Larsson & Similitude

[tspeer]

I haven't mentioned it. Proposed abstract is below. You can find the paper I presented at the last CSYS at http://www.basiliscus.com/CSYSpaper.pdf. The proposed paper is the latest work in support of the same project. Other related work is on my main web site http://www.tspeer.com.

I've derived the theory, but I'm only getting started on modifying the program. So I've got a lot of work to do in order to have the program working, results validated, and design studies finished.



Seakeeping Dynamics of a Cruising Trimaran Sailboat

A frequency domain method is described for determining the sea keeping dynamics of a multihull sailboat. The method is based on the U.S. Navy's Standard Ship Motion Program (SMP), a strip theory code for monohulls. SMP has been extended to mulithulls by assuming that the hulls are coupled together structurally to form a rigid body, but do not interact hydrodynamically. Any number of hulls may be considered, although results for only two, dissimilar, hulls are presented. Dynamic sail forces and
moments are also included. The method is linear, and therefore the sea states must be limited to those for which the motion is remains in the linear range of amplitudes.

Stability derivatives are generated for each hull individually using strip theory, and these derivatives relate the forces and moments about the hull reference point due to the motion of the hull. The complex coefficients for each hull are transformed from the hull reference point to the boat reference point and summed to form an equivalent set of coefficients for the entire
boat. Three transformations are necessary. The motion of the hull must be described in terms of motion about the boat reference point; the phase of the exciting forces must be shifted to account for the boat reference point being at a different point in the incident waves than the hull reference point; and all forces and moments must be transfered to the boat reference point.

Sail stability derivatives are assumed to be constant coefficients independent of frequency (no added mass effects) and are separately determined using a Morino method panel code (CMARC) for a variety of apparent wind directions. For regular seas, the true wind direction may be at any angle to the waves. For irregular seas, the true wind direction is assumed to be parallel to the predominant wave direction.

Once the zero speed coefficients have been determined for the boat, speed effects are added to the hydrodynamic derivatives. The apparent wind direction is determined from the true wind speed and direction, combined with the boat speed, and the aerodynamic contribution of the sails added to form the final coefficient matrices for the boat. The equations of motion are solved in the same manner as for a monohull.

Although each hull is symmetrical, the longitudinal and lateral-directional motions of the boat are coupled. The coupling arises because of the dissimilarity in the loading of the two hulls, even for the case of a symmetrical catamaran. A typical trimaran is even more asymmetric, since most sailing trimarans have two dissimilar hulls in the water at any given time. In addition, a multihull sailboat is invariably operating in a quartering sea, and never operates in a pure head sea. Thus, a six-degree-of-freedom solution to the equations of motion is required.

Results for a power catamaran in a head sea are presented and compared with published experimental data. Results for a cruising trimaran sailboat are presented for a variety of conditions, illustrating the coupled nature of the motion, the effects of the sail rig, and the usefulness of the method in determining the sensitivity to various design trades.

[Stephen Ditmore]

Now I remember you, Tom. It was a fascinating paper - I look forward to the update! Are you still thinking in terms of building the tri?

[tspeer]

Yes, but like most amateur projects, I'm already a year or two behind schedule. Still plugging at it, though. If I can get the VPP and seakeeping analyses done by the end of the year I'll be almost back where I should be. Money looks to be the long-term impediment - I'm only saving about half as much as I should be. But that's moot if I don't have a workable design, and I'm not there yet.

sir
i am a student of naval architecture and ship building
doing my final year project
design of a catamaran
i would be a great help if you could give me
some formula or empirical relationship
to check the initial stability of a catamaran
thankin you

[tspeer]

See Shuttleworth's stability index for a reasonable balance of sail area and stabiltiy: http://www.john-shuttleworth.com/Articles/NESTalk.html

Given the round, slender shapes of most multihulls, you can pretty much neglect any form stability from the hull and just concern yourself with the waterplane area and the change in displacement of each hull. Don't forget to consider diagonal stability (combination of pitching and heeling) - that's typically the worst case condition.

[Morgig]

The following link has an interesting section on Similitude of marine vehicles

http://ocw.mit.edu/OcwWeb/Ocean-Engi...otes/index.htm

It's also worth having a look at the rest of the MIT Opencourseware site for notes on structures, hydrodynamics etc