On my specialized Secteur I normally use 25mm or 28mm tires. About 6 months ago I mounted a Specialized, I think they called it a Gripon, nominally 28mm. This tire is mounted in a Velocity A23 rim and measures 29.5mm and is noticibly bigger than a typical 28mm tire. It fits fine but that is the maximum tire that will fit with about 2-3 mm clearance each side. If you can't judge by eye how much larger of a tire will fit, fashion a wooden wedge and slide it in between the tire and frame and mark how far in goes. Then measure the wedge at that point. Likely left and right sides will be slightly different and but add the two sides together. My guess is a 28mmm tire will fit fine. With bigger tires you will be able to drop the pressure several pounds for a more comfy ride.