# Forces on sailboats (#3)

Discussion in 'Hydrodynamics and Aerodynamics' started by Sailor Al, Jun 23, 2021.

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### Sailor AlSenior Member

(#3 because I see two earlier posts with similar title, but different question.)
We are all familiar with this diagram of the forces in the horizontal plane of a sailboat in equilibrium:

I'm interested in getting some actual numbers for the size of the force (Kg, Newtons) and the angle (degrees) for a range of racing keelboats of varying sizes and speeds.
Does anyone have any experimental data?

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### gonzoSenior Member

For the actual forces you will need to calculate them on 6 axes. The horizontal plane representation is a simplified diagram to explain the basic concepts. I am not aware of any compilation of data like what you ask for. However, is this for current raceboats? You may be able to get data from test tanks on old obsolete boats.

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### Sailor AlSenior Member

Yes, but aren't the forces in the horizontal plane the ones that ultimately win or lose races?
And yes, modern boats would be more interesting than old ones, although some old test tank results might be interesting. Do you have and references? I can't find any in my small library, Marchaj and Fossati are descriptive but not very quantitative.

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### gonzoSenior Member

No, boats operate in 3 dimensions and move in 6 axes. Every one of them is relevant to speed and direction. Modern designs that are relevant to racing are not likely to have their test data published. That is proprietary information and the source of income for the designer. Older tests results are sometimes available if you ask for them.

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### TANSLSenior Member

I was convinced that with three directions and three axes any movement of any object in space could be reproduced. Surely I am wrong, so please, why are 6 axles necessary in the case of sailing boats and what are those axes? Does that have something to do with string theory that talks about up to 11 possible dimensions? Thanks.

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### TANSLSenior Member

@philSweet , you will probably agree with me that 6 axes is not the same as 6 degrees of freedom, or do you not agree? Insisting twice on the 6 axes does not seem reasonable and arguing that the OP can be wrong by not taking into account the 6 axes is not reasonable, does it?
Maybe because I'm so jerk I couldn't think of another way to tell Gonzo, without forgiving him, to think about what he was saying.
Thank you for your kind qualification, it expresses your spirit very well.

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### tlouth7Senior Member

You can make some good estimates for various values from widely available data. For example the sideways (with respect to the hull) component of the forces you show can be inferred from the heel angle, righting moment, and difference in height between centre of effort of the rig and centre of lateral resistance.

The necessary thrust (ignoring lift induced drag from the keel, and change in drag due to heel) for a given speed can be inferred from engine values and propeller efficiency.

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### gonzoSenior Member

This is for sailboat, so engine and propeller are not relevant. The propeller is only considered for drag and turbulence.

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### Mikko BrummerSenior Member

Dolfiman likes this.
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### Sailor AlSenior Member

That's a really neat app. I fed in my boat's data and iterated till the heel angles matched and it returned some interesting numbers:

The 3.9° leeway corresponds well to the Farr 40 VPP of 3.09°.
However the 211 kgf (kilograms force?) feels small to drag a 5 ton 40 ft boat through the water at 7.2 kts with a leeway of 3.9°.
The heeling moment of 6072 is, on the other hand, much larger that I calculated from our 1400 Kg bulb at the end of a 2.7 metre keel at 19° heel: I get 1230 kGm.
Any thoughts?

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### Mikko BrummerSenior Member

Try turning auto depower on. What apparent wind are you using? From our Boatbase, I have for Farr 40: 1 deg RM 198 kgm, and with a crew 760 kg, RM at 19 deg heel 3900 kgm.

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### tlouth7Senior Member

You don't seem to have included hullform stability in your righting moment figure, which might explain the discrepancy.

Here is an interesting thought experiment. Imagine you are sailing along close hauled, under genoa alone. The only place where a forwards force is being applied to the hull of the boat is the turning block of the genoa sheet. In fact there will also be a backwards force from the sail material to the forestay foil, transmitted to the hull at the bow and via the mast and rigging. So the total thrust being provided to the boat must be less than the genoa sheet tension. And what is the value of that tension? Harken reckons 200kgf for the 41.8m^2 mentioned above, at 15kt windspeed.

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### Sailor AlSenior Member

Can someone explain RMC please? It appears to be weight/degree, but that doesn't appear to allow for the moment of the keel being proportional to the sine of the heel angle and the moment of the crew, to the cosine of the heel angle. I can't find a straightforward explanation.

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### Mikko BrummerSenior Member

RMC stand for righting moment corrected - corrected in this case means it's a measured value, not theoretical (RM). This is legacy from IOR to IMS I believe. So RMC is the righting moment at 1 degrees of heel in kg*m.

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### AJBJunior Member

Mikko et al,

Long time lurker, but here is some good numbers for a 36 foot LWL modern IRC boat. This analysis leans on a detailed VPP for a custom build, the published Farr office VPPs, the formulations used by ORC and about 40 years of fiddling around!

Without using software, these 'round numbers' reconcile well with the real world and (e.g.) Froude's original work for displacement hulls.

The design would be similar to high righting moment Farr 40 - like a cross between Farr design 277 and a Sydney 36, just a little longer LWL

Boat parameters
(and sorry for mix of dimensions, but have not converted Froude to metric)
LWL 36 feet or 11 metres
Wetted surface 30 m2 or 323 ft2
Beam 4.0 m
Disp 5400 kg
Upwind SA 110 m2 or 1,185 ft2
RM20 approx. 4000 kgm (or RM1 degree 200 kgm)

Dynamics
Sideforce 500 kg (so at average of around 4.5 kg/m2 of SA)
Heeling couple 8.0 m (distance from VCE of foils to VCE rig)
SA:Wetted surface ratio 3.66 (normal for high performance boats around 3.6)
Forward/sideforce ratio of entire rig and hull 0.25
Forward force 500 x 0.25 = 125 kg

Drag
Viscous approx. 2.0 kg/m2 at 7.2 knots , So: 30 x 2.0 = 60 kgf
Wavemaking at upwind target approximately equal to viscous, So 60 + 60 = 120 kgf
Induced and other drag sources add around 5% - say 6 kg
Total drag 126 kg

RM cross check

Heeling force 500 kg x 8 m = 4000 kgm
Disp 5400 kg
Transverse position of heeled CB at 4000/5400 from CL: 0.75 m
Transverse movement of CB at design heel is around 35% of half beam.

Froude cross check
Froude resistance in pounds:

R = fSV^1.83

Where f is a constant provided by Froude - 0.0098 for 36 foot LWL
S is wetted surface area in square feet: 30 m2 x 10.76 - 323 ft2
V is speed in knots - 7.2

R (pounds) = (.0098 x 323 x 7.2) 1.83
280 lbs/2.205
~ 126 kg

Caution ... this is Froude's number for upright, not heeled with induced and other elements added

Observations

1. Upwind target is 1.2 x root LWL - well in line with the real world
2. 20 degrees heel is real world also, with modern VPPs (e.g. Mills, Farr) all citing > 20 degrees for medium air upwind
3. The ballast ratio and bulb depth to achieve this RM are well optimised - VCG around 0.7 m below WL
4. The viscous drag figure assumes regatta quality bottom finish - say 360 wet and dry, polished. The drag number increases quite quickly with any lower standard.
5. The forces reconcile quite well - but remember, they are roundish numbers
6. The apparent wind angle will be +/- 23 degrees
7. The target speed will be more or less the same from 12 - 18 TWS, with flattened sails and more twist balancing the aero forces

All feedback welcome.

AJ

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