Righting and Heeling Arm Curves Righting and Heeling Arm Curves

To compute righting and heeling arm results, the user should issue a command of the form:


     RARM, INC, NUM, -OPTIONS

The options available are:


     -ECHO, YES/NO

     -FIX

     -NUMITER, ITER_MAX

     -TOLERANCE, HE, RO, PI

     -WAVE, WLENGTH, STEEP, CREST

     -YAW, YAW_ANGLE

     -WIND, WIND_SPEED

     -CEN_LATERAL, X, Y, Z

     -U_CURRENT, FLAG

     -W_COEFF, WC0, WC1, WC2, WC3

     -R_COEFF, RC0, RC1, RC2, RC3

     -STOP, HOW

     -WEIGHT, SF_WEIGHT

The -ECHO option controls the trace of iterations which is printed at the terminal. If YES/NO is YES, then the trace will be printed, otherwise it will not. The option, -FIX, fixes the trim of the vessel during the iterations. The option -NUMITER is used to override the default (20) number of iterations, and -TOLERANCE is used to override the default closure tolerances for heave, roll, and pitch respectively. The values are a percentage of weight for heave, and arms for the angular motions, and the defaults are 0.0001, 0.01, 0.5. Finally, the -WAVE option controls the static wave as discussed earlier.

When the command is invoked, it will rotate the vessel NUM times adding INC to the roll angle. For each increment, the program will iterate an equilibrium position for the other degrees of freedom and then compute the righting and wind heeling arms. Since the righting arm is based on the equilibrium of the buoyancy and weight of the vessel, the vessel weight must have been previously defined either in the model itself, or via an &WEIGHT command. For this command only, roll is defined as a rotation about an axis which can be changed. The default is, of course, the vessel X axis.

The -YAW option is used to compute righting arms about a skewed axis. YAW_ANGLE is the angle of the axis for computing the arms from the vessel X axis. If this option is used, then the axis for the "roll" is yawed to the angle specified. Here, the angle is measured positive from the X axis positive toward Y. If one uses a angle of 90 degrees, the "roll" axis will be moved 90 degrees toward Y and the righting arms will be about the Y axis. In other words, here a "roll" of 2 degrees will make the vessel stern go down.

In addition to computing the righting arms of the vessel, MOSES will compute the wind heeling arms when the -WIND option is used. Here, any load attributes which attract wind (#AREA, #PLATE, #TABLE, #TANKER, structural elements, or pieces) will be used with WIND_SPEED (knots) to compute a wind force. A heeling moment is computed from this force and an assumed point of application. There are three alternatives here:

The -W_COEFF and -R_COEFF options allows one to define a "heeling/restoring moment" which will be added to that computed from the load attributes. Here, WC0, WC1, WC2, and WC3 or RC0, RC1, RC2, and RC3 define that additional moments as:

     MW = ( WCO + WC1 * H + WC2 * H*H + WC3 * H*H*H) * WIND_SPEED **2
     MR = ( RCO + RC1 * H + RC2 * H*H + RC3 * H*H*H)

where H is the roll angle in degrees, and MW is in bforce-blength, and MR is in feet or meters.

The -STOP option is used to stop the computation after a specified event has occurred. If HOW is RARM then it will stop when the righting arm crosses zero. For a value of NET, termination will occur at the second intercept point. Finally, DOWN will terminate when the minimum NWT down-flooding height becomes negative.

One of the results computed during this process is the minimum height of all down-flooding points on the vessel. The user can define and alter this set of points with &DESCRIBE COMPARTMENT commands. If he has not defined a point, then the height of the vessel origin will be reported. The -WEIGHT option is used to redefine the scale factor used to convert righting moments into righting arms. By default, the apparent weight of the vessel is used. If the option is exercised, SF_WEIGHT (bforce) will be used.

At the conclusion of the command, the user is again placed in the Disposition Menu so that he can dispose of the results.