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