The stater limitations are because of overheating the starter which apart from transfering a considerable amount of energy is also receiving hi temp air in some cases like bleed starts.
L1011 starter cycle limitation as follows:
BA and GF Pilot operating notes show 2 cycles of 3 minutes on with 1 min off plus 1 cycles of 1 min then 30 minutes cool
Alternatively 5 minutes continuous then 30 min cool.
BA and GF maintenance manuals ( 71-00-00
) show the same limits with an additional limit for compressor wash which is 2 mins on 10 off reapeated twice to wash. Then 2 on 10 off repeated twice to rinse. then 2 min on to dry then 30 mins off.
Both manuals also note that regardless of the wait period time between starts is also limited by zero N3 rotation which could well be more than the 1 min
The pilot and engineer limits seem pretty close to each other to me
