Copenhagen Ship Curves - anyone know the math behind them?

Absolutely false logic. That 2" square does not physically exist inside your computer; it is just a concept and only in concept does it have any area you select...4 inches, 4m. And just like any tool, digital or mechanical, the error was in the operator's skill, not the machine.
Trust me on this as a professional engineer that drew lines plans, has used planimeters and integrators, has digitized line plans into a computer, and has developed lines in software; that doing a set of lines by hand is much faster and well within the accuracy of measurement with the finished physical product.

Here is a test, draw a random shape on a piece of paper. Determine the area by using the planimeter...time how long it takes you. Then digitize that shape into your software...again timing yourself. Now tell me which answer is more correct?

It must be remembered that digital calculations are precise, not necessarily accurate or the "correct" answer.

 

Bingo. Minimize the handwork, or use a machine that hits the required tolerance without it.

My first job CAD thru CAM and Prototype was in 1993. A friend who was an industrial designer wanted to put together a line of flat-pack plywood furniture with irregularly-curved profiles. He had drawn them on letter paper using French curves. I put his drawings on the Summagraphics tablet and picked off control points in Cadkey. I massaged the spline nodes and end tangent vectors until they looked good on the CRT. I plotted them with an HP pen plotter at full size, and they looked great. I exported the profiles as DXF with the chord height tolerance cranked up to minimize faceting. Another friend owned a contract furniture company with a big Thermwood CNC router. The $$$ controller choked because it's look-ahead abilities were junk. Lowering the chord height tolerance made for a coarse approximation of the spline, which machined fine, but looked horrible. It took hours to replace the splines with blended arcs so the CNC controller could deal with it.

Today I can take that same Cadkey file, with spline curves, process it in a $125 CAM program, and cut it on a 1985 Gerber CNC router retrofitted to run with a $500 controller that has great look-ahead routines. The parts come out great. All digital, except for edge deburring.

 

I got my fathers with some other old cool things. But I also got his ruling pens and I had to use them in drafting class before we could use the KOH-I-NOOR Rapidograph Drafting Ink Pens. What a mess!
I put inking lips on my Dixon Kemp ovals and will do that on any new Copenhagen ship curves or french curves of 1/4" thick plexiglass. Not so much for inking but also for ooching of a line because I use them in artwork also.
I am drawing a set of 5 different renders of Great White Egret and just Great Egret now and find that the Copenhagen ship curves and french curves are very useful in checking the overall shape of a birds wing in flight or at rest and many many other shapes in nature. All of those curves very pleasing to the eye and we humans are very good at seeing if something is not ergonomically correct. I am trying to do one of the birds landing on a low mist on the lake and have the mist flow away from its wings and body as it lands. Well we will see but the internet has some great images taken with high speed camera of vortices of the air flowing off birds wings and hope to find part of that in a french curves. But like every it's never that easy. We have a wetland called Eagles Bluff just down the lane that have the Great Egret on it now so I can see how far off I am.
Always ooching some line somewhere.
John

 

Your test is moot and based on false logic. It assumes I want to draw a random shape freehand in a second or two, and then measure the area. That's not close to the same as hand drawing an intermediate station between two already-drawn stations with ship curves, using your already-drawn longitudinal lines as controls, and then running an immersed area check with the planimeter.

The 2" square 'inside the computer' is 2" for all practical purposes: Presumably we've long ago selected our default drawing units in the program, configured our printer, and checked the quality of and accuracy of our print output. Really no different than me taking some time to calibrate the planimeter before using it so that it would be more accurate accurate, and then taking multiple tracings with averaging in order get a more accurate measurement of square drawn on grid paper. The precision of my measurements is to 3 decimal places, as that is what the vernier on the planimeter resolves to. If I drink less coffee and become more accustomed to the planimeter, my measurements should become more accurate. For them to become more precise, I'll need better eyesight or a planimeter with higher resolution.

 

I have no disagreement with the points raised in post #86 as far as preparing a lines drawing is concerned.What I would say is that if the object of the exercise is to reach the point where a boat can be built from what the designer has in mind,a CAD system wins every time.Its also much kinder on the knees if we can go directly from correctly offset sections to cutting the sections on a CNC router.We avoid the weeks of offsetting sections and fairing discrepancies that can't be seen at scale on the board because of the precision inherent in the computer.If the object is to produce an easily driven hull with the least resistance,either for performance or fuel saving,the same 3D model can be submitted to a CFD programme for comparison with other variants of the concept in a lot less time that a tank test model can be built.Which is a large part of the reason why planimeters and large boards can be bought on the used market for very little.

 

I still have an aesthetic issue with most of the computer generated designs. I don't care what the equation for a curve is. I do care if it is pleasing to the eye.

 

It is not about knowing the equation of a curve but about knowing the theoretical bases of what we are doing to understand it better and be able to take better advantage of the tools we have at our disposal. And, by the way, a slipper can be pleasing to the eye and not serve to smooth the shapes of a boat.

 

If we are talking about a slipper that goes on your foot, I'll go find one that will work as a drawing implement! If not, something was lost in translation .

Still waiting to hear from M/S Museum in Copenhagen. Unless I find out otherwise, I'm inclined to agree that Copenhagen Curve sets, even the production ones from the late 1800's through the early-mid 1900's were probably based on tracing and hand-smoothing off a previous copy. That said, I don't discount the evidence for ship designers proportioning drawings based on conic, logarithmic, and Euler curves prior to the late 1700's. Diagonals weren't much used and inclined heel positions weren't considered before then.

I mapped several of the numbered Copenhagen from the 1921 Dietzgen catalog onto the 1921 Keufel & Esser catalog. They aligned very well, numbered curve by numbered curve. Hmm...why? Well, probably not because of math, but because Eugene Dietzgen worked for K&E in New York prior to starting his own company in Chicago. Both companies manufactured their own products lines, but undoubtedly somebody could trace off somebody else's product. Ditto on the French curves based on the Burmester set. But I'm about 99% certain Burmester originated his 28 curves from linkages and kinematics. Cheers!

 

With a program such as Rhino it is quite easy to draw a plan view that works and a sheer view that looks pleasing and then have the program create the 3D combination.You can then use this as part of the 3D surfacing process.While it isn't related to the topic of Copenhagen curves,a present day professional has to be as productive as possible and 3D modelling has such numerous advantages that a keen man with a drawing board can't keep up and would have difficulty staying in business.

 

I take it you have never actually had to design a working vessel from an SoR in Rhino. While many take the same view as your post espouses, that is actually doing it bass ackwards and had lead to many failed businesses and the plethora of low-build abominations that dot the water. Having a set of lines and then trying to shoehorn in the arrangements leads to much more wasted time and money than than the traditional method; no matter how plausible it may be for a hollow racing daysailer. Trying to get Rhino or any surface program to work around an efficient arrangement block-out while giving a good faired set of lines takes a lot of time and effort without wasting a huge amount of space, material, and cost in the finished vessel. Digital in one-off design is only cheap because it is not real and never replaces the designers knowledge, skill, and experience...unless you want coke bottles all over again.

 

@jehardiman , I pretty much agree with you, in general. But a good professional has a great tool with CAD/CAM programs. Although it is very difficult for him to get what he needs with Rhino (or any other software), the great advantage, or one of them, is that, once the model is obtained, any modification can be made very quickly and he can make several versions and choose the most appropriate one. In the past, any modification was a tragedy. Starting with the difficulty of seeing how many drawings this modification affected and how many calculations had to be re-done.
The problem today is that people believe that they do not need to learn a profession, a work method, a work discipline, because they believe that software solves everything. Therefore, very prudently, they only ask Rhino to provide them with what Rhino provides. "The designer" does not have the ability to make his own design. Then, with a beautiful render that looks extremely similar to a boat but no one knows how it will float, they say they design boats. Well, that is, sadly, the reality.

 

I don't entirely disagree but I would point out that the computer is a tool and like any tool,it can do some things well and other things less well.I would welcome details of how a pencil on paper would do a better job,The basic equipment needs to fit inside the surface that is intended to contain it and it is much easier to switch on a surface layer to ascertain whether something like the engine foot of a generator protrudes than it is to make the same determination from a set of lines.The designer needs to know his business and apply his experience to the stated requirements.I know of no working designers who don't take advantage of the efficiency a computer brings.A good analogy would be the way in which mechanically driven saws displaced a duo of sawyers and their pitsaw.The outcome doesn't change but the process takes less time.

 

Shiver me timbers!

 

I agree that the computer is just a tool, and that it has many good uses. I see design in general trending to the "copy and paste" method. My issue is aesthetic. Also, that because software allows to, for example, design an interior and then cut it at the intersection to the hull/deck it doesn't make it good; it is only faster.

 

Whether it does it well or badly, well enough or not, is totally questionable but I don't know if you, personally, have experience using CAD/CAM software to make that comparison. What is clear is that the accuracy of the data from a given model is much greater in any software than taking it by hand.