Stress and shape analysis of a paraglider wing

The paraglider wing consists of leading-edge booms and a keel boom joined together at the nose and a flexible sail whose surface carries the aerodynamic pressure loading. The payload is suspended beneath the wing by cables which are used to control the wing. Adjusting the length of these cables controls the glide path of the wing by shifting the position of the payload with respect to the wing. The deflected shape of the sail depends on the pressure distribution over the sail; the pressure distribution in turn depends aerodynamically on the deflected shape of the sail. It is the purpose of this thesis to derive the equilibrium equations for the sail and to integrate these equations to find expressions for the stress resultants in terms of the pressure on the sail and the deflected shape of the sail. By integration of these expressions for stress resultants, along the edges of the sail, the resultant forces applied by the sail to the leading-edge booms and keel boom are found. Then, by considering the streamwise components and the components normal to the stream of the boom forces, the drag and lift forces are obtained. These expressions for the lift and drag forces, and for the boom forces, are given in terms of the boundary value of the stress resultants and can be applied for any aerodynamic theory appropriate to the speed range being considered. When the appropriate aerodynamic relationship, between pressure and deflected shape, is substituted into the boundary, conditions for stress resultant at the trailing edge of the sai1, the criterion for determining the deflected shape is obtained. Once the deflected shape is known all the other quantities can be determined. In order to show an application of the analysis, the equations were specialized for Newtonian impact theory. This theory yields a simple pressure-deflected relationship. This aerodynamic theory, which has found applications for hypersonic speeds, has been employed since it shows the application of the method in a simple manner. In addition, it has been previously for a rigid idealization of a paraglider wing and thus provides a ready means for comparison. Hence numerical results can be used to test the accuracy of the rigid idealization. These results showed that the deflected shape of the flexible paraglider wing differed considerable from the conical shape of the rigid wing over the complete range of angle of attack. The differences in shape result in different pressure distributions over the surface of the wing and as a result the lift and drag coefficients, and especially the lift-to-drag ratio, for the flexible wing were significantly different from the values for the rigid wing. The boom forces and the distribution of stress resultants over the surface of the sail were obtained. The stress resultants along radial lines were found to be proportional to the distance from the nose of the wing. The calculated stress resultants and boom forces provide a basis for design of sails, booms, shroud lines, and spreader bars for a paraglider for hypersonic flight. Effects of dihedral angle (raising or lowering of the leading-edge booms relative to the keel) were also considered. The pressure distributions, the lift and drag coefficients, and the ratio to drag were found for several dihedral angles at a given angle of attack.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Polytechnic Institute

Year dc:date.issued

1963

Author dc:creator

• Fralich, Robert W.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10919/101484

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/101484