Enjoy, welcome.
You only need the additional wire specs if designed into your product. In general, most consumer grade wire of "X" thickness of similar material, say PVC, will be similar to the MIL spec but its never really been tested for same. The actual formulation of PVC matters [ e.g. stabilizers, plasticizers] as well as the quality control of the maker.
Specs besides working voltage are a concern when you are say, hooking up direct to mains were surges and transients above "steady state" aka working voltage can happen, and want to really control for it to define the risk or arcing from dielectric breakdown. This is why the wires on most reputable surge protectors are extremely beefy to exceed most CAT ratings, so it rated to take worse case transients enough for the surge suppressive elements to do its job, usually > =CAT III for plug in surge protectors.
A rule of thumb is the dielectric breakdown occurs at least 5-10x the rated working voltage but at Vp not Vac rms. So 300V wire should withstand 1500Vp-3000Vp.
UL does not specify transient rating, AFAIK nor is it specified in the USA by the NEC, so that transient parameter is 'undefined', they are most concerned only with working voltage, temperature and the conditions the conductor will be exposed too, e.g., underground, underwater etc.,
https://www.ul.com/wp-content/uploads/2014/04/WC_MG.pdf UL wire specifications are in working voltage, not peak. Its Vac rms, so UL1007 is 300Vac rms.
UL 1015 is the equivalent of https://www.nationalwire.com/pdf/MIL-DTL-16878-1.pdf but note how much more MIL spec requires.
Thanks for clearing this up for me.
Whenever I'm shopping for hookup wire, I often will come across tables that list the specs like this:
http://www.standard-wire.com/comparison_chart_ul_wires_cables.html
So I was never too sure how to interpret the voltage rating given there's a choice between 300V and 600V. Is Mil spec meant for aviation, aerospace, military, automotive applications?
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