Air density, temperature, and range

I've noticed that there seems to be a common assumption that the only effect of cold weather on range has to do with reduced battery capacity as it gets colder plus increased heater use. However, there are other effects of cold temperatures on the mileage efficiency and range of an EV (or any other car):

•Increased aerodynamic drag due to increased air density
•Increased rolling resistance due to cold tires and gear/bearing lubrication

While I can't begin to calculate the increased rolling resistance due to cold, the air density calculations are straightforward. My tables below show the air density at various temperatures and humidity. As you would expect, increased air density increases drag and reduces mileage efficiency and range.

A factor that explains why those of us who live at high altitude get better gas and EV mileage is the reduced density of air with increased elevation:
[Bear in mind that as one goes up in elevation the temperature tends to decrease, increasing the air density somewhat. A temperature of 20ºC at 11,000 feet would be unusual, for example. So it isn't quite as simple as my table suggests. I use the example of density versus altitude at a fixed temperature and humidity to strip out the complicating factors usually present in density altitude calculations.]


The calculator I used to generate these figures may not agree precisely with other sources. However the purpose of the exercise is to show the relative difference in air density with changes in temperature or elevation and to point out that it is a significant factor in EV range.

dgpcolorado said:

Bear in mind that as one goes up in elevation the temperature tends to decrease, increasing the air density somewhat. A temperature of 20ºC at 11,000 feet would be unusual, for example. So it isn't quite as simple as my table suggests. I use the example of density versus altitude at a fixed temperature and humidity to strip out the complicating factors usually present in density altitude calculations.

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Of course, if the air density ever increased with height, the atmosphere would quickly (and sometimes rather violently) correct that.

As a general rule, air density decreases with height.

Weatherman said:

Of course, if the air density ever increased with height, the atmosphere would quickly (and sometimes rather violently) correct that.

As a general rule, air density decreases with height.

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I was referring to the fact that decreased temperature increases density somewhat from my simplified calculations. Overall air density decreases with elevation as you say, although anomalies, such as inversion layers, do occur at times. And cold, dense air in thunderstorms leads to microbursts, which can be quite violent as you suggest.

dgpcolorado said:

I've noticed that there seems to be a common assumption that the only effect of cold weather on range has to do with reduced battery capacity as it gets colder plus increased heater use.

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I'm not sure why you say this. I have considered and compensated for air density from the first range charts. The LEAF Energy app calculates air density and makes corrections (it actually averages the the highest and lowest elevations of the journey and makes a air density calculation based on that average elevation).

dgpcolorado said:

As you would expect, increased air density increases drag and reduces mileage efficiency and range.

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Agreed. But I will point out that a 10% increase in the force of drag induced by the air does NOT result in a 10% reduction in range UNLESS the air friction is the only or very dominant loss in the equation. It may be at high speeds, but at low speeds, other losses may comprise a large fraction or may even be dominant.

For instance, if air friction comprises about 50% of the energy loss at a particular speed, a 10% increase in the force of friction will result in about a 5% loss of range (not exactly, but close enough for our purposes).

RegGuheert said:

For instance, if air friction comprises about 50% of the energy loss at a particular speed, a 10% increase in the force of friction will result in about a 5% loss of range (not exactly, but close enough for our purposes).

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For an EV it is a significantly higher fraction of the overall 'losses' because there are few zero-load losses in an EV.

FWIW: It is not 'friction' with the air that is the issue. I expect that is negligible at highway speeds. Aerodynamic drag on a vehicle is simply due to the volume of air it has to push out of the way, at the speed it is pushing through the air at. That's why aero-drag power is approx a cubic function of velocity - it's the product of the kinetic energy of the air that is being accelerated as it is pushed out of the way, and the volume of air that the vehicle is displacing over a given time interval.

TonyWilliams said:

I'm not sure why you say this. I have considered and compensated for air density from the first range charts. The LEAF Energy app calculates air density and makes corrections (it actually averages the the highest and lowest elevations of the journey and makes a air density calculation based on that average elevation).

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I was referring to some recent posts that were mulling over the coming cold weather and its effect on range. They generally seem to ignore cold air and drag. I know that you understand this — all pilots do — and that it is well understood by old-timers here. But I wanted to remind newcomers that cold air has other effects besides cold batteries and heater usage. And that cold air and drag can have a significant impact on range. My hope is that my numbers will show this directly by separating it from other cold weather range factors.

So far as footnote 3 on your range chart goes, I've never been quite clear on what temperature effects it includes. My assumption is that it is based on an empirical measurement of the various cold weather factors lumped together. That isn't a criticism, better to keep it simple to increase utility of the chart. But I thought it would be interesting to tease out the cold air and drag effects on range and I, at least, found the exercise interesting. Others may disagree.

donald said:

For an EV it is a significantly higher fraction of the overall 'losses' because there are few zero-load losses in an EV.

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Sure, but that does not mean that it is a significant fraction of the total loses. While I do not have a chart for the Nissan LEAF, I have this graph from Tesla which indicates that air friction does not account for more than about 50% of the loss at 70 MPH. At 30 MPH, it appears to be only about 1/5 of the total. Of course this graph may not be accurate for any particular vehicle, but it does apparently represent approximately where Tesla believes the losses are in an EV.

RegGuheert said:

Sure, but that does not mean that it is a significant fraction of the total loses. While I do not have a chart for the Nissan LEAF, I have this graph from Tesla which indicates that air friction does not account for more than about 50% of the loss at 70 MPH. At 30 MPH, it appears to be only about 1/5 of the total. Of course this graph may not be accurate for any particular vehicle, but it does apparently represent approximately where Tesla believes the losses are in an EV.

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Interesting chart. For the purposes of cold weather the factors most subject to change would be drag, tires and, perhaps, the gearing/drive train friction. Plus HVAC if it is used.

When my range/efficiency drops in winter I can eliminate some of the usual suspects: heater use? I usually don't need to use it. Reduced battery capacity due to cold? My garaged car battery stays well above freezing most of the time. Poor traction conditions due to snow? I usually drive my LEAF on roads that are clean and dry. What's left? Cold air drag and cold tires and drive train.

I hope that we can take as a given that range/efficiency drops in cold weather. My hope from all this is to remind people, especially newcomers to the LEAF, that cold, dense air by itself can reduce range. In case they hadn't considered it. You are correct to point out that a 10% increase in drag doesn't mean a 10% decrease in overall range.

dgpcolorado said:

You are correct to point out that a 10% increase in drag doesn't mean a 10% decrease in overall range.

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Unfortunately, your chart states just the opposite, indicating that a 10% increase in drag leads to an approximately 10% reduction in range. Don't you think that is confusing for newcomers when the actual loss in range would be far below 10% and also dependent on speed?

Perhaps it would be better to leave off the range column since we cannot calculate the aerodynamic effect of the cold on range given the information at hand.

Hmmm. Methinks I will abandon my air density compensation code and just go for auto-tuning. Instead of trying to come up with the right adjustment to the drag adjustment to compensate for all those other factors (speed, tire wear, tire choice, use of ac, heater, etc), I will just keep track of the average outside temperature for every trip and build up a lookup table for the max,min, and average efficiency at each temperature experienced (maybe in 5 or 10 degree buckets). This way heater and ac use (or not) is also factored in.

RegGuheert said:

donald said:

For an EV it is a significantly higher fraction of the overall 'losses' because there are few zero-load losses in an EV.

Click to expand...

Sure, but that does not mean that it is a significant fraction of the total loses. While I do not have a chart for the Nissan LEAF, I have this graph from Tesla which indicates that air friction does not account for more than about 50% of the loss at 70 MPH. At 30 MPH, it appears to be only about 1/5 of the total. Of course this graph may not be accurate for any particular vehicle, but it does apparently represent approximately where Tesla believes the losses are in an EV.

Click to expand...

dgpcolorado said:

So far as footnote 3 on your range chart goes, I've never been quite clear on what temperature effects it includes. My assumption is that it is based on an empirical measurement of the various cold weather factors lumped together.

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Note 3 should specify BATTERY temperature.

Note 6 covers air density variations with temperature.

RegGuheert said:

where Tesla believes the losses are in an EV.

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I'll have to ask about whether that graph looks right (I know a chap that does coast-down testing for a living) - I have no idea about the tyres or the HVAC system on a Tesla (mine appears to use nothing when it is off, does the Tesla always use it?). Or you can argue that the energy rating should be when it is on full - so that'd be 60% of the consumption when the heater is at 7kW and I'm driving at 30 mph needing 3kW?

I'm not saying I don't believe it, seems about right overall, but the extra loads on the Tesla would, I expect, be higher than a smaller EV. Stands to reason. At 70, more than 50% are aero losses, and I expect that '50%' figure is at a significantly lower speed than for a smaller EV. My original point being (maybe badly expressed) is that for ICE vehicles, it'd be right to say that the aero losses would be expected to stay below 50% of losses, at legal speeds. Aero is, proportionately, more significant for an EV.

RegGuheert said:

I have this graph from Tesla which indicates that air friction ...

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It doesn't show air friction. I just explained that to you.

donald said:

RegGuheert said:

where Tesla believes the losses are in an EV.

Click to expand...

I'll have to ask about whether that graph looks right (I know a chap that does coast-down testing for a living) - I have no idea about the tyres or the HVAC system on a Tesla (mine appears to use nothing when it is off, does the Tesla always use it?). Or you can argue that the energy rating should be when it is on full - so that'd be 60% of the consumption when the heater is at 7kW and I'm driving at 30 mph needing 3kW?

I'm not saying I don't believe it, seems about right overall, but the extra loads on the Tesla would, I expect, be higher than a smaller EV. Stands to reason. At 70, more than 50% are aero losses, and I expect that '50%' figure is at a significantly lower speed than for a smaller EV. My original point being (maybe badly expressed) is that for ICE vehicles, it'd be right to say that the aero losses would be expected to stay below 50% of losses, at legal speeds. Aero is, proportionately, more significant for an EV.

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My gut feelings match yours on this issue. I would expect air friction to dominate losses well below 70 MPH. Additionally, we have separately discussed the brake losses on that chart and agreed that those numbers seemed too high. So it's possible that chart was intentionally distorted to hide their IP. If you can find out better data, or better yet, data on the LEAF, that would be very interesting.

The point remains, however: Range does not drop by the same fraction that air density increases since there are other losses that make up a speed-dependent fraction of the total loss. Of course, those losses may also increase as temperature drops, but that is a separate discussion.

donald said:

RegGuheert said:

I have this graph from Tesla which indicates that air friction ...

Click to expand...

It doesn't show air friction. I just explained that to you.

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You did, but since air friction is the common terminology, I'll continue to use that. You feel free to call it whatever you like.

RegGuheert said:

donald said:

RegGuheert said:

I have this graph from Tesla which indicates that air friction ...

Click to expand...

It doesn't show air friction. I just explained that to you.

Click to expand...

You did, but since air friction is the common terminology, I'll continue to use that. You feel free to call it whatever you like.

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CQTM - yay, another terminology nit to argue about. Next, someone is going to insist that suction doesn't exist...

dgpcolorado said:

I've noticed that there seems to be a common assumption that the only effect of cold weather on range has to do with reduced battery capacity as it gets colder plus increased heater use. However, there are other effects of cold temperatures on the mileage efficiency and range of an EV (or any other car)

Click to expand...

You raise an interesting issue. However, the Argonne AVTA study from 12 October 2012 says the ONLY thing that matters is the heater. For 20F, 72F, and 95F the amount of energy used on the City and Highway Cycles stays EXACTLY the same (Page 32). That includes inertial energy, regen, load energy, and powertrain losses. On the other hand, at 72F accessory loads use 5% of the energy and at 20F they account for 50%. The result greatly surprised me but that's what the study found. So in this case the common assumption seems to be right and temperature has no measurable effect on aerodynamic or rolling resistance losses.

It's not as if cold never matters. The ATV Lab Benchmarks from May of this year show that there is a measurable difference for a cold start. However, this is very transitory and disappears as soon as the drive train reaches operating temperatures. So on balance you shouldn't notice this. It's like a Prius getting less than 10 MPG if you drive it a very short distance when it's very cold.

SanDust said:

... The result greatly surprised me but that's what the study found. So in this case the common assumption seems to be right and temperature has no measurable effect on aerodynamic or rolling resistance losses.

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That's just wrong. We tend to put a lot of faith in government data, but they can get it wrong (or chose not to include certain parameters) just like anybody. There is a government study on the LEAF battery where they obviously tested an already degraded battery!!! But, of course, they wouldn't know that without testing more than one car and getting differences. We know it on this forum because that kind of data is so closely scrutinized.

There is a reasonably significant difference in aero drag (that you can easily measure) between a sea level road at --40 degrees (the same in F or C) and a road 6000 feet elevation driving through Colorado on a warm 90F day. Driving down the highway, air related drag is overwhelmingly the highest factor. Note the huge difference in air density in the examples... I've probably posted this a dozen times:

Sea Level, -40F, standard atmospheric pressure:
Density Altitude: NEGATIVE 7450 feet / -2260 meters
Absolute Pressure: standard 29.92 inches / 1013 hPa
Air Density: 0.0945 lb/ft3 / 1.514 kg/m3
Relative Density: 123.58%

6000 feet elevation, 90F, standard atmospheric pressure:
Density Altitude: POSITIVE 9972 feet / 3039 meters
Absolute Pressure: standard 23.979 inches / 812.01 hPa
Air Density: 0.0565 lb/ft3 / 0.906 kg/m3
Relative Density: 73.92%






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RegGuheert said:

Perhaps it would be better to leave off the range column since we cannot calculate the aerodynamic effect of the cold on range given the information at hand.

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Good point. I've changed it to reflect that it is just the change in drag, not range. Thanks for pointing out the error.

TonyWilliams said:

Note 3 should specify BATTERY temperature.

Note 6 covers air density variations with temperature.

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Interesting. I was never quite clear on that. My tables aside, that makes note 6 difficult to use for temperature adjustment without a density altitude calculator*. When doing calculations I used it just for the elevation delta, since that's the major factor in my vertical terrain around here.


* And density altitude calculators are difficult to use for a novice, IME.

dgpcolorado said:

RegGuheert said:

Perhaps it would be better to leave off the range column since we cannot calculate the aerodynamic effect of the cold on range given the information at hand.

Click to expand...

Good point. I've changed it to reflect that it is just the change in drag, not range. Thanks for pointing out the error.

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Perfect! Thanks!

And I appreciate you putting together all this data! It is quite interesting to see how much it changes.