Determining the center of lift for a deep vee hull?

How does one determine the approximate center of lift for a deep vee hull, such as on a wharram?

 

In my world, the term "lift" is associated with dynamic events, like planing, while the outcome of the static displacement of fluid is referred to as "buoyancy"; so which is it actually you are aiming at? I'm asking because a Wharram is not what I come to think of in a dynamic context, and static and dynamic centers do not coincide. But I may be wrong, since English is not my native lingua.....

 

When it's floating, it matches the center of gravity. That's what you get to decide on.

 

Sorry, I think you two misunderstood the question. I meant for the hulls acting like keels, acting as lateral resistance. I'm trying to figure out where to place the sails(center of pressure) on such a craft, and size and placement of rudders. The hulls I'm considering are symmetrical, would be similar in underwater shape to Tiki 21 hulls.

 

Now it's clearer. What you are looking for is taken, with sufficient approximation, to be the geometric center of the submerged area, seen from the side.

 

You are saying that the center of lift of such a hull is at 50% chord, as opposed to a symmetrical foil or flat plate which is 25%? I could see that the center of resistance would be at 50% if simply being pushed sideways but doesn't that change as the hull begins to create lift in motion with leeway?

 

I don't think I understood what you mean either. Excuse me.
I was talking about the center of drift, nothing to do with the center of lift, which I don't know how to calculate in a simple way.

 

Ok, then we are dealing with a dynamic case. There are two (at least) opposing influences active, both depending on aspect ratio (AR). If you imagine a deep foil with short chord, it has a high aspect ratio. With most "normal" profiles, the pressure center (center of effort et c) lies close to 25 % chord from the leading edge in this case. With diminishing AR, as with a long keel (or a naked hull), the pressure center moves forward.

BUT, with reducing AR, the lateral plane becomes less efficient as a lifting foil due to 3D flows. To create the required lift force now, it has to operate at a higher angle of attack (AOA), resulting in a rearwards transition of the pressure center. The situation is further complicated by the influence of the transverse shape of the foil, or as in dustmans question, the hull. To conclude: there is no general case or shape that is covered by a simple formula.

BUT, again, we can draw some conclusions from existing hull/sail combinations. With traditional long-keeled hulls, you will often find the sail center of effort (CE) about 15% of the keel chord fw of the center of lateral area (think "shadow area"), while for a typical fin keel, the sail CE is found roughly 5% of chord forward of the fin center of pressure (which in turn is found 25% aft of the leading edge). Numbers from Dyne, Eliasson, Heuman and Larsson.

Fiddling with the numbers very roughly, I'd expect that in the real sailing situation, the pressure center of the Wharram hull shape would occur at about 35% chord aft of the "leading edge" of the wetted body.

BUT, encore, there is a mutual influence between the two hulls when operating at a common angle of attack; their separate CE's will not be found at the same longitudinal position.

 

So what I'm left with is building a small scale boat with the same relative dimensions and experimenting with sail placement? It sounds like an accurate prediction is very difficult to make.

 

Oh yeah, this is not an easy one line answer.....A quick inspection of well behaved cats will show that the mast is placed significantly aft of a similar modern mono-hull (late 1800 hundreds keel dragging plank on edge vessels..not so much). Bow shape, stern buttocks, maximum area, demi-hull separation distance, etc are all going to make a difference. Have I mentioned that, to me, "lift" is only a not well thought out concept by people who want simple answers? Just a dot-product of the overall drag in the direction you wish it to be? Tread lightly here when wishing for a "single" absolute answer.

Edit: Xpost with dustman post #9

 

I think you're catching-on.

 

In addition to the good replies noted above, you have a whole lot more to to do.

What you are essentially seeking is "the balance". That being the location of the centre of effort (CE), the geometric centre of the sails, and the centre of lateral resistance (CLR), the centre of the underwater area.
To balance your design/boat, you are seeking to have the CE and CLR in line with each other.

Not a 5min job ....especially when taking into account heel and corresponding movement of the sails....

 

"approximate center of lift"

It is simplest to assume that it is a Vector right at the bow (Hörner, Fluid Dynamic Lift; Hörner, Fluid Dynamic Drag)

And to calculate its value ... complicated matter ... we could make an average of three estimates:

(1) profesor Kensaku Nomoto (Osaka) + a simplified version of profesor Keunig (Delft)

(2) the aeronautical enginer that desing the famous Australia II Keel in his Book

(3) a simple "slender body": A: bow half angle

 

If the bow sinks and there is "cross flow" then (Hörner) the Force can be quite large:

1.1-1.32-1.8 (!) (Hörner) x sin^2 A x cos A x q x h x 0.5 x LWL x 0.8

A: half Bow Angle
q: Dynamic Pressure
h: Hull draft

 

In this case for example at a speed of 5 knots and Leeway = 6 degrees the average of three estimates is 150 Newtons; but surely by the design of the bow is less and that force is further back (because the guy is obsessed with these things and somewhat exaggerated, surely it is less than that estimate) and, on the other hand, the wind force on the hull is further forward canceling the lateral force of the water in the hull.