Five huh...
The typical relay 3Pole KU style Potter & Brumfield 24VDC, that plugs into a socket is 1.2W
1.2W/24V = 51mA
It is guaranteed to operate at 75% of nominal voltage.
0.75 x 24 = 18V
24V - 18V = 6V
This means you can tolerate a 6V drop over the round trip circuit at the relay's current.
That equates to 6V/51mA = 117 Ohms that can be the circuit's drop.
The drop is a function of the circuit wire gauge and its resulting resistance per foot.
1100ft x 2 = 2200ft.
117 Ohms / 2200ft = 0.053 ohms/foot
Any wire with LESS THAN 0.053 Ohms/foot will work.
Looking at:
Down just a ways shows "Wire Gauge Resistance per foot".
This shows that even paltry 28AWG would allow the relays to operate in 24VDC land.
Certainly this is too small from a purely mechanical durability standpoint. But you can use low voltage door bell, heater thermostat, limited energy type cable to run the relays over this distance. 24AWG or 22AWG or 20AWG. The smaller the gauge the less likelihood of wire theft. The less expensive. Going with 120VAC can require much larger wire for code minimums costing substantially more and raising the theft aspect, conduit needs, etc.
I am not sure if you would have problems with an AC link on that distance. I can't find the document that gave the formula/table. I do know that distance is near the ragged edge.
At the high price of copper these days I suspect that needing maybe an extra set of relays/sockets if your sources are 120VAC, (and not dry contacts)and maybe two cheap power supplies is possibly less expensive than all the code required wire needed for the AC solution.
Keith Cress
Flamin Systems, Inc.-