Lets see if I understand this. 1/2 inch diameter = 4/8, then take out
3/8, leaving 1/8 divided by 2 leaves 1/16 inch for set screw thread.
Do you care if the end of the set screw extends out from the surface?
Won't catch on anything?

Seems like not many threads for a set screw.

Yep - you got it right. Actually I am using a regular screw, which does
indeed extend out from the shaft and through the hub of a plastic lawnmower
wheel. I might not be using the correct terminology here.

To help, I've uploaded a photo to this URL:
http://www.waycoolgear.com/ebay/shaft.jpg
( Note that I am not selling anything here, I just use the eBay directory to
post all my uploads like this. )

The inset photo is of the shaft itself, the rest of the photo shows in
inserted into the lawnmower wheel's hub.

Feel free to correct me on my terminology!
JCD