DATCOM allows the designer to input both area, S, and radius, R, for each body station. If we assume R is equal to half the width and height of the input body the maximum area covered is given by:

2R * 2R or 4 * R²

This formula is closely related to the formula for the area of a circle:

pi * R²

We can add a third formula for the area of a diamond:

2 * R²

In the general case, a shape number, S_n, can be calculated by:

S_n = S/R²

Since the maximum value for S is 4 * R² it follows the maximum value for S_n must be 4.

While there are many shapes possible for an S_n less than 4, I have dervived two formula to give a possible shape. Both formula converge at a circle with S_n = PI.

One formula, the blue line in the figure below is valid for PI <= S_n <= 4.0 and becomes a square at S_n = 4.0

The other formula, the red line in the figure below is valid for 2.0 <= S_n <= PI and becomes a diamond at S_n = 2.0. This formula yields result for S_n < 2.0 however, they are not accurate.

Fig.1, S_n = 1.00

Fig.2, S_n = 1.50

Fig.3, S_n = 2.00

Fig.4, S_n = 2.50

Fig.5, S_n = 3.00

Fig.6, S_n = PI

Fig.7, S_n = 3.50

Fig.8, S_n = 4.00

Fig.9, S_n = 4.50

Fig.10, S_n = 5.00