The physics of turning in a boat

Question

I am writing a small simulation of a boat (a sailboat under power rather than sail). It has a rudder and a keel and I have most of the physics working for the thrust and drag. I have modelled the drag across the boat to be higher than along the boat to reduce the sideways slip.

However it doesn't behave quite right. Am I right in saying that the keel will not only provide resistance but also contribute to taking the boat through the turn by channelling water?

The final model doesn't have to been scientifically accurate it just needs to "feel" like a boat.

Any pointers would be greatly appreciated.

Best regards and thanks in advance.

Dave

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EDIT (Originally posted as an answer by the OP)

OK, realised I'm missing the hydrodynamic "lift" generated by the keel. Seems like it acts like a sail underwater and generates a force vector proportional to the flow of water over it and the angle of that flow. The force vector is in the opposite direction to the movement of water across the keel and toward the direction the boat is pointing. In theory this should reduce the sideways slip and also pull the boat through the turn.

Would appreciate if anyone out there who knows about this stuff if they could add an answer that makes some sense of my basic understanding. I am trying to distill this down to a formula that is related to the direction the boat is pointing and the direction and speed of travel of the boat.

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OK, realised I'm missing the hydrodynamic "lift" generated by the keel. Seems like it acts like a sail underwater and generates a force vector proportional to the flow of water over it and the angle of that flow. The force vector is in the opposite direction to the movement of water across the keel and toward the direction the boat is pointing. In theory this should reduce the sideways slip and also pull the boat through the turn.

Would appreciate if anyone out there who knows about this stuff if they could add an answer that makes some sense of my basic understanding. I am trying to distill this down to a formula that is related to the direction the boat is pointing and the direction and speed of travel of the boat.

Passivism

Answer 1

When a displacement hull heels over one way (ie. to leeward), it causes the boat to turn in the opposite direction (ie. to windward); I've been told to do with the contour of the wetted area. I don't think the keel generates lift because the angle of attack through the water barely changes.

So when the boat turns, it heels outwards under centrifugal force (the centripetal force acts below center of mass, so there is a moment that tips the boat outward), and that changes the shape of the hull in the water in such a way that it acts to turn the boat slightly faster.

Another factor if the boat is under power is that the saildrive is usually directly in front of the rudder, which allows some thrust vectoring when the wash hits the rudder (ie. when the engine is going ahead, after a ½ second lag or so).

Intuitivism

Answer 2

Please, note that some hydrodynamic force components on the hull (and rudder) are proportional to the velocity squared. And the loading of the cargo is critical to the stability of the steering. For example, putting the bow deeper will make the steering more unstable and vice versa, putting more weight aft will make the boat harder to turn.

Bathe

Answer 3

Ultimately, the factors affecting steering of the displacement hull will be distance from rudder to center of mass (simple leverage); center of thrust (whether it is forward or aft of center of mass); shape and depth of the wetted surface (which will affect pressure and flow); speed (which will affect momentum and dynamic pressure); rudder size and shape (which will determine tendency to maintain the turn); and direction of applied thrust, once the turn commences.

Assuming that the rudder distance from center mass is roughly half the waterline length, and the rudder is hard over, and that the center of gravity is above the center of buoyancy, the vessel is likely to heel outboard, away from the turning center, as her bow, skewed from her original course, meets oblique resistance, and her mass attempts to continue in the original direction. If screw-driven, she will be forced to continue the offset, much as a pencil balanced on a fingertip will tip more rapidly, once it has begun to lean. Slightly lesser pressure on the inward bow will help the turn. While it is true that the after portion of the hull will tend to resist the turn, the velocity of fluid past the outboard side will be greater because, relative to the original course, it has more distance to cover than that on the inside. Furthermore, the after hull on the inboard is drawing away from fluid passing by, which, rushing in to fill the space, helps push the stern in the required direction. As to a deep fin type keel, if the heel be pronounced, the outboard face will help to slew the hull toward the center, and the reverse face will experience slight suction toward the turn's center.

If one backs headsails, the turn will be faster. If one backs engines, the "upset" will be resisted, and the turn less sharp. For the steamer, once the turn begins, it is too late: leave the engines alone. It is the same as braking and steering a motorcar: force both, fail both.

Ashore