Center screen on unit?

I going crazy about the map never centering on the unit I am moving. Is there a command that autocenters on units? Doing it manually with "c" is a pain in the....

does it really never centre? I find that it only doesn't centre if the unit is already on the screen. If I want to get a better look around the unit it's easy to scroll. Or else I press c. It's second nature now; left hand for c, right hand for mouse to command units. It used to be right hand on numpad, but in Civ4 it's easier to use the mouse.

Lets say I have a destroyer in the center of the screen, as I move it will soon disappear from the screen and I will only see the empty center where it started.

This game generally lacks choices in the options menu.

Like Brighteye, I nearly always use the right-mouse button to move the units around.

Click the center mouse button (or wheel). That will also center the screen on the active unit.