Body rotation

[CarlosK2]

Pitch Control

Locate the center of Flotation between 50% and 58% LWL, and reconcile CoB and CoG with this primordial center.

Yaw Control

Make a handful of estimates with 3-6 degrees of Yaw/Leeway and two speeds

Make sure that the sum of MM + K + R (Rudder of course without moving it, without touching it, without looking at it) results aft of CoG

This equilibrium condition was stated, for example, by Pierre Gutelle in his book; but he didn't know how to calculate it.

Here, i propose three rough estimates of the Max Michael Munk Moment, made using three different arguments.

To use them, take an arithmetic average of the three.

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1) Simplification (Professor Keuning, Delft) + (Professor Kensaku Nomoto, Osaka)

2) Simplification, JW Sloof

The Aero- and Hydromechanics of Keel Yachts https://link.springer.com/book/10.1007/978-3-319-13275-4

3) Slender body

 

[CarlosK2]

Bonus Track

"d", my way, "ea", AeroDynamic Drag Angle

"d", Andrew Claughton, Southampton, "eh", hydroDynamic Drag Angle

CLR = MM + K + R

R, In this case, Upwind, the Rudder can and should of course be moved to collaborate with the centerboard/Keel producing lateral force.

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I have added "dif" to Andrew Claughton's formula to take into account that the aerodynamic center of the sails is not exactly above the center of the sailboat.

The estimation of the Munk Moment can be placed as a vector right on the stem, for example 1 cm, it is the simplest, we can complicate the problem but it is not worth it.

 

[CarlosK2]

PDF

Professor Keuning

"The Yaw balance of Sailing Yachts upright and Heeled"

https://typeset.io/pdf/the-yaw-balance-of-sailing-yachts-upright-and-heeled-16uye8jsx2.pdf

Unfortunately I cannot find a link to the original article by Professor Kensaku Nomoto, which is from 1979 (!) and which initiates this reflection.

"K Nomoto (1979) considered this difference in the calculated versus the measured CLR to be primarily caused by the fact that the side force produced by the underwater body of the hull was not properly taken into account. He therefore proposed to add to Gerritsma's method the hydrodynamic forces acting on the fore body of the underwater hul.

These forces and moment were calculated using the so-called "slender body" theory.

In the literature this potential contribution to the yaw moment of a body in an oblique flow is known as the Munk Moment"

 

[CarlosK2]

The incredible thing about this story is that a simple reflection provided us with a powerful design tool: if we add Heel to Leeway/Yaw, the Angle of Attack is half the angle (A) of the bow + Leeway/Yaw

Who taught us that the coefficient of a "slender body" is "0.5 pi radians"

Answer: Max Michael Munk

And purists can place the result as a vector at 10% LWL

 

[CarlosK2]

Now

Now, Heel causes CoB to move aft, and therefore the bow dips, and/or a wave coming from the stern lifts the stern and dips the bow, a movement that is deeper because CoG is forward of CoF.

A rough idea is

Munk Moment (Pitch, Roll, Yaw) = 2 x Munk Moment (Roll, Yaw)

If we add

+ Munk Moment
+ K
= HydroDynamic Yaw Moment
+ AeroDynamic Yaw Moment due to the forces from the Sails
= This explains the difficulty in controlling some sailboats

The correct thing is that a sailboat has stable hydrodynamic balance (L_CLR > L_CG) and that the helmsman and the rudder only have the task of balancing the imbalance created by the sails.

 

[gonzo]

The correct thing is that a sailboat has stable hydrodynamic balance (L_CLR > L_CG) and that the helmsman and the rudder only have the task of balancing the imbalance created by the sails.

That statement is fundamentally wrong. The sea state has a much larger influence in the random movement of the boat that has to be corrected. Go sailing and it will be evident.

 

[mc_rash]

Yes, you can find the instant center (i.e the point at which motion appears to be pure rotation and no translation), but in 3 space you are not guaranteed that the point will have an axis system co-axial with the existing reference system. As I said in my first post...dust off your vector math.
Instant centre of rotation - Wikipedia https://en.wikipedia.org/wiki/Instant_centre_of_rotation

Edit: Ok maybe that was a bit harsh, but you need to understand what you would have to do is find and place an axis system such that the vectors of the buoyant, gravity, and other (i.e. sail) forces in that axis system when crossed with their location vectors result in only moments about the three primary axes. So the body will be rotating about a single point, by in all 3 axes simultaneously. However, because the buoyant and gravity forces are not in that axis system, that point would only exist for that instant (why it is called an instant center) and orientation of the vessel to the water surface. I really, really mean dust off your vector math.

Thanks, maybe that was the excact thing I was looking for. Probably I've ever heard of the instantaneous centre of rotation at school in dynamics but forgot it. However, I immediately remembered this video from The Action Lab:

Btw, don't worry you are not to harsh @jehardiman. I like learning things and follow your words interested.

@CarlosK2 interesting stuff! But maybe it's a little bit offtopic. My question is about large angle stability and not about sailing and helm balance, although there might be some correlations.

 

[DCockey]

So large angle stability is calculated without taking care for trim? I know that I overthink things often, but I doubt that trim is not taken into account when calculating transverse stability.

I assume you are interested in calculations for static stability.

Orca3D provides two options when calculated hydrostatics at specified heel angles.

1) Trim is fixed. The hull is heeled. (Updated to remove reference to CG).

2) Trim is free and the hull is heeled about an axis prarallel to the longitudinal axis, and then is trimmed.

 

[TANSL]

Static stability: a nice concept. Can we talk about movements when stability is static?

1) Trim is fixed. The hull is heeled about an axis parallel to the longitundinal axis through the CG.

2) Trim is free and the hull is heeled about an axis prarallel to the longitudinal axis, and then is trimmed.

I'm not entirely sure about the axes you think the ship rotates around. Could you use a simple graph to indicate the position of these axes you're talking about?. Thank you in advance.
I think that, together with our willing comments, we'll make @mc_rash completely lost and confused.

 

[mc_rash]

I think I understand what DCockey means.

1) Heel the hull arround longitudinal axis without adjustment for trim.

2) Heel with correction for trim (LCG = LCB, actually the subject of this thread)

I assume both options do correct for displacement .

 

[TANSL]

In my experience, no Administration accepts calculations that assume the vessel does not change trim when heeling. The equilibrium buoyancy should not be calculated without taking into account that the vessel can change its trim when heeling.
Furthermore, the axis of rotation, whatever that axis may be, does not pass through the CoG.