I need to know the smallest gauge wire i can use to carry a 12 v current at 16.5 amps that is still safe. Needs to be flexible and small enough to make a ~120 degree turn in a space ~10mm
ampacity for fixture wiring per nec code #14 --- 17A --- 0.0726 diam #16 --- 8A --- 0.0576 #18 --- 6A --- 0.0456 commercially available class B stranding (7 strands) or more flexible class C stranding (19 strands) you could probably get more flexible higher stranding wires from electronic shop you have 10mm space i don't think you have problem on bending the wires. should worry more on ampacity. i suggest use #14
You can use automotive wire rated for 24 volts and No.14 AWG. Automotive wires are stranded and flexible.
In Canada and the USA 15 amp circuits are the norm wired with # 14 cable unless the runs are very long. Up to 12 outlets can be place on one circuit but for a workshop, I would sugest no more the 4 or 5 per circuit. If you require a 20 amp circuit, it should be a dedicated circuit with the proper 20 amp receptacle. A separate 15 amp circuit for your lighting is smart in case you trip a breaker with one or more of your shop tools; you will still have lighting. The welder will require a dedicated 240 volt, 60 amp circuit Your air compressor will also require a dedicated 240 volt circuit sized accordingly to the power demand of the compressor motor. Just from what you have listed, I would suggest at least an 100 amp 240/120 volt load centre. This will give you extra room for fans, heating, etc.
18 is marginal, but should work for a short distance. If you can, use #16. it is 1.3 mm in diameter. With insulation that would be perhaps 3mm. You can get wire that is very flexible because it has more strands of thinner wire than ordinary stranded wire has. #16 speaker wire is commonly available. .
