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Old 8th Nov 2013, 19:07
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selfin
 
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Thanks for the detail Selfin - so in the context of this question, given the air mass remains the same (i.e. same pressure temperature) am I correct in saying that ro, csound and viscosity are constant (as are the airframe terms) so that CL is only a function of alpha?
Functions of several variables remain so when all but one of the variables are constrained. If a 3-variable function (alpha, Mach & Re) were chosen for the lift coefficient, the particular values selected for Mach & Re influence the desired alpha value for some required lift coefficient value. It is possible to choose a simpler single-variable function (in alpha) to model the lift coefficient and such a model is suitable for low speed aeroplanes.

In the original question the examiner appears to be content losing distinction between IAS and EAS, which is good to first order but fails to deliver satisfactory results at higher speeds and altitudes. It follows that the examiner probably does not want Mach and Reynolds numbers effects to be considered which is fine, so long as you appreciate the unstated assumption and the validity of any conclusions.

Here below I've reproduced an aircraft manufacturer's graph showing the relationship between the body alpha and the lift coefficient, at various Mach numbers, for a modern transport aeroplane. The lift coefficients in this example are linear functions of alpha while the slope parameters are close to a quadratic function in Mach number.



In summary there are two ways of viewing the practical problem of understanding the relationship between the angle of attack and the lift coefficient. For low speed aeroplanes, not operated at very high altitudes, the lift coefficient can be well modelled as a function of the angle of attack only. In all other cases that function should be expanded to include the effect of the Mach number, and the Reynolds number if necessary.
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