Mathematical method for inteligent cargo

These sorts of problems have been tackled since the early sixties quite rigorously with computers. It just takes some elbow grease. You're going to REQUIRE something like forty parameters to even get close, though, for three person canoe. Perhaps one of the linkages programs can be tortured into giving something reasonable in an afternoon.

That scale of Steve Killings feels right to me. But you have to be looking at similar craft. Comparing at fixed total displacement is crucial, don't scale the displacement with the boat. Midsection shape has almost no variability. Beam to draft varies a bit, and is where much of the variation in KM comes from. You'll want to have a very low deadrise out to 0.7*beam and beam/draft not less than 7 to get comparables from those tables.

 

Perhaps it depends on what "sort of problem" is to be solved. Dynamic analysis is not always required when there is movement. An appropriate quasi-static analysis is frequently sufficient and useful, particularly if the analysis predictions can be correlated with real-world experience.

The assumption that the seated passengers will move their torsos so that their torsos remain vertical, at least for small heel angles, sounds very reasonable and is consistent with my experiences. Tcubed's suggestion to model this as the passengers' CGs remaining in vertical alignment withtheir positions on the seats is consistent with that assumption. This allows the use of conventional hydrostatic analysis incorporating the standard model for a suspended mass.

 

As a amateur canoe designer, builder and user, and occasional kayaker I find it difficult to agree or even understand much of what has been written in later posts. In a canoe or kayak I do not ride a canoe or kayak like a bicycle and most certainly do not attempt to keep a heeling boat upright using body movement. That is what the paddle is for, there are several special strokes for this and they are described in detail in many books on the subject.

Kayakers - in particular with the narrower designs - often fit pads for bracing so they can stay on the axis of the boat, although there are exceptions such as whitewater and slalom. Performance canoers have kneeling thwarts that fit their bodies for much the same reason.

If the boat heels I go with it if it is a narrow boat like my homebuilt canoe and I stay upright if it has plenty stability like my shortest kayak which is downright fat by kayak standards. This may sound counterintuitive to non-paddlers but it's what I - and I am sure most solo paddlers - do. The exception is when taking a wave on the beam when the over-stable kayak is allowed to rock under me - the canoe simply rides over those.

Based on my practice I used static measurements such as metacentric height, seat height and cross-curves to validate a design before building. Ultimately if a design is significantly new the first trip tells far more than the computer.

A canoe or kayak is a highly personal craft that you wear like clothing rather than ride inside like a car. It has to fit.

Now to the caveate: all the above applies to solo paddling. There is a huge difference when two are in the same boat, unless they are in a semi-barge they must act as a team and this takes practice. A canoe designer must take into account the intended user: one or a team or an inexperienced family with kids aboard for the first time - it makes a difference.

Sorry about the rant . . .