How can my differential solve differential equations?
How does a camshaft work?
How does a spider add up?
What is inside my ECU computer?
And other questions answered:

http://www.eugeneleeslover.com/VIDEOS/fire_control_computer_1.html

Fascinating find there Windy. Mechanical analog(ue) computers used for fire control in the US Navy in 1953.

That's a whole decade after electronic digital computers were used for code breaking at Bletchley Park, but I guess those computers would not have been rugged enough for use on a war ship, even after ten years of development, and even if we had continued their development (which we didn't).

Mechanical computers were pretty well understood by Babbage, more than one hundred years earlier. Seems it took a very pressing need (warfare) to spur their development.

The equations being solved would not have been too easy on a thermonic valve computer and would have taken some time to perform, the analogue computers provide an instant answer - they are even faster than todays supercomputers!