What is shown below is an alternate way to represent the GM criterion, actually looking at the righting arm curve, not the GM directly. It assumes that the righting arm curve has the form of a sine cur ve and the heeling arm curve has the form of the cosine as shown in (1) and (2).

where

P= wind pressure

A= projected lateral area

H= the vertical distance from the center of the projected lateral area to the center of the underwater lateral area.

W= displacement

phi = 14 degrees or the angle at which one-half the freeboard to deck edge is immersed, whichever is lessThe angle at which the heeling arm curve and righting arm curve intersect is the angle of equilibrium. Therefore, at equilibrium

The Weather Criterion requires that (4) must be satisfied for each condition of loading and operation. Three LIMIT commands are required by GHS in order to apply this criterion.

The first LIMIT command assures that the angle of equilibrium occurs before 14 degrees or the angle at which one-half the freeboard to deck edge is immersed, whichever is less. It is defined as follows :

LIMIT(1) ANGLE from EQU to ABS 14 or HF > 0The HF keyword (short for Half Freeboard) refers to the angle at which one-half the freeboard to deck edge is immersed. In this case, the angle from equilibrium to the lesser of 14 or HF must be greate r than zero.

Before you can use the HF keyword, you must first mark the deck edge of the vessel. The deck edge is marked in Part Maker using the MARGIN command. For this criterion, the amount of the margin does not

matter. You could use zero or any other value. For example,

modify hull\hull.c margin 0 /When you view the vessel using the DISPLAY command, you should see a line marking the deck edge.

GHS does not make the assumption that the righting arm curve is a sine curve -- actual righting arms are calculated for each angle of heel. If only the angle of equilibrium is considered, it is possibl e to have a righting arm curve which satisfies LIMIT(1) above but has very little righting energy up to the angle or, in extreme cases, a negative GM at zero heel. In order to insure that the true righ ting arm curve provides as much energy as would a sine curve, a second LIMIT command is required. It is derived from (1) and (2) as follows:

The following LIMIT command can therefore be used to force the righting arm curve to be equal or better than the sine curve with regard to area (energy).

LIMIT(2) ABS RATIO from ABS 0 to ABS 14 > 0.492An additional limit is required to guarantee that stability exists beyond the angle of equilibrium. This could be a measure of the range of stability or the residual area. For example, if the range of stability is to be at least 15 degrees beyond equilibrium the limit command would be,

LIMIT(3) ANGLE from EQ to RA0 > 15To evaluate the stability of a vessel based on the Weather Criterion, you must also set the heeling moment. You can use the WIND and HMMT commands as follows:

WIND(PRESSURE)wherePHMMT WIND /C1

part. These commands will then generate the heeling arm curve as defined in (2).

Following is a simple run of commands which can be used to perform a weather criterion analysis:

READ filename REPORT WEIGHT w, l, t, v LIMIT(1) ANGLE from EQ to ABS 14 or HF > 0 LIMIT(2) ABS RATIO from ABS 0 to ABS 14 > 0.492 LIMIT(3) ANGLE from EQ to RA0 > 15 WIND(PRESSURE) P HMMT WIND /C1 HEEL = 0 RA 0,2 ... 14 /LIM

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