Developed Surfaces????

Is there any software that does the equivalent to spiling? Spiling is laying a straight batten aproximately in the middle of the panel from the bow to the stern. Then take perpendicular measurements at several points. Lay the batten over the lofting table, mark at the points measured and fair the line with a batten.

 

I did a little checking, and I've found I used the wrong terminology. What I called the "vector triple product" is really the "scalar triple product" or "mixed triple product".

For those wanting to program the relationship, here's the formula:

Let:

' indicate matrix transpose
P1 = [p1x, p1y, p1z]' coordinates of point 1
T1 = [t1x, t1y, t1z]' tangent vector of the first defining curve at point 1
P2 = [p2x, p2y, p2z]' coordinates of point 2
T2 = [t2x, t2y, t2z]' tangent vector of the second defining curve at point 2
D21 = P2-P1 vector from point 1 to point 2

D21 = [d21x, d21y, d21z]' = [p2x-p1x, p2y-p1y, p2z-p1z]'

Scalar triple product:

s21 = T2 * (T1 x D21)

s21 = t1x*t2y*d21z - t1x*t2z*d21y + t1y*t2z*d21x - t1y*t2x*d21z + t1z*t2x*d21y - t1z*t2y*d21x

s21 must be zero for the line from P1 to P2 to be on the developed surface.

The hard part is getting the tangent vectors. Typically a curve in space is defined by a separate formula for each dimension, with an independent parameter, call it "u", that runs from 0 to 1 to sweep from one end to the other. You have to differentiate each of the formulae for each dimension with respect to u to get the tangent:

T = [(d px)/(d u), (d py)/(d u), (d pz)/(d u)]'

For most curves used in CAD, the formula for the derivatives is quite straight-forward, but it depends on just what kind of curve you're using (cubic spline, B-spline, circular arc, conic section, etc). There's no need to reduce these vectors to unit vectors by taking square roots and such, since all you care about is the sign of the triple product and not its magnitude as you're searching.

 

Tom Speer’s method for finding ruling lines is basically the same approach I played with in my Visual Basic programming. It is essentially the same iterative approach discussed by T.J. Nolan in a paper titled “Computer-Aided Design of Developable Hull Surfaces” published in Marine Technology, 1971. Check out the paper “Developable Surfaces Modeled by Differential Equations and Flat Plate Layouts” by Brian Konesky at http://www.interchg.ubc.ca/konesky/paper02.PDF, where an improved method is proposed. Konesky’s complete master’s thesis on computational methods for developable surfaces can be found at http://www.interchg.ubc.ca/konesky/new_page_1.htm.

If you use Tom’s method, other things to consider are how you parametrize the curve and decide on the step/interval along the curves. Parametrizing by arc length is critical – you want to take your steps in units that measure distance along the curve parametrically, NOT just as units along one of the Cartesian axes. You also have to decide whether your search for pairs of points on the 2 “chine” curves that define ruling lines will always start on curve A, always start on curve B, or alternate from A to B.

For example, say I have a cubic spline curve A representing my sheer line that is 20 units long and a cubic spline curve B that is 10 units long representing my fairbody or keel line. First thing I do is normalize the arc length of each curve to 1, so my search for ruling lines will go from 0 (start of each curve) to 1 (end of each curve). I’ll use steps of 0.1 – 10 steps along the length of each curve. That means 10 steps at 2 units long on curve A and 10 steps at 1 unit long on curve B. You can see my resolution could be much higher on curve B. So double the number of steps to 20 along each curve if you like. You can make your steps as small and as many as you like to increase accuracy, provided you can live with longer computational time. On boats, the length of a sheer line tends to be so proportionately close to an adjacent chine or keel line that your step lengths will be pretty similar between curves A and B. A greater number of steps will give you greater accuracy – you can get by with fewer steps and ruling lines for a long skiff with gentle curves at the sheer and chines than you could for a twisted, pudgy dinghy. If I’m always starting my search from the sheer (curve A), I start at point 0. Use Tom’s method and find the corresponding point on the fairbody (curve B) that gives a ruling line. Go back to the sheer and move parametrically to point 0.1 (2 units of length). Repeat Tom’s method to find your second ruling line. Go back to the sheer and move parametrically to point 0.2 (2 more units of length, or 4 total units of length from 0). Repeat Tom’s method to find your third ruling line. Keep doing this until you get to point 1.0 on the sheer (that’ll be the other end of the sheer).

You can just as easily start your search from curve B (the fairbody). Or start from point 0 on the sheer, find your first ruling line, then go to point 0 on the fairbody and find the second ruling line, then to point 0.1 on the sheer for the third ruling line, and so on. Or start from point 0 on the sheer, find the first point on the fairbody that gives you a ruling line, move 0.1 unit of normalized arc length along the fairbody and find the next point on the sheer that gives you a ruling line, move 0.1 unit of normalized arc length along the sheer and find the next point on the fairbody that gives you a ruling line, and so on.

All these methods can run into problems. As an example, say we’re at the forward end of the chine curve on a flatiron skiff (the stem & chine intersection), just finishing a ruling line search that started from the transom and worked forward along the chine. The algorithm finds a point on the sheer well back from the bow that establishes a ruling line to the stem& chine intersection. Without special instructions, our search algorithm is stuck, because there are no more points forward along the sheer that form ruling lines with the stem& chine intersection. We still need to develop the triangular patch formed by the stem line, our last ruling line, and the remaining length of sheer line up to the tip of the bow. We now have to revise our ruling lines search to either jump up to the sheer line and look for corresponding points along the stem line, or start traveling up the stem line, searching for corresponding points along the sheer line. This would be analogous to the shifting from one cylinder or cone for developing the hull panel to another, tighter cone as you finish the area of the panel near the stem that might be used in manual drafting methods (the Kilgore method). Stems and transoms are a weak spot for plate development software; including Nautilus (it forces a straight line segment at the ends of each developable panel).

So it’s not quite rocket science, but you could gobble up a lot of hours developing – pardon the pun – a piece of software to do the job several others have done quite well for what is really a small amount of cash.

 

Good references! Konesky's approach is a good one - not only more reliable but probably faster than the iterative method.

I would tend to bunch the generators in regions where the bounding curves have their greatest curvature instead of spacing them equally along the arc length. If there is a section of the surface that's flat, the generator lines only have to define the beginning and end of the flat section. But if a bounding line has a kink, the generator lines will have to radiate out from that point until they can start marching down the new slope.

Naturally, you'd want to treat both bounding curves the same, and the differential approach does that. I haven't read Konetsky's paper in detail, yet, but I suspect his method will also bunch the generators according to the curvature of the bounding curves because the parametric "speed" slows down in regions of high curvature and goes to zero at kinks.

 

Chris,

Yeah at the moment im using CADkey 19.01 for all my hull design, while the office has Maxsurf and Hydromax for stabilty purposes, this seems like a pricey option for me as an individual.

At the moment all i really play around with is chine hulls, and the conics in Cadkey are great for that - I can develop a whole hull given 4 conics and a line!

Just means it has to be exported in to Masurf for any stabilty data.

But il have a look at the programs that you like and yes your right - once you have basic CAD knowledge it is pretty easy to jump from program to program - afterall maths is maths no matter how fancy the program is!

Chris

 

Excellent discussion in all of this.
For what it's worth, I have been using Autoship to create developable surfaces for years, and the current version does so quite well. I can NC cut parts up to 20' x 8' (max. plate size) to within ~1/16" when the resolution is set properly. Last 72' x 21' monohull had every plate part of hull and superstructure lofted neat (no trim margin) and water-jet cut. It all fits. Neatest trick is the lofting of bottom longitudinals that stay normal to the shell surface (twist so as to remain perpedicular to the plate). Draw the part edges fair, and press the button. For serious workloads, it's an expensive but worthwhile tool.

 

Well, this answers my question about software that does the equivalent to spiling.

 

Chris -

Go to to www.newavesys.com and get the trial versions of the software. I'm betting if even all you want to do is design chine hulls, you'll feel the ~$200 US for ProChines is well worth it , and that you'll drop doing your hull design and panel development in Cadkey. Cadkey will become your detail design and drawing layout tool.

 

pjwalsh:
I use engineering graph paper to sketch out a design at stages during development and adjust coefficients as needed. Such sketches are outlined by plotting some of the generated points then freehanding the rest by connecting the dots. It doesn't take long. I also make models sometimes, using stiff paper for designs defined by the surface panels or thin plywood for a model framework.

By using an equation, I can find the exact slope at any point by differentiation or calculate the length of the curve by integration. It's just something I started long ago, when I was doing a research project, and have become comfortable with.

 

I have read with interest the discussion on developable surfaces, conical development and the use of computers. This has been the topic of much discussion in our office over the years, some of us being from the hand drawn era and some of us from the computer generation. Whilst I am interested in the mathematics behind creating developable surfaces and will follow up this links and suggested reading in this tread, I feel that what people are losing sight of is that what we are after is a buildable surface. This being a surface having no or low levels of strain, thus requiring no mechanical forming. Thus is it right to have your design dictated by a purely developable surface, when one not completely developable in the pure sense is more suited. This leads to the method currently adopted by our office, were we use Maxsurf’s marker points created in the developable plate mode as a guide. Where we feel that sections are going away from what we want we adjust them as required and look at the developed plates in Workshop to see the levels of strain. So far we have had good results producing buildable plate when limiting the strain to 0.25%. This of course opens a question of the mathematics behind developing non-developable plate.

 

Morgig -

I disagree with your opinion that the thread is losing sight of what we're after is a buildable surface. Virtually all the discussion is about defining developable ruled surfaces, certainly far easier to insure "buildability" from sheet materials than surfaces with compound curvature.

All I need to do with a developable surface is check that the bending characteristics of my material are within its elastic limits at the point of greatest curvature and I can be pretty sure the hull is buildable (though I may aids to support the hull panels and bend them into shape during fabrication). I can either examine the bending characteristics from a mathematical standpoint or just grab the material and test bend it to the most extreme curvature I'm going to encounter and see what kind of fight it puts up.

Sounds like Nautilus proBasic and ProSurf do most of the checks for developability you mention using with Maxsurf. I know you can view a color gradated map of Gaussian curvature to identify areas of compund curvature in your hull panels. You then have the option of forcing developability on those areas and letting the program adjust your hull shape accordingly.

I've built a couple boats of heavily tortured 3 and 4mm marine ply, including a 20' electric proa with darn near elliptical and round bilged sections from the midbody to the stern. A very nerve wracking but cool process. Thought a software program that would take the bending characteristics of my material, test against a computer modeled hull shape, and finally give me my flat surface profiles would be very handy. Didn't exist at the time, as far as I knew, or would have been in the too-many-$$$ realm. So we just did the 1/8th scale model method with super-thin birch aircraft ply as described in Gougeon Brothers On Wooden Boat Construction. When we got models that didn't explode along the during fold-up, we scaled them up 8X and went for it. No computers involved.

 

Chris

I’m sorry but what I’m trying to say is ‘what are we after when we develop a hull using conical development’ To my mind, it a hull made up of surfaces that can be developed and cut from sheet material (wether by hand or CNC), then fitted without trimming.

I stand by the fact that I think that conical development is interesting mathematical tool, and it should be understood to at least some level, however it is a tool, much a the PC is a tool. What I’m saying is that it is now possible to get the results we want, i.e. flat developed panels that fit without forming, without having the hull shape dictated by conical development.

I don’t have any experience of Prosurf above looking at the demo, however I have compared results out of Workshop and Rhino. Someone can correct me if I’m wrong but Rhino seems to assume developability even when it is not and the results are not the same unless the panel is fully developable. I would therefore not trust the results unless the Gaussian curvature for the whole panel was zero.

I think that using a test model is a fair enough solution, however we work with large working boat 20 > 23m with 10mm or more bottom shell, I just don't think making a model each time would be cost effective. I think when it comes down to it you need to understand and trust the tools you use, be they by hand or computer.

Regards

 

While i agree with the computer is a tool - it is only a tool and not able to give us the results that we desire, take fro instance that not all chine and keel splines/arcs/conics are going to be able to be developed and the final solution might come down to trimming the Plate to more managable sections. This results in more developed plate beng used.

Chris,

I downloaded the ProChine software and was surprised how indepth it was for so little money - i think your right that the $200 is going to be well worth it for the smaller chine boats.

I havent got a hull shape yet but im working on it.


Chris

 

I had an article in Boatbuilder a few years back on the subject. I would put it on line, but I recently promised reprint rights to the Metal Boat Society for their journal (and I don't have a website). Maybe they will post it. Meanwhile, if someone emails me, I will send it in Adobe, or you can order the back issue from Boatbuilder (or better yet, join the Metal Boat Society).

However, the simple answer is that the surface has to have zero Gaussian curvature. In practical terms, this means two adjacent rulings have to be very nearly co-planar (in theory, they should be exactly co-planar, but there is always an infinite number of rulings infinitesimally close together, so that there are no really adjacent rulings). This means that any two adjacent rulings have to intersect or be parallel. A conic surface is one in which ALL rulings intersect at ONE point, but this is not necessary.

Once the rulings are found, each pair bounds a quadrilateral with all four angles and all four sides known, so the development is simply a matter of laying out each quadrilateral. This is often done as two triangles, but there are a number of other methods as well.

 

By the way, I also would like to agree that, provided the surface is actually reasonably developable (warp less than about six degrees or so), CNC cut plates will fit within a milimeter. I have thousands of pounds of steel and aluminum shell plating hung without any not fitting.

The problem is that some designers just don't understand developability, or what exactly their computer is doing, and so they have problems. You can't just use software blindly.