Trying to calculate Righting Moment

Hi,

I've been reading Principles of Yacht Design and playing with Delftship and was wondering if I'm calculating the RM correctly.

Delftship gives me the Transverse Metacentric Height which should be GM, and displacement (∆), 17.986 long tons (18,274.62 Kg).

From PoYD, RM = 27 * RM(1) * ∆/G + δrm:

GZ = GM * Sin(ϴ)
Eliasson says that for small angles GM is constant and Sin(ϴ) ~ ϴ (in radians)

So GZ = GM * ϴ(in radians) : 1 radian = 57.3degrees or 1 degree = 0.01745 rads

And RM = 27 * GM * 1 * ∆/G + δrm?

Am I tripping or is that right?

 

The righting moment (RM) of any vessel is simply = Displacement (delta) x GZ (lever)

The relationship of the righting lever, GZ, to metacentric height, GM, is as you have shown:
GZ = GM * Sin(ϴ)

So, if you have the GM, you can easily calculate the GZ from the above equation and then the RM.

Thus, im confused where you get the following?

 

RM = 27 * RM(1) * ∆/G + δrm is from page 206 of Principles of Yacht Design by Larsson and Eliasson second edition.

They talk about estimating small angles of GZ on page 44. I'm confused because they walk around the formula on p.44 but don't explicitly give it. And RM is rather important so I really want to get this right.

 

Indeed it is. Thus do not talk about Righting Moment (RM) when you end up talking about Mast design! The two are totally different.

A RM is simply = Displacement x lever = ∆.GZ

That is it!

What you end up referring to, is how to design a Mast/rigging.
To do so, a common approach is to determine - notice this, determine the RM @ 30 degrees. To establish the RM at 30 degrees, you need the GZ curve!

A typical one is shown here:



And you'll note the use of ballast (in your quote), live ballast. In other words, the crew! The crew when they move about change the RM....and what you are then starting to quote, mistakenly, is the RM when designing the Mast accounting for cre movement. Thus the RM you cite:

What is the

Look at the definition in the book:



The RM of ∆.GZ remains the same no matter what boat.

The RM for mast design on the pages you cite, is breakdowing down the masses and the levers further - that is all.

You may find a brief summary of such HERE about RM and movement of crew that affects the RM.