Sail Area vs Keel Area - Stability Calculation

DCockey · May 29, 2012

Paul B said: ↑

This is correct. Anyone can walk down to any marina in the world and watch the boats heel in their slips.

For the OP to have his calculation work the boat would have to be sitting broadside to a current that contributes a force on the keel that matches the force of the wind on the rig/sails.
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More than that.

Either the relative sizes and shapes fo the sail rig and hull would have to be such that the a force on the keel that matches the force of the wind on the rig/sails and the heeling moment of the force from the current on the keel matches the heeling moment of the force of the wind on the rig/sails
- or -
The boat would have to be constrained so that it could not move sideways but could pivot and the heeling moment of the force from the current on the keel matches the heeling moment of the force of the wind on the rig/sails.

HakimKlunker · May 30, 2012

Dabrownone said: ↑

This model has nothing to do with driving the boat forward.
...and does not move forward at all (or back, or sideways etc).
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Who wants a boat like that?
I call this a case of mathematical diarrhoea

BobBill · May 30, 2012

Dabrownone said: ↑

Ok, i'll say it as clear as possible; this isn't a dynamical equation, its a static one. Additionally, I need to amend my model to equate the torque generated by the two parts of the plate.
Therefore,
T = r x F,
Applying this to the results gives

r1^4 = d * r2^4

r1 = d^(1/4) * r2

This was actually what I had derived originally, but couldn't remember how I got it.
So this would indicate that if r1 ~ 5 * r2, then the torque generated would be balanced. While this isn't a 'real' sailboat, it indicates a relationship which is 'real'.
In regards to the 70' sailboat; most I have seen have a deep, thin keel with a very heavy bulb on the end. Considering that windage from rigging, poles, the hull above the waterline etc contributes to torque, and that the hull is designed to heel to a certain degree, and the action of the waves (which will apply a far greater torque as water is much more dense), it isn't surprising that most boats like this would heel in all conditions.
So why is this practical? Consider the other means of countering torque due to wind. These are form stability (which works to a point) and dynamic stability due to the righting action of the boats CE (which nowadays is usually down in the keel). Both of these have hard limits on their righting ability. For evidence of this, see the stability curves of any boat. Some are designed to right even with the mast less than parallel to the waves, and some would topple well before that. It indicates that as wind speed picks up, the force (and therefore torque) would increase quadratically (v^2 in the force equation), and would eventually overpower the ships ability to stabilize itself. The stability relationship I found is independent of windspeed, and will therefore dampen rotation (apply negative torque) all the time. A relationship of 5:1 sail to keel area would be hard to accomplish with modern boats, considering that everything above the water acts as 'sail' area, whereas only surfaces that dampen rotation act as 'keel' area.
Speaking of which, the 'keel' area could be any surface that resists rotation; for instance both keels in a bilge keels would have one side that resists, three keels would have three etc. As well, a flat bottom, or a chine that has been rotated below parallel with the water, would all actively resist rotating as well, providing a counter-torque to the above water action.
Ultimately, the action of the waves are the real danger, as they can toss you around far more readily than the wind, but here again the keel would at least resist this motion and slow it down, which is helpful.
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Dab, I thank you for your inquiry, and the others for contributions, as I learned.

But, Dabrownone, if static, a waste of time, to me, or, as one noted, self-abuse...real world...learn from these boyos.

BobBill · May 30, 2012

daiquiri said: ↑

In order to have moments of side forces created by the keel and by the sail cancel out each other, they would have to act in the same direction. But, as is well-known to anyone interested in the theory and practice of sailing, that is not how a sailboat works. In realty the two forces act in the opposite directions, and that's what makes the sailboat move in the straight course:

(Pic taken from: http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Edwin_Monin/web 2002nov25 Folder/slide5[1].html)

If the forces above and below water were acting both in the same direction, there would be nothing to stop the boat from drifting sideways at an increasing rate.
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Very kewl link, very kewl, Daq. Thanks.

dougfrolich · May 30, 2012

I would recomend reading Areo-Hydrodynamics and the Performance of Sailing Yachts
by Fabio Fossati
In section- 6.4 Equilibrium under sail - estimating the surface area of hull appendages
is a very nice article that goes back to the "spirit" of the origonal post.
My $.02 worth.

Paul B · May 30, 2012

dougfrolich said: ↑

I would recomend reading Areo-Hydrodynamics and the Performance of Sailing Yachts
by Fabio Fossati
In section- 6.4 Equilibrium under sail - estimating the surface area of hull appendages
is a very nice article that goes back to the "spirit" of the origonal post.
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Not really.

That section is more like the "spirit" of the diagram daiquiri has posted.

The OP is intent on proving that a large enough surface area under the waterline will somehow stop a boat from heeling.

These are two very different things.

TeddyDiver · May 30, 2012

Paul B said: ↑

The OP is intent on proving that a large enough surface area under the waterline will somehow stop a boat from heeling.
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And the reality makes it just opposite way.. more keel area, more heeling, less lateral area (no keel) less heeling

Petros · May 30, 2012

That just shows why mathamatitions working in any other field need to be supervised by people in that field.

dougfrolich · May 30, 2012

In the "spirit" meaning here is a fine preliminary math model for first estimates.
Can we be more pedantic?

BobBill · Jun 9, 2012

dougfrolich said: ↑

In the "spirit" meaning here is a fine preliminary math model for first estimates.
Can we be more pedantic?
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Why would ya? Seems to be pointless enterprise to begin with. No offense intended, but not practical, therefore pedantic, perhaps? Still, my numb head picked up some needed material via the out takes, regarding major sail plan change...

RBauer · Aug 19, 2019

I need help to determine the weighted needed in the keel for my RC model of this Wianno Senior. It is a scratch build 1”= 1’

DCockey · Aug 19, 2019

Do you want you model to float on the same waterline as the full size boat? If so the total weight of the model to be scaled appropriately from the total weight of the full size boat. The total weights to be scaled as the dimensional scale ratio cubed. So for a model built to a scale of 1" = 1' or a dimensional scale ratio of 1/12 the weight of the model needs to be 1/1728 of the weight of the boat.

My understanding is scale model boats intended for sailing frequently have keels which are deeper than the original boats keel.

Howlandwoodworks · Aug 30, 2019

Dabrownone said: ↑

The goal wasn't really to model an actual sailboat, but explore one specific aspect of a boat. The model uses approximations because i'm not really concerned with making precise predictions; the point was to understand whether there existed a point where the force applied by the wind on the 'sails' (essentially everything above the water) with the damping afforded by the 'keel' would cancel each other. I agree that the model is in no way correct, in that you wouldn't actually build a boat like this (although I should build a model and see what happens; something this simple to build may even be within my grasp). My argument is basically that the side force of the keel can damp the rotation (heeling) of the boat, and could therefore be used to define a point where the damping will cancel out the side force generated by the wind.
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If you were to Heave-To you would create a similar scenario but from a different set of circumstances. Sail configuration and angle of attack could create the stall over the keel you are looking for without creating a Frankenstein boat.

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Sail Area vs Keel Area - Stability Calculation

DCockey Senior Member

HakimKlunker Andreas der Juengere

BobBill Senior Member

BobBill Senior Member

dougfrolich Senior Member

Paul B Previous Member

TeddyDiver Gollywobbler

Petros Senior Member

dougfrolich Senior Member

BobBill Senior Member

RBauer New Member

DCockey Senior Member

Howlandwoodworks Member

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