Body rotation

And because i can't add this as an edit...

 

Nice, now we are getting somewhere interesting.

I'll dive into this the next days, ship motions was a tough course at school.

 

mc_rash,
I checked your profile and it seem you were not around for the two threads below. Read them first and then come back if you have questions. (And please ignore my snark in those threads).
Calculation of GM https://www.boatdesign.net/threads/calculation-of-gm.8852/
Metacentric Height https://www.boatdesign.net/threads/metacentric-height.27171/

 

Thanks for these threads, I like reading "old" stuff which still is and will ever be relevant. But unfortunately there is nothing really new to me. I would say I understand the concept of stability quite good, otherwise I wouldn't start programming a large angle stability tool in Rhino.

My issue to me is the following:
Forcing a hull to heel will result in a change of the submerged part of the hull (there are exemptions like a symmetrical fore and aftship with CoG amidships). Due to this change in underwater shape the CoB moves, which is necessary for transverse stability in any case, but also the longitudinal position will change. As the CoG stays the same LCG will create a trimming moment to get in line with the LCB. Although text books, study material, etc. always only show the well-known transverse 2D section of a boat when treating transverse stability, I think the 3D case should be considered and the hull will trim. I just wanted to find the point about which the hull rotates when the hull is heeled, so CoB changes, displacement and CoG stay the same but the hull is free to heave (to match the displacement) and free to pitch (to match LCG and LCB).

 

When speaking in terms of 6DOF:

x = 0 (fixed)
y = 0 (fixed)
z = f(displacement)
phi = heel angle (fixed)
theta = f(LCB, LCG)
psi = 0 (fixed)

where
-z is a function of displacement and the submerged body shape
-theta is a function of LCB and LCG
(with LCB a function of the submerged body shape)

change in z does effect theta and vice versa.

 

"My issue to me is the following:
Forcing a hull to heel will result in a change of the submerged part of the hull (...) Due to this change in underwater shape the CoB moves, which is necessary for transverse stability in any case, but also the longitudinal position will change. As the CoG stays the same LCG will create a trimming moment to get in line with the LCB."

---

E x a c t l y

That's how "Satanita", what a name, sank "Walkyrie", killing a crew member.

The Satanita - Wikipedia https://en.m.wikipedia.org/wiki/The_Satanita

(The bow-down hull trim is more pronounced if CoB is forward of CoF)

The sailboat is sailing with Leeway and, as it heels, sinks the bow: Pitch multiplies the Munk Moment due to Heel/Roll and Leeway/Yaw, such that the sailboat is uncontrollable when the hydrodynamic Yaw moment of the hull is added to the moment of the sail = Sail Force times its lever arm (h x sin heel angle)

 

The two most typical imbalances are:

1) the bow Pitch, for example -1 degree bow down, with heel/Roll

2) a tendency to Pitch both upwind and downwind due to the CoG being forward of the CoF

google

site:boatdesign.net center of flotation

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It's incredible that we've been going around like mules for a hundred years around two fuxxx axes.

 

One way to address the problem is Reyner's analysis

Denys Rayner - Wikipedia https://en.m.wikipedia.org/wiki/Denys_Rayner

The simplest way to minimize this major source of problems, which we have been experiencing for over a hundred years, is simply

CoG (slightly) aft of CoB
And
CoB (slightly) aft of CoF

L_CoG > L_CoB > L_CoF

 

Right now, it occurs to me that the following idea could be tried:

Commander Rayner's Analysis

15 degrees Heel
Area "In" minus Area "Out"

And we cut the result out of cardboard and balance it on the proverbial sharp old sailor's knife, which in the end is usually a plastic ruler.

And in the center thus found, we could place CoB.

And iterate again.

It seems to me that my lazy rule is the simplest.

Make sure CoF is no further aft than 58% LWL, and center the sailboat from this its primordial center:

The Center of Flotation

 

The long route

With two attempts, trials, we found the Displacement with heel/Roll

and from there we calculated the Longitudinal position of CoB

We saw that it had moved too far aft

We cursed our luck

Back to the beginning

And the same thing happened

In desperation, we chose the sensible path: L_CG > L_CB > L_CF

For example

L_CoG -1% or -2% LWL aft of L_CoB
and
L_CoB -1% or -2% LWL aft of L_CoF

 

We cut out the Water Plane Area from cardboard

We balance it on an old sailor's knife

And so we find the primordial center: the Center of Flotation

And from there we reconcile all the centers with the primordial center: The Center of Flotation.

This simple rule saves a huge amount of trouble.

(Why we've been going around in circles around if 2+2=4 for a hundred years is quite inexplicable)

 

The Yaw axis of rotation passes through the center of gravity or halfway between the center of gravity and CoB

The Pitch axis of rotation passes through the center of Flotation

Eternal return - Wikipedia https://en.m.wikipedia.org/wiki/Eternal_return

 

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, but 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.

 

Obviously there is a confusion here between two ways of expressing the longitudinal position of the centers

Sorry

L_CG > L_CB > L_CF

For example

L_CG +1% or +2% LWL aft of L_CB
and
L_CB +1% or +2% LWL aft of L_CF

 

From the "Satanita" case to yesterday afternoon: 150 years orbiting around two fuxxx axes

MM = Munk Moment
K: Keel
R: Rudder

Three estimates of Munk Moment due to Heel and Leeway/Yaw along three different paths

h: Hull Draft
Bwl: Beam at water line
A: bow Angle (half bow angle)
q: Dynamic pressure = 1025 kg x 1/2 Velocity^2 (m/s)

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

The point is that if we add -2 degrees of Pitch bow down, an explosive cocktail is formed: Mr. Max Michael Munk goes crazy, completely crazy, and the sailboat is uncontrollable.

It must be taken into account that when sailing downwind, these typical imbalances are two:

1) the effect of Heel/Roll on Pitch due to the mismatch between CoB and CoF

2) the propensity to Pitch due to a CoG forward of the Pitch axis of rotation which passes through CoF

It must be taken into account that waves are a gravitational and rotational phenomenon that imparts a rotational motion to the sailboat.

Eternal return - Wikipedia https://en.m.wikipedia.org/wiki/Eternal_return

From "Satanita" (XIX century) to 16 hours in summer conditions (XXI century) chained to the wheel of a brand new 45 ft yacht awarded as "best cruiser", with not one but two very expensive autopilots because the prudent owner (a naval architect by the way) installed a second autopilot