Warning
- FYI - some early AC/DC radio sets had live to mains chassis when operated from mains.
Equipment chassis is usually grounded to wiring ground via earth lead on power plug where provided.
In any sane regulatory environment, appliances without an earth lead are required by law to be "double insulated" so that internal metal parts are not touch accessible during operation. (Note: Double insulation nowadays seldom involves two layers of insulation - it is more a state of mind in manufacture and testing that leads to touch safe equipment. Usually :-). )
While a chassis should be "touch safe", never assume it is, because:
There are non-sane regulatory environments,
or ones where the authorities enforce the rules so little that they may be ignored and
It is excessively common for people to do silly and dangerous things with mains wiring, despite being aware that people are reported to have died due to such things.
Wikipedia - appliance classes
They say:
Class I
- These appliances must have their chassis connected to electrical earth (US: ground) by an earth conductor (coloured green/yellow in most countries, green in the U.S., Canada and Japan). A fault in the appliance which causes a live conductor to contact the casing will cause a current to flow in the earth conductor. This current should trip either an overcurrent device (fuse or circuit breaker (CB)) or a residual-current device (RCD) also named as residual current circuit breaker (RCCB), or (ground fault circuit interrupter (GFCI)) or also, residual current operated circuit-breaker with integral overcurrent protection (RCBO). which will cut off the supply of electricity to the appliance.
Class II - See also: double switching (and double insulated)
A Class II or double insulated electrical appliance is one which has been designed in such a way that it does not require a safety connection to electrical earth (US: ground).
The basic requirement is that no single failure can result in dangerous voltage becoming exposed so that it might cause an electric shock and that this is achieved without relying on an earthed metal casing. This is usually achieved at least in part by having two layers of insulating material surrounding live parts or by using reinforced insulation.
In Europe, a double insulated appliance must be labelled Class II, double insulated, or bear the double insulation symbol (a square inside another square)..
Class III
A Class III appliance is designed to be supplied from a separated/safety extra-low voltage (SELV) power source. The voltage from a SELV supply is low enough that under normal conditions a person can safely come into contact with it without risk of electrical shock.
The extra safety features built into Class I and Class II appliances are therefore not required. For medical devices compliance with Class III is not considered sufficient protection.
For a more general system I would do this differently. Maybe it's overkill in your case, but this isn't that hard. I've done something similar, although the power requirements were higher.
In my system I used CAN as a multi-drop bus to all the nodes. In the common configuration it uses differential signalling, which is a good idea for long distances where you could pick up common mode noise. I reserved one pair for the CAN lines. The other three pair were used for power, with a power and ground on each pair. That way the total common mode current of each twisted pair will still be close to zero. In my case I used 48 V because that is the maximum where you generally don't have to worry about safety issues much. There are plenty of microcontrollers with CAN built in, and the silicon deals with collisions and retries automatically.
In your case the power requirements are less, so 24 V might be a good choice for the power. Lots of transistors and buck regulator chips work up to 30 V. 28 V would be better if you want to push the most power and still use the cheapest power supplies at the ends, but I said 24 V because you're not pushing the limit and that's a very commonly available off the shelf power supply voltage.
At each node, put a small buck regulator. These are small and cheap nowadays. The MCP16301 can handle up to 30 V in, costs under $1, includes the switch, and comes in a nice and small SOT-23 package. Make sure to put a decent ceramic cap right at the input to the buck regulator though. The 24 V needs to be low impedance at high frequencies for the buck switcher to work. You probably want something like a 10 µF 30 V cap.
The advantage of this scheme is that you can tolerate a fairly wide power voltage at each node, but due to the higher voltage and therefore lower current, you won't have much drop. There will also be less heat at each node since the buck switcher will be more efficient than a linear regulator after you raise the power voltage enough to cover all the worst case conditions with headroom.
Another significant advantage is that there will be less ground offset between nodes, again due to the lower power current at the higher voltage.
Best Answer
You start by calculating the current: Y watt/X volt. The voltage is relevant for the cable's isolation, but not for the diameter. (That's not entirely true. If you work at Really Low voltages the voltage drop due to the cables resistance and possibly high current may become significant. Usually not for mains voltages and higher, though.)
Thicker cables has less resistance, so less power dissipation. I don't know where you read otherwise. This page has a calculator for the cable's required diameter. The same site also has tables for different kinds of cables.
There's indeed a difference between AC and DC. AC has skin effect, where the current will flow more need the outside of the cable. That "skin" is thinner as frequency gets higher, but already exists to a small extent for 50/60 Hz. So an AC cable may need a somewhat larger diameter, though this skin depth calculator gives a more than 9 mm skin depth for 50 Hz in copper, so that won't be a problem for most cables.