Electronic – AC cable for DC applications

Given that safety must always be adequate, you then want

• low final resistance,

• durability,

• low price

in descending order of priority.
If welding cable gives all 3 (as seems likely), use it.

Sheath may not be as resistant to sharp object penetration as TPS but is liable to be more drag and scuff resistant.
Test voltage may not be as high but would, I imagine, be adequate.
If you have a 100+ V battery system then you may well have regulatory requirements to meet re allowable wiring type. Maybe not.

At 130 Amp, 0.1 ohm drops 13V. In a ~ 100 V system that's ~ 13% loss.
Even 0.01 ohm gives say 1.5% loss.
Every 0.01 ohm improvement you can make adds ~= 1.5% to your available energy.

What sort of solar car has 105V, 130A peak specs ~= 14 kW Sounds like fun.

The actual equations you want were derived by Lord Kelvin for use on the transatlantic cable system, and the math is known as CABLE THEORY. Interestingly enough, a search on that will likely prove useless, as the most common hits will all be about neurons, for which the same math applies, and finding anything about real cables is difficult.

Interestly enough, the Telegraphers Equations probably do the job (http://en.wikipedia.org/wiki/Telegrapher%27s_equations). That provides all the differential equations you need to do the job. If you need to solve this simultaneously in time and distance, you'll get hyperbolic partial differential equations, and the results will be catenaries involving hyperbolic trig functions (so THAT'S why they're on caculators) if you get to the right answer.

Sorry I can't walk you through the math. It's not simple stuff.