14. Formula's and Equations

Question 1

Area of a box shaped vessel =

Answer 1

A = L x B = m2

Question 2

Water Plane Area (WPA)/ (Ships Area) =

Answer 2

WPA = L x B x Cw(Water Coefficient) = Answer in m2

(Cw)This is the actual area of the waterplane divided by the square off outside dimensions of the waterplane given as a ration.

Question 3

Total Volume (V) (For a box shaped vessel) =

Answer 3

V = L x B x D(Depth) = m3

Question 4

Under Water Volume (V) (For Box Shaped Vessel) =

Answer 4

V = L x B x d(draft) = Ans in m3

Question 5

Under water volume (V) (typical Vessel) =

Answer 5

V = L x B x d x Cb = m3

Cb (Block coefficient) is a ratio of the actual volume of the hull normally below a defined draft divdied by a blocked off volume with the same dimensions.

Question 6

Mass/Displacement or Weight =

Answer 6

Weight = Volume(V) x Density(D)

Displacement = L x B x d x RD(Relative Density) = tonnes

Question 7

Reserve Buoyancy (RB) =

Answer 7

RB = L x B x Freeboard = m3

Question 8

Freeboard (FB) =

Answer 8

Depth - Draft = m

Question 9

Tonnes Per Centimeter(TPC)/ Change in draft =

Answer 9

TPC = WPA x RD/100

Change in Draft = New Draft/Old Draft = OLD RD/New RD

Change in Draft = Weight Loaded or Discharged /TPC

Question 10

Instances when metres are not used in stability calculatons:

Answer 10

There are five instances where units other than the metre are used:

 TPC (Tonnes per Centimetre) uses centimetre (cm)

 MCTC (Moments to Change Trim by One Centimetre) uses (cm)

 Fresh Water Allowance (FWA) uses millimetres (mm)

 Summer Freeboard (distance from Deck Line (marking freeboard deck) to Load Line) is measured in millimetres (mm)

 (mm) is the unit used on the Load Line Certificate.

Question 11

Define Density and what is the Density of Salt Water:

Answer 11

Density is the relationship between the weight of a material and the amount of space it takes up.

Density of Fresh Water (FW) = 1000 kg/m³ = 1 t/m³

i.e. 1 tonne of FW = 1 m³ volume

As a comparison

 Fuel Oil (FO) is less dense at 850 kg/m³

 Salt Water (SW) is denser at 1025 kg/m³

 (To use in class later Honey is even denser at 1420 kg/m³)

FYI:

 Intermediate Fuel Oil (IFO) – variable of 900 kg/m³

 Diesel Oil (DO) – 880 kg/m³

Effect of different Densities:

• A less dense material will float on top of a denser one

e.g. oil on water

 A ship will sink to a greater draft in less dense waters

Question 12

Define Relative density:

Answer 12

Relative Density is the density of a substance compared to the density of FW.

Note in this expression the density of the substance and FW must have the SAME units. Relative density thus has no units.

Relative Density is a ratio and therefore has no units.

FO Density 850 kg/m³ = RD 0.850

FW Density 1000 kg/m³ = RD 1.000

SW Density 1025 kg/m³ = RD 1.025

Relative Density is also known as Specific Gravity (SG).

Question 13

What is a Hydrometer and what is it used for?

Answer 13

It is a tool used to measure relative density(RD) of water.