By Andras Sobester, Alexander I J Forrester
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Additional resources for Aircraft Aerodynamic. Design Geometry and Optimization
Such parametric formulations are said to be ill-posed. Incidentally, the latter is also an example of the separation of shape and scale, as defining the angles of the triangle essentially defines its shape; another piece of information is needed to give it scale. 1), but because dealing with something completely ‘sizeless’ is mathematically awkward, a simple work-around is usually employed: a length related to the geometry is designated as the unit of measure for the other lengths. For example, the geometrical elements of aerofoils are usually defined in terms of their chord length.
In other words, are we satisfied that the extent of the shape affected by changes to the values of given design variables is as local/global as we had planned? Compare, for example, B´ezier splines with nonuniform rational B-splines (NURBS). 17) will only have a local effect – moving control points on B´ezier curves will affect the entire curve. Neither type is ‘right’ or ‘wrong’ – not being clear on which type we are using is wrong. 1 introduced some of the key features that a parametric geometry must have.
Fuel burn and perhaps range are typical of this second tier. These are, however, still somewhat difficult to link directly to outer mould line geometry variables, so another level is required. Sometimes these lower level variables emerge from simple analytical models of the second-tier variables. 22) where ???? is propulsive efficiency, c is specific fuel consumption, CL is the lift coefficient and Wi and Wf are aircraft weights at the beginning and the end of the cruise segment respectively. We can immediately see a term there that makes an ideal optimization objective for the aerodynamic designer: CL ∕CD .
Aircraft Aerodynamic. Design Geometry and Optimization by Andras Sobester, Alexander I J Forrester
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