# Interested in Buying or Renting 56 Copenhagen Ship Curves

Discussion in 'Boat Design' started by digitalis, Jun 10, 2015.

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We need not get choked up about semantics. Batten/spline does not matter as long as we understand each other.

In my mind, correct or not, a spline is a flexible stick used on the drawing board and a batten serves the same purpose for the loftsman. Incidentally you can use spring steel wire in place of a wood or plastic spline on the drawing board. Wire like that is available in many diameters at model hobby shops. Quite useful for tweaking severe curves for a boat or a Cartesian graph.

The word spline has more applications than to describe a drawing board tool. Shafts of certain machines have splines, meaning that they have straight lands and grooves machined into the shaft. We also batten down the hatches in bad weather.

We could easily de-rail this thread by getting into the origins of words. Does everyone know where the terms port and starboard is said to have originated?.....never mind........... keep smiling.

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### digitalisJunior Member

Hello again,

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### digitalisJunior Member

Hi again,

I said that I was thinking about cubic polynomials, but I think no set would be complete without some curves that are second degree, viz. the conic sections. One could use a polar coordinate equation: r = ep/(1 + e*cos(theta)). We could vary p > 0 and e > 0. The value p controls the size of the conic and e is the eccentricity. If 0 < e < 1, we have an ellipse, e = 1 is a parabola, and e >1 is a hyperbola. For e = 0, we just use a compass or maybe a railroad curve. If you are familiar with drafting, you might have come across a tool called an ellipsograph. It is used to make ellipses. I came up with an idea to make a tool I gave the name conixograph because it can, I think, make all types of conics. In the future, I'd like to fill in the details of the design and write up a plan and take it to a local machinist and try to have it made. I say, "I think" because I'm not sure how well the parts would move with respect to each other. However, the principle of its operation is sound, i.e. the geometry works. Chris Redding

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### TANSLSenior Member

After all this I do not know what to say. You've overwhelmed me.
Tip: to work with polynomials defining splines, it is preferable to work with parametric equations.

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### philSweetSenior Member

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### Eric SponbergSenior Member

Hi Chris, What you propose is indeed, "anal." I do not know the history of Copenhagen ships curves, but I do know that they were never marked and graduated as you propose. Curve tangencies using ships curves were (are) always done by eye, thereby defining ships drawings as art as much or more so than science in some respects. I dare say that a quick search on the internet shows that various types of complete sets are available from time to time, some boxed, and the count varies from box to box. Even if you had a complete set of 56 (and I see on the internet some sets with more than 56 curves), when it comes down to designing, you usually only need a few. I think with my 20 count set, I probably used 10 of them most of the time, and maybe 5 all the time. I never used some of them. The original curves are all fixed lengths, and I suppose if you digitized them to make computer templates of the shapes you could make them bigger--but then they would not be "Copenhagen" ships curves, would they--they'd be "modified" Copenhagen ships curves. You don't really need to make them bigger--that's why we used splines and weights back in the old days.

Good luck on your quest. If you don't want what I have, that's fine. I will open the offer to anyone else--if anyone would like to buy my set of drafting curves and templates and such, I am happy to sell them at a reasonable price, recognizing that they are used. I am not looking to make a fortune, but rather that they go to a good home with someone who is interested in buying and using them. If I have no takers, they'll get recycled.

Eric

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### digitalisJunior Member

Thank you TANSL, you're right, I think it is eaisier/better to work with parametric equtions. I must reformulate my idea about the curves. It would be better, I see, because the parametric approach will work even if y is not a function of x like a curve that coils in on itself. A few Copenhagen curves do that. Thank you again.

Hi Phil, I know some about the trammel stuff. I know the ellipsograph is based on the trammel construction and in one of my drafting books it shows similar constructions for the parabola and hyperbola, but do you know if there were mechanical devices constructed like the ellipsograph to make the parabola and the hyperbola? Of course, there is not much demand for a tool for those curves. There is also the "fishing line" constructions for the conics. The ellipse uses only string, the parabola uses a T-square, and the hyperbola uses only a straight edge which can also be handled by a T-square. The only problem is that for the parabola and hyperbola, it requires one to put a pin in the T-square and all the curves require putting a pin in the board. The T-square pin could be done away with a track in the T-square that has a screw and a wing nut to hold the string along with a part to keep the start of the free section of string right at the straight edge. My apologies about using the pronoun 'I' all the time. It comes off like I'm full of myself. Not so. Chris

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### digitalisJunior Member

Wild Goose Chase

Hi, Phil. I think you sent me on a wild goose chase. There is no trammel method for the parabola and hyperbola? What do you mean by a "trammel tool?" Chris

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### jarmo.hakkinenJunior Member

Here's a file in which there are close tracings of ship curves. The ends of curves are not that finely shaped as originals, merely ellipses, conics and blends to close the longer sides together. For the smaller curves you need to buy some French curves. These vary in length between 60 to 520 mm, but you can scale them to your needs.

Print them out, glue to a sheet of polycarbonate, acrylic or 3 mm plywood, cut them out and sand them smooth. Sheet size is about 850 x 1250 mm. Or send the file to your local water-cutting company, and save the effort.

Polycarbonate is the best choice, it's almost unbreakable. You can make your own plywood for this purpose by gluing two hardwood veneers of your choice together with heavy paper in between them. But all plywood may warp. Acrylic is an easy material to shape, but you need to be careful in handling them.

My grandchildren played Swordplay and Pirates, so instead of having ten long curves, I now have twenty shorter ones. They were of acrylic.

Have fun!

#### Attached Files:

• ###### Ship curves.3dm
File size:
184.3 KB
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### peterjokiJunior Member

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### RenatoRenato_RJ

Set of naval curves

Hi everyone, hello Digitalis. I am Brazilian. There is a drafting equipment factory in my country called Trident and They have been manufactured all of the 56 naval curves (complete set) yet. They sale them inside a wooden box and There is a calling in its site asking for commercial representation partners. These are the links:

whitout wooden box: http://www.trident.com.br/index.php?cat=85

and the complete set with wooden box: http://www.trident.com.br/produto_conteudo.php?prod=445

Look at this shop and you get a price idea: R\$ 1238,oo ...today, more or less U\$ 357.oo:

Marty is a guy who have made pear shaped curves (a.k.a. Dixson Kemp curves): audiomarty@gmail.com He wrote these lines to me last year:

From Marty: ' Hi Renato,
This set of Dixon Kemp curves are custom made, hand finished and would be your "tools of the trade" hence a tool you would enjoy to use for a lifetime.
They are made of 2mm clear Acrylic and come in a complete set of 5. sizes shown below (all solid no internal profile)

305mm
280mm
250mm
220mm
185mm
+/- 2mm

All 5 templates, price including postage \$250aud + int. postage \$30
Marty '

There is even a book about the ship drafting curves history. If you wish I could look for it within my bookmarks. Sorry about any english language mistake. Hey Mr. Sponberg, I am a fan of you, I've been reading so many times your articles. Some of you, american, could ask Westlawn for representing that factory over your country. Cheers !

Last edited: Aug 18, 2015
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### RenatoRenato_RJ

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### RenatoRenato_RJ

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### Eric SponbergSenior Member

Thanks from Eric Sponberg, and an update

Hi Renato,

I know this is an old thread that I have not looked at in about 2 years, but thanks for the update, particularly about the book "Creating Shapes in Civil and Naval Architecture." Interestingly, the lead editor, Horst Nowacki, was one of my professors at the University of Michigan, and I think the course I took from him was about creating ships lines on a computer. And the computer at that time was the University's IBM 360-67 main frame, where we had to punch cards in a card puncher and feed them in batches along with all the hundreds of other students at the university.

As you may know, I am now retired, and my wife and I purchased my very first custom design, Corroboree, which I drew by hand back in 1984-85, back from the original owners, and we are now sailing full time, hoping to go around the world. We sold everything, including our home, furniture, cars, the lot, moved onto the boat, and left St. Augustine for good, departing 4 January, just a few months ago. We have progressed through the Bahamas, stopped for a week or so in the Dominican Republic, and we are now in Puerto Rico in Puerto Real at the west end of the island. We are going to head toward the east end, to Fajardo, where we expect to stay for a few weeks to do some repairs/upgrades and have our daughter and her husband visit.

So, thanks again for the reference to the book--that brought back memories.

#### Attached Files:

• ###### Technology and the Yacht Designer--PBB 165.pdf
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499.5 KB
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139

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### HeimfriedSenior Member

mathematical spline

Sometimes it may be useful to have a mathematical spline ready to hand.

A few month ago I wrote the attached (packed) Excel (2010) VBA folder (Splines_3_v2_engl.xlsm, Macros must be activated, no reliability).

Details are shown at the first sheet "how to use". It is originally written in German, I translated it now (hopefully correct and understandable).

#### Attached Files:

• ###### Splines3_v2_engl.zip
File size:
41.8 KB
Views:
100
Last edited: Apr 19, 2017
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