I would like to figure out these two things:
- X gauge of wire needed dependent on the current needed, and the length.
- X max length of wire dependent on the current, and the gauge.
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What you care about is called ampacity - Amperage Capacity. It is determined by the the heating limit of the wire carrying the current.
It has no dependancy on length.
IF you have 50 m of wire that is 1 \$ m\Omega \$ the and carries 100 Amps. the power loss along that 50 m is 10 W (0.001 * \$100^2\$) from \$I^2R\$. If you now double the wire length, the resistance doubles and the power loss doubles therefore the power loss per unit length stays the same.
What does matter is that the longer wire will drop more voltage across it (ESR - Equivalent series resistance) so you will loose headroom.
The way to look at it is that when you lengthen the wire, it's area also increases so it's ability to handle power also increases (more area to dump heat out of).