Model S

Table of energy consumption vs. speed

edited November 2014 in Model S
I haven't seen a simple formula for Wh/mile vs. speed, I decided to interpolate from a published graph and do some simple curve fitting. From 45 to 80 MPH, I found that

Wh/mile = MPH^2 / 30 + MPH * 5/6 + 120

fits the curve well:

MPH Curve Calulated
45 225 225
50 245 245
55 270 266.6666667
60 290 290
65 320 315
70 340 341.6666667
75 370 370
80 400 400
Does anyone have a better curve or data for quick calculations?

With this data, I can answer simple questions like: should I drive 200 miles at 60 or 75, to minimize the total time, including charging, with my single charger and no supercharger in the area?

At 60, I drive for 200 minutes, and consume 200*0.290 = 58 kWh.

At 75, I drive for 160 minutes, and consume 200*0.370 = 74 kWh.

So, the extra charging time is the time it takes to charge 16 kWh. I saved 40 minutes driving, but my single charger only charges at 10 kW, so it'll take more than an extra hour charging, making 75 MPH slower in total. A second charger would have made it faster.



  • edited November -1
    You might find the high end of the graph will vary with time of year. As the air temperatures changes its density changes which will slightly change the second order coefficient a little. But we applaud the information as it will help us all understand these fastastic inventions just a bit more. Thanks, great info!
  • edited November -1
    Using the above formula, I figured the best speed to drive assuming that charging time is included in the trip time (as it is when you have to charge on the road) as a function of the charging rate:

    Charging Best Speed Net Speed
    Rate (kW) (MPH) (MPH)
    9 47 21
    18 61 30
    36 77 42
    72 99 57
    120 100+ 69

    The difference between 9kW and 18kW shows how road trips away from superchargers really benefits from dual chargers, so long as you can find high-current L2 chargers (HWPC or J1772).

    The 36kW calculation speaks to the value of 50kW CHAdeMO charging. If we could use those, there would be no reason to conserve energy when traveling, just like when there are superchargers on the route.
  • edited November -1
    @AoneOne interesting way of looking at it. Very nice. Now if you factor in the time you save by going faster and charge using the Supercharger network, that would be even better. The average distance between superchargers along the I5 is about 125 miles. You can charge up to 170 miles in 30 minutes (or half a charge in 20 minutes... so 85kW/2 = 42.5kW in 20 minutes, 60kW in 30 minutes, 68kW in 40 minutes and 85kW in 75 minutes...that's according to the curve). For the most part, if you plan on doing a lot of travel off the supercharger network, it would be better to get dual chargers.
  • edited November -1

    To add to hpjtv, given an avg distance b/w SCs of 125 miles, going greater than 65 MPH will still net faster travel times (gain in driving time net of longer charging time) only if the charging station is at least 30 kW. Definitely ++1 on AoneOne's point that "... The 36kW calculation speaks to the value of 50kW (chargers). If we could use those, there would be no reason to conserve energy when traveling.."

    @AoneOne, my curve fitting came to:
    0.0261905 * MPH^2 + 1.70238 *MPH + 95.3571
  • edited November -1
    @Julian: were you fitting my data, or some other. If other, which data?

    I can easily believe that a least-squares fit to my data would give something different. I used a difference-of-differences method and the result fit well enough and was simple enough that I didn't pursue a "better" fit, especially given the errors inherent in extracting the data from the published graph, and that I've included none of the complicating factors like the environment or cargo weight.
  • edited November -1
    @AoneOne: you had a similar thread before. I sent you the data from the chart pretty precisely extracted. Since this is Tesla's chart, I assume it based on their data and expectations and is not hand drawn. That is, it is based on some either measurements and/or their own formula. Either way, I wouldn't want to deviate from it too far in understanding what is going on. Now, the middle part of it could be interpolated simpler, but all of it is not simple quadratic polynomial..

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