Alternate table look-up routine for real-time digital flight simulation

HE increase in complexity of flight simulators in the last decade has placed an increasingly larger computational burden on the simulation host computer. In the past, this has been dealt with by using separate processors for different tasks. This is not always financially feasible, especially in a university setting, where an entire simulation might be limited to one or two processors. While a perturbation model, sometimes used in a partial task trainer, can be regarded as a linear system, the total force and moment model of a real-time man-in-the-loop simulation requires a more complex mathematical representation of the vehicle. Coefficients and derivatives are often functions of several variables, including control surface position, angle of attack, Mach number, and several other parameters. These functions seldom can be represented in closed form by a reasonably small number of equations. Often a table is created that consists of an array of known dependent variable values, tabulated at certain known values of one or more independent variables. Table 1 is an example of such a table. On each pass through the simulation program, a search is initiated through the appropriate tables, and an interpolation between known values is performed in each of the independent variable directions. This has been shown to be one of the most computationally intense aspects of the simulation process.1 In order to retain model complexity and still achieve an acceptable frame rate, table look-up algorithms that reduce the computational load are highly desirable. Two widely used search procedures are outlined by Rolfe and Staples.2 The first, Method la, performs a top-down search between successive array values and exits once the proper interval is located. The second procedure, Method Ib, also performs a top-down search, but only if the position in the table has changed significantly. This is a method that has been used in industry.3 The search procedure is employed for each independent variable in a multidimensional table, $nd the process is repeated for each simulation pass. Once the proper location in the array is reached, an approximation of the dependent variable must be calculated. This dependent variable is considered to be a function/of n independent variables and is approximated, as F, by carrying out successive linear interpolations in each of the n directions as outlined in Refs. 2 and 3. Alternate algorithms presented in this paper reduce the table search time by performing a top-down search during only the initialization pass. On all subsequent passes, the algorithm returns to the interval where the value will most likely reside. This is accomplished by tracking the direction and the rate of