There are some empirical formulas for meander-line dipole, though not much. As I can remember, in the recent issue of Antennas and propagation magazine, there is a paper purposing a formula to assist the meander-line dipole design. The formula is developed based on a database consisted of many fullwave simulation results. However, I think the formula may not applied in your case. First, the geometry is a bit different. Second, the meander-line u plotted looks like the feed-line of the patch. Are u sure strong radiation is desired from the meander-line?