# John Letcher's Hull Design Method

Discussion in 'Software' started by EscapeArtist, Sep 15, 2021.

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### baeckmoHydrodynamics

I think there is a misinterpretation of "fairness"; a line or a surface can be perfectly fair with a combination of convexity/concavity, ie the curvature radius can switch from one side to the other, just as TANSL notes.
Fairness is a measure of how abrupt the switch is along the line/surface. If you combine two segments of circular arc one after the other, the surface is not fair; the radii change sign over an infinitesimal distance. But a sine curve may be perfectly fair with the radii going gradually from a positive to a negative value. The hydrodynamical implication is a sudden contra a gradual pressure gradient, with their different influences, fi on boundary layer detachement.

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### KayakmarathonJunior Member

Or at least different interpretations of "fair"
I define fair as the radius of a sphere tangent to the surface point as always being located inside the hull. This allows for a discontinuity of the second derivative at maximum beam for every waterline as in the example you gave. From what I remember from perusing Navier-Stokes equations there are 2nd partial derivative, so a design with my definition of fair would be more difficult to run fluid dynamic simulations, if not crash the program.

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### baeckmoHydrodynamics

..Fair enough....!

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### EscapeArtistJunior Member

As Dolfiman notes, a good definition of a "fair" hull may be lacking. I've taken it to mean that you don't wind up with a bulge or a dimple someplace like the blue areas shown in this example (from DelftShip – first impressions « Ducktape Engineering – the Viking project blog http://ducktapeengineering.org/2012/02/28/delftship-first-impressions/).

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### TANSLSenior Member

@EscapeArtist, I am convinced that you do not use trigonometric functions to define the surfaces of your hull. You probably use parametric polynomials in X, Y and Z, and for these to be infinitely differentiable they should be of order infinite + 1. I am sure that you do not use these types of polynomials, hence my question and my conviction that your statement is totally wrong.
Regarding the picture of the canoe that you show us, unfortunately the lack of smoothness in the surfaces is not only produced in the blue areas but the entire surface is full of discontinuities. It is not possible to speak of a smooth surface with certain areas to be corrected, but it must be said that the surface is not smoothed at all.
Fairing a hull is a very painstaking and tedious job, requiring very special skills. I admire the personnel who are dedicated to these tasks in the shipyards. Don't give up on your efforts and keep working.

Last edited: Sep 29, 2021
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### KayakmarathonJunior Member

I've spent some more time experimenting with Letcher's method. One design feature I want for fast kayaks is vertical bow/stern. Previously I posted such a feature introduced a hollow at the waterline near the end. Every tool has its limitations. I've found a "fix" for the hollow. If I make the minimum shear height equal or greater than the maximum half beam of the shear, then the hollow goes away when incorporating a vertical end. I tried this work-around for my parametric approach, and the end hollows also went away. Usually the beam is much wider than the shear height, so it would appear this method will have limited use. The work-around is to use a much larger overall cross section in the design and then cut the hull to the desired shear height to half-beam ratio.

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### EscapeArtistJunior Member

Interesting. Any idea how the "fix" works? Is it only valid if the freeboard(?) height is more than the max half beam, or can you push it a little?

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### KayakmarathonJunior Member

Not the freeboard, but the minimum freeboard PLUS max draft.

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### KayakmarathonJunior Member

I was using Letcher's method to design a wildwater kayak. The specs are 60 cm beam and shorter than 4.5 meters length overall. That's quite a lot of freedom to design. More recent wildwater and olympic kayaks have a vertical bow / stern , and vertical freeboard on the first 20 to 50 cm from the end. Below the waterline the cross section becomes a vee. The midship cross section is rounded vee.

I expected the widest point of every waterplane to occur at midship. Instead I ended up with a bulge as indicated in the green circle. Red and blue sections extend outboard of midship, the black line. I began to think about how this happened, so I plotted the normalized midship and end sections together. When I saw the normalized end section outboard of the normalized midsection, I realized Letcher's method involves a weighted average of the two sections, so if enough of the end section was outboard of the midship section, it was possible for this bulge to occur. See BULGE plot.

When I created a normalized end section that had all points inboard of the normalized midship section, the bulge disappeared. See the FAIR plot.

The fact Letcher's method does not work for the geometric features I wanted indicates these were never features in the designs Letcher had in mind when he developed his method.

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### tropostudioJunior Member

I loved the "meat grinder" analogy. I wasn't able to access the 1972 paper by Letcher, but after reading through Escape Artist's article, it looks like his fairing method was based on a homotopy applied to geometric curves without reference to specific ship forms or design coefficients. Elegant method. It looks like a precursor to the complexity that can be achieved with his relational geometry methods, which also aren't directly related to producing 'fair' hulls based on design coefficients. But maybe I'm missing something.

Related is Tom Speer's method for designing the hull for his Bascilicus trimaran project:
http://www.basiliscus.com/CaseStudy/geometry.html
Here the immersed hull shape is definitely tied to design coefficients. Another elegant method.

I've designed and built both strip-planked and developed ply small craft using Steve Hollister's ProSurf3. Years ago, I laid panels out using his generated offsets and and cut them by hand. Now it's with a CNC router. I'm amazed at how well the hulls go together and how fair everything ends up. When you are building with wood over stations, or any material having specific bending properties, the hull won't exactly match the NURBS surface. Cubic spline curves in CAD programs I'm familiar with don't really match the shape of a batten of uniform cross section and stiffness run through simple supports, with curvature set to 0 at ends. If you mill the form with a 5-axis CNC, different story.

It does have me me wondering about possible relationships between materials in bending, minimum energy curves and surfaces, and fluid flow...

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