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Elon Musk says 'we dug our own grave' with the Cybertruck as he warns Tesla faces enormous production challenges
(www.businessinsider.com)
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Higher voltage allows for fewer amps. Higher amps creates more heat and requires thicker cables which cost more and add weight. So it's substantially less copper since the wires don't need to be as thick.
I can't give exact numbers, but going from a 12/24v to 48v wiring harness will reduce the harness weight. I don't know if that's on a linear scale or not in terms of reduction.
A thinner wiring harness would also be easier to manage and place, e.g more bendable, less space required to place it.
It also gives you more leeway if you do want to push more amps to something without having to get into the really really big unwieldy wires that are very difficult to shape.
24v would work, but I imagine the thought is, if we need to create a whole new supply chain for automotive parts at a different voltage, why go to 24v when we can go to 48v and get even more benefits? The process is already happening, others have some hybrid 48v usage.
Someone else could comment on this, but without knowing more, I would speculate that higher voltages would even allow some sort of shrinking of the components themselves since internally they wouldn't need to support as high of amps either, but that's just my speculation.
Edit: Just some hypothetical numbers. If a wiring harness is 150lbs and lets say 48v gets it to 50lbs, that's a $375 cost savings in copper alone. That's also a ton less copper used/mined across the whole auto industry once transitioned. At 67 million cars a year, that would be 6,700,000,000 lbs of copper saved per year.