Temperature rise in undersized wire

So, this know-it-all at work orders some big honkin' Community R.25s to replace some bullhorns in a 70V PA system. Problem is, he ordered the 4-ohm version . It's no problem to switch the amps to low-Z output (they're Crown CT-410s), but the line resistance is about 1.3 ohms. This is 12-gauge wire and the nominal output power is about 240 watts. We're stuck with this until we can buy some 70V stepdown transformers to mount at the speakers; we tried it today and it worked OK for the short time we tested. But I'm horrified to think of all the power being dissipated in heating the wire. How would I go about calculating the approximate worst-case temperature rise (steady-state output)? I just want to know if we're facing a potential meltdown until we can rectify the situation.

You mean the total line and load impedance is 1.3 ohms? One would need to know the fraction that is the wire, with the worst-case being the initial run to the first load if the loads are hanging off the single run of line. A drawing of the situation would be helpful.

#12 is about 1.6 mohm/foot. Even if all the power of 240W were dissipated in a 1.3 ohm 406 foot round-trip, hence 590mW/foot, the insulation won't melt and fall off, although the wire would certainly get noticeably warm.

1.3 ohms is the total round-trip wire resistance--the speaker is 4 ohms nominal, so the total load is 5.3 ohms nominal. The rated power output of the amp is something like 243W/channel at 4 ohms.

Each speaker is home-run back to a dedicated amp channel; they're not daisy-chained.

[quote author="NewYorkDave"].... We're stuck with this until we can buy some 70V stepdown transformers to mount at the speakers.....[/quote]

You may also wish to try 100-150VA power toroids 110-24, 36 or 48V as a band aid.

Regards,
Milan

[quote author="NewYorkDave"]1.3 ohms is the total round-trip wire resistance--the speaker is 4 ohms nominal, so the total load is 5.3 ohms nominal. The rated power output of the amp is something like 243W/channel at 4 ohms.

Each speaker is home-run back to a dedicated amp channel; they're not daisy-chained.[/quote]

No problem then. With the ~31V rms amp output a given run will have a dissipation of ~45W. If that wire were all coiled up and confined the bundle would get fairly warm, but distributed over a run in typical spaces it will be fine I think. It's only 111mW/foot for a given section of the pair. And that's assuming continuous maximum drive, which is unlikely.

Inefficient, poor damping factor at the speaker, but not dangerous.