Developable surfaces

[Boysie]

I am having trouble following Kilgour's method as outlined in Fig 5 ([url]http://www.boatdesign.net/articles/developable-surfaces). I can follow steps 1 to 5 but not 6 (passing an arc through the points in the originating view). I assumed that I was to adjust my compasses to pass an arc through c, b, d and where the arc crossed the sheer between b and c would be point F, but if I do that Point F cuts the sheer at b, which can't be right.
The other issue is that Point E doesn't appear on the drawing - presumably it is at c?
Geometry isn't my strong subject and I would appreciate someone getting me sorted out please. Boysie.

[Boysie]

Oops the URL is http://www.boatdesign.net/articles/developable-surfaces sorry

[Wayne Grabow]

Is this an intellectual exercise in drafting for you, or are you trying to create a developable hull design?

[Boysie]

Hello Wayne,
Well, both actually. I have a boat plan that I want to increase the deadrise of. I am familiar with Plyboats but it is too restrictive. I'm about to download and try the Carlson Design program. But I am very keen to understand Kilgour's method nevertheless. Regards.

[BOATMIK]

Sounds like a hard job - you have to find the tangent to the edge of the plywood on one edge, then find the point on the opposite edge that is coplanar.

If the two lines are in the same plane they will intersect (unless parallel) so will have a common solution.

It really needs to be solved mathematically as the accuracy depends on doing it for a very large number of ruling lines. Drafting manually won't work - because of the additive errors - the small error of location of each ruling line will add to the edge of the flattened panel so both size and shape will be wrong.

However ... to draw it up as a learning exercise is a great thing!

One way to look at it is imagine the side of the boat and hold a flat panel of ply against the hull.

If the hull has a straight line of contact across the flat ply sheet then that section is developable and the plywood will be tangent to both the curve of the sheer and the chine.

ie coplanar.

It is an impossible (or near impossible) method for manual drafting because of the accuracy required and the large number of lines that have to be drawn.

Also I think that finding out if lines are coplanar would be very difficult using 2d methods as you have to find the drawing plane where the three lines are coplanar - and it might not exist if the surface is only close to developable.

Michael

[Wayne Grabow]

"I have a boat plan that I want to increase the deadrise of."

Increasing deadrise could be fairly easy depending on the hull type. I take it that the current design is developable. Is it single chine or multiple, rounded bottom or "V' shaped? You want to keep the current sheer line and chine dimensions, right? Increasing deadrise will force a new projection for development, so we don't need to know the exact location of the previous projection apex/apices. The general shape of the hull will probably dictate the approximate location of any conic projection foci (look for ruling lines). Do you have the exact offsets for many points along the existing chine? If so, a new projection can be selected, increasing deadrise and altering the shape of the keel, and the new keel shape can be calculated. The shape of the lower portion of transverse frames (below the chine) will also need to be recalculated. If it is a simple "V" only a few points are needed; if it is rounded more coordinates will need to be determined.

I just finished making a small change to the deadrise on a developable hull design of my own. I use mathematical methods, not graphical, so I can't help you with Kilgour.

[Boysie]

Thanks Wayne. Yes, it is developable and I have the offsets. Single chine, slightly convex V bottom. Want to use existing sheer and chine. So I presume that in effect only the keel edge and the bow below the chine will have to be developed.

[Wayne Grabow]

Not knowing specifically what type of hull you are considering (power vs sail, plumb bow vs flaring, constant deadrise vs decreasing aft, point of maximum draft, etc), I'll make this a general description. Bottom development begins at the bow. Half entry angle and bow flare are considerations in determining the type of projection or conic focal point. Ruling lines usually run forward, down and across the bow. A focal point for conic projection is often located forward and below the bow on the opposite side of the centerline. This produces a tight radius and high deadrise to the forefoot of the keel; the deadrise progressively diminishes aft. Alternately, the focus can be located at the other end of the ruling line: midships and above the chine on the same side (port or starboard) as the surface being developed. This type development results in a somewhat more gently curved forefoot and the focus amidships can be used for transition to a different type development aft. A third option is to use an oblique projection of constant 3-D slope which has intermediate properties.

I use an algebraic method of projection after first setting up an x,y,z coordinate system. X denotes length with zero being the the point where the chine meets the bow. Y is the half beam. Z is the height above some horizontal reference line; usually the lowest point on the hull. If we select a focus for conic projection with coordinates (x1,y1,z1) and want to project to a point on the chine with coordinates (x2,y2,z2), the 3-D slope is (x2-x1)y2-y1)z2-z1). At the keel, y3=0 and x3, z3, for the point of intersection, are to be determined. (x3-x1)/(x2-x1)=(y3-y1)/(y2-y1) states that coordinates change in the same proportion along a line. There is only one unknown in the preceding expression; thus, we can solve for x3, and using a similar expression, we can solve for z3. To find the coordinates of transverse frames, we can use the fact that each frame is located at some known value of X. Thus, we can solve for y3 and z3 with a known x3.

The chine line I use is a constructed exact mathematical curve. Thus, the chosen coordinates are exact and plentiful making for easy, accurate projections and a simple connect-the-dots creation of the hull shape. Certainly more can be said, but Kilgour is probably starting to look more desirable already, so I'll end it here for now.

[Gilbert]

I have an autolisp routine that uses Kilgore's method to give ruling lines between two 3d curves. Did you just want to understand how to use his method graphically? Or did you want to know if your new bottom is developable? Or??

[Boysie]

Wayne - Thanks for going to all that trouble for me. I'll need to study it.
Gilbert - Yes I want to understand how to use Kilgour's method graphically please.
And of course it would help to know if the new bottom is developable. I realise now that I just can't use this method to answer both questions. This is a 19 ft boat, so perhaps I could make a quarter size half-breadth model and test it for developability.
PS: This is all Christopher D. Barry P.E.'s fault. He wrote the article I referred to. (Joke).

[Gilbert]

You should be able to do both.
Unfortunately, the illustration in the article posted is very small. Kilgore's article in FISHING VESSELS OF THE WORLD 3 has clearer illustrations as I recall. If you can find a copy, it should help you understand the graphical method.
It is quite common for a chine to keel surface to be developable. The questions are 1) does this give me the shape for the sections I want and 2) can we bend the material we want to use around this shape.

[Boysie]

Gilbert, I right-clicked on Fig 5 and sent it to the desktop and the diagram printed out to spread across an A4 sheet, clear enough to see, but it is incomplete.
Since I started this thread something has been bugging me that I have seen an article on the subject sometime in the distant past and you have cleared it up for me: I used to have that book but it got lost in one of the 5 house moves we've had since then.
I think Wooden Boat has some archival material on the web. I'll have a hunt there.
Thanks a lot.