America's Fighters of the 1980s - F-16 & F-18 by Robert C. Stern

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By Robert C. Stern

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7, as defined by the following matrix of vertex coordinates: V ¼ ð v1 0 0 ¼ @0 0 v2 1 0 0 v3 1 0 1 v4 0 0 1 v5 0 1 0 v6 1 1 0 1 1 1 v8 Þ v7 1 0 1A 1 ð2:23Þ Assuming that the xy-plane is originally horizontal (with the z-axis pointing vertically upwards), the entire object can be rotated through an angle of 30° or p/6 radians about the x-axis by applying the following transformation: 0 V ¼ Rx ðÀp=6ÞV For instance, this is the type of calculation that would be required to define the spatial position of an aircraft fuel tank at a bank angle of 30°, starting from a convenient datum frame.

16):    x1 cos y ¼ y1 Àsin y sin y cos y  x0 y0  ð2:17Þ As previously, the result obtained in the xy-plane can be expanded to include the z-axis. 17) can be rewritten, as follows: 0 1 0 cos y x1 z-Projection: @ y1 A¼@ Àsin y 0 z1 sin y cos y 0 10 1 0 x0 0 A@ y0 A 1 z0 ð2:18Þ Once again, the transformation can be inverted by applying an elementary projection through a negative opposite angle, which means that the transformation matrix is transposed. 18), it should be clear that rotation and projection are equivalent mathematical processes.

Without being overly assertive about this particular categorisation, it is one of a number of ways of highlighting scientific and technical aspects that come together in design. In short, a vehicle is a mobile platform with a load-bearing structure of frames, panels and effectors (that determine shape, strength and stiffness) together with an array of enclosures, apertures and interfaces. It is surrounded by an environment that determines its configuration, its means of propulsion and so on. The remaining elements relate to the way in which the vehicle is mechanised for its intended role and involves the selection of appropriate technologies.

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