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Charge required to climb 1000 feet

Discussion in 'Model S: Battery & Charging' started by derekt75, Jan 23, 2013.

  1. derekt75

    derekt75 Member

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    To get from home to work, I spend about 10 miles on a freeway with a gradual 200 foot elevation gain. Gaining 20 feet per mile seems somewhat inconsequential, and yet I draw about 400 Wh/mile on the freeway on my way to work, and about 300 Wh/mile on the freeway on my way home. It got me to thinking about how much energy it takes to go up or down a hill.

    2110 kg * 9.8 m/s[SUP]2[/SUP] * (1 hr / 3600 s) * (1 m / 3.28 ft) = 1.75 W∙h / ft

    So for every 1000' you climb, you should burn at least 1.75 kWh.
    Equivalently, a 1000' climb should cost about 6 miles of rated range.


    In my case, the 20' per mile should cost me about 25 Wh/mile on the way up and give me about 25 Wh/mile on the way down, but that only seems to account for half of the difference that I see emprically. It's usually colder on my way to work than on my way home, so that might account for some more of the difference.

    Anyway, I thought others might be interested in the math.

    Derek
     
  2. Zextraterrestrial

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    When I did my last roadtrip I tried to slow down a bit on the up hills and crest the top traveling as slow as comfortable ~ 50-55, with no traffic behind. On the down hills I'd hold the accel on just enough to have no power draw and coast down hill until I hit a speed that was too fast for the law then use a little regen but only when it was necessary. That seems to improve hilly driving quite a lot. - you can never get better energy use using regen while going down a hill than coasting down
    It will piss people off though if you have traffic around! The S has some amazing coasting capabilities...try N sometime on a hill
     
  3. vfx

    vfx Well-Known Member

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    I do 2000 foot Roadster climb that measures out at 9 miles. I loose 6 going up, using 15 miles, and gain 4 going down using 5 miles- rarely drive that one for economy, either way.
     
  4. derekt75

    derekt75 Member

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    The Roadster weighs only 1200 kg, though, so it should need less energy to climb a hill. Instead of 3.5 kWh for a 2000' climb, it should only need 2 kWh.
     
  5. ChadS

    ChadS Petroleum is for sissies

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    I just took a 3,000 mile trip that went over many passes. The numbers I was using for planning were 7 miles used for every 1,000 feet of elevation gain, and 4 miles gained on the way back down. Seemed to work pretty darn good, although I wasn't taking precise measurements and of course all sorts of things varied - temperature, wind, road conditions, etc.

    Zex, I agree that coasting is theoretically more efficient than regen. But in addition to the problem you noted of possibly going way too fast, there is also wind drag. At some point you're better off using regen than losing energy due to wind drag, although I'm not up to the math (and also don't have enough data about the car, like regen efficiency) to figure out just where that point is.

    Even if you don't put the car in neutral to fully coast, by holding down the accelerator to maintain a desired speed, you use regen where desired, and even if not full coasting you are partly coasting and using less energy to cover the miles, so you get some of the miles back without an energy conversion penalty. But as long as there is regen and/or wind drag, you won't get all of the miles back.
     
  6. jomo25

    jomo25 P4398

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    Yes, my Roadster-owning friend says that his experience matches the theoretical calculation as you have it. Of course all other factors (temp, drive style, etc all make a difference too) but all things being equal, the calculation works for estimation purposes.

    And you will never get 100% back in regen downhill what you take out for climbs.

    Finally, don't forget to add the weight of people and cargo in your weight variable.
     
  7. derekt75

    derekt75 Member

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    Good point. That would make it slightly higher than 1.8 W∙h/ft for me.
     
  8. Zextraterrestrial

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    I think the drag gets 'bad' above 55 mph but the car will coast really fast on a long 6-7% grade maybe to 90mph or more even. It would be neat to figure out where optimized efficiency is. I have a almost perfectly graded hill to the north of me (7% I think & ~ 5 miles) that I might get up to someday to try but I should contact CHP first. (and I can maybe get an accurate profile of it too)

    I still think you are better off not using regen at all down a hill if you can. but you will 'obviously' get better range if you are traveling slower. Ideally crest a hill at ~ 0mph and completely roll down the other side.
     
  9. gregincal

    gregincal Active Member

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    Yes, but going over a mountain pass that technique doesn't work so well. The first 10 miles of my commute has a 1800 foot elevation gain, and the next 10 miles goes down the same amount. I don't quite have my car yet, but I'm going to be interested to see what the wH/m is. The speed limit is 50mph, so that should help. The last 10 miles is 65mph level (usually drive 70), so the question is whether going over the hill or driving on the freeway consumes more energy.
     
  10. Palomarbob

    Palomarbob New Member

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    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Max range or efficiency is at about ~ 20 mph
    so crest hills at ~ 20 mph
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     
  11. smorgasbord

    smorgasbord Active Member

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    I had started another thread that I'm too lazy to dig up, but the consensus is that regen is more efficient than going fast down long hills. You burn off more energy going 75 versus 35 than you lose using regen at 35.

    ICE/Hybrids have a different efficiency profile than EVs.
     
  12. ThortsMD

    ThortsMD Member

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    Last week I traveled from Steven's Pass, WA (elevation 4019) to Seattle. Along the way (steeply) downhill, I gained rated miles and only reached my the initial rated miles I left the pass with 38 miles (at Startup, at 604 ft elevation) later. I traveled in cool (45-ish) temps and dry pavement and (mostly) at the posted speed limit (varied between 45 and 60, up to 75 in the steepest fun parts).

    My surprising experience suggests that if you have a steep grade and work the pedal well, you should be able to do well with the regen.
     
  13. pnaecker

    pnaecker Member

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    You neglected efficiency. Figure the output is about 90% efficient (hopefully). So you will at most get .9 of this figure, or about 2 kWhr per thousand feet, which is about 7 range miles per thousand feet of climb. Other folks have measured something closer to 12 range miles per thousand.
     

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