[suhoca]

I'm trying to explain the relative rates of these different bridgehead sulfonates.
I would have thought that the norbene derivatives would have had a faster rate because they can form a norbenyl cation - but apparently not.
Any tips very much appreciated.

{Mod Edit: typo}

[pgk]

Think about steric hindrance.
PS: “Acetolysis” and not “Acetonlysis”, neither “Acetonolysis”.

[pgk]

Thinking twice and given that students ought to answer questions and not to criticize or to revise the said questions, I think it is more correct to accept that acetonolysis (solvolysis) of the bicyclo-norbonyl/norbornenyl alkylosulfonate esters occurs hereby and not their acetolysis.
Besides, the formation of a norbornane/norbornene cation is possible because it is favored on the bridgehead carbon atoms of bridged rings, regardless if being secondary ones:
Bridgehead solvolytic reactivity. A unified data set to test molecular mechanics, J. Org. Chem., (1985), 50(26), 5852-5855
https://pubs.acs.org/doi/abs/10.1021/jo00350a080