:confused: What is the ampacity of 10 AWG GXL (125 C) wire in "free air" when used on a 120 VAC (nominal) circuit? Also, what is a good definition of "free air"?

Free air is like an overhead span.

Where would you possibly be using wire in free air??

The wires are used as internal wires in a transfer swith. They are in a 12x10x4 enclosure BUT not in a raceway, cable or buried application (like NEC Table 310.16). Would the enclosure be considered a raceway or conduit?

No, it would be considered an enclosure. #10 is typically rated at 30 amps. There are considerations- How many wires in the enclosure? How many CURRENT carrying wires are in the enclousre?

A total of 18 10AWG wires carrying 50 Amps each (worst case) to/from the relays. There are also 8 16AWG wires carrying < 200 mA for the control circuit. The NEC 310.17 chart would allow 55 Amps (in free air, at 30 C) for 90 C wire. GXL is 125 C but the chart does not have that column.

50 amps is a lot of current for #10. Intermittently it may be OK but personally, I wouldn't use #10. In close confines the ampacity drops due to heat considerations. Remember "FREE AIR". Means the wires are able to dissipate any heat generated by the current draw. Can the enclosure be ventilated in some way to help with heat?