Marine Kit - 3 Ship Stability

Ship Stability Activity General Guide Lines: This activity will demonstrate the effect of center of gravity and center of buoyancy on ship’s 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.

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.

Center of Buoyancy and Gravity CG Displaced Water CB

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

Terminology

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

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).

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

Day 1: Part - A, Center of Buoyancy (CB) (Contd.) Model parallel to water level 3. Move the weights until the foam model is level with respect to the water line. 4. Mark the circle inside washer with a marker. Remove the washers and take the foam model out of tank. 10

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.

Day 1: Part - A, Center of Buoyancy (CB) (Contd.) 6. Note down the X and Y coordinates of the CB on X-Y grid of the model. 5. Mark the center of circle as CB. 12

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.

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

V Volume of Water Displaced Water Level Draft = Thickness V=Volume of Displaced Water Rear View of the Foam Model

Work Sheet 1. h1 = cm, h2 = cm, b1 = cm 2. A1 = 0.5 * h1 * b1 = sq.cm 4. Area = A =A1 + A2 = 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. h1 A1 A2 h2 b1

Note: You can either have washers of Type-1 / Type-2 in your Kit. Work Sheet ( Contd.) 8. Coordinates of Center of Buoyancy: XB = cm, YB = cm 9. Number of washers required to find weight of displaced water = N = (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 Type-2 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 O.D I.D

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.

Day 2: Effect of Salinity of Water Water Level Draft Draft in Fresh Water Draft in Saline Water

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

Draft Comparison – Effect of Salinity Fresh Water Water Level Saline Water In salt water, the buoyancy is higher than the fresh water