Copenhagen Ship Curves - anyone know the math behind them?

Years ago, it was essential for a person with an expert in the field, with very good vision in space, to decide that "that" was pleasing to the eye. Nowadays, with much less practical experience, but knowing well the multiple tools that specialized software puts at our disposal, it is possible to obtain much smoother shapes than before. And it is not only about obtaining something pleasing to the eye but also, and above all, about creating pieces that fit together perfectly, thus avoiding a lot of labor in error correction.
The tortured shapes that ship hulls have today, without CAD/CAM, would have been impossible to achieve, both because of the time that would have been needed to obtain them and because of the precision achieved.

 

Yeah, but....most are still going to...
1) layout and scribe with a spline
2) mark with chalk
3) cut with a gas axe
4) form with a hammer
5) bend, beat, and clamp to fit
6) weld with stick
7) paint to match
.....sub millimeter precision and curve following is a pipe dream for most fabricators....

 

Probably because, for whatever reason (and there may be many reasons), they do not use current technologies that are neither so expensive, since it saves a lot of costs, nor are they so complicated for a professional who knows the trade. And you can always outsource that work.

 

I have used the Copenhagen Ship Curves (CSC) #42 at 1/3 scale that will make NACA 0015 and 1/2 scale #42 for the TMB EPH foil shapes as well as a modified Kemp curve to create NSS and NACA 0015.
Good enough for what I do and at the bottom of most of my planes in very small print is "All Drawings are Diagrammatic". They are as accuate as need for the task at hand.
Euler Method: Leonhard Euler, who first proposed it in his book Institutionum Calculi Integralis (published 1768–1770).
Copenhagen ship curves have been made since at least 1817. chicken or egg
I find them most useful in rendering sails leaches curves, sheer lines etc... If you hold the curve up at the angle of the viewers perspective of the curve and sight down the curve you can see the distorted curves with out a 3D program. I do this when drawing object as well as using Lawson perspective charts to render curves viewed from different angles of perspective if needed.
Poor folks have poor ways.

 

That's pretty slick! Re. Euler, are you referring to the Euler Spiral developed from the conversations between Euler and Bernoulli? The 'Curve whose curvature is linearly dependent on distance along the curve?' As mentioned by several in this thread, it would be obvious to apply bending moments to a simple beam and at some point 'lock' those curves into a static template that can be easily moved and re-used. Its kind of funny to think that all the beautiful analytic curves drawn out in scientific literature were probably using some other 'fair' 2d template to blend through the data points. 'Objectivity' is relative to the tools available, and what the author wants to emphasize