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Energy density and range calculation Electric Vehicle

  1. Feb 12, 2013 #1
    I want to calculate the range of an Electric Vehicle (EV) with a Li-ion battery of 200 Wh/kg.

    Parameters
    v= 50 km/h = 14 m/s
    A= 0.8 m2
    d = 500 m
    efficiency = η= 85%
    mc = 900 kg incl. 100 kg battery
    ρ = 1.3 kg/m3

    First I have calculated the power of the EV with a speed of 50 km/h and 100 kg battery.

    Power car= 1/2η [m v^3/d+ρAv^3 ]=1/(2×0.85) [1000×〖14〗^3/500+ 1.3 ×0.8×〖14〗^3 ]

    Power car = 4.91 kW


    Energy density battery = 200 Wh/kg. With a 100 kg = 20 kWh

    Driving time on a full charge (hours)=(power of battery (kWh))/(power of car (kW))=20/4.91= 4.07 hours

    Range (km)=Speed (km⁄h)×time (h)= 50 ×4.07 = 204 km

    Is this correct? I am not sure if you can divide the power of battery with power of car.
     
  2. jcsd
  3. Feb 12, 2013 #2

    SteamKing

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Looks good.
     
  4. Feb 12, 2013 #3
    Re: HELP! Energy density and range calculation Electric Vehicle

    Well, the problem is that if I do the same calculation with a 200 kg of battery (mass car is then 1100) then the range would be less. I don't think that this is correct, the range should be more of course.
     
  5. Feb 12, 2013 #4

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Where does 500m come from? You appear to have calculated the average power needed to go from rest to 50k/h over some negligible distance, then maintain speed for 500m. How does that equate to the power needed over the whole driving range? Is the assumption that you will have to stop on average every 500m?
    You gave car mass as 900kg including 100kg battery, but you've added the battery weight on to get 1000kg.
    Are you sure? Try getting the general algebraic expression before plugging any numbers in.
     
  6. Feb 13, 2013 #5

    SteamKing

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    Re: HELP! Energy density and range calculation Electric Vehicle

    If the original mass of the car was 900 kg including the 100 kg battery, how can putting in a 200 kg battery (in place of the 100 kg battery) make the car's mass 1100 kg?
     
  7. Feb 13, 2013 #6
    Re: HELP! Energy density and range calculation Electric Vehicle

    The 500m is the distance between two stops. This is very common in the city. The car that I am talking about drives only in the city and you need to stop every 500m (traffic).
    The mass of the car is 900 kg and 100 kg battery (thus 1000 kg). If the battery is 200 kg the total mass will be 1100 kg. In the calculation I have done it correct, but in the given parameters it is not correct.

    There is something about this calculation that is not correct. But I can't quite figure out what the problem is. If the car stops every 500m there is a lot of energy lost due to braking, but how then can you drive about 200 km (calculated)?

    Thank you, I hope it is clear what I have done.
     
  8. Feb 13, 2013 #7

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    You seem to be taking the drag coefficient as 1, whereas at http://en.wikipedia.org/wiki/Drag_(physics)#Drag_at_high_velocity it says .25 to .45. Using your numbers (including 14m/s instead of 50kph) in a spreadsheet I get the same result as you for 100kg of battery, but when I change it to 200kg I get a range of 385km. That seems reasonable in proportion.
    Putting in a drag coefft of .35, and an exact 50kph, the range (for 100kg battery) increases to 268km. On top of that, you're taking the driving pattern to be full speed or nothing. Allowing for likely patterns of acceleration and deceleration might add 5%.
    So I can't find a good reason to say you're overestimating the range.
     
    Last edited: Feb 13, 2013
  9. Feb 13, 2013 #8
    Re: HELP! Energy density and range calculation Electric Vehicle

    I understand the calculation errors you've mentioned above, I have corrected for that. But I don't get more range for more kg battery.
    If you look at the formula's more mass of car means more power needed and therefore less range, because the driving time will be less (and thus less distance).
     
  10. Feb 13, 2013 #9

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    That's not the result I get, using your formula. Pls post your working for that case.
     
  11. Feb 13, 2013 #10
    Re: HELP! Energy density and range calculation Electric Vehicle

    Could not insert table.
     
    Last edited: Feb 13, 2013
  12. Feb 13, 2013 #11
    Re: HELP! Energy density and range calculation Electric Vehicle

    Here is the table with the parameters (the parameters are OK, they are not the problem).

    v= 50 km/h = 14 m/s
    Effective area = C(d)A= 1 m2
    d = 500 m
    efficiency = η= 85%
    mc = 1000 kg (100kg battery) or 1100 kg (200 kg battery)
    ρ = 1.3 kg/m3

    100 kg battery (total mass 1000kg):

    power car (kW) 5,33
    time (h) 3,75
    range (km) 187,74


    Formula's:

    Power (kW): ((1/(2*0,85))*(1000*(14^3/500)+1,3*1*14^3))/1000
    Time (h) = 20/5,33
    Range (km) = 3,75 * 50

    For the 200 kg (total mass 1100kg) battery I get these answers:

    power car (kW) 5,65
    time (h) 3,54
    range (km) 177,01
     
    Last edited: Feb 13, 2013
  13. Feb 13, 2013 #12

    CWatters

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Can you explain how you arrived at that equation?

    0.5 ρ Av^3 looks like the instantaneous drag in Watts. However you can't just set v=50kph because the car is accelerating? Means V and hence drag isn't constant.

    0.5 m v^3/d looks like KE / time ? eg 0.5mv^2 * v/d. Which again looks wrong because the velocity isn't constant.

    I think you need to plot a graph of velocity v time for the 500m segment and integrate it to get the energy consumed. If we call that E500 (in Joules). Then

    Range = 500 * Battery Capacity (in Joules) /E500

    PS: You don't say how fast the car accelerates to 50kph and that will certainly alter the average speed and power consumption....just as it does for a gas car.
     
  14. Feb 13, 2013 #13

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Bianca's model considers that the car cruises at a steady 50kph for 500m intervals. The acceleration and deceleration stages in each interval are presumed unimportant. My estimate is they'll not make more than a 5% difference to the answer.
     
  15. Feb 13, 2013 #14

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Yes, but I don't, and I keep asking you to post your working that gets those answers.
    Here's from my spreadsheet:
    Code (Text):

    Var Item            Units   Formula sc 1    sc 2
    eta efficiency                          0.85    0.85
    mc  car mass        kg              900 900
    mb  battery mass    kg              100 200
    k   energy density  J/g             720 720
    A   x area          m2              0.8 0.8
    rho air density     kg/m3               1.3 1.3
    v   cruise          m/s             14  14
    c   drag coeff                      1   1
    d   drag            W   c*v^3*rho*A/2   1426.88 1426.88
    s   cruise dist     m               500 500
    ec  energy/cruise   J   (mc+mb)*v^2/2   98000   107800
    p   power demand    W   (ec*v/s+d)/eta  4907    5230
    t   range time      s   mb*k/p      14673   27535
        range           m   t*v             205424  385488
     
     
  16. Feb 14, 2013 #15

    CWatters

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    Re: HELP! Energy density and range calculation Electric Vehicle

    In which case what does this term represent in his equation?

    0.5 m v^3/d
     
  17. Feb 14, 2013 #16

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Average power. d = interval distance = 500m. KE generated then lost over each 500m interval (.5 mv2) / time of each interval (d/v) = mv3/2d.
     
  18. Feb 14, 2013 #17

    CWatters

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    Re: HELP! Energy density and range calculation Electric Vehicle

    Edited:

    Humm ok I think I understand. He's including the energy needed to accelerate from 0-50 every 500m BUT he's assuming that it gets to 50 so quickly that for most of the distance it's doing close to 50?
     
    Last edited: Feb 14, 2013
  19. Feb 14, 2013 #18

    haruspex

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    Re: HELP! Energy density and range calculation Electric Vehicle

    That's my understanding; and, correspondingly, coming to a sudden stop at the end of each 500m.
    The main issue in the post is that the calculated range seemed to go down when the battery size was increased. Using the same data and equations, I was not able to reproduce that, but I don't seem to be able to get Bianca to post the details of the second calculation.
     
  20. Feb 15, 2013 #19

    CWatters

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    His equation shows both power consumption and battery capacity are proportional to mass so not possible for range to go down.

    Only way for it to go down would be if power consumption was proportional to mass squared or something like that.
     
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