Properties of the Admittance

Eq. 4 is the basic transfer function for the infinite lifting surface. Eq. 3 is an integral form of H (k) obtained from the concept of strip theory; H (k) must be calculated only once, and can be used for an arbitrary body. The strip theory is based on the assumption that the downwash velocity at one spanwise location does not affect the downwash at a nearby position. It is evident that

lim H (k) = 1, (10)

k^0

which is coherent with the definition of admittance, Eq. 1. There exist val­ues of the gust speed ratio that yield values of the admittance larger than the unity, though H (k) is always finite. When the forcing frequency is signifi­cantly lower that the natural frequency of the aerodynamic system, the transfer function is equal to unity.

Eq. 3 shows that at a given frequency the admittance is inversely propor­tional to the profile width. The leading edge is invariant to yawing or stretch­ing. This can also be inferred from the transfer function.

Integration of the equations is generally done numerically, but for a limited number of cases there exist closed-form solutions.