Question About Gz

Discussion in 'Stability' started by mcm, May 3, 2013.

  1. mcm
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    mcm Senior Member

    For small angles of heel it is accurate enough to use the un-heeled metacenter to measure the GM x SINE for GZ, BUT what about 20*-30* angle of heel ?

    Are those angles of heel also small enough to use the un-heeled metacenter to get an accurate enough GM x SINE for my GZ ?
     
  2. Ad Hoc
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    Ad Hoc Naval Architect

    No.
    For those angles you are into "large angle stability", see below for definition why:

    metacentric curve def.jpg metacentric curves.jpg
     
  3. mcm
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    mcm Senior Member

    Thanks Ad Hoc,
    So now i have to develop new water-planes at these greater angles of heel while maintaining the same displacement,,, ouch!
     
  4. chayan
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    chayan Chayan Chakraborty, Naval Architect.

    For large angle of heel, you may follow the Attwood's formula to find the GZ.
     
  5. mcm
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    mcm Senior Member

    thanks chayan,

    concerning attwood's formula GZ=[v(hh')/V] - BG sine (theta)

    what is the definition of wedge (v) ?
    and what is the definition of hh' ?
     
  6. Crowsnest
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    Crowsnest Junior Member

    Gz

    Best, and by the way, accurate standard approach ,for GZ calculation is by means of CrossCurves and CG(Center of Gravity possition).

    CrossCurves(KN) depend on hull shape. Hence must be derived, for a set of heeling angles/Displacements, from the hull design.

    Most ship design softwares have the capability for those curves calculation. Making the work, by hand is long, and by the way, nowadays, a nosence.

    KN curves, are referred to the Base Line (K) and not to the CG, hence do not depend on loading conditions. As said before, only on design shape.
    Take a look to the attached pic. A hull is heeled an angle t, while floating on the plane defined by F-F'.
    With a righted ship, the Buoyancy center (C), was located at C1, but once heeled, it moves to C2.
    This is well known. By drawing the floating vector through C2, the intersection with the longitudinal center plane, will return the Metacenter possition(M).
    But due to the hull shape, the motion of C, does not behave as a circle arc centered on M. Hence Metracentic height cannot be directly deduced.
    But, once again. We have the KN(CrossCurves) provided by the designer or self-obtained in any way.
    Provided that the intention is to draw/calculate, the GZ curve for a given displacement.
    Read along the KN curve that fits the desired displacement (or interpolate between adjacent values), its value for each angle.
    Just having a look to the pic again, it becomes obvious that:

    GZ(t)= KN(t)- KG sin(t) with:
    GZ(t) GZ for the heeling angle t.
    KN(t) CrossCurve value for displacement/heeling angle(t)
    KG Vertical coordinate of the Center of Gravity, measured from the base line(K) in Righted Ship conditions.

    If the Center of Gravity has transversal coordinate, its not located on the Longitudinal center plane, (TG), then:
    GZ(t)= KN(t) - KG sin(t) - TG cos(t)

    [​IMG]

    Once checked that the GZ curve fullfills the required criteria, its time for Computing and checking the Dynamic curve, that is directly obtained by numerical integration from GZs.

    Hope this helps.

    Regards
     
  7. mcm
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    mcm Senior Member

    Thanks Crowsnest,

    i don't have the software, so i have to do it the hard way.

    i do have the new heeled waterline, but, since the 20 deg. heeled underwater shape of the hull is no longer symmetrical port to starboard, it's going to take me some time to figure out the new transverse and vertical center of buoyancy.

    in the end i want to figure out the KN cross-curves for the full range of heeling angles.
     
  8. mcm
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    mcm Senior Member

    To derive the new heeled centers of vertical and transverse buoyancy when at large angles of heel, Larson and Rolfson in "The Principles of Yacht Design" recommend the cardboard cut-out method.

    But i find it hard to visualize their description.
    They say cut-out each underwater hull section in cardboard, glue them together in correct sequence, then rotate the glued sections on a needle while using a plumb-bob.

    What ?

    I can visualize balancing the cut-out sections on a knife edge vertically and then horizontally to derive the new heeled transverse and then vertical centers of buoyancy.

    But where an how do you rotate the cut-out sections on a needle, and how does the plumb-bob come into it.

    I wish they had given a step by step illustration of this method which they say is accurate enough.
     
  9. Crowsnest
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    Crowsnest Junior Member

    Free Soft

    If you have the lines plans, its possible to remake them in FreeShip. This software has the capability for computing all hydorstatic and many of the dynamic datas of the ship. By the way it's Free.

    Albeit, working by hand, is the better way to get a good base knowledge, granting the accuracy of results, becomes easier by using a computer.

    Best regards and don't hersitate asking any time you need it.
     
  10. Crowsnest
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    Crowsnest Junior Member

    Methods

    There are lots of methods and formulas that try to give an aswer to this subject.
    Take into account that all of them are aproximative and only valid for a given Kind/type of ship.
    When using this kind of solutions, its a key question to use the formula/methodology that fits the hull under study.

    The only accurate, general way, is working from the offsets table, numerical and/or graphic methods, which by the way, is the path that computational procedures use.

    Of course the hull symetry is broken when the ship is heeled. When and how much are things that directly depend on the design. Extrictly speaking symmetry is broken from the very first beggining of heeling, excepting the case of "revolution bodies" hulls.

    Regards
     
  11. TANSL
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    TANSL Senior Member

    You can do something very similar, but much faster and more accurate, with AutoCAD:
    1.-You draw each frame, the depth you want, the transform to region and you ask AutoCAD to calculate their physical properties. You get well the area, the center of gravity, development and something more, for each frame.
    2.-These values, duly placed in Excel, of integrity by the Simpson method or by the method that you like. This will give you the volume, center of buoyancy, the wet surface and some coefficients.
    3 - Doing the same, with various drafts and heeling, you can get KN curves. It is very laborious, but much less than if you do it by hand by the method of cutting cardboard, and much more accurate and complete.
    Regards
     
  12. mcm
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    mcm Senior Member

    Thanks Crowsnest and Tansl for the Freeship and Autocad suggestions.

    However, because my interest is not professional, but simply casual personal knowledge, i am trying to avoid the learning curve regarding software.

    If i can correctly grasp the basic stability ideas by using simple paper, pencil, and calculator upon no more than an example or two (such as Larson and Rolfsson's example) i will be satisfied.
     

  13. Crowsnest
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    Crowsnest Junior Member

    mcm
    OK, you're wellcome.

    Tansl
    Agreed

    Regards
     
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