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24 hour EV range record in Model S possible?

Discussion in 'Model S' started by Banahogg, Apr 9, 2013.

  1. Banahogg

    Banahogg Member

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    I was watching JB's talk at cleantech and he mentions around 33-34 minutes in that Model S owners are doing a significant fraction of the current EV range record just driving their cars home using the superchargers as just part of the expected infrastructure. I couldn't let that pass without doing some back-of-the-envelope math...

    Google maps shows 116 miles and about 1 hour 37 to get from Harris Ranch to Tejon Ranch (+/- 1 minute for the different directions). If you assume 40 minutes to charge, which should be fairly conservative for going 70 between the two, then you can fit 10 full legs in 24 hours, or 1160 miles. The record is 1172.

    So, if one were either willing to go over 70 on I-5 to cut the driving time (from the data we have, the tradeoff point where it's better to slow down and supercharge less is well over 70mph) or cut the charge time by timing the charging carefully to maximize charging in the fastest part of the battery, adding another 12 miles in 24 hours seems quite doable.

    Food for thought :)
     
  2. PureAmps

    PureAmps Model S P85 (#2817)

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    Easily beatable in the Model S with superchargers. I just did 480 miles in 11 hours this past Saturday, and 1.5 hours of that was spent on a J1772 charging @ 30amps. I drove in very strong headwinds and climbed over 4000 vertical feet. Even with all of that I could have covered 1047 miles in 24 hours at that rate, just 125 miles short of the record. Take out the wind, hills, and slow chargers and 1172 miles could easily be done in 24 hours with a Model S and superchargers.

    You'd probably have to do some math to figure out the optimum driving speed vs charging time/range if you were to do "laps" between Tejon and Harris, but I bet you could get 11-12 runs completed. So about 1276-1392 miles. Of course, all it would take is one speeding ticket and your record breaking attempt would be over. ;)

    It seems like kind of a boring way to spend a day, though. I'd rather wait until they have a 1200+ mile stretch of road covered with superchargers, and just drive from point A to B.
     
  3. stevezzzz

    stevezzzz R;SigS;P85D;SigX

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    Thought experiment: what's the theoretical maximum 24-hour range of an 85kWh Model S using Superchargers limited to 90kW charging?

    I'll start: my assumptions include a banked, sea level, windless circular track that's large enough in diameter so that g-loading doesn't materially affect rolling resistance. There are dedicated Superchargers located at one mile intervals around the track: no waiting to plug in when you decide it's time to charge. Factory stock, standard S85 w/ 19" wheels and tires.

    OK, let's drive: what's the protocol that maximizes overall cross country speed? I know from my experience flying gliders cross-country that to optimize cross-country average speed you should drive at a speed that results in a battery drain equivalent to the rate of charge you'll see when you stop, 90 kW. What's that speed? You should obviously start the attempt at the highest SOC you can get and end the 24 hours with 0% SOC (or should it perhaps be the lowest SOC that allows you to pull 90kW continuous? You don't have to care if you damage the battery: imagine that this is a factory-supported record attempt). When do you stop to charge, and when do you leave the charger and get back on the track? Again, from my glider experience, I say you should leave the charger as soon as the rate of charge starts to tail off below 90kW; but what is the SOC when that happens?

    Anybody want to figure out how far you'll get in 24 hours? Post your assumptions and your calculations, please.
     
  4. richkae

    richkae VIN587

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    #4 richkae, Apr 10, 2013
    Last edited: Apr 10, 2013
    I'll start with the Roadster efficiency and range spreadsheet and then make a Model S version by multiplying the Roadster wh/mi numbers by 1.25
    ( This gives you a 300 mile range at 52mph. Pretty close. The curves for aero resistance, rolling resistance, drivetrain resistance are all probably slighlty different from the Roadster, but this is close enough )
    Then calculate the power consumed to travel at each speed, then ratio of driving to charging for each speed/power level assuming 90kW charging, then calculate the portion of 24 hours you could spend driving.
    This ignores charging transition time and time to accelerate and decelerate. It also assumes 90kW charging means 100% efficiency so 90kWh is added to the battery in an hour.
    My spreadsheet shows the peak miles per 24 hours comes at 100mph. At 100mph you consume 62kW to cruise and spend 59% of time driving and 41% charging. Over the 24 hour period you go 1421 miles.
    Since you get to start full and end empty you get 1477 miles instead because you spend 22.63 hours doing the cycling, and the 1.37 hours driving 100mph until the battery is dead. ( Of course the car wont really let you go 100mph when the battery is near dead, so the real result would be slightly less )


    Having a real transistion cost and acceleration cost would push the "best" mph down, because fewer transitions are better.
    I bet a real world number is closer to 1330 miles at 70mph with 30 minutes wasted in 5 driving-charging-driving transitions. At 70mph you get 1366 theoretical miles, with 18.98 hours driving and 5.02 hours charging.
     
  5. Ben W

    Ben W P85 #61, Roadster #108

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    #5 Ben W, Apr 10, 2013
    Last edited: Apr 10, 2013
    This is a decent rule of thumb, but not necessarily exact. For instance, if you're charging off super-slow 110v/12a (1.3kW), which takes 4 days to charge, your ideal speed will still be about 25mph, which drains about 5kW continuous while driving. The "sweet spot" is rather the speed at which going one extra mile per hour "breaks even" as far as extra recharge time required.

    Breaking out the math: let's define the function p(v) to be the power (in kW) required to maintain velocity v in MPH.

    Then assuming 90kW continuous supercharge, superchargers 90 miles apart (becaues it makes the math work out cleaner), and no overhead time for stopping to plug in, the "cycle time" t(v) from leaving one supercharger to leaving the next supercharger can be calculated as:

    t(v) = (time spent driving) + (time spent charging) = (90 / v) + ((p(v) / 90) * (90 / v)) = (90 + p(v)) / v.

    Using calculus (yes we're going there) to solve this equation, we want to set the derivative of the function t(v) equal to zero:

    t'(v)= p'(v) / v - (90 + p(v)) / v^2 = (v * p'(v) - 90 - p(v)) / v^2 = 0.

    From here, we can simply crunch the power vs speed data to find the approximate speed v for which this is true.

    For the Roadster, I found this graph: http://kilowatt-age.com/yahoo_site_admin/assets/images/image003.323212833_std.jpg

    and let's assume the Model S uses 25% more power than the Roadster at any given speed.

    So from the graph, we can eyeball some data points:

    70mph: Wh/mi = 300 * 1.25 = 375, continuous power p(70mph) = 375 * 70 = 26.25 kW
    80mph: Wh/mi = 360 * 1.25 = 450, continuous power p(80mph) = 450 * 80 = 36 kW
    90mph: Wh/mi = 425 * 1.25 = 530, continuous power p(90mph) = 530 * 90 = 47.7 kW
    100mph: Wh/mi = 500 * 1.25 = 625, continuous power p(100mph) = 625 * 100 = 62.5 kW
    110mph: Wh/mi = 570 * 1.25 = 712, continuous power p(110mph) = 712 * 110 = 78.3 kW
    120mph: Wh/mi = 660 * 1.25 = 825, continuous power p(120mph) = 825 * 120 = 99 kW

    and from these numbers we can numerically approximate p'(v), which is simply the marginal increased power required to go one extra mph:

    p'(80mph) ~= (p(90) - p(70)) / 20 = 1.073 kW / MPH
    p'(90mph) ~= (p(100) - p(80)) / 20 = 1.325 kW / MPH
    p'(100mph) ~= (p(110) - p(90)) / 20 = 1.53 kW / MPH
    p'(110mph) ~= (p(120) - p(100)) / 20 = 1.825 kW / MPH

    So recalling that t'(v) = (v * p'(v) - 90 - p(v)) / v^2, we can plug these in and calculate:

    t'(80mph) = (80 * 1.073 - 90 - 36) / 6400 = -0.00628
    t'(90mph) = (90 * 1.325 - 90 - 47.7) / 8100 = -0.00228
    t'(100mph) = (100 * 1.53 - 90 - 62.5) / 10000 = 0.00005
    t'(110mph) = (110 * 1.825 - 90 - 78.3) / 12100 = 0.00268

    and we have our clear winner: 100mph is extremely close to optimal. (Drat, I so wanted it to be 88mph!)

    The t'(v) calculations above can be interpreted as "number of hours saved for each drive/charge cycle for a 1mph increase in speed", so e.g. at 80mph, you can calculate that driving an extra 1mph faster would save you 0.00628 hours = 23 seconds per drive/charge cycle. However, increasing your speed from 110mph to 111mph would penalize you 0.00268 hours = 10 seconds per cycle. What's your time worth? ;)

    The continuous power draw at 100mph is roughly 62.5kW, which means that for optimal cross-country speed, you'll spend about 60% of your time driving and about 40% charging.

    By comparison, I had similarly calculated a few years ago that the "sweet spot" for the Roadster, using 17kW charging (70a/240v), was about 55mph.

    Someone check my arithmetic?
     
  6. stevezzzz

    stevezzzz R;SigS;P85D;SigX

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    Thanks, richkae and BenW; very cool that you approached the problem differently yet your numbers are in close agreement. It's interesting that the optimum speed of 100 mph is lower than my glider rule of thumb would predict (between 110 and 120 mph). Another rule of thumb from glider cross-country flying is that cruising between thermals (charging stops) at 10 knots below the optimum speed is much less detrimental to your average cross-country speed than going 10 knots too fast.

    Of course, the fastest cross-country speeds in glider flying are achieved not in classic thermal soaring (where you stop and circle in thermals to gain altitude) but by finding 'streets' of lift that allow you to gain altitude (recharge) while flying in a straight line, making progress in the direction of your goal. Can you say "inductive charging while driving"? :biggrin:
     
  7. vfx

    vfx Well-Known Member

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    Would it be possible to do this on a track?
     
  8. Banahogg

    Banahogg Member

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    Only if the track had a supercharger on it. Plus, I think it'd be cooler to do break the record "in the wild" rather than on a closed track.

    I'll have to read through the arithmetic posts in more detail when I have a minute...
     
  9. ggr

    ggr Roadster R80 537, SigS P85 29

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    Even though my company is working on inductive charging, I'm not a big believer in charging while driving. I think if you're going to wire up all the roads anyway, you might as well just push the cars directly... linear accelerators.
     
  10. drbradfo

    drbradfo Member

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    I believe the Fremont factory has a track and a supercharger near it. :)
     
  11. richkae

    richkae VIN587

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    What about a hybrid system where the roads are wired for inductive charging and a small battery in the car.
    You put wires only on the main roads and highways, and your battery allows you to leave the main road and venture onto side roads. Your battery size determines how far you can go from a main road.
    If you could charge ridiculously fast, then you would put charge stripes on the road that are as long as you need to fully charge the car as it passes over. Then you put them every few miles and at every on and offramp.
     
  12. wraithnot

    wraithnot Model S VIN #5785

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    Here is my crude, back of the envelope calculation of how far I'd be able to go if you drove as I have on previous road trips and there was an ideal placement of superchargers:

    With a full range charge, I get 270 miles of rated range. Driving at approximately 75 mph, I tend to get almost exactly 80% of rated range (216 miles of actual range). If I drove the car to near empty, I should be able to get a half charge (108 miles of actual range at 75 mph) in 30 minutes. The part would get 216 miles and take 2.88 hours. Each additional cycle would cover 108 miles and take 1.44 hours + 0.5 hours = 1.94 hours. The last leg would end once 24 hours was reached.

    cycle miles hours
    0 216.00 2.88
    1 324.00 4.82
    2 432.00 6.76
    3 540.00 8.70
    4 648.00 10.64
    5 756.00 12.58
    6 864.00 14.52
    7 972.00 16.46
    8 1080.00 18.40
    9 1188.00 20.34
    10 1296.00 22.28
    11 1387.50 24.00
    So at the end of 24 hours, I'd be able to go about 1,390 miles. Although in real life I wouldn't want to run the battery down quite this much, transitions between charging and 75 mph would take a few minutes, and supercharger placement isn't ideal. Perhaps I'll try a silly road trip like this the next time my wife is out of town :)

    But seeing how close an EV can get to the "Cannonball run" New York to LA record of 31 hours and 4 minutes (The Pedal-to-the-Metal, Totally Illegal, Cross-Country Sprint for Glory ) would be a much better test of how close EVs are getting to gasoline powered cars! Once they build out the supercharger network, something like 48 hours in a model S should be possible without breaking too many traffic laws . . .
     
  13. Tesla 940

    Tesla 940 Member

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    I'm far more interested in considering the logistics of this type of attempt today. Harris Ranch / Teton Ranch isn't ideal because of the potential for strong winds and the 4K climb / descent. If I were to attempt this here is what I would want:

    1. Acknowledgement from Tesla of the attempt so that I could "rope off" one or even two of the SCs at each location 30 - 45 minutes before the car is expected to arrive. Roping off two would ensure that at least one is working when the car actually arrives.
    2. At least one person at each location for the duration of the attempt. One advantage is that the person could be connecting the charge cord before the driver even exits the car. Other duties would include explaining the attempt to people wondering why the SCs are not available, monitoring traffic in the area.
    3. At least two drivers.
    4. Perform a few trial runs so I know what real life energy usage is in each direction and at various speeds.
    5. Monitor weather conditions to avoid heat (100+), cold, and wind - probably either Spring or Fall.
    6. Research traffic patterns to determine the least crowded time of the week/year. Especially truck traffic.
    7. Radar detectors.
    8. Food/rest rooms shouldn't be a problem - everyone just needs realize that charging times will be short and every second counts.
    9. Monitor traffic in/out of the SC areas to avoid unnecessary delays getting back onto I5 (not behind a truck).

    What did I miss?
     
  14. Johan

    Johan Took a TSLA bear test. Came back negative.

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    Having fun doing it? :)

    Np really you seem to have thought of most things. I would consider bringing a spare wheel.
     
  15. Tesla 940

    Tesla 940 Member

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    I thought about that but if you get a flat any chance of setting a new record is over.
     
  16. Zextraterrestrial

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    make sue you get the 2 spots that share superchargers so you're not sharing power ever
     
  17. Banahogg

    Banahogg Member

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    Tejon is on the north side of the grapevine, so you don't do the full climb. Tejon is about at 1k feet, which isn't ideal, but probably as good as you're going to get outside of FL :)

    The fact that they superchargers are close together is a good thing since most of the charging will happen in the faster bottom half of the battery.

    From looking at Average Weather For Lemoore, California, USA - WeatherSpark (closest station to Coalinga), the average wind down at the bottom doesn't look too bad, though I agree that there are definitely some windy days out on I-5.
     
  18. wraithnot

    wraithnot Model S VIN #5785

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    If someone really wants to take a serious shot at the record, I'm sure they could crowd source a bunch of helpers. If you could recruit two Model S owners at each supercharger location you plan to use, they could occupy a pair of superchargers with their cars whenever you get near and then unplug and move one of the cars right as the driver attempting the record pulls up. A simple sign in the back window of each occupying car that says something like "Reserved for EV range world record attempt- follow us on twitter @EV_Range_Record" would both keep people from getting too pissed off and generate some excitement about the attempt.

    A couple of practice runs between each supercharger location to gather data before the attempt would probably be needed to make sure any given plan would have a good chance of working.
     
  19. Thumper

    Thumper Member

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    But we know 120 kw is on the way. How does that compute?
     
  20. Ben W

    Ben W P85 #61, Roadster #108

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    Redoing my calculations based on a 120kW charger, the optimal speed increases to about 109mph. Of course, these calculations ignore charging losses, which have to be factored in. Assuming the 120kW charger actually delivers 100kW of usable energy into the batteries (and 20kW is lost as heat), then the optimal speed decreases to about 103mph. (And the optimal speed with 90kW chargers, delivering ~75kW of usable charge, decreases to about 95mph.)
     

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