Aim:
The aim of this experiment is to identify the metacentric height of a ship model.
Theory:
Meta-centric height is an important parameter for analyzing ship stability. This is the distance between the ship’s metacenter and the center of gravity. The metacenter is the intersection of the vertical line passing through the center of buoyancy,
of the ship in the vertical position, and the corresponding line in the inclined position. The metacentric height determines the stability of the ship. If the metacenter height is high, the ship is more stable, and if it is low, the ship is less stable.
Apparatus and materials required:
We require the following apparatus and tools for determining the meta-centric height of a ship model.
- Ship model
- Container filled with water
- Plumb line
- Ruler
- Weighing scale
Procedure:
- First of all, collect all the required materials and apparatus as mentioned above.
- Weigh the ship model and record its weight.
- Now, place the ship model in a container filled with water.
- Make sure that the ship model is floating upright and is not touching the sides or bottom of the container.
- Measure the height of the ship model from the waterline to the top of the model.
- Slightly tilt the container on one side and let the ship model heel to an angle of 5 degrees.
- Allow the ship model to come to rest and measure the angle of heel with the help of a ruler.
- Measure the distance between the waterline and the new center of buoyancy of the ship model.
- Repeat steps 6-8 for angles of heel of 10, 15 and 20 degrees respectively.
- Calculate the metacentric height using the following formula. GM = (I/V)*((T/Tanθ)^2)
Where,
GM = Metacentric height
I = Moment of inertia of the ship’s water level
V = Volume of the vessel
T = Draught of the ship (Ship current)
θ = Angle of heel
Data analysis:
Calculate the water level moment of inertia of the ship model and the volume of the ship model using the following formulas:
I = (1/12)BL^3
V = BLT
Where,
B = Width of the ship model
L = Length of the ship model
T = Draught of the ship model
Substitute the GM values into the formula and calculate the metacentric height of each base angle.
Discussion:
The metacentric height of a ship is an important factor in determining its stability. A high metacentric height indicates that the ship is more stable, while a low metacentric height indicates that the ship is less stable.
The metacentric height is affected by several factors, such as the shape and size of the ship, the location of the center of gravity, and the weight distribution of the ship.
Results:
The meta-centric height of the ship model can be calculated for each angle of the heel. The results can be plotted on a graph showing the relationship between the meta-centric height and the angle of the heel.
Precautions:
- Ensure that the ship model is not touching the sides or bottom line of the container.
- Measure the height of the ship model and the angle of the heel accurately.
- Ensure that the container is leveled properly before each measurement.
- Conduct the experiment in a safe and controlled environment.
Conclusion:
The metacentric height of a ship is an important factor in determining its stability. An experiment to determine the metacentric height of a ship model can be performed using the above procedure.
With the help of the results, the stability of the ship can be analyzed, and the necessary adjustments can be made to improve its stability. In order to obtain reliable results, it is important to ensure that the test is performed accurately and with appropriate precautions.
The meta-centeric height can be calculated for different heel angles to get a better idea of the stability characteristics of the ship. In general, this test is essential for a ship’s stability analysis and design.
