Lab 2

Buoyancy

Prelab

Read the lab procedure carefully.
Print this datasheet and bring it to the lab.
Bring a computer or calculator as there will be calculations done during the lab.
This spreadsheet will help calculate your floatation parameters. Fill in the red sections. Be sure to include the worksheet with your report.
- You cannot edit the master worksheet, but you may download a copy and edit it locally. Do not request access to edit.
- You are responsible for showing, and explaining the actual equations used in your report. The sheet is only a convenience.

Purpose

To calculate and test the buoyancy and stability of the S.S. Ivan Curry. Bonus points will be awarded according to the value of your design to the company (height of the observation deck).

Theory

When objects float, they displace some of the fluid in which they are floating. The weight of the fluid displaced equals the buoyant force which in turn equals the weight of the object such that:

Fb = w & γf Vd = γo Vo

where:

Fb is the buoyant force (N)

w is the object's weight (N)

γf is the specific weight of the fluid (N/m3)

Vd is the volume of fluid displaced by the object (m3)

γo is the specific weight of the object (N/m3)

Vo is the volume of the object (m3)

A floating object is stable when its metacenter mc is located above its center of gravity cg. The location of the metacenter is found by first locating the center of buoyancy cb, which acts through the centroid of the displaced volume. The distance from the center of buoyancy to the metacenter MB is:

MB = I/Vd

where:

MB is the distance from the metacenter to the center of buoyancy (m)

I is the least moment of inertia of the horizontal section of the floating object at the fluid surface (m4)

Vd is the volume of fluid displaced (m3)

The center of gravity of the floating object acts through the centroid, or if the floating object is composed of multiple shapes, the center of gravity is a composite of the individual centers of gravity relative to x, y, and z coordinates such that:

xc = Σxw / Σw yc = Σyw / Σw zc = Σzw / Σw

where:

xc, yc, zc is the location of the center of gravity of the entire body relative to the bottom of the vessel (m)

x, y, z is the location of the center of gravity of each individual body relative to the bottom of the vessel (m)

w is the weight of the individual body (N)

If the bottom of the floating object serves as the reference, the relative locations in terms of the vertical axis y is:

Note: Image not to scale and may not be representative of your design.

In general, if yCB>yCG, the body is stable, If yCB<yCG, the body is unstable, but the degree of tolerance a vessel has is determined by the distances and relative forces of each.

It is helpful to imagine a seesaw, where the buoyant force acts on one side, and the gravitational force on the other. Any pairing of these is theoretically stable so long as the fulcrum is in the right position. The larger the relative force of one versus the other, the closer is must be to the fulcrum to balance. In the case of a floating body, the fulcrum is the Metacentre. The metacentre is the point about which the ship tends to spin.

The resulting system, from an engineering view is a pair of moments. One contributed by the mass acting at the distance from the metacentre to the centre of gravity, and the other by the buoyant force, acting at from the metacentre to the centre of buoyancy. So long as these are balanced ( the sum of the moments is zero) the ship is "static" and stable.

Since the masses of the construction materials are fixed, and therefore the resulting buoyant force and force of gravity results from them is as well. We can only alter the placement of these materials in the hopes of designing a better ship.

By raising or lowering the observation deck height, we raise or lower the metacentre and thus alter the moments contributed by each force.

Procedure

Part 1: Buoyancy

Record the data as required below.
Measure the depth of submergence of the styrofoam hull alone.
Measure the depth of submergence of the wooden block alone.

Part 2- Stability

You have been charged with the responsibility of building the S.S. Ivan Curry, a tour boat that will travel the waters of the Bay of Fundy.

The vessel is to be constructed of:

1 styrofoam hull,
1 wooden 2x4 block
2 threaded rods and an assortment of washers and nuts.

Tourists will pay top dollar for the best view, however, your competitors are also in the process of designing boats with great views. Your objective is to build your ship in a manner that maximizes the height of the observation deck above a calm water surface without endangering the lives of the passengers.

Calculate the maximum possible height of the observation deck. you should calculate (using the excel sheet, fill in red sections):
- The depth the vessel will submerge
- Centre of Buoyance CB
- Water Displaced.
- Inertial Moment.
- MB
- ymc
Using the center of mass equation (in the y direction in the above equation) find the height of the top of the wooden block.
Build your vessel according to these specifications.
- The construction is as follows starting at the very bottom of the rods add:
  - 1 nut, medium washer, and large washer to each.
  - Insert the rods through the styrofoam block so that it sits on the nuts/washer assembly. then repeat the washers /nut in reverse order.
  - You should use 2 nuts, 2 medium washers, and two large washers on each rod in the process and have the styrofoam secured between them.
  - Repeat a similar setup near the top of the rods using small and medium washers instead, with the wooden block this time.
  - Adjust the height of the nuts and wooden block so that the top of the wooden block matches the height you suggest.
- DO NOT ATTEMPT TO FLOAT YOUR VESSEL UNTIL YOUR WORK HAS BEEN REPORTED AND SIGNED.
- The team whose deck is closest to the maximum height possible for their vessel properties will score a bonus.
Test your calculations by floating your vessel.
- If adjustments are required, make them at this time.
- Continue making adjustments until the passengers' lives are not endangered and you have maximized the view.
- Measure the new height, be sure to mention the original guess and final safe height on your data sheet.
Have your stable ship verified and disassemble.
Lastly, measure the depth of submergence of the entire constructed ship.

Results

Part 1- Buoyancy
- The calculated and observed depths of submergence of both objects, and the vessel assembled.
Part 2- Stability
- The calculated center of gravity, center of buoyancy, and metacenter from baseline.
  - Include the supporting calculations from the excel sheet with proper variables rather than cell equations.
  - Produce a drawing like that in theory section with labels and values similar to the one above. (may be done freehand and scanned)
The calculated height of the deck for stability and the experimental height for stability.

Questions

Comment on any differences between the calculated and observed stability height. State any reasons why you feel a difference may exist.
List 2 ways to increase the stability of your ship without lowering the observation deck.

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