Hi Silv, although this is not a barn door tracker the idea is similar i built this curved bolt clock drive some time ago using this formula, which can be applied to and diameter of threaded rod and thread pitch arrangement, one must however use a 1 rev/minute motor, which i had made for me some time ago as well.
Anyway this may give you some ideas.
Leon.
Formula for building a Camera Clock Drive, using a one revolution per/minute motor and a curved threaded rod with a pitch of 24 to the inch.
Formula
Radius = 1436.5 x ( n / 2 pie t ) where n = 1 and t = 24
Radius = 1436.5 x ( 1 / 2 22 / 7 x 24 )
Radius = 1436.5 x ( 1 / 6.285714 x 24 )
Radius = 1436.5 x ( 1 / 150.85713 )
Radius = 1436.5 x ( 0.0066287 )
Radius = 9.52212 inches, (241.86184 mm)
Motor revolution must be (one) 1 per / minute
Threaded rod pitch in this case is 24, other diameter and pitch can be used
This formula works very well and is accurate to a least 30 minutes plus, of time exposure