GHS BULLETIN
Wind and Rolling Calculations

1/2018

In the presence of wind pressure, a vessel may need to have enough righting energy available to absorb the kinetic energy due to a roll from a point to the windward of its equilibrium heel. GHS provides a mechanism for setting such a windward heel angle so that these energies can be compared.

With a heeling moment in effect (see the HMMT command), the equilibrium heel angle can be found simply by issuing the SOLVE command (without parameters). If the roll angle to windward of equilibrium is known, the heel angle can then be decremented simply by giving the command
```  HEEL *-r
```
where r is the desired roll angle.

A more powerful way of handling the roll angle is provided by the ROLL command. For example,
```  ROLL r
HEEL *-ROLL
```
does about the same thing as the HEEL *-r command, except that it always moves the heel angle in the direction opposite to the initial heel angle. Further, if the actual value of r is to be calculated from the present condition according to the IMO rolling formula, then the ROLL command may be given once in the form
```  ROLL IMO
```
and the actual value of r will be calculated when it is needed from the then-present condition.

A typical sequence of commands to check the energy available to resist an IMO roll would be:
```  ROLL IMO
WIND 53.4
HMMT WIND /CONST
SOLVE
HEEL *-ROLL
RA /AREA
```

If an increase in the heeling moment (due to a gust of wind) occurs at the rolled angle, it can be modeled by using a /GUST parameter on the HMMT command. The issuance of the HEEL *-ROLL command then automatically causes the heeling moments to be multiplied by the gust factor from then on -- until another HMMT command is issued. For example,
```  ...
HMMT WIND /CONST /GUST: 1.5
SOLVE
HEEL *-ROLL  `<-- The gust factor does not take effect until after this.
RA /AREA
```

When using the MAXVCG process, the roll angle and gust factor are automatically applied in the proper sequence. Thus
```  ROLL IMO
WIND 53.4
HMMT WIND /CONST /GUST: 1.5
SOLVE MAXVCG
```
is all that is necessary.

Further, the MAXVCG command automatically recalculates the wind moments at each new draft when they are based on the lateral plane. Hence
```  ROLL IMO
HMMT WIND /CONST /GUST: 1.5
MAXVCG ...
```
produces maximum VCG curves for a stability criterion involving the ROLL angle.

The LIMIT command, used for establishing stability criteria, accepts the keyword ROLL as an angle, in which case it actually refers to the *-ROLL angle. For example,
```  LIMIT RESIDUAL RATIO FROM ROLL TO ABS 50 OR RA0 > 1
LIMIT RESIDUAL RATIO FROM ROLL TO FLD or RA0 > 1
```
expresses the IMO criterion for severe wind and rolling.

When you want to run the righting-arm curve either to port or starboard, depending on the vessel's initial (non-wind) list, things get a little more complicated. The MAXVCG process handles this automatically; but when you are doing an individual righting-arm curve you have to make sure that certain commands are in the correct order. The procedure is as follows.
```  1. With the heeling moment off, solve for the equilibrium heel angle.
2. Set the ANGLES direction accordingly.
3. Set the heeling moment.
4. Set the HMMT direction according to the heel angle.
5. Solve for the equilibrium heel (with steady wind).
6. Apply the roll.
7. Do the RA /LIM command.
```
Here is an example.
```  HMMT OFF
SOLVE
ANGLES *
HMMT WIND/CONST/GUST:1.5
HMMT *
SOLVE
HEEL=*-ROLL
RA /LIM
```

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Copyright (C) 2011 Creative Systems, Inc.