I always got a huge kick out of watching
this video that explains how the massive mechanical calculators they used to solve firing problems worked. It's 40 minutes long, but I've yet to meet an ME who didn't finish the whole thing once they started.
Some of the mechanisms are so cool, I made a really simple one as a Christmas gift. Essentially you move the pin to the angle you want to find the sine of, and by reading the location of the pin you can find the sine of that angle. By picking a location on the scale and then reading the angle you can find inverse sines too. And if you remember your trig identities (probably should've inscribed these on the face, they are hard to remember!) you can really do a whole lot more. I figured there are enough engineers here someone would be bound to get a kick out of it.
Video, in case my explanation doesn't make sense.
