I routinely use EZNEC to design antennas printed on a substrate. I do
the basic design then apply a fudge factor to the conductor width and
length derived from comparisons between model results and measurements
of real antennas. Final designs usually take some adjustment even at
that. However, I haven't tried this for any antenna that depends
strongly on coupling between elements, such as a Yagi, because the
mutual coupling will also be affected by the substrate and won't be so
easy to approximate. In the case of a log periodic, I'd adjust the model
transmission line to try and get the same Z0 and velocity factor as the
line on the substrate, which you might have to determine by measurement.
That would help, but you'd still be lacking accurate mutual coupling
information. At best, I think, a model would get you in the ballpark,
with a final design requiring some tweaking.

Roy Lewallen, W7EL