I greatly appreciate all of the contributions to date – each has opened a new area to look into, and some have taken me down quite a diversionary path!
Going back to where this all began, I began this journey (which is still only just begun) wondering how the ship designers of old determined the height of the load waterline when they were designing the ship. In looking through various descriptions of the design process in a number of treatises and books from the 18th and early 19th centuries, and then comparing to a small sampling of plans, it appeared that the LWL was not necessarily used to design the vessel, but rather was a goal for how the ship should float. The majority of the plans used design waterlines along with buttock lines and station lines to transfer the shape of the frames and other timbers to the mould loft floor. A quick (and very simplified) review of the principal lines used in these plans:
Design waterlines – horizontal lines on the Sheer and Body Plan, curved profiles on the half breadth. Represent fixed distance above the baseline and are usually parallel to the keel.
Buttock Lines – curved lines on the Sheer Plan, horizontal lines on the Half Breadth plan and vertical lines on the body plan. Represent the shape at fixed distances parallel to the centerline of the ship.
Station Lines – vertical lines on the Sheer Plan and the Half Breadth Plan, curved profiles on the Body plan. Represent the shape of the ship at fixed locations fore and aft of the midship frame.
The LWL may, but more often did not, match one of the design waterlines. Since it wasn’t needed to loft the frames, when was it added and how was it determined?
To know the amount of water a ship will draw (that is, how deeply it will sit in the water), the weight of the ship is the primary consideration. The weight then is used to determine the amount (volume) of water that will be displaced – regardless of the shape of the ship (that is, a rectangular shape will displace the same amount of water as a ship shaped ship at the same weight). In most references I have looked at covering 1700 to 1850, the British standard was about 64 pounds per cubic foot of seawater.
Once the weight and the volume were known, what remained was to determine the level on the ship where the volume below the water matched the volume of seawater. That may seem simple, but proved far more complex in practice!
Determining the weight of a ship was, also, an interesting exercise. In theory, by knowing the density (weight per cubic volume) of each material used, and then determining the volume of each item used in the construction (bolts, treenails, frames, beams, planks, and so on, with a different value for each type of wood, that also varied with the dryness and changed over time) the builder could determine the light weight. Then all that was needed was to do the same for the crew (and their personal effects), food, water, masts, spars, blocks, rigging, powder, guns, small arms, lamps, candles, and on and on to determine the fully burdened weight. Not likely to happen – far too much to even attempt that!
Another method was that of equivalency – for a given class of ship, determine the height at which it floats empty, then load everything that would be needed and see how much it settled. By determining the difference (how much lower it sat in the water), the additional volume displaced (assuming a fairly simple shape for simplicity in most cases) represented the additional weight above and beyond the ship itself. From various activities such as this, Sutherland (among others) offered a set of assumptions to use in determining the weight of the vessel empty and fully loaded. Not totally, accurate, but a starting point! This was a “close enough” approximation, but only for vessels of similar shape and dimensions. The assumptions fall apart when either is altered more than a small amount.
Which, of course, brings me back to the beginning – in the absence of mathematical methods (which the shipbuilders did not like, based on many reports and descriptions from the 18th century – both in France and in Britain), other than “looks about right based on the last one I built”, how would they be able, before launch, to have any certainty that the ship would ride where they intended – whether merchant or war ship?
So, there you have it – the “why do this” that is driving me forward! What have I learned so far? Much about the development of the science, a bit of the history of the first Royal School of Naval Architecture (Reverend Inmon and John Fincham were key players there), the resistance to these changes during the time of Captain Symonds as the Surveyor of the Navy, and the influence of France, Spain, The Netherlands and Sweden in advancing the understanding of the science (and applying to shipbuilding long before the British). Also that it appears the Americans were followers for many years with little in the way of contribution to the science until the 19th century. I have also learnt much about the development of mathematics between the time of Archimedes and the mid-19th century. Not to mention (well, okay – I’ll mention it) the value of colleagues who can translate other languages!
The quest goes on, and the questions continue to accumulate – please feel free to add to the list and, if you can, shed some light on those darker areas that are yet to be illuminated!