Pressure distribution on a hull in a slanted flow ...

Indeed, as most do, to 'explain' their theory better.

But the point is/was, that Munk moment is associated with the reaction/behaviour of a fully submerged body to an inline flow.
The separation of flow of fluid at the fore body and after body creates the pitch up moment, which if said body has insufficient restoring force, destabilises the body...think sub's and swaths.

A yacht, is not a fully submerged body.

 

I agree. Airplanes with keels make the best boats.

 

I don't know whether this video might help our original enquirer but it might justify a bit of his time to evaluate the possibilities .

 

Munk moment is an inviscid phenomena, not resulting from separation. There can also be a moment due to separation.

MIT Open Course notes: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://ocw.mit.edu/courses/2-154-m...004/a13938a09eb13e7d8be464545141aaab_lec8.pdf

8.2 Munk Moment
Any shape other than a sphere generates a moment when inclined in an inviscid flow. d’Alembert’s paradox predicts zero net force, but not necessarily a zero moment. This Munk moment arises for a simple reason, the asymmetric location of the stagnation points, where pressure is highest on the front of the body (decelerating flow) and lowest on the back (accelerating flow). The Munk moment is always destabilizing, in the sense that it acts to turn the vehicle perpendicular to the flow. Consider a symmetric body with added mass components Axx along the vehicle (slender) xaxis (forward), and Azz along the vehicle’s z-axis z (up). We will limit the present discussion to the vertical plane, but similar arguments can be used to describe the horizontal plane. Let ∂ represent the angle of attack, taken to be positive with the nose up – this equates to a negative pitch angle δ in vehicle coordinates, if it is moving horizontally.
(See equations in link.)
The added mass terms Azz and Axx can be estimated from analytical expressions (available only for regular shapes such as ellipsoids), from numerical calculation, or from slender body approximation (to follow).

8.3 Separation Moment
In a viscous fluid, flow over a streamlined body is similar to that of potential flow, with the exceptions of the boundary layer, and a small region near the trailing end. In this latter area, a helical vortex may form and convect downstream. Since vortices correlate with low pressure, the effect of such a vortex is stabilizing, but it also induces drag. The formation of the vortex depends on the angle of attack, and it may cover a larger area (increasing the stabilizing moment and drag) for a larger angle of attack. ....​

 

The usual expressions for calculating Munk Moment of regular shapes are for fully submerged flow. The same phenomena exists for bodies which are not fully submerged, but with the added effects of free surface wave generation.

 

Do you have references for such?

 

PNA 1988, Vol III, Section 9.4 Page 238 has a discussion of the differences due to free surface effects.

What is your reference for:

The applicability of the solution for a submerged ellipsoid as shown in Lamb 1945 is a different question than whether the same phenomena with with the added effects of free surface wave generation exist for bodies which are not fully submerged. The latter is what my comment which you quoted was about, not the former.

 

So a yacht, is not a fully submerged body, the vast majority of the time on a good day.

I see your point.

 

Correct.
Since in PNA the authors are attempting to use the Munk moment (and a bastardisation of the theory) to generate hydrodynamic coefficients, for predicting/estimating the control of a vessel.

 

My opinion is that you are both correct within the limits of the direction you approach it from. I still remember the days where this problem would have been solved by sources and sinks and a mirror surface (circa 1984 when I graduated), so it was applicable as the body was effectively "fully submerged". Even recently when I retired (2018) there wasn't a "good solution" to the whole problem of viscous flow pressures on the body surfaces at (or near) the air-water interface under random waves and orientation. Hell, the best we could do was to use model derived coefficients. As I said at the beginning, you could force AeroHydro to do it for a fixed angle in planer water, or conversely you could use WAMIT to give you a moment due to the waves from any angle but no way on. This and the TBL are the next peaks in the mountain range we must overcome.