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Consumption and efficiency differences climbing various grades

Discussion in 'Model X: Driving Dynamics' started by ohmman, Dec 5, 2016.

  1. ohmman

    ohmman Maximum Plaid Member

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    In @JimVandegriff's excellent trailer-pulling report, we noted a climb that seemed to defy the standards of consumption. That is, we noticed that, according to Jim's records, he seemed to consume more energy climbing a steep grade than he did climbing similar elevations on a more shallow grade.

    The question was raised (by me) whether a nominal unit of climb (let's call it 1000ft) could cost more in terms of consumption depending on the percentage grade.

    @ecarfan points out that the actual physics of motion seem to support the inverse. Since there is less rolling resistance to climb 1000 feet over a shorter distance, it seems like one would do better. @vandacca points out that it may have to do with efficiencies related to torque or heat created by the work being done.

    I thought it would be useful to split out and discuss separately. My recollection tells me that AC induction motors are actually most efficient at full load, so that would remove the motor from the equation. I believe @ecarfan has it right with regards to the actual physics of moving an object. There's a horizontal and vertical component. What about battery discharge efficiency? Does anyone want to chime in about that?
     
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  2. cpa

    cpa Active Member

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    Ohmman, since I know ZERO about these sorts of things, let me throw some softballs out there to all the physicists:

    I do not believe that all grades are equal. Highways undulate. Some grades are mostly straight and others have lots of curves. Many of the curves are banked. Many roads have multiple lanes for ascent along these curves. Temperatures affect air density which affects the amount of energy used. Clearly to me these are variables that would affect the amount of energy needed to climb a given distance.

    Would not these variables affect the energy needed to climb an X% grade over Y miles?
     
  3. Saghost

    Saghost Active Member

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    I'm not sure I've seen enough data to make an assessment. I would tend to agree that the physics suggest more efficiency on steeper hills, not less.

    I am pretty sure there's a misunderstanding going on, though - the 20 miles climbing and only 35 remaining is connected with reporting ~1.75 kWh/mile in the worst cases.

    That would mean ~80 usable kWh would give you ~45 miles, and that 20 actual miles of climbing in that worst case would eat up 35 kWh at most - maybe a hundred rated miles not the 220+ you thought he was reporting.

    I'm pretty sure that the "35 miles remaining" is either instant or predicted average for some increment off of the energy screen if he kept climbing the hill, not rated miles.
     
  4. ohmman

    ohmman Maximum Plaid Member

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    I agree, grades are not equal. Switchbacks could really hit the consumption if you have to slow to a near stop, then accelerate out of them repeatedly. Also, most grades have both ups and downs on the eventual way up. So you may climb more for the net elevation gain. I was trying to isolate for that by charting his grade, which appears to be nearly straight up. But it doesn't tell me anything about switchbacks.

    Yes, I have continued to wonder if there wasn't some typo or accidental misrecording on that segment. Jim has done such a great job recording and sharing, I didn't want to call him out on it. But it would give me a lot more confidence in getting an Airstream if that were the case.
     
  5. aesculus

    aesculus Still Trying to Figure this All Out

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    Was the speed the same in both cases?

    W = mgvt sin(θ)

    Assuming gravity and the mass of the vehicle did not change you are left with the speed (v), the amount of time (t) or the slope (θ) that makes one energy consumption different than the other. And in the case of time and speed, wind and rolling resistance will have different effects.

    This is an interesting article from a cyclists perspective:

    Gradients and cycling: how much harder are steeper climbs?
     
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  6. Saghost

    Saghost Active Member

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    That's only the loads side. You also have to look at the car side - motor efficiency vs power/torque @ speed, losses in wiring, battery voltage sag, etc.
     
  7. polymathic

    polymathic Member

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    With no math or physics, as someone who puts more miles on his bike than on his car in a give year, I can tell you that the steeper it gets, the more energy it takes. A long gradual climb takes less energy than a short steep one.
     
  8. ecarfan

    ecarfan Well-Known Member

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    If your description of how much energy is required to climb a steep grade compared to a more gentle grade is based on your cycling experience, my opinion is that your subjective evaluation does not apply to the physics of powering a vehicle.
     
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  9. David99

    David99 Active Member

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    Speed is a very important part. Air drag makes up the largest part of the energy consumption at highway speeds. Pulling a trailer air drag becomes an even larger part. So without having read through the other discussions, if the driving speed on the two drives was different, that would have to be considered.

    One other factor is the ohmic losses. Double the power from the drive train causes 4 times the ohmic losses. Since the steeper drive requires a higher power, the losses are much higher.
     
  10. ohmman

    ohmman Maximum Plaid Member

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    Ohmman wants to hear more about these ohmic losses. I can't see a way to quantify them - any ideas? It doesn't look like they're likely to be a very big part of the puzzle, from what I can tell, but it does look interesting.
     
  11. JimVandegriff

    JimVandegriff Member

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    Calling Jim out is warranted! I did not keep the notes I was taking that day on the ascent of the 4th of July pass. I do remember I kept writing down higher and higher consumption numbers as we ascended, and the 35 miles remaining was exactly as Saghost suggested - a projection of current consumption numbers applied to the continuation of the trip. But what is interesting to me is that the mileage we drove that day ended up averaging 660 wh/m despite the 1.75 Kwh/m at the summit. My general experience was that we had more range possible than I thought we would have (especially with dry road conditions.)
    I'm going to keep better track of consumption and other factors on our next trip (starting in March.)
     
  12. David99

    David99 Active Member

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    Without going into too much detail, electricity is measured in Volt and Ampere, the two aspects of electricity. Power (Watt) is the product of Volt * Ampere. So for example the Model S/X battery has 360 Volt. Let's say we drive with 20 kW power, that means at 360 Volt there is 55 Ampere. 360 * 55 = 20 kW. Ohmic losses depend only on Ampere, not Volt. If you now need 40 kW, you need twice the Ampere which causes 4 times the ohmic losses. at 80 kW we have 16 times the losses and so on. Overall the losses are pretty small, but you can see that as you need a lot of power the losses go up dramatically. What makes it even worse, as you pull more power out of the battery, the voltage drops. That's just how batteries work. The more you make them work, the more the voltage drops. At full acceleration, the voltage drops under 300 Volt. To get the power the battery now has to deliver a higher Ampere number which causes even more losses.

    The voltage also drops with lower state of charge. So as the battery is more empty your losses are higher.
     
  13. ecarfan

    ecarfan Well-Known Member

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    David, thanks for your post. It seems to me the key is to quantify the ohmic loss for the kW draw at freeway speed on a level road and then we get a sense of how much it will be on a steep grade.

    It is not yet clear to me if ohmic losses are a significant factor when calculating energy usage on a 10% grade vs. a 5% grade, for example (assuming everything else being equal during the two drives).
     
  14. ohmman

    ohmman Maximum Plaid Member

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    The quantification is the difficult part for me as well, though I do thank David for the bird's eye view. I remember most of the electrical relationships from my physics courses in college, but don't recall covering ohmic loss. Of course, that was decades ago.

    Anyway, it seems that Jim has let us know the data may be suspect to start. The 35 miles of range remaining were the consumption app's estimate based on current usage, not the range remaining in the battery. Phew!

    I do think this is something to keep an eye on. I log my telemetry locally, and will try to find some similar roads with steeper grades, and control for temperature, speed, etc. If nothing else, it'll be an interesting exercise.
     
  15. cpa

    cpa Active Member

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    You have plenty of roads in your immediate area to make your observations and record your data, Ohmman. You can snake your way into Lake County from Calistoga. You can take the back door to Lake County up SR16 west of Woodland and then go west on SR20. If you want some steeper grades, try SR108 or SR 4 (both now closed for winter) across the Sierra. I believe that the grade on 108 east of Sonora Pass is up to 26%. Highway 4 is fun as it is about 1 1/2 lanes for 20 miles or so. I drove SR4 this past May twelve hours after CalTrans reopened the highway for summer travel. Even saw a Chippie going the other way!

    Driving north on 395 from Bishop, there is Sherwin Summit south of Mammoth Lakes Junction and Conway Summit north of the Lundy Lake turnoff. The climb up Sherwin is straight and steady while the climb up Conway is sweeping and steady. I do not believe that there are any descents with either of these climbs.
     
  16. David99

    David99 Active Member

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    That's where it gets difficult. I don't have any numbers from the Model S/X that could be used to make estimates. I know the car does report motor/inverter efficiency on the CAN bus, but I don't have access to it. It would be pretty straight forward if we had access to this data and driving in different conditions and see how it affect efficiency. One other factor I just thought of is the active cooling. When the battery reaches a certain temperature, active cooling kicks in. It's basically an AC dedicated to cool the battery. This would take up additional energy which brings down overall efficiency as well. Passive cooling might just be enough to go up a small incline, but active cooling might be needed for climbing a steeper road.
     
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  17. EV-lutioin

    EV-lutioin Active Member

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    Ohmic loss.... ohms or resistance due to heating presumably from the increased load caused by steeper grades. I love all this physics talk. Keep it going boys (and girls)!
     
  18. Saxman

    Saxman Member

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    I totally agree with you.

    I'm a road cyclist in the Colorado mountains and can more easily climb a 5 mile 6% grade than a 2 mile 10% grade.
     
  19. ohmman

    ohmman Maximum Plaid Member

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    I feel that this is less about the mechanics of the slope and more about the human ability to output higher power. Since humans and Teslas manage power output differently, I'm not sure it's a valid point of reference.

    All that said, I do love tackling a good climb. :)
     
  20. landis

    landis Member

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    It's not the point of reference but the principle.

    The mistake of the early posts in this thread was assumption of idealized physics environment (i.e. spheres on frictionless surfaces.)
    Reminded by the 'Bing Bang Theory' episode with Physics seminar/jokes on idealized spheres I saw rerun last night.

    It is reasonable to assume a very steep climb also puts the car in a different range with more heat losses as suggested up thread.

    I only have a B.S. in physics and math from almost forty years ago so I am not claiming any expertise here. ;-)

    (I would affirm posts up thread that attribute most of the 'surprise drop' with the estimated range based on recently traveled miles.)

    It would be very interesting to have some data points once (for both estimated range and remaining capacity in %) every 30 seconds for 5 minutes or so before and after cresting the peak.
     

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