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but why aren't the hollowing sweeps applied directly to the bilge sweeps?
(Because then you get) less harmonious surface.
Please also note I have used the term "surface", as opposed to "curve".
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but why aren't the hollowing sweeps applied directly to the bilge sweeps?
.Can you give me an idea how this process must have been carried out? How can the sketchy, downscaled main frame be turned into a full size template? My imagination comes to a complete halt here. Perhaps you can shed some light on this matter.
First, it is probably worth using an example of tracing the stempost taken from van Yk's 1697 work, which demonstrates that geometric design methods were indeed used.
In the description to the engraving above, on page 58, there is a thorough explanation of how to obtain the circular curve of a stempost, knowing in advance the height and rake of the stempost; the final shape of the arc of the stempost being obtained with a compass. This could have been a normal compass for drawings made to scale, or a string compass for real scale tracing.
Indeed, as you point out, in many cases it would have been inconvenient or even impossible to use a radius and a compass. Particularly in such cases, the designer could easily measure on the drawing (or calculate mathematically if he was proficient in calculations) the so-called deflection arrow. After scaling it to the actual scale, he could use this value when collecting timbers, for making a working templates or for giving instructions to carpenters. To give a simple example: we want to buy 52 timbers with a length of 9 feet and a deflection (in the middle) of 1 foot.
In this way, the two approaches, the geometric and the practical, combine and complement each other in a harmonious, even essential way.