aerodynamic characteristics of arbitrary configurations

The VSAERO low order panel method formulation is described for the calculation of subsonic aerodynamic characteristics of general configurations. The method is based on piecewise constant doublet and source singularities. Two forms of the internal Dirichlet boundary condition are discussed and the source distribution is determined by the external Neumann boundary condition. A number of basic test cases are examined. Calculations are compared with higher order solutions for a number of cases. It is demonstrated that for comparable density of control points where the boundary conditions are satisfied, the low order method gives comparable accuracy to the higher order solutions. It is also shown that problems associated with some earlier low order panel methods, e.g., leakage in internal flows and junctions and also poor trailing edge solutions, do not appear for the present method. Further, the application of the Kutta conditions is extremely simple; no extra equation or trailing edge velocity point is required. The method has very low computing costs and this has made it practical for application to nonlinear problems requiring iterative solutions for wake shape and surface boundary layer effects