Designing a symmetrical hull under heel

I see, you do not talk about the "metacenter" but about the "false metacenter". But you will agree with me on what to say " metacenter is the point on the center plane of the boat directly above the center of buoyancy" It is not clearing up the issue. (Be careful with Wikipedia, it is not uncommon to find inaccuracies in its definitions, for a naval architecture technician it is preferable to look for other sources).
As the metacenter is not the subject of this thread, I am going to stop intervening in such a pleasant conversation.
By the way, merry christmas.

 

Skipping references to metacenter, etc, the righting moment arm of a hull which is a portion of a body of revolution with the axis of revolution parallel to the waterplane will be the (distance from the CG to the axis of revolution) * sine (heel angle).

Corrected.

 

Something is missing in that equation, do not you think?

 

Correct. It should have been righting moment arm. I'll correct it. Thanks.

 

If I understand the original posters query, the aim is to produce a hull shape that does not change longitudinal trim when heeled (i.e. does not go "bow down" or becomes hard mouthed or display other undesirable handling problems).

If so, T Harrison Butler wrote a book a while ago - 1945 - called Cruising yachts Design and Performance. He relied on the Metacentric Shelf theory* to produce hulls that, when heeled, remained perfectly balanced and with neutral steering characteristics. His designs do indeed display an uncanny tendency to remain on course when heeled with the tiller unattended and to display pleasant handling characteristics. I believe that the book is still in print but second hand copies are readily available. My copy is the 4th edition.

Essentially, the theory is that, as the hull heels, it will put more of the hull volume into the water around midships and take some of the hull volume out of the water at the ends. Provided that the volumes at the ends are about the same and the volume immersed is approximately symmetrical around the hull midpoint, then no change in trim occurs. Makes sense, no? He illustrates the "shelf" by a sketch showing the volume immersed below a line (presumably the waterline) and the volumes removed above the waterline so it looks like a lazy sort of sine wave, if that makes sense.

I also have a PDF copy of a final year dissertation by John Harlock called Metacentric Analysis in Yacht Design which amplifies the explanation given in the book. I can't find it on the net (I think it is from the T Harrison Butler owners association but nowadays I can't remember what I had for breakfast and there are only corn flakes in the cupboard!) but if anyone is interested, I can e-mail them a copy.

Note that the designs are traditional long keeled yachts and the book addresses in detail how to design such a hull. If you want to scale up the dimensions of a laser dinghy to 30 foot LOD, put a lid on it to gain full standing headroom and a fin keel to keep it upright, then his writings may not be applicable. However, that is something to try out and/or research.

*Peace, fellow yachties. I know that all naval architects dismiss the concept as being fundamentally flawed and "it doesn't work" but as Professor Heinkel said about the bumble bee, it is scientifically impossible for the bumble bee to fly. However, the bumble bee doesn't know that. And neither does a boat built from one of T Harrison Butlers plans know that the theory doesn't work.

 

I would be very interested in a copy of the Harlock thesis. My email is boebert@swcp.com You may be interested in the paper on Turner's theory I attached to post #11 in this thread.

Cheers,

Earl