cross curves

gianlisi
2006-04-25
2013-04-19
  • gianlisi
    gianlisi
    2006-04-25

    Hi marven,

    just a question:
    how the cross curves calculation is supposed to be used in order to obtain the rigthing moment?

    Is that GM*KN*sin(phi)?, so that just GM is supposed to be calculated apart?

    In case... GM = KM-GK? Is K the keel y?

    Many thanks

    gianluca

     
    • gianlisi
      gianlisi
      2006-04-25

      forgot... are results of the cross curves an axpossimation (like the DSYHS) or a calculation based on the model geometry itself?

      once more thanks

      gianluca

       
      • Marven
        Marven
        2006-04-25

        These are exact hydrostatic properties, not an estimation or approximation.

         
        • Thanks for the very useful explanation... but then, what do I have to moltiplicate to the data obtained by the cross curve calculation (which gives a force) to obtain the rigthing moment?
          gianluca

          ps: I maybe wrote bad... my KN meant KiloNewton! :-) sorry...

           
          • Marven
            Marven
            2006-04-26

            The result of the crosscurves calculation is a distance, not a force.
            Subtract VCG*sin(phi) from that to obtain the righting arm GZ.
            To obtain the righting momen from that finally multiply as follows:

            Righting moment RM=GZ*Displ*g where g is the gravitational acceleraton. If displ. is in tons then the righting moment is in Kilo Newton.

             
            • I had understood really nothing... now it's clear!

              gianluca

               
              • Marven
                Marven
                2006-04-27

                Good!

                 
                • Marven,
                  Congratuations on a marvelous product
                  Please tell, are the cross curves calculated to free trim or fixed trim?
                  Thank you

                  Ian

                   
    • Marven
      Marven
      2006-04-25

      GM is the metacentric height when heel is (almost) zero. In that particular case GM=KM-KG. Under larger angles of heel the metacentric height shifts and is called the virtual metacenter (denoted by N). Its height above the keel is KN. If you know the height of your center of gravity above the keel (KG) than you can calculate the righting arm as follows:

      GZ=KN sin(ø)-KG*sin(ø)

      where ø is the heeling angle

       
      • I have always believed the formulation for the determination of GZ is : GZ=KN-KG*sin(ø); (ø)is the heeling angle. So my question is : the cross curves results are KN or KN*sin(ø);
        Thanks for your answer.
        Jean-Claude (PSCO)

         
        • Marven
          Marven
          2006-09-11

          No, GZ=KN*sin(ø)-KG*sin(ø)

           
    • Toni
      Toni
      2006-04-30

      Could someone explain what the cross curve is ?

      For example, in kayak design I used 0.1 tons (100kg) displacement and got 0.11 kN at 20 degree, 0.18 kN at 40 degree.

      So; in first values, I'm assuming the kayak is tilted 20 degrees, it still has displacement (load) of 100kg's and the hull shape creates 110 N force that is trying to tilt the kayak back to horisontal position.

      But what does that 0.11 kN really mean? Is it force at definite distance from roll axis? Or is it something else?

       
    • Both are correct!!!!!

      In Marvins Case he denoted the new Metacenter by KN
      hence GZ = KN*Sin (theta) - KG cos (theta)

      In the conventional sense, KN is the perpendicular distance from the Keel Point (Intersection of CL with BaseLine) to the Line of Action of Buoyancy (Heeled Condition)

      hence in this case GZ = KN - KG sin (theta)

                                  '. :
                                   '.:
                                   M : Marvin denotes this as N
                                     :'.
                                     :phi
                                     :   '.
                                     :    '.
        GZ = KN - KG Sin (theta)     :      :
                                     :       '.
        since from figure            :        '.
        GZ = PN                      :       90 . Z
        PN = KN - KP                 :      ..'' '.
        and KP = KG sin (phi)        :  ..''      '.
                                  G  .''            :
                                     ::              '.
                                     :phi             '.
                                     :  :               '.
                                     :   :             90'. N
                                     :    :            ..'':
                                     :     :       ..''     '.
                                     :    90:  ..''          '.
                                     :     ..P.
                                   K : ..''
                 '''''''''''''''''''''''''''''''''''''''''''''''BL
                                     :
                                     ' CL

      RP