How valid is Marchaj area under the stability curve for catamarans?

Discussion in 'Stability' started by UpOnStands, Oct 10, 2017.

  1. Ad Hoc
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    Ad Hoc Naval Architect

    There has only been one questions I have asked. But you elected to answer a question I did not ask and unrelated.
    So back to the question at hand...

    Thus, your question of:
    You now have your answer.
     
  2. UpOnStands
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    UpOnStands Senior Member

    ummm, maybe, maybe not
    This is a cross sectional view of Shuttleworth Spectrum 42.
    Green area is roughly calculated to be 34 sq cm.
    Orange area is 68 sq cm with 13 degree heel.
    Sorry, but how does the Marchaj graph account for these changes in hydrostatic balance?
    Believe that is why Richard Woods referred to a theoretical crane lifting the windward hull.

    Just added the 3rd image showing the original displacement with 13 degree heel. Very little, if any, change in the hydrostatic balance.
     

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  3. Ad Hoc
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    Ad Hoc Naval Architect

    Well, now you know what occurs when the hull rotates and if a multihull, when one hull comes out of the water..the other hull must accommodate a new waterline as it supports the entire weight of the vessel on just the one hull.

    We calculate this effect using a GZ curve and it is done sequentially from 0 - 90 or 0 - 180 degrees (depending upon hull type) at 10 degree intervals, or similar like below:

    Typ GZ Curve for monohull yacht.jpg

    Then knowing the wind force is applied at a particular location on the sail, this force x the distance from the load application point to the waterline is a lever = a moment. This is called the wind heel moment.

    So we now plot this wind moment onto the GZ curve as shown below:

    Typ Wind heeel on GZ.jpg

    So where this wind heel moment curve intersects with the GZ curve, we get the angle of heel of the boat. That's it, simple.
     
  4. UpOnStands
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    UpOnStands Senior Member

    Back in the office again -- thanks for the explanation.

    No allowance is made for wind loading on the superstructure or indeed the hull itself?
     
  5. Ad Hoc
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    Ad Hoc Naval Architect

    Yes it is..and, depending upon the style/design of the deckhouse/superstructure, it can have some or little effect. The images you show above, for example, the shape of these coach roofs have been wind tunnel tested and shown to have minimal effect on the stability. But it is just one of the aspects that the naval arch must take into consideration when assessing the stability of the vessel.
     
  6. UpOnStands
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    UpOnStands Senior Member

    interesting to know how accurately all the interaction forces can be calculated, but that is for another day
    rough analysis indicates that the Spectrum 42 lifts a hull at just 7-8 degrees of heel so the recommendation is to reef early?
    Thanks for the assistance.
     
  7. UpOnStands
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    UpOnStands Senior Member

    So, new day.
    The RM curve for a catamaran is basically a really steep curve to some max value reached at, for lightweight vessel, 8-12 degrees. The rest of the curve is of little import since wind loads sufficient to reach RMmax will of course tip it over right quick. This is quite different from a monohull which interacts significantly over a very wide range of heel angles.
    Has anyone seen detailed wind load plots for a conventional catamaran?
    The wind load curve provided by Ad Hoc is, I assume for a monohull.
     
  8. Ad Hoc
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    Ad Hoc Naval Architect

    The procedures for a monohull and catamaran are the same. Just different results that's all.

    Thus, the naval arch must demonstrate as such.

    No no no...ALL the curve is very important - that goes into dynamic stability and energy.

    The height of the Wind moment curve is dependent upon what wind speed one is using and also the projected profile area at each angle of heel.
     
  9. UpOnStands
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    UpOnStands Senior Member

    Theoretically true but in practice? A captain with his catamaran heeled at 50 degrees is not going to be impressed with the vanishing small levels of energy available for righting the vessel.
    Take 20 degrees of heel, so flying a hull. Is the remaining righting moment energy of any import? Theoretically yes but in practice? Since the hull is already flying the wind is more than strong enough to continue to heel the vessel until capsize.
    If the wind suddenly eases or the captain is able to release sheets or bear up in time, or the vessel naturally responds then the remaining righting energy becomes significant.
    Reminded of a discussion on the multihull boat forum where a large open bridegedeck cat' was being discussed. Suggestion was made to add a flat dodger but with no windows so air could pass through - minimal increase in wind loading? Except as the vessel heels and then suddenly the dodger presents significant surface area to the wind.
    That is why I would be interested to actually see a professionally derived wind loading plot. What would it look like? curves for wind speed from 10 knots to 45 knots at 5 knot intervals?
     
  10. Ad Hoc
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    Ad Hoc Naval Architect

    Sorry, wrong again.

    Looking at the wind moment curve applied to the righting moment GZ curve above, where is says first intercept, this would be the steady angle of heel. Your 20 degrees if you like. If the wind continues and the vessel is heeled to 50 degrees, to where is says downflooding angle (call this the 50 degrees), the area under the curve of the righting moment from the instantaneous angle of heel to the 50 degree line (downflooding angle) above the wind moment curve must be the same or greater than the area from zero angle to the first intercept....regardless of the location of the avs.

    Thus plotting the curve and the wind lever gives a picture of how much work is being done...and how much energy the vessel has...and in varying wind speeds.
     
  11. UpOnStands
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    UpOnStands Senior Member

    Sorry, I choose 20 degrees as it is significantly beyond the RMmax.
    Just to keep it clear, I am assuming the vessel has has ready passed through RMmax (which for most cats would <15%) and has now reached 20 degrees - not steady state at all.
     
  12. Ad Hoc
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    Ad Hoc Naval Architect

    It is called a steady angle of heel.

    The area under the curve irrespective where RMax is, is the important feature. You seem not to grasp this.
     
  13. UpOnStands
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    UpOnStands Senior Member

    I am trying to link theory with the real world.
    Since this cat has lifted its hull the wind force exceeds that needed to reach RMmax . The wind continues to lift the hull as the RM decreases after RMmax. The wind is constant, the hull is rotating. Describe the theory.
     
  14. Ad Hoc
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    Ad Hoc Naval Architect

    If the wind moment is greater than the righting moment...its over!

    That's why we study the effects of wind and its implications on a design...and how to mitigate it, or prevent it.
     

  15. UpOnStands
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    UpOnStands Senior Member

    Bon, simple answer to a simple question.
    Back to the "Wave Rider" capsize in Tasmania. Was the design the problem?
    Hull design or sail design?
    Apart from unstayed masts and furling systems, can we create a sail design that is self load spilling?
     
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