Determining the center of lift for a deep vee hull?

J.W. Slooff

It makes a nice and always interesting tangle that simplifying i have summarized in 2) = 2 Leeway in radians x q x Displacement in m^3 x 0.8 / (0.5 x LWL)

 

A simple estimate: a "slender body".

After all we are estimating (a variant of) the so called "Munk's Moment"

Max Munk - Wikipedia https://en.m.wikipedia.org/wiki/Max_Munk

so let's follow Munk and Hörner and ...

0.5 Alpha (radians) x pi x h^2 x q

Alpha = half bow Angle
h: hull depth
q: Dynamic Pressure = 0.5 x 1025 kg x Velocity^2

To the bow Angle we could add "Leeway":

0.5 x (AoA, Angle of Attack = bow Angle + Leeway) x number "Pi" x h^2 x q

 

But this assumes that the "slender body" is like a cylinder, as if it were a javelin or a pen. If the Bow is very sharp and if on top of that it sinks / pitches then the Force is much larger.

 

All these mathematics are gibberish to me. I can do basic math well but these equations might as well be an alien transmission from alpha centauri.

I understand the behavior of foils fairly well but I have read several places that thin, very low aspect foils, such as a boat hull as described, have a center of lift further back than, for example, a naca 0018.

A Wharram Pahi has a very similar underwater hull shape to what I'm considering, perhaps I should figure out where they are placing their sails as a jumping off point.

Sometimes it seems like building models is easier/faster than trying to do all the math, and that models are necessary anyways.

That is exactly what I'm after here. I'm assuming you are using the term CLR to mean the center of lift of the hull and all appendages as a whole? If I were to assume the center of the underwater area is my reference point that wouldn't take into account the lift distribution?

 

As noted here:

 

But the center of the underwater area is a different thing than the center of lift of a hull under motion with an angle of attack. Why would the center of lift be the same as the center of lateral area? If i put the CE in line with the center of lateral plane area I suspect i would have serious weather helm. I'm not sure exactly what you are trying to tell me here. Not trying to be argumentative, just don't know what center of lateral plane has to do with anything. What we are after is the center of lift, same as we use the center of lift of a sail plan to determine its placement.

 

That it is.

The CE – centre of effort – is sometimes called centre of pressure, it is the resultant total aerodynamic force of the sail; at the given angle of attack of the sail to the wind direction.
And, again, the CLR is total hydrodynamic force, which must be balanced by the CE.

Because it determines the balanced boat. In the same way having what is called directional stability in non-sailing vessels.

For example, if the resultant aero force, Ft of the sail, or now we call it the CE, is aft of the CLR, you must apply helm to react against the “couple” and hence the moment of Ft x distance. The distance being the separation between the CE and CLR.

 

I understand about balancing the forces, and what the CE of a sail is. What I don't understand is how to determine the location of the CLR(center of lift) for this type of hull. I'm basically looking for the longitudinal CE of the hull.

What is confusing me about what you are saying is talking about center of lateral resistance(CLR; the center of the lift forces created by the hulls and rudders), and then talk about placing the CE over the center of lateral plane area, rather than placing it over the CLR, to attain balance.

 

Im not sure how many times I can keep saying this, it is the Centre of Lateral Resistance, CLR, not LIFT!

That's your issue why you're going wrong.

 

You are saying to place the CE of the sails over the center of lateral plane area, which you are equating to be the CLR? On a Wharram the sail CE is well forward of center of underwater lateral plane area(CLR as you are defining it).

 

Have you calculated this or estimated this or read this?
And is this at one heel angle or across many, and at what speeds v angle?

 

I looked at pictures of side profile of wharrams and took a tape measure to my computer screen. I could not exactly pinpoint the CE, but I can guarantee it was well forward of midship with the sails sheeted in. The mast beam was almost 2/3 of the way forward on the waterline. To say nothing of the skegs and rudders which would push the "CLR" even further aft. The hulls are symmetrical. I'm not sure that heel has a lot of relevance on a catamaran. The twisting moment of the sail I guess could need to be counteracted somewhat a little more forward placement of the CE and varies with wind speed, but I imagine that's not a significant factor, especially for a cat that tracks well with little rocker. (On a side note, tubby monohulls must be ridiculously hard to balance)

 

Fluid Mechanics (1920: Ludwig Prandtl and Max Michael Munk) in two kicks:

High Pressure (H) depends on Angle of Attack (AoA)

Low Pressure (L) depends on the Curve

The Lift Center of the High Pressure is very close to the Attack edge.

Low Pressure Lift Center is around the Bend.

 

Fluid Mechanics (1925) Advanced Course

first case: Wing profile of an Airplane (1925)

second case: Munk's Moment: a Submarine maneuvering or a Sailboat upwind

 

The terrible copy-and-paste divinity has propagated this drawing which is drawn exactly backwards