# Development of intersection of two cones and two planes.

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

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### Mr EfficiencySenior Member

The reality is, this "method" is too restrictive for best results, in terms of what shapes you can arrive at, it is enough of a limitation that you are constrained by the need to have a developable surface, without it also having it needing to be described precisely by mathematical equations.

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### TANSLSenior Member

Shame to limit shapes of a boat to get them from developable surfaces. Typically, at least for me, has always been to design a boat with suitable forms, from technical and aesthetical point of view. If then you have to apply some of the methods of approximate development of non-developable plates, you apply and go. No need to be a math expert to use these methods, enough to have some knowledge of a loftman work.

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### WgrabowNew Member

Mr. Efficiency & TANSL, I absolutely agree with both of you. I am a small time hobbyist who plays with this approach for the fun of it; it is inadequate for general purposes.

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### DCockeySenior Member

A ruled surface is a surface which can be formed from non-intersecting straight lines. All developable surfaces are ruled surfaces but not all ruled surfaces are developable surfaces. In addition to being a ruled surface a developable surface must satisfy a no-twist along the ruling lines requirement.

This is an example of a ruled surface which is not a developable surface. It is possible to create a developable surface with one edge being part of a circle and the opposite edge with the form y=x6 but the ruling lines would not be as described.

Yes, developable surfaces are not restricted to cones.

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### NoEyeDeerSenior Member

Hmm, well I suppose the question becomes "How developable is developable enough?", because I'm sure a lot of us have made plywood go around shapes that have twist on the ruling lines.

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### BOATMIKDeeply flawed human being

I've used a few different ones. But mostly I use hullform which is now public domain.

The observation about the deviations from the computed shape seem to be general, particularly when panels are twisted much, but I would like to hear of any different experience.

If panels don't have much twist then the stress on the ply is very much less and you don't see great deviations from the computed shapes.

MIK

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### BOATMIKDeeply flawed human being

I did like the Knud Riemers quote about what is required to be a yacht designer ... a sharp pencil and a clean white shirt.

This is not necessarily a comment on what you do Wgrabow, but about the general discussion

In a way you could say EVERYONE builds boats that are mathematical solutions to the developability problem.

In my case, and most of us using software, it is absolutely mathematical, so that any boats coming from it are in fact purely mathematical.

A spline ... wood or an appropriate mathematical entity have more or less the same behaviour.

So ... all mathematics. At the same time building lots of boats and getting feedback from plans purchasers really does feed back nicely into computer development of hull shapes. Watching people learn software I often seem to say the same things I say when using battens around nails.

They are a very good fit. As they must be

Moving on to other stuff ...

As far as using a few pure mathematical shapes to produce developable surfaces, that part works fine. I can see the attraction from the original post.

But the problem becomes progressively more complex as performance is required to be optimised. With two intersecting cones or cylinders and probably a third cylinder representing the bottom of the boat and a plane representing the waterline it is possible to solve a general case for volume.

But it is not going to be particularly simple. Mathematical software can probably do it in a moment. But begs the question ... why one type of mathematical software and not another (some sort of marine CAD)

A short cut for the pure shapes would be to do the calc to the centreline plane and the waterline plane giving only two curved surfaces to deal with.

One problem will be fore and aft symmetry. The method will force a high degree of symmetry that will tend to match only particular types of boats rather than a general case.

There are certain advantages of a less constrained approach ... like altering rocker radius through the length of the boat, or moving the centre of buoyancy to where it was needed for some reason just as two common examples.

Either way this is a very interesting discussion. Thanks to all participants.

MIK

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### BOATMIKDeeply flawed human being

There are two general approaches it seems. (I'm very interested in any experience otherwise because that would ideal).

I've used both.

One is to accept the panel shapes given by the computer and wire them up to make the boat. Most errors from the compounding of twisted panels will generally close up to be bridgeable with epoxy. The finished shape will not be so exactly representative of the design shape but will be perfectly buildable and with care ... not too different. The more careful designers will seek carefully measured corrections and manually edit the panels to reflect the minor edge alignment errors.

The other method is to make an accurate strongback to make sure the original shape is recreated and then use the panel shapes as a first trial on the strongback. The errors of alignment can be quite large - say up to 8 to 20mm in 16ft (4.8m) canoes if there are heavily twisted panels (ie near horizontal midships then vertical to align with the stem/s at the ends). That way you get the designed shape - volumes, prismatic, matching class rules etc etc but have to make big changes to the panel shapes.

Note the two types of error.

Those from compounding of the ply or other things the software is not able to account for. Any computational method will be weak in some areas because plywood does not act like an infinitely strainable anisotropic entity of no thickness.

The other are minor edge errors where the panels are brought into alignment and gaps of a few millimetres appear here and there. In experience these are very unlikely in the mid body or near a transom stern, but start appearing in conventional bow areas.

MIK

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### BOATMIKDeeply flawed human being

This probably describes the reason why older boat designs tended to be very type formed. To avoid both logarithms and problems that could not be calculated.

To move away from standard methods or jump up to significantly larger size involved decades or centuries of trial and error building.

An example are Gothic Cathedrals ... if you've ever been in one you'll know how breathtaking they are. But they basically went on what they knew and if something fell down they would rebuild it until it stood up. In particular the buttresses on the outside would be built heavier to prevent the tendency of the main structure to buckle outwards.

Trial and error would have been the main tool in developing different types and solving the problem of larger structures.

I'm living in the Philippines the last three years. I've travelled around a little so far but have been astounded by the knowledge inherent in different local boats types. You can go to the next bay and boats may well be completely different.

I was at a boat show earlier this year plugging the idea of home built boats. A well educated Filipino (it turned out he was a university lecturer) asked me if I was going to teach village Filipinos how to build better boats.

My reply was that I would rather give them a big stack of plywood and leave them for a couple of years or a decade.

Their own locally built boats are incredibly brilliant. Sadly there is a move from above that thinks that fibreglass boats are better - which kills the local innovation - everything is centralised. And the locals can build four plywood boats (which they can repair and rebuild or change at minimal cost) for the price of one 'glass boat.

But that is by the by .. point is the cost of low teching the development is that you need time.

That is the value of logarithms and advanced methods. We can project with greater certainty without quite the same risk of failure.

If you have a century to spare for an innovation an abacus might be a very useful instrument.

MIK

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### NoEyeDeerSenior Member

Really, if anyone can be bothered, it should be possible to write software that will accurately predict how actual plywood will behave. The relevant moduli are known, as are panel layouts, etc, so with enough frigging around an algorithm that predicts the behaviour of (example) 6mm 5-ply gaboon should be feasible. You should also be able to extrapolate the principle to deal with a range of species, thicknesses and veneer counts.

Seems to me that it comes down to the stress levels. Of that ply that is, not the builder. Throwing a bit of compound into narrow planks is easy. Carrying the same curvature out to a greater width isn't, and the edges are likely to buckle, among other things. Same with twist. You can twist the hell out of narrow planks (Javelin garboards in the old days, for example*) but you'd never get the same twist into a plank two feet wide.

*For those who weren't in Oz then, the trick used to be to fasten the garboard almost to the bow, then pour methylated spirits on the end and set it on fire. Heat softens lignin. Garboard end twists up to 90 degrees. Alcohol doesn't burn hot enough to trash the plywood. No worries.

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### NoEyeDeerSenior Member

This is why I warned the OP that things rapidly get quite complex if you're not happy with the most basic of results. Modern design apps are generally pretty well thought out, and offer a lot of flexibility without having to know much (if any) mathematics.

However, sometimes they can be limiting too. I can't remember which thread it was, but some of the pros here were grumbling about hull design apps in general. The gist of it was that often an app would be good most of the time, but every so often you'd hit a problem it couldn't deal with. You'd end up spending so much time fighting it, trying to get it to do what you wanted instead of what it wanted, that it was sometimes better to shift the project to another app which would handle the particular problem. Of course, this second app would have its own weaknesses too. The consensus seemed to be that really you needed half a dozen or so different hull design apps to handle any case.

Now the basic system suggested by the OP is very limiting, due to the constraints of the system of equations behind it, but it seems that to some degree most hull design apps will hit this problem sooner or later. They're all based on a system of equations chosen by the software's author, according to what he or she thought was most useful, but humans rarely think of absolutely everything.

ETA: BTW you actually could easily get a high degree of longitudinal asymmetry with the system the OP was thinking of, if you were cunning about how you laid out your vertices.

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### gonzoSenior Member

There is another method that works very fast. That is to make a model with a stiff enough material. Also, designing with battens develops shapes that can be planked. Don't let a computer hamper your creativity. The programs were developed by programmers not shipwrights.

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### TANSLSenior Member

There is nothing, I think, what did the ancient loftmen can not currently be done with cad programs. What is true is that if you do not know crafting, the software will not.
No designer who works with computers think a software can "hamper" his creativity. Instead, a creative person, with a good program has many more possibilities to realize his creativity in specific designs. In addition, he can do so much more quickly and without error involving a tragedy (in time or money).
Beg to differ again but that has absolutely no basis. A good program is always developed by a team in which there are various technical in each of the subjects. One of these technicians is responsible for translating technical language into machine language. Everything else, comprising 90% of the merit of the program is developed by people who know a lot of mathematics, descriptive geometry, naval architecture, etc ... and also for people with extensive practical experience in shipbuilding.

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### DCockeySenior Member

If "panels are twisted much" then the surface probably is not actually developable.

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### gonzoSenior Member

There is no computer program in existence that can give me the infinite curves of a batten. They all work with approximations. Also, they don't come close to fairing as full size lofting does.

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