Righting Moment Question -

I'm having some trouble visualizing this, so I am going to ask here!

Suppose I have a hull design which, at such and such an angle of heel, has some specific righting moment, and some certain GZ. The quantities are not important.

Suppose now I add 1 pound of weight to the boat, at the center of gravity. Assume that GZ doesn't really change appreciably. CG and GZ are the same, the only difference is that there's another pound of weight on the hull.

I should get more righting moment, correct? The question is this:

do I get 1 pound x GZ -- the additional weight at the end of the righting arm

OR

do I get 2 pounds x GZ -- the additional 1 pound pushing down at CG, and the additional 1 pound of buoyancy pushing up, GZ away from CG?

I guess another way to ask is: does adding a pound of mass to the boat add just the pound, or do I get a couple that's twice that big?

 

amolitor righting moment is weight (disp) X distance( GZ) as you wrote, its easy just do the math.

 

You get slightly less than a pound. Maybe very, very, slightly less.

The reason for this is because the boat is now riding slightly lower in the water, increasing the depth of its underwater sections. What this means in most monohulls is that the GZ actually does change because more underwater area is being added to the high side as well as to the low side, causing the Center of Buoyancy to shift not quite as far to the low side as before.

There are exceptions.

A boat with flaring sides is one. It is an exception because, as the boat gets loaded down, the Beam Waterline increases keeping the proportion of Beam to Depth pretty much the same.

A banks dory is an extreme example of this.

When it is launched from the mother ship, it has two men and maybe a couple hundred pounds of fishing gear. When it returns, it may have as much as a thousand pounds of fish on board as well as the two men and the fishing gear.

Another possible exception would be a boat where the CG is below the Center of Buoyancy, such as an old Victorian 'plank on edge' design, where the Beam is considerably less than the hull Depth.

I only bring this up to possibly help prevent mistaken assumptions that could lead at best to disappointment and at worst to tragedy.

In one of my own design studies, I discovered that the righting moment of my proposed design increased very little, if at all, once all the cruising gear and stores were loaded aboard. The displacement went up but the Righting Arm (GZ) actually shrank.