# Development of intersection of two cones and two planes.

Discussion in 'Boat Design' started by pdmclean, Nov 19, 2014.

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### pdmcleanJunior Member

@NoEyeDeer
Why the cone?
Because portions of it are developable and this lends itself to ease of construction.
I started with a lens shaped cylinder with a flat bottom, but I'm trying to get away from the flat bottom and introduce some curves. (Before that I considered an angular punt-shaped thing, partly for ease of construction.)
Also, I'd like to learn a bit more about quadratic equations and piecing them together.
Of course, these shapes are quite arbitrary.

I raise the golden mean in jest, of course, the golden mean has some nice properties but its use in design (aesthetic or functional) is usually fallacious.

I don't pretend for this family of design to be optimal in any sense. I'm happy to forgo x% of performance. If wanted a good boat I'd go about it another way.

I don't have much experience with cad-type software - the program I used above is geogebra - a geometry package. Can anyone recommend a free package for a learner to use?

Also, I find much of the nautical terminology a bit impenetrable - why not just use 'left' and 'right' like the rest of humanity.

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### pdmcleanJunior Member

Really? Not even for pedagogical purposes? It doesn't help the designer to know how his tool works?

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### NoEyeDeerSenior Member

Ok, but you don't need a true cone to get a developable surface. That picture Mik posted is a good example. Basically, you just need it to have straight lines drawn across it at some angles so that the lines don't intersect. If you have this, you have a developable surface.

As an example, off the top of my head, if the lower line was part of a circle and the upper line was of the form y=x6, and you divided each line into the same number of segments and drew straight lines between the corresponding points, that would be developable too.

So, you aren't restricted to cones and can get more useful and interesting shapes. The expansion of such shapes is a bit trickier to calculate, but most design apps are set up to do it for you.

I use Delftship, and it's pretty good IMO. There's a free version available which would get you off to a good start. http://www.delftship.net/delftship/

And boaties use port and starboard because landlubbers are wrong.

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### NoEyeDeerSenior Member

Oh, and to save PAR and others the trouble of giving the perennial warning to beginners: any design app will only do what you tell it to do, so if you tell it to draw a terrible boat it will merrily comply. It's still down to your knowledge and ability.

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### pdmcleanJunior Member

Really? Where does this fit in the list: http://en.wikipedia.org/wiki/Developable_surface

Or is it a "PolySurfaces and Freeform Curves" (see http://www.rhino3.de/design/modeling/developable/

I'll have a look at Delftship.

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### WgrabowNew Member

Great discussion from people with a wealth of experience. But how many here have actually designed and built a boat using a purely mathematical technique? I started using such an approach about forty years ago (when it made sense). I think that most overestimate the difficulty. As with any approach, you get better with time. For me it seems pretty simple: a \$20 calculator and basic algebra.

I have written some blog posts to describe the method in more detail, but I think it just puts most readers to sleep. Just want you to know that it works. The numbers don't control the process; you select the numbers. At the website developable-surface-boat-designs.blogspot.com if you go to the entry of May 2006, you can see some pictures of early designs. Then you can skip to entries from this past summer to see the latest boat.

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### TANSLSenior Member

The paraboloid hyperbolic is a non-developable ruled surface.

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### TANSLSenior Member

Do not quite understand what you mean but I think that with a \$ 20 calculator, you've designed not even a bicycle.

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### gonzoSenior Member

You don't even need a calculator. A slide rule or a table of logarithm will suffice to do all the calculations. They are only convenient tools to help a designer. An experienced shipwright can simply build a boat.

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### NoEyeDeerSenior Member

Yes, I did a couple of small boats this way years ago. I was using a Hewlett-Packard programmable though, which saved a lot of donkey work and enabled quite sophisticated systems of equations to be set up fairly easily. I have to say that for complex systems of equations, the old Reverse Polish Notation used by those calculators absolutely rocks compared to standard algebraic.

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### NoEyeDeerSenior Member

With an axe too. Don't need any of them new-fangled planes and stuff.

[/viking shipwright]

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### NoEyeDeerSenior Member

Ok, fair point. I was just giving him the short version.

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### WgrabowNew Member

I designed my first boat using a slide rule. The HP programmable was about \$500 at that time. By the time I did my second boat, calculator prices had dropped dramatically and I took advantage of it.

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### NoEyeDeerSenior Member

I think I paid \$576 for mine at the time. That figure seems to be stuck in my head. I remember it wasn't exactly cheap. Handy gizmo though. I had it set up to do pretty much everything. Offsets, to inside or outside of planking, at any station, waterline, buttock or arbitrary diagonal you liked, as well as basic hydrostatics (displacement, prismatic, upright and heeled CB, including corrections for heeled longitudinal trim, and a couple other things IIRC). Basically it was almost a little pocket-sized CAD system. The abysmal amount of RAM meant getting results out took a while for some things (inside offsets in particular, due to the iterative loop required for the planking thickness subtraction). I never set it up to deal with things like radiused garboards either, which was a bit limiting if you wanted something like a traditional keelboat. Still, for a self-written pile of equations it wasn't half bad at the time.

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### TANSLSenior Member

The Chinese, back in the fourteenth century, made boats up to 100 m in length and only had the Chinese abacus.
With or without the table of logarithm?

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