By Andras Sobester, Alexander I J Forrester
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Extra info for Aircraft Aerodynamic. Design Geometry and Optimization
Put another way, they can be derived from the two curves (upper and lower) making up the side profile of the fuselage: the scaling variable is the difference between the two and the Z-wise positioning variable is the lower curve. 12. Any number of mathematical formulations could be used to define all of these curves, subject to any number of design variables. 11 we merely show a possible instance of one possible parameterization. There is no limit here to adding additional flexibility via the parameterization of these streamwise functions.
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.
7 to construct a Boeing 747-style double-deck fuselage cross-section. To enable an optimizer to include this type of section in a design search, we need to make a subtle tweak to the formulation: we need to add the possibility of closing the profile with a common tangent (shown here with a dash–dot line). e. we also want the optimizer to visit solutions that leave the cusp between the lobes exposed), we have to pay with the usual currency of flexibility enhancements: increased dimensionality. Thankfully, this time we can get away with a binary variable (common tangent to the two lobes present or not); but even this results in a doubling of the design space, and thus a doubling of the cost of the design search – not a step to be taken lightly.