Often, it is not worth it to try to find a closed function modeling the aerodynamics. In such cases, the the simulator can obtain the forces and moments from a tabular data obtained from flight or wind tunnel tests.
Table 1 lists a simple example of a table. The table lists a drag polar typical of a wing with a laminar flow airfoil. To determine the drag, the simulator determines which two points in the table the angle of attack is between, and then calculates the drag by linear interpolation. To speed up the interpolation, the slope of each segment is often precomputed and stored in the table as well .
C_{X} | |
(deg) | |
-10 | -0.0134 |
-8 | -0.0108 |
-6 | -0.0094 |
-4 | -0.0082 |
-2 | -0.0072 |
0 | -0.0052 |
2 | -0.0053 |
4 | -0.0055 |
6 | -0.0116 |
8 | -0.0175 |
10 | -0.0230 |
Aerodynamic force is generally a function of more the one variable;
therefore, flight simulators use multidimensional tables.
Theoretically, the table could have a dimension for each variable the
force coefficient is a function of. For example, C_{M} may be
expressed as
Fortunately, the effects of some variables are not influenced, or are influenced only weakly, by other variables. For example, the effect of on pitching moment is not influenced by , and vice versa. Thus, and never need to appear in the same table. This allows the large table to be broken into several smaller tables, each limited to three or four dimensions. The tabular model sums the contributions from each table.
A tabular aerodynamic model has been used to simulate an
F/A-18
.
Equation 64 presents an
example of an extremely simplified version of the model for the yawing
moment:
The main problem with tabular models is the lack of smoothness. For example, the C_{X} curve from Table 1 is nondifferentiable at the tabulated points, and its derivative is discontinuous. Flight simulators can remedy this somewhat by using tables with smaller increments. Another technique is to use higher-order interpolation.