During the Battle of Leyte Gulf during World War II, the U.S. invaded the Philippines, forcing a Japanese response. Knowing that the U.S. had superior naval power in the theater, the Japanese employed a series of decoys hoping to draw the main U.S. force out of position. Near the end of the third day of the battle this strategy worked, and the U.S. Third Fleet was drawn nearly 100 miles out of position.
The Japanese fleet then launched an attack directly on the American invasion force, which was protected by the U.S. Seventh Fleet. The Seventh Fleet was equipped to support a marine landing, not to engage in a heavy sea battle. The commander of the Seventh Fleet realized that his only chance to save the invasion force was to delay the Japanese several hours until the Third Fleet could return. Lacking air support and heavy guns, he decided that his only hope was to sacrifice his destroyers.
An order was given: ``Attack overwhelming forces with little probability of survival.''
The guns of the U.S. destroyers were not powerful enough to be of any use against the armor of the Japanese battleships. Further, the destroyers could withstand only one direct hit from the battleships' main guns, which fired salvos of 3000-pound shells. The only effective weapon that the destroyers had were torpedos, but they could only be used at an extremely close range.
By zigzagging erratically, the destroyers were able to close to within torpedo range and fire all of their torpedos. Although three out of the four destroyers were sunk while retreating, the damage to the Japanese fleet was so great that it was forced to withdraw.
The fact that speed and maneuverability could be so effectively utilized was somewhat contrary to the conventional wisdom of the day. It caused naval architects to focus on these features for decades to come.
In this lesson we will study the problem of determining the power required to give modern destroyers their speed and maneuverability. To do this, we will have to come up with a mathematical model for a destroyer as well as a mathematical description of the kind of course that we'd like our destroyer to follow. Along the way, we'll learn about some of the support that Maple provides for doing calculus, learn what it means to abstract an expression into a function, and see an example of a rather complicated function composed out of simple pieces.