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Actually, this relatively ‘late’ period is beyond my immediate interest in the subject, yet, prompted by a hunch, or rather encouraged by the hull shapes quite characteristic of Northern style of design, I decided to take a closer look at this case as well. Specifically, it concerns Joshua Humphreys' design proposal for the intended ‘Constitution’ class of frigates (many thanks for @Martes for providing this information), i.e. a design from around 1800.
Preliminary tests confirm that Joshua Humphreys did indeed design ships using one of the sub-variants (parabolic) of the general Northern tradition, yet, for greater certainty, a similar analysis can be performed for his 1776 frigate Randolph as well, of which the original plan has been preserved in the archives. Until now, the design methods employed by American shipbuilders of that period were not recognised, and this issue was merely speculated upon by various authors dealing with the subject on premises other than the actual, comprehensive analysis of the design lines. Needless to say, without conclusive results.
Finding the right design method allows for the correction, with unprecedented certainty and precision, of the not very precisely hand-drawn hull lines, which is quite characteristic of manual drafting, and without resorting to clumsy synchronisation of waterlines, buttock lines and cross-section lines in order to make the surfaces fair, and which, as is often the case, still further distorts the original shapes intended by the designer.
In addition, the design method found can also be used for rational and realistic reconstructions of other vessels, based on their known general dimensions, from that time and place, or at least those designed by Humphreys himself.
It can also be added that the plans from the era of captured American vessels, as well as those of other countries, drawn up by the British, although on the one hand may quite well reflect the general shapes of the hulls, and even be quite sufficient for practical applications such as the construction of ‘duplicates’ of such ships, yet, on the other hand, they cannot represent the original shapes very accurately, because for the purposes of making these secondary plans, other design methods were used by the British, which inevitably generated different specificity of shapes, and as a result, only better or worse approximations of the original shapes could be created.
Below are the results of the tests carried out. The red lines, superimposed on Humphreys' original plan (American archives), were generated according to the design method found. As can be seen, they coincide quite satisfactorily with the lines on the plan, except, partly, for the so-called hollowing/bottom curves, which either made some trouble due to their slightly greater complexity to draw, or – more likely – the possibility that in order to speed up the drawing process they could have been drawn in the ‘express’ mode, i.e. without following the formally correct geometric procedures (hence the need for verification diagonals).
The presented results of the shape study are preliminary, which means that the reconstruction still needs to be refined in a consistent manner according to the very precise course of the main longitudinal design lines (after their prior, already more exact determination), which will ultimately guarantee flawlessly fair hull surfaces that are also consistent with the designer's intentions.
As a final note, it can be said that most of the key design lines forming the basis of the project have been removed from the drawing (and, as a result, they need to be painstakingly recreated), leaving only the resultant and verification lines.
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.. but I should appreciate that - as I should not purchase more books anyhow!
