Department of Mechanical and Design Engineering
HYDROSTATIC STABILITY OF FLOATING BODIES
Lab #1 - Part A & Part B
Righting Arm - Inclining Experiment
Instructions
1. This part of the lab covers the Righting Arm theory that will be examined experimentally in this lab.
2. The results of Part A of the Lab to be handed over to your instructor at the beginning of the Part B lab.
3. If you can, answer the questions without referring to your notes. Only refer to them when you are confused or fail to understand a concept. This will greatly improve your understanding of the concepts the lab is designed to reinforce.
4. Use a copy of the Excel Sheet (Stability. Xls) provided at the L Drive to analyse the data collected from the Lab experiment.
5. All work must be shown on your lab for proper credit. This means that you must show generalized equations, substitution of numbers, units and final answers. Engineering is communication. Work that is neat and shows logical progression is easier to grade.
Student Information
Name: ..
Student No:
Course:
Date: .
Aim:
Reinforce the students understanding of the righting Arm theory.
Demonstrate the effect that an increase in KG has on stability.
Show how the change in stability caused by an increase in height if centre of Gravity (KG) can be predicted.
Part A
Apparatus:
Rectangular Pontoon
This is made of acrylic material and consists of a Mast with Two horizontal slots. These slots also have stepped recesses provided for securing the adjustable weight.
Adjustable Weight
This is made of Stainless steel. It can be clamped to different positions on the mast using the slot provided on the weight.
Protractor Device
This is fixed at the top of the mast. The needle freely moves over the angle graduations marked on the mast.
Water Tank
The tank is to be filled with water. This tank would be used for floating and heeling the pontoon.
Theory
The pontoon is going to be heeled by shifting the initial position of the weight horizontally to another position. This shifting of weight produces a couple.
You will recall that a couple is a particular type of moment defined as:
.a pair of equal and opposite forces separated by a distance.
a. What is the effect of a couple on a body? .
b. What are the units of a couple?.................................................................
When the Pontoon is heeled to a particular angle you will find that it remains at that heel without further rotation or translation. Is the model in static equilibrium?
Why?
...
On the Figure 1 show the direction of the forces that create the couple.
Show the Righting arm between these two forces. Call this distance GZ.
Figure 1 Simplified View of Heeling Model
On the axis at Figure 3 plot the curve of statical stability (heeling to one side only) for a ship with the following stability characteristics. Ensure to label all axes.
Range of stability = 0 - 880
Angle of maximum righting arm = 500
Maximum Righting Arm = 3.5 ft
Righting arm at 300 of heel = 2.0 ft
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Figure 2 Axis for Plotting Curve of Statical Stability
When creating this curve for a full scale ship, it is not possible to rig apparatus such as that described earlier. How is the curve of statical stability produced for a full scale ship?
...
...
When creating this curve for a full scale ship, the centre of gravity of the ship will be raised thereby increasing KG. The effect this can upon the curve if statical stability will be measured. It should be possible to predict this effect by an analysis of the heeling ship shown diagrammatically at Figure 3.
Figure 3 The Heeling ship with a vertical shift in the center of Gravity
Use Figure 3 to derive an equation for the new righting arm (G1Z1) after a vertical shift in the center of gravity from (GZ). Your equation should include the old righting arm (G0Z0) and the Angle of heel (f).
From your answer above, what effect do you believe an increase in the distance KG will have upon the stability of a ship? .................
...
Construction of the curve for statistical stability for normally loaded condition ( Weight mounted at Base Slot.)
PART - A
Perform the Following Steps.
a. Make sure all the weights and protractor are secure on the model. Make sure the water tank is not overfilled with water, which may cause it to overflow during experiment. Fill the tank to 2/3 of its height.
b. Float the model in its normally loaded condition so that it floats without tilting to either side. At this stage the GZ = 0. Note that the protractor needle is at Zero.
c. Remove the weight from the current position and mount it on the adjacent groove to the right.
d. Record the heeling Angle (f).
e. Now remove the weight from the present groove and mount on the next groove to the right. Note down the Heeling angle as you did before.
f. Repeat the above process by changing position of the weight horizontally to the remaining three slots.
g. Enter the values in the Part A Table of the Excel Sheet.
h. The Excel Program will calculate the Righting Arm (GZ) for each of the Heeling angle entered and produce the Stability Diagram.
i. Study the Chart and complete the following table.
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Observations made from Stability Diagram |
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Range of Stability |
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Maximum Righting Arm |
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Angle of Max RA |
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PART - B
The model can be caused to have a vertical rise in G by moving he adjustable weight to the upper horizontal slot provided. Take the Weight from the bottom slot and clamp to the centre groove of the upper slot.
Now repeat the process you performed earlier to find the curve of statical stability. Use the PART B table to record the heeling angle data.
Study the new curve and complete the following table.
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Observations made from Stability Diagram |
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Range of Stability |
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Maximum Righting Arm |
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Angle of Max RA |
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Compare the curves produced by the above two conditions Normally loaded and Raised G .
In which condition is the model more stable?
Why ? ..
What deduction can you make regarding the effect of an increase in KG on the stability of a ship?
...
...
Take a print out of the Tables at both conditions and Stability diagram from the Excel sheet and attach to this Lab sheet.
Submit the Report at the Department office.
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