Wednesday, October 23, 2013

Driving Tesla Model S as fast as you can with Supercharging.

With Tesla adding an Autobahn tuning package, it made me wonder if driving fast in a Model S would just leave you hanging around the SuperCharger more often.  Perhaps a little bit of calculation can shed some light.

First, I started with a graph from Tesla of battery consumption versus speed.  Unfortunately that graph only went up to 80 mph, so I had to extend it (yes I know that exponential is probably not exactly correct, but it's close).
Having that data, I needed to make some assumptions about the Superchargers.  If they are 120 KW, they can charge an 85KWH battery in 0.708 hours.  Sure, I know it would take much longer than that because the last 20% of charge is slow, but I'm just trying to get a rough estimate here.

So with some simple math, we can figure out the "running time" and the "charging time" and compute an "aggregate MPH".






Running Charging Total
Speed
range Time Time Time Agrregate 
miles/hour WH/miles (miles) hours hours Hours MPH
10 220 386 38.6 0.71 39.34 9.8
15 195 436 29.1 0.71 29.77 14.6
20 190 447 22.4 0.71 23.08 19.4
25 190 447 17.9 0.71 18.60 24.0
30 195 436 14.5 0.71 15.24 28.6
35 200 425 12.1 0.71 12.85 33.1
40 215 395 9.9 0.71 10.59 37.3
45 225 378 8.4 0.71 9.10 41.5
50 245 347 6.9 0.71 7.65 45.4
55 265 321 5.8 0.71 6.54 49.0
60 285 298 5.0 0.71 5.68 52.5
65 315 270 4.2 0.71 4.86 55.5
70 340 250 3.6 0.71 4.28 58.4
75 365 233 3.1 0.71 3.81 61.1
80 400 213 2.7 0.71 3.36 63.2
85 429 198 2.3 0.71 3.04 65.2
90 463 183 2.0 0.71 2.75 66.8
95 501 170 1.8 0.71 2.49 68.0
100 542 157 1.6 0.71 2.28 68.9
105 586 145 1.4 0.71 2.09 69.4
110 633 134 1.2 0.71 1.93 69.6
115 684 124 1.1 0.71 1.79 69.4
120 740 115 1.0 0.71 1.67 69.0
125 800 106 0.8 0.71 1.56 68.2
130 865 98 0.8 0.71 1.46 67.1

That puts the optimal speed (in a time sense) at an impressive 110 mph.   Realistically, optimal speed will probably be a slower than that due to charging issues.

Unfortunately, the aggregate speed is only 69 mph considering the charging time.  It will mean driving for 1.2 hours and then charging for 0.71 hours.  That might be slightly painful.

The only thing worse, would be to go for optimal efficiency and drive at 25 miles./hour which would be 17.9 hours of driving and 0.71 hours of charging.  Bathroom break anyone?



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