I wanted to build my own gabion fence (35 metres wide x 975mm high x 525mm deep) starting from scratch. I wanted it to be an artisan project, so I built my own spiral winder from parts of machinery I had lying around the farm. The cogs came from a Massey Harris seed drill, and I used a length of acme thread as I wanted the spirals to be even, consistent and regular to make them easier to wind onto the mesh. I used hog rings to hold the mesh together prior to winding the spirals.
If building your own, it is important to remember that the lead shaft needs to turn a bit faster than the winding shaft so that the carrier arm moves at least the thickness diameter of the wire per revolution. I used 3.15mm fencing wire. Looking at the figures there was a 2:1 ratio involved, and I would use 3/4" acme 6 TPI thread if purchasing a length. If using round bar for the winding shaft and stretching pole I would use 25mm and 20mm respectively as this would still give a 5mm differential to allow the coil to stretch.
I was fortunate enough that everything I had, worked and gave me approximately 1 to 1.5 turns per 75mm mesh square. There were no mathematical calculations involved apart from the number of turns required!