Arbitrary Motion of a Profile in Supersonic Flow

In a supersonic flow, the aerodynamic response of a profile to an arbitrary motion is function of the free stream Mach number and is obtained by means of the Wagner function and the Kussner function where the former is the response to a sudden angle of attack change and the latter is the response to an arbitrary gust. Here, we are going to use /(s) for the Wagner function and v(s) for the Kussner function as usual.

With Wagner function and ao:

cL(s) =2 nao /(s) (5.54)

Similarly, for a gust of magnitude wo with Kussner function:

cLg(s) = 2naJUj-x(s) (5.55)

Here, s is the reduced time based on the half chord. The approximate expo­nential forms for the Wagner and Kussner function read as follows.

/(s) = b1e bl s + b2e b2s + b3e Ьз*

Here, the numerical values for the coefficients and the exponents are given in Table 5.2 as provide by Mozalsky and O’Connell (1962).

Fig. 5.18 Pertinent dimen­sions of a slender body