Can Cp Increase When A Boat Heels

The discussions around heeling a scow have typically mentioned reducing wetted surface area for more speed. Wetted surface area would definitely be a factor at speeds less than hull speed.

I've been wondering if the prismatic coefficient of a heeled scow might be significantly higher than the Cp of a flat scow? Would the Cp due to the immersion of the round bilges be higher than the Cp of a flat bottom boat?

With enough sail power, a boat with a higher Cp can sustain a higher hull speed (see attached graph).

Might that explain a scow's sudden increase in speed when heeled?

 

The answer is going to be "it depends" isn't it?

Which Scow?

I think you also need to consider waterline beam, wave impact effects and all the rest of it. An extreme scow, when heeled, has a radically different effective immersed hull shape, so its unsurprising there's a similarly large change in its behaviour. My gut feeling is that effective waterline beam could be at least as significant as Cp when a wide scow heels, but I've no evidence whatsoever to support that guess.

In the past I've got too hooked up on Cp in my head. These days my suspicion is that its a useful shorthand for comparing some aspects of basically similar hulls, but I'm not sure its very useful for making comparisons between very different styles of boats. Cp in conjunction with length give you some good clues about how long the displacement wave system kicked up by the boat is going to be, but I don't think it should be regarded as much more than a rule of thumb guideline.

 

Yes it can if designed so..

 

As Teddy says; Yes it can if designed so.

I come down on the side of aspect ratio....L/b advantages over Cp considerations.

If a scow or other boat can, by whatever means, including heeling, lengthen and narrow it's WL, then some elements of physics come into play. When a more gradual distribution of areas is present, there are acceleration advantages. Consider that some mass of water is to be displaced in a certain length of time. That brings us to the familiar equation; F=Ma. Acceleration being a time rate of change process.

Never mind all that. It is clear enough that long skinny multihulls go more quickly than their shorter, fatter monohull counterparts.

None of that is to imply that Cp is to be dismissed. However, Cp is most applicable to hulls operating some where below or near their hull speeds. Inland Lakes scow exceed hull speed routinely.

 

You can think of a scow as the morphing of a dinghy into a catamaran that was stopped half way. So it has many of the attributes of both a dinghy and a catamaran. When heeled, the scow has a long, slender hull and the waterplane is located a substantial distance from the centerline. The prismatic may well change, but the difference in wetted area and righting moment are far more important.

I didn't experience a sudden increase in speed when my scow (an M16) was heeled. It was more a matter of optimizing the performance for the conditions. And, of course, offwind when the wind is up, one sails a scow flat so it planes.

 

What I was anticipating was an Order-of-Magnitude 'O' statement suggesting that a long slender waterplane with circular cross-sections tends towards a higher Cp than a hull with a short wide oval displacement.

You know, something like 'O' @ heeled => (chine radius)^2 vs 'O' @ not heeled => (beam - chine radius)^2. Or, something abstract like that.

I'm too lazy to do the math myself.

 

You're not going to get anything like that.
Consider on the one hand a craft with lots of rocker on the keel, but near horizontal buttock lines at waterline beam, and very wide none or barely immersed bow and stern. That might have a moderate cp when upright and a higher one when heeled.
OTOH a boat with a very flat rocker line but relatively narrow bow and stern might go the other way.