How to plan route with elevation in mind?

[TonyWilliams]

One of the great things about the Leaf is that the power of the car has little bearing on the absolute altitude unlike an ICE car which loses HP as it operates at higher elevation (assuming non-turbo charged).

And won't overheat going up the hill.

 

[DaveEV]

So let's say we assume a conservative 1.7 kWh for each 1000 ft of climbing - perhaps it'd be useful to indicate how many miles range you'll lose because of it? Of course, this will vary depending on speed - the faster you go the effects of climbing should be less (as a percentage) since you're expending more energy pushing wind.

So for example, using the Range-Speed-Bars table let's say you're doing about 43 mph. Normally this would get you as far as 108 miles, but every 1000 ft of climbing will reduce your range by 9 miles.

At 50 mph every 1000 ft of climbing will reduce your range by 8 miles.
At 60 mph every 1000 ft of climbing will reduce your range by 7 miles
At 70 mph every 1000 ft of climbing will reduce your range by 6 miles.

(I rounded up there to be even more conservative).

Then (assuming 1 kWh gained when descending) when descending, you'd pick up this many more miles at these speeds (rounding to lower 0.5 mile again to be conservative):
43 mph +5 miles
50 mph +4.5 miles
60 mph +4 miles
70 mph +3 miles

So if I'm planning a 70 mile trip with 4000 ft of climbing and 2000 ft of descent and planning on driving about 50 mph.

96 mi - 4.5 mi * 4 + 4.5 mi * 2 = 87 miles. Looks like I should make it with room to spare.

What about at 60 mph?

81 mi - 4 mi * 4 + 4 mi * 2 = 73 miles. Looks like I'll be rolling in after the very low battery warning if I'm lucky.

Rough extrapolation to 55 mph?

88 mi - 4.25 mi * 4 + 4.25 mi * 2 = 79 miles. Should barely have one bar remaining if all goes well... Limiting max speed to 55 mph and going slower when possible ought to make it with some room to spare.

 

[abasile]

One of the great things about the Leaf is that the power of the car has little bearing on the absolute altitude unlike an ICE car which loses HP as it operates at higher elevation (assuming non-turbo charged).

Efficiency is actually better at altitude due to the reduced aero drag.

We regularly do a 5000' climb over 16 miles to reach our house. With four of us in the car (myself, my wife, and our young children), plus groceries, that drive requires about 6.5 bars of charge averaging 35-40 mph. If we start the climb with eight full bars, we make it home with two bars, but the second bar isn't full.

To drive 16 flatland miles at a constant 35-40 mph, 1.5 bars of charge would be more than enough. So we're using maybe a tad more than one additional bar per 1000' climbed.

 

[DaveEV]

So we're using maybe a tad more than one additional bar per 1000' climbed.

Seems like your usage is fitting the current estimates...

1 bar ~= 1.7 kWh
40 mph ~= 5.5 mi / kWh
1000' climb ~= 1bar ~= 1.7 kWh

16 mi at 40 mph = ~2.9 kWh or ~1.7 bars
5000' climb = ~5 bars or ~8.5 kWh

Total: ~11.4 kWh or ~6.7 bars to travel 16 miles up 5000' at ~40 mph.

Or pretty close to your estimate of 6.5 bars.

 

[abasile]

The potential energy calculations work out closer to 1.3 kWh per 1000', or slightly higher given passengers/cargo. Check out LEAFer's calcs: http://www.mynissanleaf.com/viewtopic.php?f=24&t=309&p=6025" onclick="window.open(this.href);return false;

Perhaps 1.6 or 1.7 kWh per 1000' is closer to the real world value due to battery and motor losses. In any case, it doesn't hurt to be conservative.

 

[edatoakrun]

The potential energy calculations work out closer to 1.3 kWh per 1000', or slightly higher given passengers/cargo. Check out LEAFer's calcs: http://www.mynissanleaf.com/viewtopic.php?f=24&t=309&p=6025" onclick="window.open(this.href);return false;

Perhaps 1.6 or 1.7 kWh per 1000' is closer to the real world value due to battery and motor losses. In any case, it doesn't hurt to be conservative.

This will never be a constant over different roads, requiring different use of the power-train.

For a long time, I also thought I was consuming about 1 bar for each 1,000 ft of ascent, based largely on my "commute" experience, on a narrow winding road requiring frequent acceleration and regen "micro" events, lowering total efficiency. With more experience on more "efficient" mountain roads, those with more constant grades and speeds, I now believe that 800 ft per bar (with about 300 lbs of passengers and cargo-you may be carrying more on average) may be a better average estimate, for "highway" conditions.

Someone may want do the math for 800 ft in a 3650 lb vehicle and see the results in kWh. Since I have neither an accurate SOC meter, nor know the actual available battery capacity, I find the per bar estimate to be more useful (and a lot easier to do) while driving.

 

[abasile]

For a long time, I also thought I was consuming about 1 bar for each 1,000 ft of ascent, based on my "commute" experience, on a narrow winding road requiring frequent acceleration and regen "micro" events, lowering total efficiency. With more experience on more "efficient" mountain roads, those with more constant grades and speeds, I now believe that 800 ft per bar (with about 300 lbs of passengers and cargo-you may be carrying more on average) may be a better average estimate.

In my case, California Highway 330 is a pretty efficient road. It is well graded with a 55 mph speed limit and no especially tight curves. There is no need for regen, except for a small section of CA-18 at the end of our drive home.

The "problem" with a nicer road, however, is that one is likely to drive faster and consequently use more energy on the climb. Indeed, driving 45-55 mph up CA-330 seems to use one additional bar compared to 35-40 mph.

When driving 35-40 mph, 1000 ft./bar is closer to what I observe than 800 ft./bar. If I were using as much as one additional bar per 800 feet climbed, then the 5000' ascent would require 6.25 additional bars on top of the energy required to drive 16 flatland miles. And I can't drive 16 flatland miles on 0.25 bar!

Someone may want do the math for a 3650 lb vehicle and see how close that comes to 1.3 kWh.

Here's the calculation: 3650lb * 0.454kg/lb * 9.8m/s/s * 1000ft * 0.3048m/ft / 3600s/h / 1000Wh/kWh = 1.375 kWh

 

[edatoakrun]

It sounds like we are seeing very close to the same results. As I said, I'm reporting my experience at higher speeds, more like 55 mph on average.

That's about as slowly as I can safely drive on the mostly 2 lane 55 mph highways around here, and I still have to speed up occasionaly, when a log truck traveling at 60+ mph gets on my tail.

For a long time, I also thought I was consuming about 1 bar for each 1,000 ft of ascent, based on my "commute" experience, on a narrow winding road requiring frequent acceleration and regen "micro" events, lowering total efficiency. With more experience on more "efficient" mountain roads, those with more constant grades and speeds, I now believe that 800 ft per bar (with about 300 lbs of passengers and cargo-you may be carrying more on average) may be a better average estimate.

In my case, California Highway 330 is a pretty efficient road. It is well graded with a 55 mph speed limit and no especially tight curves. There is no need for regen, except for a small section of CA-18 at the end of our drive home.

The "problem" with a nicer road, however, is that one is likely to drive faster and consequently use more energy on the climb. Indeed, driving 45-55 mph up CA-330 seems to use one additional bar compared to 35-40 mph.
When driving 35-40 mph, 1000 ft./bar is closer to what I observe than 800 ft./bar. If I were using as much as one additional bar per 800 feet climbed, then the 5000' ascent would require 6.25 additional bars on top of the energy required to drive 16 flatland miles. And I can't drive 16 flatland miles on 0.25 bar!

Someone may want do the math for a 3650 lb vehicle and see how close that comes to 1.3 kWh.

Here's the calculation: 3650lb * 0.454kg/lb * 9.8m/s/s * 1000ft * 0.3048m/ft / 3600s/h / 1000Wh/kWh = 1.375 kWh

 

[Stunt822]

So, no web site to calculate total gain on route? i'm not much interested in graphics, just number, like - on your way you'll have to climb X and descend Y feet?

 

[yoobb]

I haven't had time to read the entire thread, but so far, I haven't seen the direct answer, using physics equations.

First, the mass of the LEAF is 1521 kg. Add 79 kg of driver and luggage for 1600 kg of loaded mass.

The usable capacity of the LEAF battery = 24 kWh * 0.95 depth of discharge * 3.6e6 J/kWh = 82.08e6 J.

For every 1,000 meters of elevation gain, the energy used is:

1600 kg * 1,000 m * 9.81 m/s2 = 15.696e6 J.

If you were driving straight up, using energy only for elevation gain, your vertical range would be:

82.08e6 J / (15.696e6 J / 1,000 m) = 5,229 m.

Keep in mind you'll regain energy on the downhill portions. I'll assume 30% regenerative braking efficiency.

If you're going to climb a hill 2614.5 m high, then come down the other side, you'll use half of your battery capacity (41.04e6 J) to get up the hill, then recover 30% of that (12.31e6 J) coming down the hill on the other side, for a net use of 28.7e6 J. After accounting for the climbing and descending, you'll have 53.38e6 J left for all the other losses.

Assuming you get 80 miles range on flat driving (which I do), your energy use per horizontal mile is 1.026e6 J/mi. Your range, with the hill, will be 53.38e6 J / (1.026e6 J / mi) = 52 miles.

 

[TonyWilliams]

The usable capacity of the LEAF battery = 24 kWh * 0.95 depth of discharge * 3.6e6 J/kWh = 82.08e6 J.

How did you arrive at this number (in bold)?

 

[dgpcolorado]

One of the great things about the Leaf is that the power of the car has little bearing on the absolute altitude unlike an ICE car which loses HP as it operates at higher elevation (assuming non-turbo charged).

Efficiency is actually better at altitude due to the reduced aero drag...

Yes, the air density decreases as altitude increases and that can significantly reduce drag, especially at highway speeds. I discovered this for myself years ago when I would take my ICE car down to sea level and see my gas mileage drop sharply.

Some rough numbers for the reduction in air density versus altitude, other conditions being equal (temperature, humidity, weather air pressure):
Sea Level (0)
1000 feet -4%
2000 feet -7%
3000 feet -10%
4000 feet -14%
5000 feet -17%*
6000 feet -20%
7000 feet -23%
8000 feet -26%
9000 feet -29%
10,000 feet -31%

Of course there are other factors that affect air density: cold air is more dense than warm air and dry air is more dense than humid air (as any pilot learns). But, in general, there are way fewer air molecules to push out of the way where I live (7670') than at sea level. The lowest altitude my Leaf will reach in normal use, without a charge station network, will be ~5800' for grocery shopping.

Other confounding factors are road conditions, EVNow has reported reduced range on wet roads and I would expect reduced efficiency when driving in snow or on dirt/gravel. I guess I'll find out whether the altitude benefit will compensate for the other factors.

[Miscellaneous fact: the lowest elevation in Colorado is 3315 feet, where the Arickaree River flows into Nebraska.]


* (This is one of the reasons baseballs fly farther and curve balls don't "curve" at Coors Field in Denver)

 

[abasile]

Other confounding factors are road conditions, EVNow has reported reduced range on wet roads and I would expect reduced efficiency when driving in snow or on dirt/gravel. I guess I'll find out whether the altitude benefit will compensate for the other factors.

On a recent, 52 mile round trip drive to a trailhead (see http://www.mynissanleaf.com/viewtopic.php?f=31&t=3512&start=51" onclick="window.open(this.href);return false, we covered the distance on roughly 6.5 bars of charge. At that rate of usage, we could have charged to 100% and (barely) done the drive twice, for a total of 104 miles on a full charge. The kicker is that I was making relatively little effort to drive efficiently, there were significant ups and downs, many curves, and three of the miles were on a somewhat rocky dirt road. Except for the dirt road portion where I drove 10mph or less, I stayed close to the speed limit which varied from 35-50 mph. Of course, we were at 6000' - 7400' altitude for the entire drive.

 

[TonyWilliams]

Some rough numbers for the reduction in air density versus altitude, other conditions being equal (temperature, humidity, weather air pressure):
Sea Level (0)
1000 feet -4%
2000 feet -7%
3000 feet -10%
4000 feet -14%
5000 feet -17%*
6000 feet -20%
7000 feet -23%
8000 feet -26%
9000 feet -29%
10,000 feet -31%

The conditions are not accurate for equal temperatures and pressures. The density altitude percentages you specify are based on standard conditions at that altitude.

A rule of thumb for standard temperature is to subtract 2C per each 1000 feet higher in altitude. "Standard" temperature at sea level is 15C (60F), so where you live, at about 8000 feet, the standard temperature would 8 * 2 = 16 degrees Celcius less than 15C, or -1C.

So, you can use this calculator to plug in:

> 8000 feet (2438 meters)

> 30 (-1C) temperature

> 29.92 inches (1013mb)

> 0 dew point for this example

The answer you'll get is very close to 8000 feet density altitude. That's standard conditions that will equal the approximate 26% reduction in air density. If the temperature were 15C at sea level, and then 15C at 8000 feet, the difference in density altitude would be about 10,000 feet, or about 31%.

When you're in that big airplane at 30,000 feet, and see on the info screen that it's -45C outside, that fits the rule of thumb, 15 - (30 * 2) = -45.

Also, air pressure are not the same. There is a rule of thumb of 1 inch of mercury pressure loss per thousand feet increase in altitude. So, your 8000 foot mountain home would only have a standard pressure of:

29.92 [inches at sea level] - (8 * 1) = 21.92

The pressures reported by the weatherman and aviation "METAR" reports are corrected for altitude, therefore would report 29.92 (QNH). Only one airline, that I'm aware of, in the western world used "QFE", or actual pressure at Field Elevation; American Airlines. Every time they landed, the altimeter would read "0". Some former Soviet and Chinese countries also use QFE.

A crash of a U.S. Air Force aircraft in eastern Europe was attributed to mistaking QFE for QNH.

 

[dgpcolorado]

The conditions are not accurate for equal temperatures and pressures. The density altitude percentages you specify are based on standard conditions at that altitude...

You are correct, of course. I specifically chose standard conditions to eliminate variations due to the temperature lapse rate, and the like, to make the many moving parts in the calculation more straightforward. So, yes, I assumed the same temperature up high as down low, which is not typically the case (my highest temperature this summer was 92ºF, BTW, so it isn't always cold here). And I was trying to focus on air density since that is more relevant to drag than pressure, although all are linked.

I flew sailplanes and airplanes for many years and am keenly aware of pressure altimeter variations from day to day, even hour to hour when a front is moving through. I was trying, perhaps unsuccessfully, to come up with a sort of baseline density variation at STP*, even if it is a bit artificial. Once one factors in variations in temperature, humidity, barometric pressure and the like, the calculations get complex, as you know. However, adjusting for temperature, as you suggest, gives numbers that are more relevant.

I like the calculator that you linked to; it is better than the ones I found. I present a new table below that uses a fixed barometric pressure and humidity but varies the temperature at the standard lapse rate.

*[For those who don't recognize the term: STP = Standard Temperature and Pressure.]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Air density versus altitude using lapse rate:
Sea Level 100%
1000 feet 97%
2000 feet 94%
3000 feet 91%
4000 feet 89%
5000 feet 86%
6000 feet 84%
7000 feet 81%
8000 feet 79%
9000 feet 76%
10,000 feet 74%
11,000 feet 72%
12,000 feet 69%

 

[planet4ever]

The usable capacity of the LEAF battery = 24 kWh * 0.95 depth of discharge * 3.6e6 J/kWh = 82.08e6 J.

That would be 22.8kWh usable. I was among those who argued early on for 24kWh usable, but I think most of us have had to bow to the reality of measurements that show about 21kWh usable, almost certainly less than 22kWh.

Keep in mind you'll regain energy on the downhill portions. I'll assume 30% regenerative braking efficiency.

Regen efficiency has been hotly debated, and of course there are losses in the generator/motor, the charger/inverter, and the battery itself. One camp may still be claiming that it can't possibly be as high as 50%, while I have seen a claim of having measured 80%. I think 80% is too high, but just watching the Energy Usage display I am impressed with what it says I am recovering. In my opinion 30% is far less likely than 70%.

Ray

 

[adrianco]

Carwings records the actual usage for each trip made in the Leaf, so if there was a way to aggregate all the data that Nissan is collecting, they could map out the KWh needed to go on a trip that included hills and freeway driving.

I live at 2400ft, work 10 miles away near sea level, half the distance is on the freeway. Carwings shows that I need to start out at 80% charge to get regen on the way down the hill, and that I use 5-6KWh to get home. I drive the car hard over these distances, I'm not trying to save power and I don't bother charging at work unless I'm going further afield during the day.

Laurel's commute is about 40 miles each way (down to sea level and more freeway speed driving) , total daily use about 18KWh, but she always charges at work to make sure she doesn't cut it fine on the way home, and doesn't have to use ECO mode.

I have crept home in ECO mode a few times after longer trips, got down to near zero remaining. Our overall average is 3.2miles/KWh last time I looked.

 

[HighDesertDriver]

Just a quick data point for our first extended drive from Palmdale CA to Valencia CA. The objective was Chick-Fil-A at the Valencia Mall. Except in the Valencia area, the roads are 2-lane, curvy, and (at the time) empty.

-- Used this table: http://www.mynissanleaf.com/viewtopic.php?f=31&t=4295" onclick="window.open(this.href);return false; to estimate power consumption
-- Ball-parked the elevation changes using the Google functions mentioned on the first page of this thread: Total climb segments of 1100' and total descent segments of 2700'. (I just approximated the elevations from the route profile. No micrometer here.)
-- Outside air temps of ~77F outbound during the net loss of elevation, ~67F return during the return net gain of elevation.
-- Generally planned on 40-45mph, but actually varied 35-55mph, depending whether straight or lots of turns
-- Battery temperatures stable in mid-range both directions
-- Climate control set to Auto both directions
-- Same roads both directions, 29 miles each way, good pavement
-- Left house with 100% charge. The climb over the first set of small hills left sufficient room for regen on the other side. The first bar disappeared at ~4 miles and from then on none of the regen bubbles were locked out.

Pre-drive planning predicted arrival at Chick-Fil-A about in the middle of the 9th bar. We lost the 10th bar about 2 miles before arriving, so planning was conservative. Arrival back home was predicted to be just into the 2nd bar, but we pulled int the garage in the middle of the 3rd. Taking into account the surplus from the outbound leg, return planning was remarkably close.

Conclusion: The table works quite well. Thank you, Tony Williams, and all contributors who's comments helped refine it. I'm sure there was more than a small bit of luck involved in getting so close on one's first try, but it builds confidence for the next trip.

 

[TonyWilliams]

Just a quick data point for our first extended drive from Palmdale CA to Valencia CA. The objective was Chick-Fil-A at the Valencia Mall......
Conclusion: The table works quite well. Thank you, Tony Williams, and all contributors who's comments helped refine it. I'm sure there was more than a small bit of luck involved in getting so close on one's first try, but it builds confidence for the next trip.

You're welcome. I'm going to guess you averaged 4.3 miles/kWh ??? That would leave you with about 30 miles still in the gas tank.

Truly excellent use of available info. I did very similar planning for this trip and this trip.

I'm glad you like the chart. My plan has become to be able to plan these trips to use the full (meager) range of the vehicle. And to stress to folks that the GuessOmeter is a waste of time, until such day that Nissan decides to actually fix it. They did fix the discrepancies in CarWings, so you never know.

Tony

 

[HighDesertDriver]

I neglected to reset anything except the trip odometer so I don't have a precise miles/kWh number. Interestingly, Carwings showed the charge at 17% which seems to have been at odds with 3 bars showing.