Marine Kit - 3 Ship Stability Alok K. Verma 06/09 Lean Institute ODU 1 Ship Stability Activity General Guide Lines: This activity will demonstrate the effect of center of gravity and center of buoyancy on ships stability. This activity requires 2 class periods. At the end of the activity please erase all marks on the foam model. First we look at the terminology related to ships which will be helpful in the activity. Alok K. Verma 06/09 Lean Institute ODU

2 Terminology Center of Buoyancy (CB): It is the center of the volume of water displaced by a floating body. Center of Gravity (CG): It is the point on the body where all the weight of the body can be considered to be concentrated. Both points are shown in the following slide as points CB and CG respectively. Alok K. Verma 06/09 Lean Institute ODU 3 Center of Buoyancy and Gravity

CG Displaced Water CB Alok K. Verma 06/09 Lean Institute ODU 4 Terminology Displacement of ship = Weight of the displaced water. Draft: Vertical distance measured from waterline to keel (deepest point of ship). Reserve Buoyancy: Volume of watertight portion above waterline. Freeboard: Vertical distance from waterline to main deck.

These are illustrated in the next slide Alok K. Verma 06/09 Lean Institute ODU 5 Terminology Alok K. Verma 06/09 Lean Institute ODU 6 Archimedes Principle A ship sinks until the weight of the water displaced by the underwater volume is equal to the weight of the ship Force of Gravity: G = mship * g = Wship Force of Buoyancy: B = water * Vdisplaced g = aceeleration due to gravity 9.81 m/sec2

= specific weight of water 9.81 KgN/m3 62.4 lbs/ft3 Alok K. Verma 06/09 Lean Institute ODU 7 Day 1: Part A, Locating Center of Buoyancy (CB) Use the foam ship model with X-Y grid printed on the top surface. Fill the tank up to the mark and place the model in the tank.

Place the weights (3 washers) at different locations on the grid, locate the position where model remains level with respect to the water line, indicating the position of center of buoyancy in X- Y plane. Mark the location by drawing circle inside the washer with a marker (Draw lightly so you do not create an impression on the foam model). Alok K. Verma 06/09 Lean Institute ODU 8 Day 1: Part - A, Locating Center of Buoyancy ( CB) Model not parallel to water level 1. Fill the tank with water until the

marked line. Place the model in the tank. Check the level of the model from all sides. 2. Place the weight (three washers) on foam model at any point and check whether model is level with water line. 9 Alok K. Verma 06/09 Lean Institute ODU Day 1: Part - A, Center of Buoyancy (CB) (Contd.) Model parallel to water level 3. Move the weights until the 4. Mark the circle inside washer

foam model is level with with a marker. Remove the respect to the water line. washers and take the foam model out of tank. 10 Alok K. Verma 06/09 Lean Institute ODU Day 1: Part- A, Locating Center of Buoyancy (CB) (Contd.) Take the foam model out of water and mark the center of the circle as the center of buoyancy (CB).

(Use the marker provided in the kit) Record the X & Y coordinates of CB. Note the coordinates on the worksheet to one decimal place. (Use the ruler in the kit to measure the location of CB) Each grid is a 1cm x 1cm square. Alok K. Verma 06/09 Lean Institute ODU 11 Day 1: Part - A, Center of Buoyancy (CB) (Contd.) 5. Mark the center of circle as CB. 6. Note down the X and Y coordinates of the CB on

X-Y grid of the model. 12 Alok K. Verma 06/09 Lean Institute ODU Day 1: Part-B, Finding Weight of the Displaced Water In this activity we place weights (washers) at the location of CB on the model until the water line is at the top surface of the model. (Water should not cover the top surface.) At this point the weight of the washers is equal to the weight of the displaced water. (Weight of the foam model is very small) Count the washers needed and multiply by the weight of each washer to obtain total weight. This is the weight of the water displaced by the model. Next, we calculate the weight of the displaced water mathematically. Alok K. Verma 06/09 Lean Institute ODU

13 Day 1: Part B, Finding the Weight of Displaced Water Water Level 7. Place the foam model in 8. Place weights at the CB until the the water tank. Check the model is submerged such that only level of model from all top surface remains above water. sides. (Make sure there is no water on top surface). Count the washers. 14

Alok K. Verma 06/09 Lean Institute ODU Volume of Water Displaced Draft = Thickness V Water Level V=Volume of Displaced Water Rear View of the Foam Model

Alok K. Verma 06/09 Lean Institute ODU 15 Work Sheet 1. h1 = cm, h2 = 2. A1 = 0.5 * h1 * b1 = cm, b1 = cm

sq.cm 3. A2 = h2 * b1 = sq. cm 4. Area = A =A1 + A2 = A1 h1 sq. cm 5. Thickness = cm

6. Thus, Volume(V) of water displaced by the model : V = A * Thickness = cu. cm 7. Convert units from cu. cm. to cu. m. A2 b1 Alok K. Verma 06/09 Lean Institute ODU h2 16 Work Sheet ( Contd.) 8.

Coordinates of Center of Buoyancy: X B = cm, YB = 9. Number of washers required to find weight of displaced water = N = cm (Weight of each washer = 0.030 kg or 0.041 kg) 10. Weight of washers = N * = kg

(Compare the answers for weight of washers and the weight of displaced water. Are they equal ? ) Note: You can either have washers of Type-1 / Type-2 in your Kit. Type-1 O.D Type-2 I.D Outer Diameter (O.D) = 50 mm Outer Diameter (O.D) = 44 mm Inner Diameter (I.D) = 21 mm Inner Diameter (I.D) = 18 mm

Weight = 0.041 kg Weight = 0.030 kg Alok K. Verma 06/09 Lean Institute ODU 17 Day 2: Effect of Salinity of Water Previous activity is repeated for the saline water. A salt packet containing two cups of salt is provided in the kit along with a cup which can be used for stirring the water. Make sure the salt has dissolved evenly. Place the model in the salt water. Place the same amount of weight used in the previous section on the model (at CB).

Note the change in the draft. Alok K. Verma 06/09 Lean Institute ODU 18 Day 2: Effect of Salinity of Water Water Level Draft Draft in Fresh Water Alok K. Verma 06/09 Lean Institute ODU Draft in Saline Water 19

Day 2 : Effect of Salinity Water Level Level difference in red lines indicate the draft change Water Line 1. Fill the water till marked line. Mix two cups of salt in the tank. 20 2. Place the same number of washers at the CB, used for finding weight of displaced water. Observe the change in

draft. Alok K. Verma 06/09 Lean Institute ODU Draft Comparison Effect of Salinity Fresh Water Water Level Saline Water In salt water, the buoyancy is higher than the fresh water Alok K. Verma 06/09 Lean Institute ODU 21