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Derivatives are evaluated about the trim condition because

  • A.The derivatives would otherwise have the wrong units for use in the equations
  • B.The equations of motion are linearised for small perturbations about that condition
  • C.The wind tunnel can only be run at one speed
  • D.The aeroplane never departs from trim in service

Answer: B

Linearisation is the whole basis of the method: the aerodynamic forces are expanded as a Taylor series about trim and truncated after the first-order terms, whose coefficients are the derivatives. That is why a set of derivatives is quoted for a stated speed, altitude and configuration, and why a different flight condition needs a different set. Tunnel capability has nothing to do with it. Aeroplanes leave trim constantly, which is precisely why the perturbation equations are needed. The units follow from the definition rather than from the choice of reference.

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