How to Design Our Prandtl Wing Shape

¶ … PrandtlPlane aircraft configuration is based on the concept of "Best Wing System." The best wing, according to Frediani et al. (2012) is the lifting system with the minimum induced drag. A large amount of aerodynamic analyses is needed to develop this best wing and the most recent improved version was that set up by the Univ. Of Pisa in 2012 named MSD (Multiple Shape Design); it has been set up to generate any aerodynamic PrandtlPlane configuration (Frediani et al., 2003).

The MSD calculates the best conditions for the Prandtl wing which include the following:

- The total surface area of the Prandtl Wing must have the same surface area as the White Knight Two from Virgin Galactic for comparison purposes

- The lift on both wings of the Prandtl Wing must each have the same lift

The lift distribution on each wing section must be elliptical (two sections per wing, two wings = 4 sections total)

Frediani et al. (2012) applied it on a two seat ultra-light aircraft, but as they note, with modifications their conclusions can be applied to any aircraft.

The first factor of importance is an aerodynamic design that reduces drag. This reduces pollution and noise and is essential for any commercial aircraft (Schneider, pp. 9-16,). Much of the drag is due to friction drag and induced drag. Induced drag depends on the lift distribution the wing span. The commercial aircrafts too aim to cut down on Direct Operative Costs. All of these factors define wing design. According to Prandtl, the lifting system with the minimum induced drag, is a wing box in the front view (Frediani, & Montanari, 28).

The MSD code that the University of Pisa used was parametric in order to accord accurate calculation. The Euler analysis also was used and this showed that the plane should be designed in such a way that it should avert shock waves on the rear wing.

Any computation also has to take into consideration ach of the following aspects of the plane:

-identification of the four main lines (center, top, side, bottom),

-sketch of the four main lines, exported in (.dat) file format.

-identification of control sections and bays

-sketch of control sections, exported in (.dat) file format

-generation of the body geometry by means of NURBS interpolation.

This is what the MSD code does (Frediani et al. (2012 ).

In order to achieve stability and control, the wing must be designed with the same principles as that used for the body of the aircraft (Cleynen, 3) The wing is created by adding one bay to the other connected at each end from first to last airfoil. Airfoil is designed by sweep, twist, dihedron and is attached to each end of the wing in order to achieve full sweep and to reduce drag.

Each bay (i.e. wing of the plane) is generated by extrusion (i.e. A process that is used to create objects of a fixed, cross-sectional profile). The process of working all this out geometrically is achieved by piece-wise NURBS interpolation (Wolkovitch, pp.649-670).

In a PrandtlPlane configuration, the geometrical design of the wings are called 'rounds' since they are made up of horizontal and vertical wings, joined by round trunks of wings. These 'rounds' are mathematically important since they help define the aerodynamic results of the plane. Each of the 'round' (form let's say the beginning on the horizontal wing to the end on the vertical wing) operate and are designed according to certain laws. Each (such as the airfoil, radius of curvature, etc.,) also changes with laws of air flight. The shape and grid of the round elements are therefore defined by a set of parameters which are changed during the optimization process. Each curve of these rounds is calculated with reference to a control polygon that is defined by three control points.

The entire Prandtl Best Wing optimization has to primarily consider 3 aspects: possible transonic phenomena, static stability of flight requirement and structural design. Each of these has to be taken into consideration to design the most effective wing.

In order to consider compressibility effects, a CFD Euler analysis is conducted. Static stability of flight can also influence aerodynamic efficiency so the two components are studied and worked on together. Finally, the structural design of the lifting system too is particularly important due to factors o new materials or the innovative design of the wing box sections. The wing has to be detached a certain distance from the fuselage to reduce noise. This is worked out mathematically too. The front wing, therefore, may have to be more loaded than he rear one. This depends on the aircraft.

In the research conducted by (Frediani et al. (2012) they learned that:

In order to control the stability of flight, the lift repartition (between the wings) and the lift distribution (along the span), we need to modify both the twist angles along the span and the geometrical parameters of the wing (chord distributions, sweep angles, etc.). By modifying all these parameters, it resulted that the best repartition of lift associated with static stability of flight was of the order of 70% on front wing and 30% on rear wing. (p.9)