Road bike on crushed limestone/gravel trails : bicycling
On road bikes, this gap may not be much bigger than 28mm or so. The 2nd factor is brakes. Brakes made for a bike with narrow road tires may not fit around a really wide tire. The easiest way is to try it out. Ask the LBS if you can borrow a 28-32mm tire (Even used) to see if it rubs on your frame and brakes. 1.