Copenhagen Ship Curves - anyone know the math behind them?

Of course that statement is true, the craftsman selects the proper tool for the job....but often, for anything much more than simple bookkeeping, the computer is not it...and anyone who believes different (i.e. the computer can do everything) is just fooling themselves (i.e. glue on pizza).

This, in my opinion, is the major fallacy in much present day thinking about automation. It conflates automation with fabrication, and fabrication with design. Yes, a head saw turns out hundreds of 2x4's in a day....but craftsmen still have to place them to build a house. Sure you could automate the ability of a software program to space the studs in a drawing...but how does the designer decide where the doors and windows are? Sure, you could standardize a wall sections or rafters to be pre-fabed in a automated factory.... but what if you need something specific? When your product is thousands of the same thing, full on automation with an acceptable failure rate is financially competitive and therefore selected by non-technical managers.....boats and ships which are still basically hand built one at a time and need to work every time, not so much. Rickover pointed out this perception problem back in 1982.

 

@jehardiman , you're getting philosophical and that's not my specialty. Better I go to sleep.

 

Here it is with some maybe bow buttlocks.
Are there some kind of drawings/instruction somewhere for them?

 

I love it, except the 3'rd station up from the bottom has a butt-ugly kink just above the keel line> I could fix that in Stephen Hollister's 'ProSurf'

 

Copenhagen ship curves would be diagrammatic representation of a ships lines.

Top part of the K&E page could be: Sheer, Waterlines and Buttlocks.
Middle: some ornamentation-naval heraldry for the stern and gunwales and a lot of maybes in between..
Bottom: row looks like ribs of different small craft

The K&E or others layout may not me intuitive to there usages.



Bottom photo is of 3 different sizes sets I use 1:1, 1:2 and 1:3 scaled sets of the Burning's.
The 1:3 scale Burning set is on the board below.
Head scratching, who lost the instruction.

 

Captain and officers quarters had different embellishments found in quarters and on the stern and gunwales of a quality ship.
Or you might put these in the bottom corner of your rendering with your name and contact information.

 

I thought those little joggles at the ends of the curves were so you could interlock them to draw a longer curve.

 

Unless someone knows of some instructions. I am just throwing stuff at the wall to see what sticks.

I used Copenhagen ship curves on the waterlines as guides and to transfer lines from models laser lines back to the Line Plans to double check but found the laser lines were not that accurate, most likely user error. I did waterlines heeling to 10, 20 and 30 degrees of hull for Curves of Displacement check and set the model in a water tank to check if the center of effort and center of lateral resistance were in alignment.
A model was a great tool for me and the scaled boat of 6' to 7' LOA fit the standard size Copenhagen ship curves fairly well.

 

It's always refreshing to see somebody acknowledge that ownership of a laser level isn't always and automatically a guarantee of accuracy.Similarly I don't think I would ever follow a Copenhagen curve slavishly without some assurance that it really is the perfect shape for the job.The flow of water past the hull may not be aware of how it is supposed to behave in relation to the shape of the curve.

 

@Howlandwoodworks - just giving you a hard time about the use of the curves. I think it was jhardiman who mentioned the tiny ogee's at the end of curves were often used for millwork detailing. Your 'reverse engineering' of how to use the curves makes sense. 'By any means necessary' to fit through control points, right?

Agreed on the laser level with both you and @wetfeet. Nice process, nevertheless. I bet it gives plenty enough accuracy and precision for calculating displacement at heeled conditions. It could help with further fairing on a drawing table.

Still haven't gotten a reply from M/S Maritime Museum in Denmark. I may try contacting another curator or historian there. I did some preliminary curve fitting to scans of Copenhagen's in the 1921 Dietzgen and Keufel & Esser catalogs. I limited myself to conics and logarithmic spirals, figuring that would fit the math used by ship designers up through the late 1700's. It's easy to get local fits on a part of a Copenhagen, but the scan resolution is poor. Trying to determine limits for start and stop of a 'piecewise segment' is also an 'eyeball guess,' and adding the next 'piece' and checking whether that curve is just C1 continuous (tangent) or C2 continuous (both tangent and curvature) is another deal entirely.

 

Possibly a 'fair slipper?'



Definitely not a
'fair slipper...'

 

LOL
As gonzo says, always right in his comments: "I do care if it is pleasing to the eye."

 

Is that a quip or a pun? I'll let it slip by.

Seriously, though, I think that there are many methods of arriving at a fair curve. CADD and Excel generate curves very fast. However, they are limited to what the software allows them to. A person with a good eye will correct those curves for beauty with a spline or Copenhagen curves. My opinion is about aesthetics.

 

After inquiries to two curators at the M/S Maritime Museum of Denmark regarding Copenhagen curves, I haven't received any replies. I'll put the question of a mathematical basis for them to rest.

I am still intrigued with finding more information on the Burmeister curves that are the basis for the commonly used 'French Curve' sets. There is no way that a preeminent kinematician of the 1800's,with his knowledge of mechanical linkages and geometry, would defaulted to 'by eye' to put together a curve set. How he went about it is the question - he apparently didn't write about the project.

Researching the question has added to my library, which now has copies of Abell's The Shipwright's Trade, Chapman's Treatise on Ship Building, Deane's Doctrine of Naval Architecture,1670, Kemp's Yacht Architecture, and L. Francis Herreschoff's Capt. Nat Herreshoff: The Wizard of Bristol. Additionally, I've assembled an assortment of papers by naval historians and historic model ship builders who have done in-depth 'reverse-engineering' of historic ship drawings and wrecks to ascertain methods used to design them. Based on an admittedly cursory review of most of these, I think the following affirmations are valid:

• In the 1500 and 1600's, a good deal of European ship design was based on prescribed sets of rules and lines were drawn using geometric methods based on blended arcs, conics, and logarithmic curves. Some methods were well-documented and published, others were held as 'trade secrets.'

• As engineering methods became more sophisticated in the 1700's (Euler, numerical integration methods from calculus, etc.), stability calculations included heeled conditions. Although a hull could still be drawn with previous geometric methods, the shape of heeled lines didn't follow those methods. Coupled with developments in fluid mechanics, other means had to be used to draw the lines. This is coincident with increased reliance on 'irregular curve templates' and splines for ship design.

• Further advances in machining, engineering, and fluid flow in the 1800's resulted in hull forms being drawn (or in the case of Herreschoff, carved) using planimeters, manufactured sets of irregular curves (Copenhagen's, 'French curves), scale rules, and some really advanced math. Designs were still recorded as pencil on paper (or in a half hull). This would hold true until the development of computational geometry in the mid 20'th century. I'll stop there, as the discussions about merits of hand drawing vs computers are so partisan.

If anyone wants more info for the literature I've mentioned, feel free to message me.

 

I would seriously doubt that a more comprehensive study of the topic has ever been undertaken, or ever will be.I don't remember too much of relevance in the Herreshoff biography, but maybe his "Common Sense of Yacht Design" would have provided some hints, I particularly enjoyed his recommendation of a particular brand of two foot rule because it was handy for prodding the window open on a warm day.