at any one time you only need a few pieces of information:
- are you currently in a run
- length of the current run
- maximum length of run encountered so far
if you are not in a run and you encounter a T then move on to the next entry
if you are in a run and you encounter a T then compare the length of the current run to the maximum so far to determine if you have a new record. Afterwards either way mark yourself as no longer being in a run. then move on to the next entry.
if you are in a run and encounter a H then increment the length of the current run. Then move on to the next entry.
I left out a detail that you should be able to catch.
You can get away with using just two variables aside from the loop index.