Soviet Warships

You are an intelligence officer for the US Navy. Secret agents have managed to gather information on a number of Soviet warships, which you have compiled into a table:

Name             Type                       length (m)      mass (tonnes)
------------------------------------------------------------------------
Kiev             aircraft carrier                            38,000
Dzerzhinsky      guided missile carrier                      15,450
Moskva           helicopter carrier                          14,500
Azov             guided missile carrier                       8,200
Bedovy           guided missile destroyer                     3,000
Sokol            escort ship                                  1,500
Gangutets        escort ship                                    950
Poti class       corvette                                       560
P-4 class        torpedo patrol boat                             22

You have a contact in Moscow (Boris) who can tell you the lengths of these ships, but the communications are difficult; you can ask for no more than four lengths before the line is discovered and destroyed.

The Secretary of the Navy comes into your office and says, "We've just heard that the Soviets have developed a new type of warship, codenamed Dolphin. We need to know how long this new ship is, so that we can recognize it in satellite photos of the drydock. Lieutenant Jones is working on some intercepted messages. He thinks he can figure out the mass of the Dolphin ... but what we need is the length, not mass."

Your job is to figure out the length of the Dolphin. Your tools are paper, pencil, and graph paper.

The rules:

break into teams of two
one member of each team will use linear graph paper; the other member will use log-log paper
each team can ask Boris for the lengths of 4 ships from the list above -- you have to decide which 4
based on that information, each person should make a graph showing length (in meters) on the x-axis and mass (in tonnes) on the y-axis
after having made the graphs, get the mass of the Dolphin from Lieutenant Jones
use your graphs to estimate the length of the Dolphin

Questions:

How should you pick the 4 ships in order to make the best estimate of an unknown ship?
What sort of pattern do the points make on the linear paper?
What sort of pattern do the points make on log-log paper?
Which paper makes estimating the mass of the Dolphin easier? Why?
What is the slope of the line connecting the points on the log-log paper?
Write an equation showing log(mass) on the left side and log(length) on the right side, with the appropriate coefficient on the right side.
Write an equation showing mass on the left side and length on the right side, with the appropriate exponent on the right side.
What is the value of the exponent? What should it be? Why?

The team which comes closest to the actual length of the Dolphin will win a prize.

Bonus! The ship codenamed Dolphin in this exercise is a real Soviet warship from the sixties and seventies. Somewhere on campus is a reference which describes this class of ship, and gives the names of the real ships in this class. Anyone who provides me with one of these real names before next week's class will win a prize.

Last modified 11/2/2000 by MWR