Advanced questions regarding CoE - CLR balance of small boats

It sails over my head right now, but maybe it's useful to you . . .

PDF - The Hydrodynamics of Hull, Keel and Rudder - Chapter 5

the below quote comes from PDF page 40 (of 44)​

‘‘ . . . . . . . . The influence of the free surface

Just as is the case with the induced resistance of a wing there is also an influence of the free surface on the lift generating properties ofa wing. This is represented inthe 'equivalent keel' approach by mirroring the extended keel around the waterline. By doing so the effective aspect ratio of the equivalent keel is more than doubled when compared to the geometrical aspect ratio ofthe actual keel. As soon as the yacht gets heeled however the pressure distribution over the keel is influenced by the presence of the free surface.

This effect is also influenced by the characteristics of the hull above the keel, i.e. a wide and shallow hull will tend to move the keel closer to the free surface when heeled than a narrow and deep hull. The latter however will also have less of an 'end plate' effect on the keel. . . . . . . . . . . ’’

P.S. - the above comes from, and there's more of it at . . . .

Delft University of Technology (TU Delft)

---> Mechanical, Maritime and Materials Engineering (3ME)​

---> Department of Maritime and Transportation Technology (M&TT)​

---> Digital Library​

 

The approximate effect of the water surface on the flow can be approximated using the mirror analogy.
The flow on the underwater foil is the same as the flow on the real foil associated with a foil wich is its symmetrical
relating to the water plane. So if the depth of the foil is d, its aspect ratio A corresponds to 2d.

 

Remember that the simple CLE/CLE balance formulas do not properly model the basic balance of forces and moments of a boat sailing. The sails are not on centerline, and if the boat is heeled both the sails, and the keel/centerboard and rudder move off of centerline. Trying to improve the formulas by improving the physics of individual components of the boat may not improve the overall results without moving to a 3D model of the forces and moments.

 

DCokey , I agree but I answered only to the question about CLR location of 2 combined foils. Heeling on a monohull gives weather helm, due to
the lateral offset of aero thrust force and hydro drag, on a catamaran lifting a hull it is just the opposite at low heeling angle !

 

Hey, sorry for reviving the old thread, I was away from this part of the project for a while. Now I came back, and I still can't wrap my head around this. I went through several aerodynamic textbooks, but the formulas they have for lift coefficients don't take the aspect ratio, nor the shape of the foil surface, into account.
I'm sorry to bother you with this, but could you please explain how exactly do I calculate lift coefficient for a particular foil shape (centerboard and skeg)?

 

See these well known books :
Theory of wing sections, Ira Abott and Albert E Doenhoff, Chapter I
or
Aerodynamics, Aeronautics, and Flight Mechanics of the Airplane, BW Mc Cormick
or
Fluid dynamics Lift, Hoerner
or
Aerodynamic of the airplane, Schlichting and Truckenbrodt

or every other basic textbook on wing aerodynamics.................................

 

Well, I found graphs like these:



But I haven't been able to find any that would predict CL for an aspect ratio as low as 0.176 (the skeg on my boat). Have I missed something else that you wanted me to find in those books? I've been at this for several days now, and most of that stuff is way over my head.

EDIT: I got some opinions from aeronautical engineers who said that if the foils are more or less flat (no NACA stuff), then aspect ratio barely influences the efficiency of these foils, and the Center of Lift (or Lateral Resistance in this case) is as simple as a combined center of areas. Would you agree?

 

You can find experimental data on low aspect ratio delta wings here :
Fluid dynamic lift, Hoerner, Chapter XVIII

 

Turns out to be online; Chapter XVIII starts at PDF page 415 of 507.

 

Thank you both. I will try to make some sense of it.

 

I have a couple of proposals:
1/
a) regarding the boomless sheeting, mike drummond said it, the forces are internal within the boat / rig, it is the sail area and shape that determine the turning moment, not the mainsheet arrangement.
b) boomless sheeting on a cat rig boat like you pictured has a long foot with large camber in an arc, I suppose the max draft will be relatively aft. End boom sheeting usually pulls the foot fairly tight, and flat, at the bottom of the sail. A jib will also pull the COE forward as it unloads the mainsail.
c) For any aerofoil, you have Drag, Lift and Moment coefficients ie Cd, Cl, and Cm. A flat plate will have a low (zero?) Cm whereas a cambered plate will have a moment coefficient that increases with curvature.
d) you could roughly estimate the change in Cm between a flat and curved sheet and add that difference into the mix

2/ I'm sure the aspect ratio does affect the lift produced for a given angle of attack. tabulated values are generally for 2 dimensional foils.
I thought there may have been a foil spreadsheet that includes it somewhere in these forums? The formula isn't terribly complicated iirc.

3/ Sharing the load between rudder and centreboard is faster (assuming an efficient rudder) but makes boathandling less pleasant and more difficult if its extreme...