What I mean is, for, say, a Sherman to be kept operational, what as required besides the tank and its crew? How many men and machines were required behind the front to supply the fuel, ammo, parts and repair, and so on?
I'd be especially interested in comparisons between various vehicles, ie the difference in supporting a Tiger II vs. a Panzer III, as well as countries to boot. How much more (or less) did the US need to support a Sherman compared to the Soviets with a T-34?
As a follow up question, were tanks simply driven to the battle where they were needed? It seems like a waste of fuel but I can't think of an alternative.
The Red Army had many kinds of tank units with varying support structures, so let's take one of the smallest types: an Independent Tank Brigade formed in November of 1943.
The very smallest structure in the brigade with any support tail is the battalion. The battalion consists of two companies of 10 T-34 tanks each, plus one T-34 tank for the battalion commander. In addition to the T-34s, the battalion has 1 light car and 12 trucks.
Supporting these tanks are a technical support platoon (48 men), quartermaster squad (5 men), and the battalion medical group(4 men). Out of the 148 soldiers in the platoon, only the T-34 crews (80 men) are doing the actual fighting, a bit more than half.
In addition to three such battalions, the tank brigade contains a motorized infantry battalion (507 men), which are as important to keeping the tank alive in battle as any mechanic, but your question doesn't seem to be about these guys so we'll skip them. There is also an AA machinegun company (48 men), a command company (164 men, 3 armoured cars), the technical support company (123 men) and a medical platoon (14 men).
In total, there are 1346 men in the brigade, but only those 20 T-34s per tank battalion are doing actual fighting, so that's a tooth-to-tail ratio of about 1:5. For each guy in a tank, there are 5 making sure that the tank can do its job properly.
Shtat 010/500-506
Follow up: If a tank broke down, did the crew stick around to wait for repairs or where they given another tank asap?