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Super chargers for Chicago to south florida

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If you have an 85, I imagine both of those gaps should be doable. Take the time to do a range charge before setting off and monitor your predicted arrival charge so you can adjust your speed as needed. (Note: I haven't done any supercharger trips yet so this is all just theoretical for me!)
 
EV Trip Planner calls for 230 rated miles or 69 kWh to make the trip from London to Chattanooga at 72F. I find their estimates to be slightly conservative so a range charge can get you there. Plenty of 30A chargers in TN if you need to stop for an hour to top off.