# Nonlinear Aerodynamic Models

In the high AoA regime, flow separation and stall occur and the airloads become highly nonlinear functions of AoA. Therefore, the mathematical representation of the air­foil characteristics in this regime becomes more difficult. Usually this cannot be easily accomplished by using simple polynomial curve fits to the test data. However, mathemat­ically representing the nonlinear airfoil characteristics by means of analytic functions or equations can still be accomplished in several different ways. These methods need to be relatively parsimonious because they will be included inside the blade element models used for the rotor analysis; this means that computational efficiency is always paramount simply because of the very large number of times such models are accessed during a typical rotor calculation.

7.11.3 Table Look-Up

One common way of representing nonlinear airfoil characteristics is to store the measured airfoil data as tables. Generally, one table must be provided for each Mach number. A computer program can be written to manipulate these data and to extract interpolated values of Ci (or C„),Cm, and Cd for any specified AoA and Mach number. This is a procedure used by large comprehensive rotor analyses, and it is also used for flight simulation work where there may be a need for real-time evaluation of the blade airloads and so brevity of calculation is paramount, but without accepting a large loss of physical accuracy.

Representative experimental results for Q versus a for a rotor airfoil at Mach numbers of 0.3, 0.4, and 0.5 are shown in Fig. 7.48. The results for the intermediate Mach number of 0.4 were found by linear interpolation between the results at = 0.3 and Mqq = 0.5. It will be seen that, in the low a range, the results are accurate, but for conditions near stall less reliable results may be produced. If the measurements are spaced at sufficiently small increments in Mach number, then the resulting interpolated data using this kind of scheme is normally viable.