No, Giga Texas already has a bty cell making facility under construction. They'll be ready to make 4680s in Austin at the same time as the first vehicle is ready to go.
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Fremont Kato Roadrunner is ~10GWh/yr capacity. That's enough for about ~100K Models S/X, which is the planned capacity of the new line with 2 shifts, per Elon. Compare vs Fremont:
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Have to quibble slightly with Joe's comment that Giga Texas will have 2.5x the capacity of Kato Roadrunner: there will be exactly 1 prototype line at Kato Rd, and Tesla says each production line will have 20 GWh/yr capacity. So my quibble is that you can't have 2.5 lines: it's always an integer multiple of the base number as you add more duplicate lines. IE: you could have 2 lines or 3 lines, but not 2.5 lines.
So, since the nameplate capacity is larger for the production bty lines, let's say Austin will have 2 bty lines (not 3) in the space allocated above. So that's 2x20GWh/yr capacity, enough for 500K Models Y if each comes with an 80KWh pack (which is what is shipping now from Fremont with 2170s). And that's exactly how many you'd get from a 10K/week GA line for Model Y. Book 'em!
Giga Texas has 4 square miles of land in its boundries. TX gonna git big, Bigger, BIGGEST...
Cheers!