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An extract from A Closed-Form Solution for Noise Contours, Scientific and Technical Information Branch (NASA), Ames Research Center, NASA Technical Paper 1432, 1979 (48 pgs)

In this report is described an analytical approach for generating noise contours that overcomes the difficulties of existing programs. Although many noise-contour programs are available, they require large computers and a sustained major effort for use, are complex and slow, and are generally not desirable for interactive use for on-line piloted-simulator use. The method developed here is valid for arbitrarily complex paths and reveals the importance of various factors that influence contour shape and size. The calculations are simple enough to be implemented on a small, hand-held programmable calculator, and a program for the HP-67 calculator is illustrated. The method is fast, simple, and gives the area, the contour, and its extremities for arbitrary flight paths for both takeoffs and landings.

The equations for the relevant characteristics of the noise contours can be implemented on a small hand-held programmable calculator. In this way the necessity to access a large central computer system is avoided. In this section we describe the implementation of the contour calculations for one of the common programmable calculators, the Hewlett-Packard
Because of the limitation of programming memory in the
HP-67, the program was accomplished in two parts: the contour-area and the contour plotting programs.
The area program calculates and sums the area of the noise contour due to each segment and also calculates some quantities necessary for determining the noise contour. The contour-plotting program determines the y values of the contour associated with an input value x. Instructions for using each of these programs are given in figures 1 and 2 for takeoffs and landings. Some discussion of the combined use of the two programs is required because there are two possible options. The first option, illustrated in figure 3(a), is used when the number of segments in the flight path is four or less. The area program must be run first because it calculates quantities that are required by the contour-plotting program. Next, the contour-plotting program is loaded and the contour is plotted . The second option, illustrated in figure 3(b), is the more general case. It must be used when the flight path consists of more than four segments; it can also be used when the user wants to postpone plotting the contour to a later time regardless of the number of segments. With this option, after the area program calculations have been completed for the first four segments, the area and the intermediate quantities are written on a magnetic card. The user then goes back to repeat the procedure with more segments until the complete flight path is finished. Later, when it is desired to plot the contour, the contour-plotting program and the intermediate quantities previously computed are loaded in the calculator and the contour is plotted.
For those interested in the details of the program, a flow chart and a listing of the area program are given in figures 4 and 5, respectively; figures 6 and 7 provide the same information for the plotting program.

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