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Bonjean Curve Method

This discussion on "Bonjean Curve Method" is in the Events during Sinking & Subsequent Forensics section; For the engineering types on the board, could someone provide me with a concise and ...

      
   
  1. #1
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    For the engineering types on the board, could someone provide me with a concise and understandable explanation of the Bonjean Curve Method as it applies to Edward Wilding's calculation of 12 square feet of aggregate hull openings? Wilding mentions the Bonjean Curve method but does not provide any further details or clarification.

    --Nate R.

  2. #2
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    Nate-- Bonjean curves are a representation of the area of the transverse sections of a ship at successive waterlines. They are normally plotted as a fair cure on a profile of the ship.

    "Waterline" in this case does not mean the physical load waterline, but rather a horizontal plane running fore-and-aft. Think of them as the layers of frosting in a multi-layer wedding cake. When combined with other lines called "sections" and "buttocks," a 3-dimensional curved ship can be represented on a flat sheet of paper. The three--waterlines, buttocks, and sections--are combined in one drawing called the "lines drawing."

    When plotted on a profile of the vessek, each Bonjean curve begins on the base of the station it represents. It rises and curves forward on the profile, indicating the transverse area of the hull at that location on the hull. Bonjean curves can also be plotted on graph paper.

    Bonjean curves are used in calculating the volume of displacement and the center of buoyancy at any waterline, or angle of trim. Most often they are used in stability calculations, determining the capacity of the ship, or in launching calculations.

    --David G. Brown

  3. #3
    Noel F.Jones
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    Bonjean curves form part of the set of hydrostatic curves provided to the vessel by the builder. The underwater volume of a vessel and her longitudinal centre of buoyancy can be derived from her Bonjean curves.

    Customarily, a ship is divided into a number of equidistant stations, usually ten (note that these stations are not necessarily coincident with her watertight bulkheads).

    Bonjean curves are curves of immersed cross-sectional area plotted against draught and are drawn on the profile of the ship at each station. Thus waterlines at any angle to the vessel's baseline can be superimposed upon the profile. It then becomes possible to read off the immersed areas by drawing lines parallel with the baseline from the intercept of the waterline with the section to the Bonjean curve for that section. The use of Bonjean curves thus enables the volume to be found for waterlines that are not parallel to the baseline.

    Since the resultant is a volume of displacement your Mr Wilding must then have gone one to adduce some COEFFICIENT OF PERMEABILITY for each station to arrive at a volume of inundation. From the summation of such inundations at two representative waterlines (presumably as per witness observation) and the elapsed time between them, it is possible to compute a rate of inundation and thereby arrive at a notional summation of the areas of all the breaches in the hull, in this case, 12 square feet.

    As to the validity of his computation, how your Mr Wilding dealt with the effect of the changing head of water as the vessel settled I would not know.

    I seem to recall that the eponymous Monsieur Bonjean was a French naval officer.

    Noel

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    Noel -- this discussion is so entertaining that perhaps we could take our act on the road. I'm sure we have lost most of the ET contributors--or at least put them to sleep.

    The significance of this is that Wilding used a standard method technique of naval architects as the basis of his calculations. The same curves are still used for similar purposes today.

    You mention the problem of the coeffficient of permiability. In effect, a "fudge factor." This factor is an attempt to approximate how the internal components of the ship restrict the flow of water.

    Other variables include the duration over which the flooding occurred and its location. On both of these, it appears that Wilding was misled by the data provided by Lord Mersey. In specific, Wilding was told that boiler room #6 flooded perhaps 20 minutes earlier than it did. And, he was told that hold #2 and the forepeak tank were not flooded.

    What is curious is that Wilding's initial calculations--using Bonjean curves--showed that Titanic should not have foundered. So, Wilding dutifully changed the flooding pattern until it matched the results desired. It was this second set of calculations that became the basis for his famous "12 square feet" estimate of the damage.

    -- David G. Brown

  5. #5
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    Daved, Noel, while I'm no mathmatician, I'm not having a problem following what you two are saying. Keep it up guys...I'm learning something.

  6. #6
    Tom Pappas
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    In this case, it might be inferred that the Bonjean Curves were deficient. It was said for many years that "according to the Principles of Aerodynamics, the bumblebee cannot fly." Then vortex lift was discovered, and the Principles were modified to "save the phenomenon," as the ancient Greeks would say.

  7. #7
    Brian Hawley
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    Along with Mike I am still reading, although I must say I had to read Dave's and Noel's post twice. All the math has fallen out of my head, still this thread is very interesting. Especially that Wilding had to recalculate his figures, and the issue of internal fittings impeding flooding.

    Brian

  8. #8
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    Tom -- The Bonjean curves were accurate enough. They are not a theoretical construct, but a realistic method of describing vessels. Wilding undoubtedly had a full set of Bonjean curves for Titanic produced as part of the ship's construction. They were needed to launch the vessel without damage.

    As to percolation...well, that's where the black arts come into play. There are various "fudge factors" which are used for various types of ships and/or cargoes. These approximate reality, but are not reality--sort of like computer projections of tomorrow's weather.

    --David G. Brown

  9. #9
    Noel F.Jones
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    "As to percolation...well, that's where the black arts come into play. There are various "fudge factors" which are used for various types of ships and/or cargoes. These approximate reality, but are not reality--sort of like computer projections of tomorrow's weather."

    Quite. There are promulgated in the textbooks various parameters of permeability depending upon the use to which a compartment is put. Considering the infinitely variable conditions of lading of such as a tweendeck or lower hold containing general cargo, once you get past the design stage 'permeability' must border on wild guesswork.

    Especially when you consider that the vessel's stations are somewhat arbitrary and don't necessarily conveniently encompass whole compartments.

    Mr Wilding must have been in possession of a deal of detailed information to arrive at his '12 square feet' - which I would take with a large pinch of salt.

    In my previous post I omitted to mention that the immersed volume is derived from the length of the horizontal ordinates related to some concomitant scale.

    I also omitted to add that "the above does not purport to be a definitive or complete exposition of the procedure"!

    Noel


  10. #10
    Noel F.Jones
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    On seeing that the ET Discussion Board is veritably a-buzz with this gripping topic I feel compelled, at risk of some considerable re-iteration, to re-address it in more measured terms than hitherto, the better to answer Nathan Robison's original query....


    Bonjean curves form part of the set of hydrostatic curves put aboard by the builder. The underwater volume of a vessel and her longitudinal centre of buoyancy can be derived from inter alia her Bonjean curves whenever she floats on an uneven keel.

    At the design stage the drafted profile of a ship is customarily divided into several (usually ten) equidistant sections, referred to as 'stations'. For each station a Bonjean curve is got out and inscribed on the profile. Those stations at the extremities where curvature is severe can be further divided into sub-stations. Note that a ship's stations do not necessarily coincide with her w/t compartments.

    The Bonjean Curve of Section is a fair curve generated by wrangling the 'five, eight, minus one' rule on a tabulated work sheet in accordance with the formulae handed down to us by M.Bonjean.

    The curve initially allows the determination of the median immersed cross-sectional area of each station to any oblique waterline superimposed upon the profile. This is done via a system of rectangular Cartesian co-ordinates whereby the y-axis represents the vertical distance between baseline and maindeck and the x-axis returns the corresponding immersed area, the curve springing from the axial origin. The abscissa thus generated (that is, the rectangular or horizontal distance between the intercept of the waterline with the curve) represents the immersed area, discernible in practice by dropping an ordinate to the graduated x-axis.

    Having thus determined the immersed cross-sectional area to the given oblique waterline, the prismatic projection of that area throughout the length of the station will render the corresponding immersed volume and therefore the volume of displacement to that waterline. The findings can be adjusted for angles of heel by taking a mean of port and starboard draughts. Having thus determined the volume, the mass of displacement can be determined from the prevailing specific gravity (i.e., sea- or fresh water).

    As to Mr Wilding's aspirations to aggregate the total area of the breaches in Titanic's hull, since the Bonjean curves can provide the volume of displacement for each station it would then be necessary for him to adduce some coefficient of permeability for each station to arrive at a volume of inundation. From the aggregation of such inundations at two representative waterlines and the elapsed time between them, it would be possible to compute a rate of inundation and thereby arrive at a notional aggregation of the areas of all the breaches in the hull. In the present case this seems to have been 12 square feet.

    However, while of value at the design stage and thereafter in managing the operational conditions of lading of the ship, I would not have thought Bonjean curves of much practical value in determining the damaged condition of a ship. Better recourse would be had to her 'floodable length' (a known quantity, being that flooded length which takes her down to her margin line and no further). That and the soundings, which themselves would directly return the rate of inundation.

    That is probably what Thomas Andrews succinctly did in the present case. Rather than redundantly computing to two successive waterlines, on being notified of the carpenter's soundings he could simply work back to the time of the collision to determine the rates of inundation for the affected w/t compartments (never mind theoretical 'stations').

    From the outset he would have know that the Titanic's floodable length had been exceeded. The most urgent requirement therefore was to estimate the time left for her to remain afloat and tenable. From the determined rate of inundation and the capacity of the pumps to meet it he was able to give Captain Smith such a time.

    All this without reference to my textbooks! albeit I can see them out of the corner of my eye fulminating on the shelf and threatening due retribution after I've sent off this post.

    Reverting to Mr Wilding's recourse to Bonjean curves in his attempt to aggregate the area of the breaches through which the sea entered, I see him as overly reliant upon dubious evidence as to waterlines, elapsed times and the permeability of the bilged compartments. There are various parameters promulgated in the textbooks for permeability depending upon the use to which a compartment is put but these can be very approximate in actual service. Remember also that 'stations' survive from the design stage and do not necessarily conveniently coincide with compartmentation, let alone w/t subdivision.

    Wilding probably took recourse to Bonjean curves because the soundings book did not survive to help him, even assuming it was filled in (the damage control soundings probably arrived at the bridge on such as the back of a fag packet in the time-honoured manner).

    I note Edward Wilding was a qualified naval architect on the H&W design team and it must therefore be assumed he knew precisely what he was talking about when he put forward his computation. I've been unable to trace the context but presumably he was being asked to supply an answer to a specific question and went about it will nilly. I cannot see however that such a retrospective calculation had any material bearing on the casualty or the prevention of future such casualties.

    Note that the above does not purport to be a definitive or complete exposition of the concept or the procedures.

    Ever anxious to prise apart the synapses with more essential information with which to face down the vicissitudes of life, I am trying to track down a biography or obituary of the originator of Bonjean curves (we speak of little else where I come from). The name, as far as I can ascertain, originates in Provence and should be accorded the French pronunciation. Short of my asking the RINA or its French equivalent, can anybody help?

    I could continue with this peroration but others are advising me to end it now, their reasoning being that the arrival of the Horlicks trolley is imminent.

    Noel

 

 
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