Rates of reaction can be affected by the size of rings. Essentially each reaction should be studied on a case-by-case basis but some general trends have been seen.  Molecular mechanics calculations of strain energy differences SI between a sp2 and sp3 state in cycloalkanes show linear correlations with rates ( as logk ) of many reactions involving the transition between sp2 and sp3 states, such as ketone reduction, alcohol oxidation or nucleophilic substitution, the contribution of transannular strain is below 3 %. 
Rings with transannular strain have faster S1, S2, and free radical reactions compared to most smaller and normal sized rings. Five membered rings show an exception to this trend. On the other hand, some nucleophilic addition reactions involving addition to a carbonyl group in general show the opposite trend. Smaller and normal rings, with five membered rings being the anomaly, have faster reaction rates while those with transannular strain are slower.
One specific example of a study of rates of reactions for an S1 reaction is shown on the right. Various sized rings, ranging from four to seventeen members, were used to compare the relative rates and better understand the effect of transannular strain on this reaction. The solvolysis reaction in acetic acid involved the formation of a carbocation as the chloride ion leaves the cyclic molecule. This study fits the general trend seen above that rings with transannular strain show increased reactions rates compared to smaller rings in S1 reactions.