Ship Longtitudinal Centre of Gravity Position

Question

This question is designed to get help from someone (with some important important questions), so that I can get an understanding on why I cannot quite get the correct answer for this question Longtitudinal Centre of Gravity for Ship Cargo.

Also establishing if I have actually answered Longtitudinal Centre of Gravity for Ship Cargo question correctly and maybe the answer from the textbook is not quite correct.

---

If the Longtitudinal Centre of Gravity of a ship (without added load) is behind (aft) of it's Longtitudinal Centre of Flotation, does this affect a ships change in aft draft ?

For change in draft aft calculations, does added weight always have to be added at Longtitudinal Centre of Flotation, parallel sinkage calculated there and then change in trim calculation for movement of weight to it's actual position done from there ?

or

Can an Added weight be positioned at the ships original Longtitudinal Centre of Gravity, Parallel sinkage calculated at LCG and then the change in trim calculation for movement of weight to it's actual position done from there ?

I am thinking of a situation when it is calculated that a cargo load is to be positioned aft of the ship Longtitudinal Centre of Gravity, when the ship Longtitudinal Centre of Gravity is behind Longtitudinal Centre of Flotation.

Answer 1

Your first suggestion is the correct one, so let's have a look at why.

When dealing with longitudinal stability of ships, it is crucial to be aware of the difference between the center of flotation $F$, the center of gravity $G$ and the center of buoyancy $B$.

1. The center of flotation $F$
   • is the center of gravity of the waterplane area
   • is the point about which rotation (trim) takes place, and hence where the trimming moment is taken about
   • is where the force from extra buoyancy will attack if weight is added to the ship (the extra buoyancy is due to the change in the vessels draft when adding weight)
   • is dependent on the geometry/curvature of the vessel, meaning that different drafts will will have different locations of the center of floatation
   • (is dependent on the trim angle, but since the trim usually is small, we tend to neglify this dependency)
2. The center of gravity $G$
   • is the longitudinal center of gravity of the vessel
   • is where the gravitational force of the vessel will attack
3. The center of buoyancy $B$
   • is where the total buoyancy force of the vessel will attack

Hence, if adding a weight to the ship, imagine it first being placed at the center of flotation, calculate the parallel sinkage, then move it to the correct location and calculate the trim angle about the new center of flotation (when the added mass is small, giving a small parallel sinkage, it is often sufficient to assume that the center of flotation does not change).

Consequently, it does not matter where the center of gravity is located with respect to the center of flotation, if following the procedure above.

In the below image, $M_L$ denotes the longitudinal metacenter, which will not be further explained in this answer.

Lastly, I will suggest those curious to dive into the appropriate literature for more details on the topic of longitudinal stability of ships. My suggestion includes, but is not limited to the book; Ship Stability for Masters and Mates by C.B. Barrass and D.R. Derrett.