John Letcher's Hull Design Method

John Letcher got a PhD in Aerodynamics from CalTech in 1966, sailed across the Pacific six times - twice single-handedly in a 20 ft boat, formed AeroHydro (makers of MultiSurf and SurfaceWorks) and served as the senior scientist on the 1987 America's Cup Stars & Stripes. In 1972, he published a paper, "A New Approach to Lofting and Fairing" in the Marine Technology Society Journal, which described a method for generating a hull using only six curves - sheer, freeboard, profile, two sections and a homotopy to smoothly transition between the sections. I was curious to know if it might be possible to recreate his ideas using current software tools. In 1972, he was undoubtedly using a slide rule to do the calculations, but today's computers are far more capable. A decade prior to his paper, Pierre Bezier applied polynomials defined by a set of control points to create surfaces for Renault autos. Combining these, and using open source software (Octave, Geogebra, DelftShip/FREE!ship) I was able to recreate a bit of mathematical history, and wrote it up in "Yacht Design with Mathematics". This isn't meant to replace any modern software tools, but you might like to try drawing a hull using this method. Below are images of the curves in Geogebra and the hull in DelftShip. All of the code is available on GitHub.

 

Modern softwares do not look for the surface of the hull but rather generate several surfaces (patches), the one that best fits the hull in each area, and they achieve that the union between these patches is uniform: equal tangents and equal curvatures in the lines of joining the patches together.
I am not convinced that a current hull could be defined with only 6 curves. But for J-class sailboats, for example, it could be a very valid tool.

 

TANSL, I don't think this is likely to compete well with current CAD programs either, but I thought it would be instructive to see what Letcher was attempting in his article. His basic idea is still valid though in that each section has to be topologically "close" to adjacent sections and has to fit within the bounds of the sheer, freeboard and profile curves. My guess is that he expected to use more than two sections and more than one homotopy to achieve the smooth hull surface.

 

No, he was using a digital computer and his method was actually a coding framework for fully "digital" lines in the days where lines plans where hand digitized (everyone who has worked a puck raise their hand...). I know code existed for it in FORTRAN on IBM360's well BPC. And really, "mathematical" methods existed well before any digital computing was applied to them in the 1950's and 60's .... Chapman's displacement parabola curve methods, Colin Archer's wave form theory, Taylor's Standard series, interwar polyconic development, etc. These are all methods designed to generate a fair hull of know dimensions. Back in the elegant days where you had to determine where to place sources and sinks instead of throwing the shape into a meat grinder and allowing several million really fast but not really insightful widgets put it all back together again.

 

An interesting project and thanks for letting us know about Letcher's paper.

 

John Letcher was a remarkable person. He gave a course on use of his method at the Maine Maritime Academy in Castine, Maine. I and 3 or 4 other Coast Guard people took that course in 1984. His software was based on b-splines, and according to him he first developed the idea using a simple hand held calculator. When we took the course he was using a Radio Shack TRS-80 computer and the program was written in Basic. However, it didn't take long before he moved on to developing software for use on DOS computers and windows. It was a really good system. You had to define points on the curve (much like Freeship) and it drew a smooth curve through the points. Lots of points, lots of curves and you could define a hull shape. It was a bit cumbersome compared to current software but it worked and a was a breakthrough at the time.

 

While looking through an early 1990's NRL bibliography of then existent computer methods, I actually tracked down a PDF of a Oct 1982 (approx 1 year after the IBM PC introduction) essay of Letcher's early (pre 1985 Aero-Hydro) thoughts. Pretty much state of the art when I was a in my last years as a NA student at UofM. We had four (yes 4) top of the line IBM PC with COLOR(!) monitors and 2 (!) 320k floppies, start the program and "go away for an hour" indeed. There are two things of note in the essay, first is the references, second is that the essay was either typed or used a daisy-wheel (though my money is on a Selectric).

https://repository.tudelft.nl/islan...4c2-862d-0251dec2429b/datastream/OBJ/download

 

Very interesting. For the purposes of my thesis I developed a software to parametrically design a hard-chine planing hull with three main curves (sheer, chine, center line) and two sections. My first attempt was to derive intermediate sections using a "section shape transition" function but I ended up deriving a surface without intermediate sections using a Sweep surface method. This method applies several transformations to the original or a set of sections and places them to new positions while keeping the ends attached to the "sweep rail curves". Users of Rhino may be familiar with this.

 

Thanks for the link to the paper. It's another great look back into the early days of computing.

 

I've developed a similar approach using NURBS for the midship and both ends, while connecting the midship to the ends with 3D chines of parabolic waterlines, elliptic fore keel profile, and parabolic aft keel profile. My method allows me to control how much cross section vee in the fore and aft independent of each other. One thing I have noticed in a hull where the midship is mapped to a vertical end is a concave waterline midship that becomes convex at the end. Letcher's method could be adapted to accomplish independent section vee control by applying the method first to the fore section, then to the aft. Using standard math functions for sheer, waterplane and profile in Letcher's method would improve accuracy of analysis and lofting at desired sections. I'm going to experiment with Letcher's approach on a spreadsheet.

 

I was not aware of this Letcher'method, very interesting. It turns out that I apply a very similar method for Gene-Hull, with however an important difference for the sections : instead of defining 2 sections + a homotopy function A(x), I use 3 sections (fore, midship, aft) of which shape of each requires the input of 3 adimensional parameters + of course the sheer point and the keel one. Then, a second degree function is automatically defined, for each parameter at any x, based on the 3 input values (fore, mid, aft). So, instead of input an A(x) function which is not very natural , the user input the midship section which is more significant for a naval architect, and then the second degree functions generated for the parameters assure automatically a good fairing of the whole.

In addition to this basic approach, I added the "alfa" and the "scow" transformations :
- "alfa" is an angle which "open" the sheer line using a rotation with the bow end as center and acting only on the y values (so actually a true-false rotation). This transformation allows to change a classic narrow hull body into a more modern beamy one.
- "scow" introduce a roundness of the bow waterlines, which can be small (the roundness resulting from the bow real construction) or large (a truly scow bow) .

Here attached the formulations as used for the hull body in Gene-Hull Sailboat 3.2 (an application developed on a spreadsheet under Open Office Calc) with examples of the use of "alfa", of "scow" and of the various sections shapes made possible with 3 parameters.

 

I implemented Letcher's hull approach in a spreadsheet using simple line/ circle sections, and parabolic sheer/beam/keel curves. It does have the same limitation I have observed in techniques I've developed using parametric family of curves to generate a fair hull. If the keel does not meet the sheer/beam line at a single point at the bow; then the method will generate a hollow in the waterplane near the bow. If the midship beam to draft ratio is greater than (or equal to) 1.0, and the stern beam to draft ratio is less than 1.0; then a hollow in the waterplane near the stern will occur.

I need to spend more time running more experiments on Letcher's method since it does create no water plane hollows under certain circumstances.

 

I've noticed some small hollow areas as well. The problem seems to be that while the curves are infinitely differentiable, if any one of them has a first derivative that changes sign somewhere then the hull isn't fair. I've been considering checking for non-convexity and somehow adjusting the control points to enforce fairness.

 

How is that possible?

But that is totally normal on the surfaces of a hull, tangents can change sign, or go through null values, at many points, which normally form a line on the hull.

 

To have a "fair" hull needs a definition, which is not simple : fair for the hydrodynamic should be the guideline, because with modern fiberglass construction, any shape of hull body can be built. Concavities can exist in a good hull body, e.g. waterline fore ends (very classic lines), or a double concave keel line (also classic, ... and modern with the Sun Fast 3300), or even a double concave sheer line : non conventional but one can demonstrate (in the illustration here attached) that could lead also to perfect waterlines of the hull body when heeled.