Developed Surfaces????

I've been looking around on the internet for a while now trying to find technical articles on developing surfeces in 3D CAD (or even the hand-drafting methods) but i have yet to find any examples.

I know that Maxsurf is "kinda" able to develop surfaces but so far i do not trust it as the results it give me are rather funny.

While i can use the maxsurf results for a general starting control point for the developed surface.

I currently use a program CADKEY to do all of my modelling and drawing.

Thanks for your help

Chris

 

I also have a probably misplaced skepticism about the algoritms used to create developable surfaces in hull modelling programs. I have lately been fooling around with creating developable surfaces in Rhino using the plain jane multiconic techniques I learned back in the era of drafting by hand.

This way I can choose the locations of the cone apex (apeces?) myself, and can draw the rulling lines manually, then create a surface through them. It is sorta slow, but I am definitely getting a feeling for how to wring subtle changes in the shape of a developable surface.

There are plenty of references on creating developable surfaces in sheet metal handbooks. I have good one by S.S Rable called "Ship and Aircraft Fairing And Development" It is not realy specific to hull shapes but the basics are there.

Skenes (Kinney) also has a page on the single apex technique

 

There is always the old and tried half model. I know, it's archaic. However, having a model in your hand is very different from looking at a computer screen. Also, you can take dimensions right off the model. I love making models, so it may just be a rationalization.

 

That is the current method that i use to fair and develop the hull shapes. Kinda slow as you said - but alot quicker with CAD (compared to hand drawing)

Thanks pjwash - would you happen to know the the www of the site on apex development.

 

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.

 

Ship and Sircraft Fairing

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.

 

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.

 

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?

 

Developable design

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.

 

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.

 

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

 

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!

 

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.

 

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 -

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!