Q & A #171 Residual Area Ratio Calculation

To find the values of area A and B that are used in the RESIDUAL RATIO, you need to find the rows in the Righting Arm table that correspond to EQU and the smaller angle of the following three: 50 degrees, downflooding (FLD), and the angle of vanishing stability (RA0). In this case, the downflooding angle and the second intercept occur at an angle larger than 50 degrees.

The cumulative residual areas are located in the 7th column in the table. Since the area region labeled A begins at the first angle in the righting arm table, the total area for this region is simple the cumulative area at the angle that corresponds to the end of this regions. Area A stops at equilibrium so we can simply look at the value in column seven that corresponds to the row where the value in column 6 is zero. GHS uses the convention that residual area is negative if the absolute righting arm curve is less than the heeling arm curve. So the cumulative area from the start of the curve up to the angle of equilibrium (12.88s) is reported as a negative 15.92 foot-degrees. Finding the area for region B involves subtraction. Remembering that this area column is cumulative, if we simply take the area from column 7 that corresponds to the row whose angle terminates region B, we will be getting the total area from the start of the curve until 50 degrees. Since region B starts at equilibrium, not the first angle in the table, we need to subtract off the residual area from the start of the curve to equilibrium, which is the area of region A. So we take the area value corresponding to the terminating angle for region B and from that subtract the area value for region A.

Area value from table corresponding to angle which terminates region A: -15.92 The start of region A is the same at the starting angle of the table so area for region A = abs(-15.92) Area value from table corresponding to angle which terminates region B: 19.48 This cumulative area value includes region A so it needs to be subtracted out. Area region B: = 19.48 - (-15.92) = 19.48 + 15.92 = 35.4 Ratio of area B / area A = 35.4 / 15.92 = 2.224

To see the example run file that prints the values of area A and B in the report, click here.

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