Whenever possible we should remove all distinction between science education and �real� science.

Part 1: The Stiffness of a Toy Boat

click images

Above Left: City Lights - reefed under light winds because these are novice sailors and because the nylon sail had stretched. Right: Two successful models, waterproof and constructed from discarded manila folders.

This is perhaps my best example of how boatbuilding can combine the usefulness of science education with the excitement of original research. First, I tasked a number of students with finding a method for making waterproof toy boats �on the cheap�. Most were college students, but a high school sophomore, his mother, and younger sister also attended the evening boatbuilding effort that met one evening per week.

click image

"every wrong attempt discarded is often a step forward" ... Thomas Edison

The first attempt used those ubiquitous overhead transparencies that come with textbooks. That failure is shown just in front of the coffee cup. One success, sitting one the soda can, was a manila folder coated with paraffin wax. This idea was introduced by James, an elementary education major with a strong interest in science. A student with initials TRR proposed using foam sheets. But that was too expensive for my tastes. A number of failures involved coating cardboard or manila folder paper with various glues. We wanted very much to make a boat using school glue, but she always became waterlogged and sank in a few hours.

For me the most useful way to construct a toy boat appropriate for research is to cut panels out of manila folder paper and coat her with waterproof polyurethane glue. Though not appropriate for middle school children, polyurethane was the primary glue used to make City Lights, the (real) boat shown at the top of this page.

If you inspect the boat in the lower right corner of the first image, you will see the manila/polyurethane boat, along with fishing weights and a straw. The fishing weights along one side were used to vary the applied torque on the boat, causing her to tilt to one side. This was suggested by the mother of the two pre-college children as she was watching us struggle with a different scheme that used pennies we found in the lab. The straw was her son�s idea as a way to measure the angle of tilt. (I think we ended up using uncooked spaghetti.)

There was a reason I wanted all this done. After reading various confusing and sometimes even conflicting explanations for how water ballast stabilizes a sailboat, I decided to try my hand at calculation. It is somewhat counterintuitive that water, which is neutrally buoyant, could stabilize a sailboat. Though beyond the scope of all my collaborators, the calculation shown below should be understandable by any physics major. It predicts a linear relationship between applied torque and angle of tilt, up to the point where the bottom corner leaves the water. Hence the line in the graph terminates at this critical angle.

�

The experimental data were taken by an adult student, Debra, who had more manual dexterity than possessed by the pre-college students. An excellent college algebra student, she lacked the background to fully understand the theory. But we did have a lengthy discussion about whether it was significant that her data did not seem to cross the origin. I think I convinced Debra not to worry about it, and that the graph is an excellent match to the data. Was I right? We need more investigation, perhaps with computer models, to be sure.

Derivation of the stiffness for a rectangular block with beam, B, and length, L:

Begin with the left half (where the boat rises).� By Archidemes principle there is less buoyant force by an amount equal to the volume of the triangle times the weight of the water it would take to fill that volume.� Taking B/2 to be the base of this triangle and, b to be the height, the force equals:

Torque is the product of force and lever arm, which is the distance from the centerline of the boat to the center of the triangle.� But the center of a triangle is 2/3 of the way the apex of the triangle to the midpoint of the other side.� Hence the lever arm is B/3.� There is an equal torque on the other side (where the boat sinks) that also contributes.� Hence we multiply this force by 2B/3 to get a net torque of:

Note the strong dependence on beam.� A boat with 10% more beam has over 30% more stiffness.� Using calculus we can get the same result by integrating the torque associated with the change in pressure, P, at the bottom:

(Here we used the well-known formula relating pressure to depth.)� Use this result to create an integral over the beam as a function of length and use Simpson�s rule:

where the beam is evaluated at the bow, the stern, and exactly at the middle.� If the boat comes to a point at the front, B₀=0.