Future FleetScience Topics: Buoyancy, Density and Volume

Future

Fleet

SESSION ONE

History of Failed Ships

History of Failed Ships• What is the economic cost of a failed ship

design?Student Responses

History of Failed Ships• What is the human cost of a failed ship

design?Student Responses

History of Failed Ships• How can the tragic losses in the article be

prevented?Student Responses

History of Failed Ships• Is it possible to know how much a ship will

cost before you build it?Student Responses

History of Failed Ships• Can an unsinkable ship be designed?

Student Responses

History of Failed Ships• Is it possible for a tragedy at sea to happen

today, even with current technology? Student Responses

Lets Explore

Exploration Teams• Assigning the teams• Roles

– Task manager– Activity recorder – Life Line – Evaluator

Task manager• Keep group members

focused

Activity recorder• Records what the group

does and what questions the members have

Life Line• Can leave the group to

seek help

Evaluator• Judge the

effectiveness of the group

• Report back only to the group

The Stations

•How Metal "Boats" Float (5 min)•Liquid Density and Lava Lamp (5 min)•Soda Can Pirouette (5 min)

Students should move to their teams now and begin the exploration

TIME IS UPPlease return to your seats

REPORT• Each group should now report on the

following:– Name one thing you learned that has not been mentioned yet

Student Responses

Definitions and Calculations• Density• Displacement Mass• Buoyancy• Center of Gravity• Center of Buoyancy• Metacenter

Density

D = M / VSolve the equation for mass

M = D x V

Mass can now be calculated

- The degree of compactness of a substance- Mass per unit of Volume

The Density of WaterDensity is influenced by depth, temperature,

and salinity.

Look at the Salinity Map

Salinity Map

Look at the Temperature Map

Temperature Map

Displacement MassThe mass of a fluid (as water) displaced by a floating body (as a ship) of equal mass

460 mega kilograms of water To stay afloatA 460 mega kilogram ship Needs to Displace

The Calculation of Displacement Mass1) Find the density of water of operational area

Density is influenced by depth, temperature, and salinity

We will use about 34 PSU* Salinity as an

operational areaSalinity Map

We will use about 30 degrees Celsius as

an operational areaTemperature Map

At 20m depth the density will be

1.021 g/cm3

*PSU * Salinity is measured by conductivity (how easily electricity flows through a seawater sample).

The Calculation of Displacement Mass2) Find the volume of water being displaced

Take the cross sectional area height x width 30 m x 5m

5 m

30m

3 m

x 3m and multiply by the 3rd dimension

to find volume

This gives us a Volume of 450 m3

The Calculation of Displacement Mass3) Find the displacement mass M = V x D

Volume of Water (cm3) x Density (g / cm3)

(450 m3 x 1,000,000 cm3 / m3 ) x 1.021 g/cm3

459450000 g

Weight vs. Mass

So the volume can displace a mass of 459450000 gramsor a weight of

459450000 g x (1kg/1000 g) * 9.8 m/s2 = 4,502,610 N

or 459450000 g x (1kg/1000 g) * 2.2lbs/kg=

1,010,790 lbs or 505.4 Tons

- Weight is a force- Force in general is mass times acceleration

Buoyancy

What is Buoyancy?Buoyancy is the upward force that a fluid exertson an object less dense then itself.

As mass is added, the boat displaces more water until the weight of the

displaced water equals the weight of the boat; then the boat sinks.

Archimedes's principle.An object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

Put picture of floating boy here

5 m

30m

3 m

A 500 Ton ship needs to displace a volume of 450m3 to avoid sinking

Summary of Buoyancy and Displacement

Displacement of irregular shapes

Use graph paperto approximate the cross sectional area

Then find the displacement mass

Center of GravityWhat is the Center of Gravity?The center of gravity is the geometric property that represents the average location of the weight of an object.

We can balance the scale by moving thefulcrum to the center

of gravity.

How do we find the Center of Gravity?1) Hang the object from a

point2) Hang a weighted

string from the point and when it comes to a rest draw a line

3) Repeat with another point on the shape

Center of Buoyancy• Is the center of gravity of the displaced water• The center of buoyancy changes as the ship rolls and

pitches• The balance between center of buoyancy and center

of gravity affects stability of the ship

Metacenter

Ship

Water

Center of Gravity

Center of Buoyancy

Ship rolled at a small angle

New center of buoyancy

Line of force for new centerof buoyancy perpendicular to water line

The intersection of the two linesof force form the metacenter

The distance from the metacenter (M) to the center of gravity (G) is called the metacentric height (GM).

G

M

Metacenter• A positive GM is needed to make a stable ship• The higher the GM the more stable the ship• The higher the GM the faster the ship will

right itself. If this number becomes too high the ride will become rough.

Elaborate• Work in your teams to

come up with general guidelines for ship design.

Exit Ticket• Find the displacement of mass of a ship

segment with cross sectional dimensions of 30m by 8 m and a length of 10m.

Student Responses

SESSION TWO

Build a Prototype

The Littoral Class • Future Ships of the Navy

The Littoral Class • Why did the Navy use two different designs?

Student Responses

The Littoral Class • What need is the Navy trying to address?

Student Responses

The Littoral Class • What aspects of the design of the ships

address the needs of the Navy?Student Responses

The Littoral Class • Why do you think using all new 21st century

technology was important to these features?Student Responses

LCS and PiratesClick me to see Somalia

Click meTo see video

The Littoral Class • How could the LCS class ships help support

operations in the region? Student Responses

The design requirements• Length must be 128 cm• Width 32 cm• Displacement depth 4.3 cm• Hull shape up to the

designers but ship must be stable and must displace its weight in water

Design Time

Planning and calculations Build Time

25min 35min

Evaluate• The students will work in their design team on a brief

description of their prototype. • In this description the students should address the aspects of

their prototype that are most closely related to a real ship (displacement and buoyancy).

• Students should then give themselves a confidence rating. This should represent how successful the ship will be in a full scale prototype. Focusing only on aspects related to a real ship, students should answer the question - “Is the design of their prototype worth spending several million dollars to test at full scale?”

• The students should answer the question - “Is the design of their prototype worth spending several million dollars to test at full scale?”

SESSION THREE

Testing our Design

Presentations• Each group will have 3 minutes to present

their design to the class using the evaluation from Session 2

Evaluation of design• Each team will put their prototype in the water tank

and have it tested by the instructor.• All students will record data on a rubric for each

prototype. • There are three categories:

o Percentage error between predicted water line and actual water line (tank can have dye or food coloring in it to help denote the actual water line for measurement)

o Stability test under wave creation. Three levels of intensity for waves should be tested by dropping a weight in the water a short distance from the ship.

o Overall design appeal and creativity – this is subjective

Improving on designTeams are to go back together and reevaluate their calculations to determine the following:•Explanations for percentage error •Stability of their prototype and what improvements could be made•If they were to make another prototype what would they do differently?

The Littoral Class • We looked at stability and buoyancy. What

other variables might have to be addressed in building of a prototype?

Student Responses

The Littoral Class • How will designing versatile and flexible ships

prepare us to handle the future?

Student Responses

The Littoral Class • Given the safety concerns about some

modern cruise ships, how might one prevent future accidents like the Costa Concordia?

Student Responses

Congratulations on finishing your designs of