Location of aerodynamic center. 1. The dependence is linear for any aspect ratio wing ( )

Drag.

Lift.

1. The dependence is linear for any aspect ratio wing ().

2. With increasing of the value of a derivative grows and at tends to the airfoil characteristic (Fig. 6.4). This tendency takes place faster than in subsonic flow, that is explained by limited area of the lateral edges influence at .

3. The value of derivative decreases and tends to with increasing of Mach numbers , that is connected to narrowing of Mach cones at growth of and reduction of lateral edges influence (Fig. 6.5). It is possible to assume, that already at (difference is less than at , at - less than ).

Fig. 6.4. Dependence at

Fig. 6.5. Dependence at

4. The ratio is the universal dependence on reduced aspect ratio .

There is only pressure drag which determines wave drag and induced drag in an inviscid supersonic flow. As the wing leading edge is supersonic, then there is no sucking force and (for flat wing). As and , then ; . At that influence of onto at is weaker than in subsonic flow (for example at ). The wave drag is defined by airfoil drag and multiplier which is taking into account span finite. Let's notice, that in case of unswept wing, the same multiplier is included in the formula for (6.4). As well as , the value of parameter with increasing of and (more precisely ). It is explained by narrowing of Mach cone and reduction of lateral edges influence. It is possible to consider that at (error ). The ratio is depended only on reduced aspect ratio and factor of the airfoil plan form i.e. .

Fig. 6.6

"Loss" of lift in the wing areas falling inside of Mach cones will cause displacement of pressure center and aerodynamic center forward, to the leading edge, in comparison with location of the airfoil aerodynamic center (Fig. 6.6). The location of aerodynamic center is a function of aspect ratio .

At . Approximately at with an error less than . At difference from - .

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