Note on Metacentric Diagrams

Discussion in 'Stability' started by AaronJohnson, Jul 23, 2011.

  1. AaronJohnson
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    AaronJohnson Junior Member

    I’m trying to get a copy of an article from 1941 by John Joseph Welch. I’ve put a request through inter-library loan, but unfortunately I’m not that patient!!! The article is called:

    Note on Metacentric Diagrams
    by J. J. Welch
    The Shipbuilder and Marine Engine-Builder
    July 1941

    The article is also published in:

    The Journal of the American Society for Naval Engineers
    Volume 53, Issue 4, pages 811-822, November 1941

    Any help would be greatly appreciated!
     
  2. hoytedow
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    hoytedow Wood Butcher

  3. AaronJohnson
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    AaronJohnson Junior Member

    I did find that... I’m not that keen on purchasing stuff online though! On another note: does anyone know if the information is relevant to sailboat hull design? I believe the basic premise is to design the hull so that the locus of the curvature of the curve of flotation is located at the metacenter. The small addition or subtraction of weight in this design would not change the characteristics of stability of the hull? Any thoughts?
     
  4. MikeJohns
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    MikeJohns Senior Member

    Metacentric diagrams

    I scanned this in for you, hope this helps elucidate the subject.

    From the book available here:
    http://www.nauticalbooks.co.uk/site/bookdetails.asp?id=103

    cheers
    Mike

    These days with the ease of altering and analysing the hullform instantly I'd be more inclined to look to the GZ curve than try and design to metacentric curves of form.
     

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  5. AaronJohnson
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    AaronJohnson Junior Member

    Thank you Mike,

    Those pages were very helpful. So, as I understand it, the metacentric diagrams are useful only in cargo vessels with varying drafts (as it graphs the height above or below the waterline of the metacentre at different displacements), but not for other vessels with fixed displacement?

    Is a sailboat’s metacentre always highest at zero degrees of heel? And what are the typical values? I’ve calculated the metacentres for simple shapes (box and parabolic cylinder) and those shapes show the reverse.
     
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  6. TeddyDiver
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    TeddyDiver Gollywobbler

    No.. they are useful to all vessels. Unfortunately they aren't published generally..
    And no again.. it depends of the cross sectional shape and VCG. And it naturally changes some depending of the loadings you refer to..
    BR Teddy
     

  7. AaronJohnson
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    AaronJohnson Junior Member

    When I was working out the shape of the transverse metacentric curve for the simple shapes I mentioned (box and parabolic cylinder) I noticed that the shape of the buoyancy curve for both shapes was a parabola. The flotation curve was also a parabola for the parabolic cylinder and a single point for the box. Does anyone know what the family of curves are that produce parabolic buoyancy curves and flotation curves? (I’m making the assumption that the single point for the flotation curve of the box is a parabola of zero width.) Or is it simply that the box is a cut off parabola of infinite depth so that its sides are vertical?
     
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