Developed Surfaces???? [Archive]

pjwalsh

08-21-2003, 11:35 PM

I do not know of any website describing these techniques - might be a nice project to put one together for someone who understands this sort of thing thoroughly. I use the previously mentioned books along with just trying things out in Rhino.

You can do a simple multiconic surface development by drawing two edges of the surface, say chine and keel in 3-
d, then divide each curve into an equal number of segments. draw a straight line between corresponding segment ends on each curve, then use your 3-d modelling software to create a surface through these straight lines. Some trial and error will give you an idea of the best way to divide the chine and keel to achieve the sections you desire. I think not every pair of edge curves will give you a developable surface though.

Could also start with a single curve, say the keel, and pick an apex location. then draw straight lines between the apex point and segments of the keel line. Create a surface through the straight lines. Then you can cut this surface with an inclined plane to create a chine line. Kinda unpredictable in the shape of the chine though.

I think the Barnaby text on naval architecture has some writing on this too, but I don't have a copy.

Phil Bolger places the apex near the middle of the chine then draws ruling lines radiating toward the keel. He says it results in a deeper forefoot than is generally possible placing the apex outside and forward of the hull. Haven't tried this yet myself.

Paul B

08-22-2003, 02:46 PM

Hi Chris,

I have a copy of the S. S Rable book that PJ has mentioned for sale in the Marketplace forum.

I know you're in OZ, so shipping might be a cost issue. Let me know if you are interested.

tspeer

08-22-2003, 03:49 PM

Originally posted by pjwalsh
...You can do a simple multiconic surface development by drawing two edges of the surface, say chine and keel in 3-
d, then divide each curve into an equal number of segments. draw a straight line between corresponding segment ends on each curve, then use your 3-d modelling software to create a surface through these straight lines. ...

This will not give you a developed surface, although it does give you a ruled surface.

In order to create a developed surface, the lines between the two curves must connect points which have the same slope. If you don't follow this principle, you get the "starved horse" look to the surface.

You can see the reason for this if you consider two skewed straight lines as your defining curves. Drawing lines at regular intervals between them results in a hyperbolic paraboloid - definitely not a developed surface.

Another way to picture it is to consider the developed surface to be made up of hinged slats, like a roll-top desk lid. Each slat should sit on the defining curves so that the curve touches the slat at the midpoint of the slat end and the tangent to the curve will lie in the plane of the slat. Since the slat is not twisted, the tangents of both curves must lie in the same plane.

So what you need to do is to pick a point on one curve, then generate the tangent line at that point. Pick a point on the other curve and get its tangent. Slide the second point along the curve until the two tangent lines intersect or are parallel. Now you can connect the two points to form one line generating your developed surface. Pick another point on the first line and repeat. You will probably want to bunch the points closer together in regions where the curves have the greatest curvature.

An equivalent criterion would be to form the normal vector of the plane consisting of the tangent line to the first curve and the point on the second curve. This normal vector is the cross product of the tangent vector and the vector between the two points. When the dot product of the normal vector and the tangent of the second curve goes to zero, that's your point. In other words, the vector triple product of the two tangents and the line connecting the two points has to be zero.

If you search along the second line until the triple product changes sign, you've bracketed the point and a secant search should home in on it quickly. These are all computationally simple operations, so it shouldn't take all that long to generate the developed surface to an acceptable degree of accuracy.

pjwalsh

08-22-2003, 11:52 PM

Tom,

That might explain some of the funny results I have been getting here and there.

Do I understand you correctly that the slopes at the points on each defining curve must be identical and calculated in the same plane? So the normal vector at point 1 is identical to the normal vector at point 2, and the in plane angle between the tangent of each of the defining curves and the ruling line is identical?

Guest

08-23-2003, 12:18 AM

Physical models, graphic plotting, and mathematical methods (with or without a computer) may each be the optimal method in certain situations. I use all three, but prefer the mathematical method (no computer, just a programmable calculator) for most tasks. I usually start by defining a chine line along the middle of a side, then project upwards to form the sheer and deck and downwards to define other chines and the keel. For example, Y=22.5 (X squared)/(105 squared) when plotted for values of X=0, 7, 14, 21, etc. will give corresponding values of Y=0, 0.1 ,0.4 ,0.9, etc. This is a form of the trajectory curve, a smooth parabolic curve. The end slope of that curve is 2(22.5)/105 or 3/7. A curve such as this is gentle enough to easily bend most real world materials to follow it. It also furnishes many convenient closely-spaced points to plot and project to establish other surfaces. I also usually add a straight segment at the end of each curve because elastic real life materials do not maintain a curve to their very end but are normally straight between their last two points of fastening. A similar curve, or other relation can be defined to establish curvature in the third, Z, dimension. When projecting, a surface must be defined for projections to intersect. Using X for length, Y for beam, and Z for height above a base line, Y=0 is an example of a simple way of defining the centerline when projecting to establish the keel shape.

On my last boat built, I used a conic projection to establish a sharp forefoot. The closer a projection is to the apex, the more severe the curvature imparted. Next time I plan to use a parallel projection where X,Y,Z vary in the relation 8:3.8:1 (as an example) which will be easier to plank with the thicker stock I plan to use.

I don't want to go into all the forms of projection, but if you just pick up a piece of paper and see how many way you can wrap it, using multiple apices connected by ruling lines, projecting both toward and away from apices or using an apex that changes position along a ruling line for each segment projected, it is amazing how many different shapes can be generated.

Mathematical methods allow easy changes by just changing a constant in an equation or a coordinate of an apex. They provide exact output. Not much of a batten is needed for fairing when you can bend the batten across many exact points spaced only inches apart. The frame spacing can be easily changed as long as your basic requirements for displacement, stability and such are fulfilled. The better I can define a shape, the easier I can build it.

tspeer

08-23-2003, 01:39 AM

Originally posted by pjwalsh
...Do I understand you correctly that the slopes at the points on each defining curve must be identical and calculated in the same plane? So the normal vector at point 1 is identical to the normal vector at point 2, and the in plane angle between the tangent of each of the defining curves and the ruling line is identical?

The normal vectors will be parallel because the tangent vectors and the line are all in the same plane. The in-plane angles between the tangent vectors and the line can be anything. Visualize a board instead of the line sitting on curved wires. You can rotate the wires about the normal vectors at the contact points and the board will still sit there as before.

The tangent vectors don't have to be parallel - they can point toward or away from each other or be parallel. If the two defining curves lie in parallel planes, then the slopes would be identical at each end of the line. But the curves will generally lie in different planes or twist through space.

So "same slope" is the qualitative description to get the feel of the situation, but "vector triple product = 0" is the precise definition you can code from.

This makes sense from another perspective, too. The triple product is the volume described by the connecting line and tangent vectors as edges. What you're trying to do is collapse that volume like pressing an open-ended cardboard box into a plane by sweeping point 2 along its curve.

Here's another good illustration. You know those wicker stools that are made with two sets of reeds running at an angle from the base to the rim? One set is angled like they were originally straight and then the rim and base twisted relative to each other, while the other set runs the other way. All the defining lines are straight and evenly spaced around the circular base and rim. But a cross section taken in a plane radiating out from the axis is a hyperbola. The tangent lines where a given reed connects to the rim and base are rotated relative to each other and don't lie in the same plane.

But consider the untwisted case. If the reeds connect points on the rim and base that have parallel tangents, the side of the stool is a cone - which is a developed surface.

b_rodwell

08-23-2003, 03:18 AM

I used Rhino to create a developable surface for a flat plate construction catamaran. I first had to work out where I wanted my 'cones' and where I wanted my 'cylinders'.

For the 'cones' I used the 2 rail sweep command. The first rail was a conventional smooth curve; the second rail was so short it was almost a point. Connect the ends of the rails and sweep. Then you take the last straight edge and add another 'cone' to it or a 'cylinder'. The 'cylinders' were made by extruding thestraight edge along one curve.

I was able to build a completely developable surface this way (it was the side of the hull). I checked it at the end by looking at the guassian curvature of the whole surface. Rhino said it was fine.

Brian Rodwell:)

ChrisGibbs

08-23-2003, 08:36 AM

thanks guys! Well that has certainly expanded my limited knowledge of developed surfaces!

Now just have to find the time to sit down and try each method to see which one works the best for me!

pjwalsh

08-23-2003, 10:12 AM

Thanks for the clear explanation Tom,

It appears that the multiconic technique I wrote about earlier (as described by S.S. Rabl in "Problems in Small Boat Design") does not comply with the triple product = zero criterion. Actually looking more closely at the technique you can see that it does not require that the apices of adjacent cones lie on the same line, creating the situation you described of two skewed straight lines. The requirement for the apices to lie on the same line corresponds to the requirement for the two tangent vectors to have the same directions (triple product equal to zero).

Guest, I am intrigued by the idea of defining edge curves with an equation, but do you not find it difficult to visualize the shape this way? I suppose you can change the coefficients to suit the curve you are looking for but how do you check this visually?

Thanks all.

terhohalme

08-23-2003, 11:45 AM

I have made many plywood hulls using Rhinos unroll command to edge surface or loft surface. Though knowing the manual method I have never used apexes or other aids unrolling rhinos surfaces. If the two curves (for example keel line and chine line) have a low amount of points (say five) the surface unrolls nicely and the error is smaller than manufacturing tolerance. The plies have been fitted perfectly. Rhino has a developable surface option in loft surface, but it makes sometimes useless surfaces.

Chris Krumm

08-24-2003, 12:16 PM

Chris -

I also use Cadkey, both as my general modeling and drafting software at work and for playing around with boat designs. I do not recommend it for designing and fairing hull shapes or for developing flat panels for hulls. Spend a couple hundred bucks for Nautilus ProChines if all you want to do is design chined hulls; or better yet, spend a couple hundred more bucks for their ProBasic software and you can work with round bilged, chined, and any combination of round bilge with chined surfaces. You'll get easy to use tools for checking hull fairness and hydrostatics, along with accurate panel developments. You can export DXF and IGES files for all designed curves and surfaces into Cadkey or any other CAD software. The exported offsets and DXF patterns from ProChines have been dead-on for constructing a couple of multi-chine sea kayaks, 2 skiffs, and a 20' round-bilge electric launch.

Cadkey 21 now includes full trimmed surfaces capabilities, along with a utility for "unrolling" copound curved or developable surfaces to a 2D pattern. I believe it works by generating a triangular surface mesh aproximation of your NURBS or bicubic surface to a user-defined tolerance. It then unfolds that triangular mesh onto a plane, starting from the approximate parametric center of the surface. Its final step is to trace a closed cubic spline around the perimeter of the unwrapped triangles to give you a 2D flat pattern. Ought to be accurate for developable surfaces, butprobably full of errors for a coumpound surface since it has know way of knowing physical properties fabrication methods you'd apply to your sheet materials. And Cadkey's still lacking built-in routines for fairing and hydrostatics that you'll get in any decent entry-level boat design software from Nautilus, Vacanti, or Maxsurf.

Tom Speer's explanation of developabale surfaces is great. I have played around with developing a Visual Basic app for doing the same procedures. It's a fun project, but not trivial by the time you work in all the graphics programming, interface design, and error checking you need to have a nice tool. It certainly isn't the way to go if what you really want to do is design and build a small boat or two. Nautilus, Vacanti, and others have made programs available at a very reasonable pric. I daresay if you're at all computer and CAD literate, you can get up to speed with them as fast as you can learn the tricks for conic projection and lines fairing for manual drafting and lofting. And before I hear cries of protest from traditionalists, I love to work out designs with splines & ship curves on paper as well!

gonzo

08-24-2003, 01:52 PM

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.

tspeer

08-24-2003, 08:07 PM

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.

Chris Krumm

08-25-2003, 12:24 AM

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.

tspeer

08-25-2003, 02:41 PM

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.

ChrisGibbs

08-25-2003, 06:24 PM

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

Guest

08-26-2003, 12:54 AM

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.

gonzo

08-26-2003, 08:55 AM

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

Chris Krumm

08-26-2003, 01:25 PM

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.

Wayne Grabow

08-26-2003, 09:45 PM

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.

Morgig

08-28-2003, 06:25 AM

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.

Chris Krumm

08-28-2003, 08:50 AM

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.

Morgig

08-28-2003, 11:07 AM

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

ChrisGibbs

08-28-2003, 06:04 PM

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

CDBarry

09-01-2003, 05:37 PM

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.

CDBarry

09-01-2003, 05:43 PM

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.

Chris Krumm

09-02-2003, 06:08 PM

Morgig -

I think we're in 100% agreement. This discussion has ranged over the process and mathematics of checking for developability along with a number of references to current software that will do the job for you from as little as $200 into the thousands-of-dollars range.

programs by New Wave Systems, for example, give you gaussian curvature maps to check for developability along with plate expansions. It'll even force developability on patches of the hull if you like, provided you can live with it adjusting your hull lines.

Understand how you don't want to mess with trimming thick plates on big boats. Prosurf and ProBasic have been used to build some large tugs, brges, and who knows what else, along with the plywood projects of us amateurs.

The software is a tool for most of us. Some earn their bread with the tools, others play with the tools, and yet others play with making the tools.

Ian

05-16-2004, 12:41 PM

I know that you have received a great number of very interesting and very technical replies--but on the off-chance that you just want to get going with something functional--I suggest that you look into a program called Plyboats. It is very cheap, very easy to use, more flexible than it at first appears--and the results are buildable.

carlg

05-17-2004, 10:52 AM

I'll second Plyboats. In spite of its low cost, which is now around $40 to $50, it is extremely useful for plywood hulls. I've built five boats using Plyboats and all the panels have fit perfectly.

It's unfortunate that the program is passed over in forum discussions.

Andrew Mason

05-20-2004, 09:06 AM

I think Morgig makes a valid point that is not widely appreciated by many designers. The perfectly developable surface is usually not the surface that is most desirable from the point of view of the designer. Typically on a powerboat hull with twist in the bottom panel forward, the truly developable panels have too much convex curvature to be ideal.

However, by modifying the sections toward a more ideal shape, it is often possible to come up with a surface that is just as buildable as the truly developable surface. The reason for this is that we are not dealing with inelastic materials, even steel plate has some elasticity that allows it to be persuaded into a slightly non developable shape.

This is one reason that we take the approach we have in Maxsurf. We show, using marker points, where the true developable surface will lie, and the designer chooses whether to have his surface conform to those points or whether to deviate from them.

This approach also allows another important design function - the ability to intentionally make a portion of a surface non-developable. For example, on the topsides of a typical powerboat hull, the aft 2/3 of the surface may be perfectly developable. Up forward, however, the designer may choose to sacrifice developability to create a significant amount of topside flare. Maxsurf allows the designer to do this within a single surface, and to measure the amount of strain (i.e. compound curvature) in the resulting plates. Apart from small boats, this is a typical requirement of steel and aluminium workboats - make as much of the boat as developable as possible, but sacrifice developability in those areas that have a critical influence on seaworthiness and performance.

Remarkably, the use of Maxsurf to design surfaces that are practically developable has resulted in examples that were easier to build than truly developable design. The example I can give was one builder in the N.W. U.S. who was building a workboat with a deep forefoot at the bow. This is a hard shape to get developable but it can be done with fairly full sections. One plate in the bow, although developable, needed to be formed around a radius of curvature of about 1 meter. When the design was modified to give straighter sections and less developable plates, the minimum radius of curvature increased to around 2 meters, resulting in less force being required during the plating process.

We recommend with Maxsurf and Workshop that if a plate is developed and has a maximum internal strain of less that 0.25%, the plate can be considered to be practically developable. We have had builders who have relaxed this recommendation to 0.4% with good results. As a result I have concluded that the enforcement of perfect developability by many programs is an artificially strict requirement that results in the unnecessary compromise of seakeeping and resistance characteristics for many designs.

As an additional point, I have not used Plyboats, only seen printouts, but the impression I got from these was that it only did straight section designs. This is fine for untwisted panels, but results in large discrepancies from the developable surface when a panel is twisted. Ironically, I think that the reason that Plyboats has produced many reasonable boats is for exactly the reasons described above - the inherent elasticity of plywood allows a panel to be tortured into a shape that is not developable, allowing the straight sectioned designed to be panelled effectively while retaining straight sections.

Tim_Hastie

05-20-2004, 12:31 PM

I currently use AUTOSHIP and have so for many years. I build metal boats from 20' to 65' . I have found AUOTSHIP to be perfect every time. Keeping in mind "Garbage in---garbage out"

maximillian

07-14-2004, 09:06 AM

i'm currently doing a final year project on creating a database on 'development of developable surface area'. since knowledge in this topic is very shallow, and i've to start from scratch. i need some advice where needed to write a program, using parameters such as common elements, directrixes etc, to determine whether a surface is developable.

Chris Krumm

07-14-2004, 07:27 PM

Maximillian -

Read the earlier posts in this thread, particularly those by tspeers (Tom Speers). Also look for my references and links to the Brian Konesky papers. I think that points you in the right direction regarding the math and background on methods that could be implemented in computer algorithms.

Chris Krumm

Andrew Mason

07-14-2004, 11:36 PM

If you mean that you wish to analyse and existing surface for developability, rather than creating a developable surface from scratch, the procedure is straighforward but does require some math.

The definitive test for developability is whether the Gaussian curvature of all points on the surface is zero. Gaussian curvature is simply the product of the two principal curvatures at a given point of the surface. The principle curvatures are the maximum curvature and the minimum curvature, by definition the directions that these two curvatures run in are always exactly 90 degrees to one another (a perfectly flat surface is a special case, the principal curvatures are both zero, the Gaussian curvature is also zero, and the principal curvature directions are undefined)

For a developable surface, the minimum curvature is zero, in other words the surface is straight in one direction. This is the familiar directrix or ruling of the standard development methods. The curvature in the perpendicular direction may be positive, negative or zero, but the product of the two curvatures (i.e. the Gaussian curvature) will always be zero.

To test for developability analytically, you need to know the principal curvatures for any point on the surface. To calculate the principal curvatures you need to know the first and second derivatives of the surface in the u and w parametric directions.

The calculation of the principal curvatures from the partial derivatives is covered in the book "Geometric Modeling" by Michael E Mortensen (pp 280-285).

The calculation of the partial derivatives of a NURBS surface is covered in several books, including "Mathematical Elements for Computer Aided Design" by David F. Rogers, "An Introduction to NURBS" bt David F. Rogers, "The NURBS book" by Les Piegl and Wayne Tiller.

maximillian

08-01-2004, 12:28 PM

Thanks so much, Andrew and Chris.

Chris, i see that you've played with the surface using Visual basic. i'm now doing the same too, but not much progress. i've yet to define a specific objective for my project. but i'm planning to proceed with developable for all the hull, most probably using fixed apex for all the connicle. and i've yet to manage to access to the Konesky's paper. Basically, what do you find in your program(Visual basic), i means what's the inputs (parameter) and outputs?

BIG MAC

08-01-2004, 02:58 PM

if you have a hard time following this, it's because i can't explain it - not because it's difficult.

1. take your lines and create ruled surfaces. this divides the curves into triangles with vetices lying on the curves. the more divisions you make with the rulesurf variable, the more points you will have on the curves.
2. get in a 3d view that is convenient, exlplode the surface to get individual lines.
3. copy the first triangle, bow or stern, and move it a little away from the curves
4. reset the user coordinate system to align with the single triangle you just copied.
you now will only use 3 commands: distance, circle, and line.
5. here is where a very simple procedure may get hard to explain. you have your 3d curves divided into 3d lines forming triangles and you have the one copied tringle, now parallel to the coordinate system. on the curves, you are going to measure the length (distance command) of the next lines next to the first triangle. any units are fine so set units to decimal and accuracy to thousandths to save some keystrokes. the distance comand will give you several distances - the actual line length, length in the x axis (as though it were in the corodinate plane, which it isn't), lenth on the y axis, etc. just use the actual line length. pick a line of the next adjacent triangle on the curve and measure its length and then draw a circle on the single triangle with the same diameter, from the same vertex. on the curves, measure the distance to the next line's endpoint form the other vertiex and draw a circle of that radius from the corresponding vertex of the single triangle. where the circles intersect is the endoint of that next line of the adjacent triangle - so draw a line from there back to the single triangle. this is now that next line projected into the current xy plane. keep doing this for all lines of the triangles of the curve and you have your projection. the more divisions you create with the rulesurf command, the more lines you have to process and the smoother the reult will be.

maximillian

10-17-2004, 11:52 AM

i knew that to obtain the developablility, the Gaussian curve must be zero. the problem however, is that i'm trying to develop the surface from scratch. The most important part now is the math algorithms to represent the surface. i'm currently trying to use spline, such as B-spline or bezier to define the space curves between the surface, say, the chine and keel. I've also obtained some constraints from the Konesky's paper for developable surface. Is it possible to determine the algorithms for the surface, under these constraints? or do i need to obtain it through the sweep surface?

Jeff D.

10-29-2004, 01:50 PM

Wonderful discussion on developable surfaces, but I wonder if you'll indulge me trying to work backwards for a moment.

For the sake of arguement, let's say that I have the lines drawings for a vessel not necessarily designed to be built from sheet material. Let's further assume that the drawings are in AutoCad, or some other 2-D drafting program, so I can do conical projections the old fashioned way, but with a bit better accuracy. Mathematically, I could also determine the equations of the lines, as they are all simple radiused curves. No splines, higher order curves, etc.

As opposed to using cones to generate lines, which would insure a developable surface, I have been trying to find cone locations which correspond to the existing lines, thereby insuring that the existing surface is buildable from sheet material. Trial and error isn't working. At least I don't think it is, but there is always the possibility that I am trying to prove the developability of an undevelopable surface!

Does anyone have any suggested techniques, mathematical or graphical, to verify that a surface is developable if given the lines drawing?

Thanks in advance for your help,

Jeff

maximillian

11-02-2004, 06:14 AM

it is always good to prove the developability of all the surface, or at least make it developable.
But i do think that working backward (Kilgore's method) is very tedious and inaccurate. Furthermore, all you are doing is actually multiconic development method.
What i am trying to develop is a set of simple algorithm to represent the surfaces of the hull, using spline function as a beginning, and its derivatives for conditions. this is relatively simpler and more accurate compare to graphical methodology.
so there's no need to going back on the Kilgore's method.
Even so, your comment has been very helpful.
Thanks.

Gilbert

11-06-2004, 02:45 PM

Kilgore's method is not a multiconic development method. It is the rotation of two 3d lines about the axis of of a tangent point on one of the 3d lines to determine a ruling line which is tangent to a point on the other 3d line. I am not aware of a more accurate method. Most of the computer software I've seen that claim to generate ruling lines are a joke. And it's obvious when they are a joke that they are not using Kilgore's method. What use would you have for software that does not work "backward" as you put it when you want to know if the surface is developable?
My 2c.
Gilbert

bholtermann

11-24-2004, 03:14 PM

Hi Guys,
I am new to the site just today and am trying to reply to a question I saw about CAD CAM and a router to make some small models... I have a CNC machine in the garage and am willing to help if I can.
In my experience pretty boats are mostly elipses, one or more together. I have used Design CAD to prepare section views. This is the way boats are ofter presented with cross cuts running from sem to stern. BobCAD can surface it from there.
I would need DXF files so if you can get that far, or if I can help let just me know? I've been around boats all my life and do not expect that to change any time soon.
Thanks,
Bruce
bholtermann@sealeze.com

bholtermann

11-24-2004, 03:59 PM

Hi Chris,
I am new to this site but not to boats. There is a product called BobCAD that can generate a surface from the section views of a boat. I have been using DesignDAC with elipse fuctions as they are used a lot in pretty boats. They can be imported to BobCAD via DXF files and machined with the model upside down, Keel up.
If I can help let me know. I have a CNC router I got to make small boat hulls.
Best Regards,
Bruce
bhltermann@sealeze.com

patrik111

03-23-2006, 11:33 AM

What sort of gaussian curvature could I tolerate when designing a hull to be built in 3-4mm tortured ply?

If I place a sheet of playwood on a flat surface but add a distance in the middle, the gaussian curvature of the playwood does not as far as I understand it equal zero if the all edges of the sheet touch the flat surface.

Where could I find information on how much gaussian curvature is achievable?

Br

Patrik

Andrew Mason

03-23-2006, 11:02 PM

Patrik

It's not a matter of how much Gaussian curvature you can tolerate, it is dependent on the amount of elongation required in the panel once it is developed.

When you take develop a doubly curved panel with positive Gaussian curvature, center of the panel will need to be stretched to form the curved shape, whereas with a negative Gaussian curvature panel the edges of the panel will need to stretch.

As you make the panel larger, the amount of elongation required increases. If the amount of elongation needed is less than the natural elasticity of the panel material, the panel will can be regarded as being developable for practical purposes, even though the Gaussian curvature is non-zero. It is these elongation or strain values that you need top look at.

As panel sizes get smaller it becomes easier to accomodate the elongations required, so with steel or aluminium vessels it is often possible to handle double curvature by breaking the panel up into smaller plates. This is not really viable for a plywood boat where typically you will scarph together smaller sheets of ply to make one piece that can cover the whole panel.

So, in summary, you can't tell much from the magnitude of Gaussian curvature, you really need to develop out the panel in a program such as Workshop and look at whether the maximum strain values fall below certain values.

Typically for steel and aluminium I recommend minimum strains in the developed plate of less than 0.25%, although some Maxsurf users have had success up to 0.4%. I don't have a value to recommend for plywood, but expect that it would be slightly higher than this.

Hope this helps

Andrew