Question:

I have some questions concerning the "wave" function in GHS. How does the wave action apply force to the buoyant shape?

What phase angle is the worse for degrading the stability?

What does the output indicate when the righting moment is still positive but the Origin depth is negative. One of the phase angles that I tried in my quest to understand its usage created a righting arm that oscillates between positive and negative values. Why?

Answer:

The wave function in GHS transforms the waterplane into a curved surface. Buoyancy force and its center of action are calculated in the same way; i.e. the buoyancy force is equal to the weight of the volume of displaced water and the CB is the centroid of that volume.

We are still dealing with an hydrostatic analysis. Inertial and frictional forces are not addressed. Therefore you cannot use the wave to simulate the dynamics of the vessel in a seaway. There are "seakeeping" software programs which use time- or frequency-domain analysis to predict ship motions, but these are rarely used for ship stability work.

Standard practice, or what you might call "the state of the art", in ship stability is to use a flat waterplane and static calculations but require such an excess of energy under the righting moment curve that the ship will not capsize in expected real-life seaways. The level of energy required for a particular ship is usually set by statutory regulations. These are the result of experience and the analysis of casualties. In other words, we bridge the gap between the flat-water analysis and the real world by empirical stability criteria referenced to flat water but predicting survivability in stormy seas.

The primary use of the static wave as it appears in GHS is to predict increases in hull-girder bending moments when the wave length is about the same as the vessel length and the angle of encounter is zero. It is also interesting to look at the effects on stability in the same kind of waves, but this is not required by any of the standard stability criteria that I am aware of.

When the angle of encounter is 90 degrees and the wavelength is long compared to the width of the ship, you are essentially advancing the heel angle with regard to the water beyond the heel angle with regard to gravity. Some GHS users have found this useful for generating data to be used in dynamic analysis with other software. Unless you have some basis for stability criteria on this kind of wave, I don't think it would be useful as a measure of static stability.

The phase angle determines the location of the crest of the wave with respect to the origin of the vessel. If you want to see where the waterline is being drawn on any section of any component, use the COMPONENT /SECTION command. It will show the depth and heel perturbations relative to the nominal waterplane.

Stability criteria for small vessels such as the one you are dealing with are not as well developed as they are for larger ships. Many small craft will not pass the standard stability criteria since they depend on limited exposure to bad weather and good seamanship for their survival. In the USA, most of the stability regulations are found in CFR 46 part 170. You might find something there you could apply, but you will find much of it addressing characteristics of vessels that are quite different from what you are dealing with.

Ultimately, unless you embark on a model-testing project or a detailed hydrodynamic simulation including inertial forces, you will be faced with making decisions based on your own criteria such as a reasonable range of stability under a given wind heeling moment. Another thing you might look at is whether there is enough energy under the righting moment curve to absorb the energy of a roll to windward. For example, suppose a wave rolls the vessel 20 degrees to windward. You would want to see positive area emerging before some reasonable heel angle as it rolls to the other side:

HEEL = -20
HMMT WIND
RA /AREA