# practical developable surface design

Discussion in 'Boat Design' started by mod flod, Oct 13, 2007.

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### mod flodNew Member

Hey guys,
I can't seem to understand how to come up with developable lines. I read and reread posts on the forum, I understand tangents, radians and apices. I own and have read Ship and fairing development by Rabl. I understand how to tell if a surface is gonna be developable or not as well as how to unroll it.
What I don't understand is how to design lines that are gonna be. Let's say I start with the sheerline, how do I then go about to draw a chine that I know is gonna give me developable topsides? Math formula? It's hard to believe trial and error is the key... easier to believe I overlooked something in my reading!
JF

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### NojjanAll thumbs...

Get some software that do it, don't make life harder than it has to be. Rhino for instance is really good at it. BR / J

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### Wayne GrabowSenior Member

I have a method for creating developable hull shapes which works well for me, without using any software program, but other people seem to have their eyes glaze over when I start to describe it. I am an amateur but have designed and built seven boats so far using this method. I haven't read Rabl, but did look at drafting and sheet metal texts. I started by bending a wire into a curve, putting a light source behind it, and projecting that curve unto a flat surface at various angles. The light source simulated an apex, the wire simulates a defined curve, and the flat surface is the projected plane as in a drawing. This allowed me to visualize what I was trying to do. To get a defined curve you need a mathematical equation; I have found that a parabolic curve works well for me; you are welcome to look for something which may suit you better. The mathematical curve is defined in an x,y,z coordinate system and each apex is also defined at the x,y,z location of your choosing depending on what shape you are trying to create. Multiple apices can be linked by ruling lines to create more complex shapes using multiple curvatures within a single surface. Choosen points on the defined curve have x,y,z coordinates and each point when combined with the apex provides two points needed to define a unique line which can then be projected to find its intersection with any other surface. The result is a projected shape defined by many projected points of intersection. Then it is simply a matter of "connect the dots" to create continuous surface boundaries. I usually start by defining the shape of the principle chine; then I project downward to define the keel and upward to define the sheer or an intermediate chine. I can define the deck surface independently; the actual sheer line is then the intersection of the hull side with the deck surface. Have your eyes glazed over yet? If not, I have some pictures and further discussion on a website.

Hey, it works for me. Next boat I build will be a 20' by 5'8" power launch with a flared bow, tumblehome stern, cambered deck, and rockered keel. Each surface includes at least three different projections. Because all dimensions are computed mathematically, lofting to insure fairness is not needed.

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### kengromeSenior Member

So is FreeShip, and it is ... free!

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### hbrJunior Member

link between wire and parabole function

Appreciated the reply of Wayne a lot
on the one hand, failed to understand the link between the wire and the mathematics.
Wayne can you further explain this a little bit further since i am missing the link between a wire and a full 3D surface.
if you could provide me with some extra light -
on the other hand you refer to a website and Q&A about the subject, looking forward to use the URL

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### Wayne GrabowSenior Member

The wire was strictly used for visualization when I first started thinking about this subject. It helped demonstrate what a given curve would look like when projected from an apex onto another surface in various trial orientations. I never use it anymore; it was not mathematical; it simply helped me picture what a 3-D curve looked like when projected onto a surface in various orientations.

What type boat are you trying to design? Rather than talk about theory, perhaps reviewing the decisions and steps in creating one design may be helpful.

developable-surface-boat-designs.blogspot.com

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### mod flodNew Member

Hey Wayne,
I guess you hit the spot with the math formula, I just have a hard time visualizing how to put it in practice. Once I have the principal chine curve that I built using the mathematic formula, then I project it to a point which I intersect with a line, let's say with the centerline, and that will automatically give me the keel curve?
JF
Nice website btw

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### Wayne GrabowSenior Member

"I just have a hard time visualizing how to put it in practice."- so did I initially. "Once I have the principal chine curve that I built using the mathematic formula, then I project it to a point which I intersect with a line, let's say with the centerline, and that will automatically give me the keel curve?" You project multiple points on the chine curve toward or away from your apex as appropriate (depending on where you choose to locate the apex) until they intersect with a plane (i. e., the midline) or other surface to define multiple points on that surface creating a line on intersection (your keel curve). Similarly, many points of intersection with the frame locations (chosen at any convenient curve segment locations) will define the frame shapes.

As an example: I wanted a hull about 5' wide at the waterline and 20' long. I started by considering the forward chine. (When you create a curve, it is usually wise to include a straight segment at the end of the curve. You need a fulcrum to create torque, and there is no fulcrum at the end of a wood board to create continuous curvature.) I selected a curve of length 105" and a total offset of 22.5". Then I divided the curve length into 15 equal segments. 15 squared is 225. 22.5" divided by 225 equals 0.1" which becomes the lateral offset incremental unit. The B/L ratio of this curve is 3/14 and thus its end slope is 3/7 (one of the endearing properties of this type curve is that the slope at any point is always twice the B/L to that point) ; then I added a straight segment of 14" which then adds 6" to the total offset. So now I have a total curve of 119" and a maximum (half) beam of 28.5" Starting amidships the beam is 28.5"; moving 7" forward the beam is 28.4"; next is 28.1"; then 27.6" and so on. We are subtracting the # of segments squared times 0.1" each time we move forward one segment. At the end of 105" we have moved forward 15 segments; 15 squared is 225; 225 times 0.1 equals 22.5" which when subtracted from 28.5" gives us the remaining 6" offset of our 14" straight segment.

I want the chine to curve upward as it goes forward so I choose a vertical offset incremental unit of 0.05" for a total vertical offset of 14.25" over the entire length of the curve. Now I have a defined curve with exact coordinates every 7"; it could be further refined to exact coordinates every 3.5" with only slight effort. It doesn't take much of a batten to connect points so closely spaced.

Classically, you then choose an apex located below and forward of the bow and across the midline for projecting to define the keel. I have read that P. Bolger uses an apex located above and near midships on the same side as the curve. I have used both at different times, but, in this instance, I selected to use a parallel projection which requires no apex and created the shape I wanted. In selecting the apex location or other projection, you need to consider the bow half angle (i. e., 3/7), the desired deadrise (determined by displacement and stability considerations), and the desired bow shape. If you locate the apex close to the surface you are creating, expect rather sharp curvature in that area.

Have your eyes glazed over yet?

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