This US Navy training video at GENE SLOVERS US NAVY PAGES website shows how the 1950s mechanical fire control computers worked. It is explained simply enough for a layman to understand. I found it fascinating to watch. It is crazy to think that the ballistic software on my $199 iPod Touch can do nearly everything that this huge mechanical device did.
UPDATE: Part 2 can be watched online here. Thanks to Steve for the link.Related