Section 1. Aerodynamics of lifting surfaces

Topic 5. The aerodynamic characteristics of
Wings in gas subsonic flow

As it was spoken earlier, aerodynamics of subsonic speeds is limited by Mach numbers .

Potential of speeds of disturb flow satisfies to linearized equation of gas dynamics in a linearized subsonic flow

. (5.1)

Let's pass to new variables, so to receive the Laplas equation for speed potential in incompressible fluid. Then, assuming flow parameters and aerodynamic characteristics in incompressible fluid as known, we shall connect them to the required characteristics in a subsonic gas flow.

The passage to incompressible flow is performed by replacement of coordinates:

(5.2)

where variables with an index correspond to coordinates in incompressible gas flow. At that and .

For the pressure factor in incompressible flow we have and . Finally we receive:

. (5.3)

Therefore, the aerodynamic characteristics connected to pressure forces are determined analogously:

, , . (5.4)

It is necessary to emphasize that the characteristics , and correspond to the transformed wing (Fig. 5.1) at passage to incompressible flow, i.e. to a wing with geometry , and . Let's define these parameters:

Fig. 5.1. a) - initial wing; b) - transformed wing.

, , , , , , , - reduced aspect ratio, ,

Now it is possible to obtain the aerodynamic characteristics of the specified wing in subsonic flow, knowing the aerodynamic characteristics of the transformed wing in a flow of incompressible fluid. Let's notice, that the we consider linear components of and . Therefore it is possible to write and instead of and in the formulae (5.4).

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