Determining the center of lift for a deep vee hull?

"I'm trying to calculate the area needed for a keel for a 60 foot yacht. (...)
What I'm doing wrong"

keel Lift vs side Force help??? https://www.boatdesign.net/threads/keel-lift-vs-side-force-help.12530/

"The thing is that I'm getting very low Lift values for my keel"

 

First of all you have to move the rudder

the load, the work, has to be divided between the centerboard/Keel and the rudder, for example 70% centerboard and 30% rudder or even 60-40 and in some extreme cases 50-50.

And secondly you have to take into account the interaction between the hull and the daggerboard (HK).

 

These calculations can be done in a sophisticated way or we can do it the old lazy way.

The Old Lazy Way

Lift Coefficient 2d = 0.10 for each degree of angle of attack

Lift Coefficient 3D = 0.9 x Cl2d / (1 + (2 / AR))

AR = Aspect Ratio

Force = CL x Dynamic Pressure (q) x Area (A)

And the lazy way for the Hull effect on the centerboard (HK) is on the one hand to lengthen the Area of the centerboard to the Waterline and, on the other hand, to multiply the AR of the centerboard x 2

 

Rudder Blade Angle of Attack is for example: +5 degrees Rudder Blade + 5 degrees Leeway - DownWash

(which here from aeronautics to nautics would have to be called SideWash)

And the Down-wash (SideWash) can be calculated or it can be assumed roughly = 0.5 x Leeway

Also keep in mind that the water speed seen by the rudder blade is lower = 0.9 x Velocity

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This is why it is a good idea to take the rudder blade to one side to get rid of the keel, i.e. two blades.

 

Upwind ... the Keel Downwash (SideWash) is irrelevant, as the rudder blade goes a few degrees to leeward.

Downwind ... the off-center rudder blade is more effective as its response to Yaw is stronger.

And

if the stern is wide, then a single rudder blade works very poorly with a heeled sailboat.

 

CarlosK2, this is an awesome analysis.

Sorry I have been absent, I will be back this weekend to look all this over with more attention. Things are really hectic over the last little while.

 

(Froude 0.5)

We have seen the Yaw Axis (albeit in a somewhat disorganized way while i myself was getting clear on this tangle).

But in the background there is an even more important Axis: Pitch.

Here the Forces we have are:

A=1) Hydrodynamic Force of Vertical Lift, force due to High pressure and depends on the Angle of Attack

B=2) An unnamed Force that Savitsky calls Hydro Static and, on the other hand, Hörner calls Hydro Dynamic.

(Due to the accumulation of water: a wedge. Obviously in a high speed motor boat (Froude > 0.8-1) the approach is that of Savitsky 1964; but here let's say it is a Savitsky 2025 for sailboats.)


C=5) Lift Force in this case inverse: Suction due to Low pressure and that depends on the curve.



3) Force of the Earth
4) Force of the Ocean

 

It is a heuristic model (that with effort and care can even calculate although not very accurately) so I think it is better to leave it as a heuristic model for understanding and comprehension.

Force A) depends on the Angle of Attack and the width, beam, squared of the Spray (and the reduction if the lifting surface is not flat but V-shaped, see Savitsky 1964).

Force B) depends on the Angle of Attack and the width, Beam (BWL) squared.

Force C) depends on the width of the water exit and 'arrow / chord' in Arc seen in profile.

 

This model for sailboats is only valid for 0.5 Froude and 0.6 Froude.

If the velocity increases, vectors 1 and 2 become a single vector. And if the velocity continues to increase then vectors 1, 2 and 4 become a single vector (= Savitsky, 1964)

0.5-0.6 Froude are key velocities because on the one hand they are the typical velocities of a surf riding with small waves and, on the other hand, it is the take-off velocity for a big and glorious surf with a big ocean wave: surf gliding.

 

The Calculus problem

The problem is that one thing is the Forces represented by those Vectors and another question is the shape of the Hull wave.

A crude supposition that occurs to me is to multiply the result by 2: if the estimation of the Forces gives us Bow Up +1 degree maybe we can suppose +2, in any case when making these estimations although they are not precise we are understanding the matter.

I mean that it is better to think with Numbers even if they are quite imprecise. Between thinking with confusing words and having a good CFD ... I think there is a middle ground. In my father's time (may he rest in peace) they used slide rules, and airplanes flew.