How Much Weight Can Your Boat Float?

Objective

The goal of this project is to determine how much weight can be supported by boat hulls of various volumes.

Introduction

You know from experience that if you drop a steel bolt in a bucket of water that it will sink like a rock to the bottom. On the other hand, you know that ships made of steel can float. How does it work?

What determines whether an object floats or sinks? It's the density (mass per unit volume) of the object compared to the density of the liquid. If the object is more dense than the fluid, it will sink. If the object is less dense than the fluid, it will float. If the object has the same density as the fluid it will neither sink nor float.

With a steel-hulled ship, it is the shape of the ship's hull that matters. The hull encloses a volume of air, so that the total density, defined as:

(mass of steel hull + mass of enclosed air) / volume,

is less than that of water.

Archimedes discovered that an object immersed in water displaces a volume of water equal to the volume of the object (see Junior Engineering, 1997, for the whole story). The displaced water creates an upward force on the object. If the weight of the displaced water is greater than the weight of the object, the object will float.

In this project you will make some boat hulls of various shapes and sizes using simple materials (like aluminum foil and tape). Can you predict how many pennies each of your boats will support without sinking?

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

weight,
volume,
density,
buoyancy,
displacement.

Bibliography

Here are some good background resources on buoyancy:
- Junior Engineering, 1997. "Buoyancy," Utah State University [accessed December 29, 2006] http://www.engineering.usu.edu/jrestate/workshops/buoyancy/buoyancy.php.
- Wikipedia contributors, 2006. "Buoyancy," Wikipedia, The Free Encyclopedia [accessed December 29, 2006] http://en.wikipedia.org/w/index.php?title=Buoyancy&oldid=97455729.
Here's an article to get you thinking about what happens if the fluid in which the object is immersed has a density lower or higher than that of water:
Phillips, T., 2005. "Rainbows on Titan," Science@NASA [accessed December 29, 2006] http://science.nasa.gov/headlines/y2005/25feb_titan2.htm.
The following link shows you how to make a Cartesian Diver, which will make an interesting demonstration of buoyancy you can use along with your display board (requires Adobe Acrobat Reader):
Terrific Science Press, 2005. "Cartesian Divers," Terrific Science Press [accessed December 29, 2006] http://www.terrificscience.org/ncw/2005/pdf/Cartesian%20Divers.pdf.

Materials and Equipment

For building the boats you can use:

cellophane tape (e.g. "Scotch" tape), and
aluminum foil.

For measuring the volume of the boats, you will need either:

a ruler (for measuring the dimensions of the boat in order to calculate its volume), or
dry rice kernels and
a glass measuring cup with metric markings (or a graduated cylinder).

For testing the buoyancy of the boats you will need:

a container (e.g., sink, tub, bucket, dishpan) with water,
pennies.

Experimental Procedure

Use the foil and tape to construct boat hulls with different shapes.
1. You can fold or even cut the aluminum foil if you wish to obtain the desired shape.
2. It is important to insure that there are no leaks!
3. Try building several different boats using the same amount of aluminum foil for each.
4. Also try building several different boats using different amounts of aluminum foil.
Calculate the volume of each boat hull. Below are two alternative methods you could use. (Or, you could use both methods, and compare your results. Which method is more accurate?)
1. Ruler Method
  - Use the ruler to measure the length, width, and height of your boat hull.
  - Volume (in cm³ equals length × width × height (each measured in cm).
  - If parts of the hull have an irregular shape, measure the volume piece-wise. Use triangles to approximate any areas of the hull that are curved or angled. Use rectangular prisms for regular areas of the hull. Calculate the volume of each (imagined) subsection. Add up the volumes of the individual regions to get the total volume for each hull.
2. Dry Rice Method
  - Carefully fill the boat hull with dry rice. The rice should be level with the top of the hull.
  - Being careful not to damage the hull, pour the dry rice into the measuring cup (or graduated cylinder).
  - Gently shake the cup (or cylinder) to level the rice.
  - Read the volume of the dry rice, in mL. This is the volume of your boat hull.
Measure the buoyancy of each boat hull.
1. Carefully float the hull in the container of water.
2. Gently add one penny at a time. Note that some boat shapes will be "tippier" than others. For these you will have to pay careful attention to balancing the load (left to right, front and back—or port to starboard, fore and aft, if you're feeling nautical) as you add pennies.
3. Keep adding pennies until the boat finally sinks. Count how many pennies each boat could support before sinking (i.e., the penny that sank the boat does not count.
Make a graph of buoyancy, measured in number of pennies supported (y-axis) vs. boat hull volume, in cm³ (x-axis). What do your results tell you about the relationship between buoyancy (amount of weight a boat can support) and volume of the boat hull?

Variations

By measuring the average weight of a penny, you can convert your buoyancy measurement from number of pennies to grams. If you don't have a scale at school or home, you can probably find a scale to use at the post office. Find out how much 10 or 20 pennies weigh (together). Calculate the average weight of a penny by dividing the total weight by the number of pennies. Now for each boat, you can multiply the number of pennies it could support by the average weight of a penny to convert your buoyancy measure to grams. Thinking about what you learned about displacement, how do think the buoyancy in grams will compare to the boat hull volume in cm³?
It would be difficult to bring a bathtub to the science fair in order to demonstrate your project, but there is a nice demonstration of buoyancy which you can show in a clear plastic soda bottle: a Cartesian Diver (Terrific Science Press, 2005).
Use other materials for building the boat hulls. For example, waxed half-gallon cartons (for milk or juice) can be cut open and unfolded to produce sheets of waterproof material. To make folds to create the desired hull shape, first score the material with a blunt stylus—the classic Bic pens with the blue plastic caps have a great shape for this. Keep the cap on and use it to score the waxed paperboard before folding.
Here's a "thought experiment" for more advanced students to try. NASA's Cassini spacecraft sent the European Space Agency's Huygens probe to the surface of Saturn's moon, Titan, where it found evidence that the surface contains large bodies of liquid methane (Phillips, 2005). On Earth, methane (CH₄) is typically not liquid at all, and is known most commonly as 'natural gas.' On Titan, where the surface temperature is −179°C, water would be solid and methane is a flowing liquid. What is the density of liquid methane? How does the density of liquid methane compare to the density of water? If your boat could float 100 pennies in water, how many pennies would it support (on Earth) in a container filled with liquid methane? An actual experiment you could do would be to re-do the experiment with a liquid that has a density different than that of water. Cooking oil would be a good choice. Though the difference in density is not nearly as dramatic as for liquid methane, it's a lot easier to obtain and safer to work with! How does the buoyancy of each boat hull in vegetable oil (measured by the number of pennies it can support) compare to its buoyancy in water?

Sources

This project is based on: