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## Mountain driving - some numbers

## Mountain driving - some numbers

Yesterday, I took a drive from Pasadena, CA up to Mt. Baldy, partially as a recreational outing, partially to test the Model S's mountain performance. My wife kept notes so we could see how the charge status would be affected.

Firstly, let me say that mountain driving with the Model S is every bit as much fun as you'd expect. Cornering is marvelous, uphill passing pure entertainment, and - as it turns out - range is not as severely affected as at least I had expected.

Miles are rounded, so there are small inaccuracies, but nothing of consequence.

The first leg was 24 miles of freeway along the foothills, with little relative elevation change (+1000 ft), cruise at 74mph, which averaged out to 65 mph including local driving. The rated range decreased from 187 to 155, 32 miles range loss for the 24 miles driven - the higher speed took its toll, as I expected. I averaged about 350 or 360 wH/mile.

The climb to Mt Baldy Village is a 9 mile drive to about 4200 ft., so we gained 2200 ft in elevation. The rated range went from 155 to 129, which gives us a "climbing penalty" of slightly below 8 miles of range per 1000 ft gained. (155-9=146, 146-129=17, 17/2.2 = 7.7miles/1000ft) The average speed of the climb to that point was about 35-40 mph.

Then came a steep climb up to the bottom of the ski lifts, from 4200 ft to 6500 ft in just under 5 miles. That dropped the rated range from 129 to 110. The "climb penalty" was less this time (6.1 miles/1000ft), perhaps because the average speed was much lower (24 mph).

Now came the surprising part: I knew the car re-generates power on the way down, but I was curious to find out how much. So I drove down without using the brakes except for a couple of little taps. After the the 14 mile descent the rated range had increased from 110 to 124!

So, the average "climb penalty" on the way up was about -6.3 miles/1000 ft, the average descent gain was over +5 miles/1000 ft, and in total, the net range loss for the 28 miles in the mountains was only 3 miles more than rated range miles, less therefore, than I would have seen if I had driven those mountain miles on a flat freeway at 75 mph. That, I have to say, blew me away. That's *very* efficient energy recovery!

By the time I got home, the average Wh/mile read 308, and I had 102 miles rated range left. This means that my 24 mile freeway drive reduced the range only by 22 miles, and that the whole 77 mile trip cost me 85 rated miles - most of the overage caused by the higher than EPA freeway speed.

By the way: In retrospect, the extra 8 miles of range loss on my first leg now seem totally accounted for, and then some, because I did climb 1000 ft in these first 24 miles, and with a 6 mile range loss per 1000 ft, that means that I only lost 2 miles due to speed. This also was reflected in the lower than expected range loss on my freeway drive home, even though it didn't give me the full 5 miles range gain I would have had with regeneration.

This car continues to impress me in new ways every day.

Crow| March 4, 2013Thanks for the report but I am wondering if you can provide a few more details. Are you reporting rated or projected? Average or instant? If average, over how many miles?

Cattledog| March 4, 2013diegoP - Grew up in Arcadia, know that drive well. Sort of unbelievable on the avreage of 308 Wh/mi! I think I drive too fast...

diegoPasadena| March 4, 2013I used rated miles, not ideal. The wH figures are averages from the beginning of the trip. I have readings from the climb, but since the flat drive was distorting the figures I didn't use them. I should have read the average wH/mile for a 5 mile range. Oh well, I'll do it on my next drive.

shop| March 4, 2013I found a similar result going up and then down the Tejon pass south into LA. You gain back a lot more range than you might think going downhill. Very impressive indeed.

gregv64| March 4, 2013My daily commute is over an 1800 foot pass. I start at about sea level and end at about sea level in about 20 miles, then have another 10 miles of flat freeway. The mountain pass portion of my commute at about 60mph takes about the same average energy as the level portion at about 70mph. I average about 330 wh/mile for my commute. Needless to say, I'm very pleased with this (my Audi A3 hatchback got about 27 mpg for the same commute).

robkal007| March 4, 2013I concur with these numbers, but there is a caveat. If you don't come down you don't get it back. We left Harris Ranch for Tejon Rnch SC with an extra 20 miles Rated Range. Drove well and thought we had it made 20 miles out with 30 miles Rated Range, but Tejon Rnch is 6-700 feet uphill from 20 miles out and we arrived with 1 (one!) mile left. Remember Tejon is at about 1000 ft of elevation. Of course that makes it easy to get to Long Beach (sea level) with only an extra 20 miles!

winfriedwilcke| March 4, 2013I live on a nearly 2000' hill over Silicon Valley, which I climb/descend daily during my commute and therefore am interested in the subject.

A bit of physics, which will lead to a handy rule of thumb for mountain driving....

Potential Energy U = m * g* H where m is the mass of the loaded car (say 2300 kg with 2 persons for the MS), g = 9.81 m/sec^2 is the earth's gravitational constant and H is the height gained or lost.

Lets set H = 100 m ( ~ 310 feet), which it makes it easy to scale for your situation. Let's further assume that the drive train is 90% efficient, then

==> the potential energy required to climb 100m (vertical distance) is 0.7 kWh. <===

After playing with some data I recorded, I found that a pretty good approximation for calculating the energy needed to drive x miles with an altitude gain of H is to figure the energy you need to drive a distance X AS IF YOU WERE DRIVING ON FLAT GROUND and then add 0.7 kWh for every 100 m vertical altitude gained. In other words, E(total) = E(flat ground) + E(climb)

Note that 0.7 kWh is about 2.5 miles for most driving on flat ground, so another way to say this is:

===> If you drive x miles with an altitude gain of H meters, then add 2.5 miles to x "for each 100 meters you gain in altitude" . This gives you an apparent distance y, which the battery experiences on this climbing drive.

Example (from my commute): x = 6 miles, H = 650m. Hence y = 6 + 6.5 * 2.5 = 22.2 miles

The MS will use up as much energy on this (steep) climb as if it were driven 22.2 miles on flat ground.

I measured the rate of energy returned and found that well over 80% is returned to the battery. Fantastic!

I'd be interested if other Tesla users can confirm these results.

diegoPasadena| March 5, 2013winfriedwilcke

Your figure of "2.5 miles to x "for each 100 meters you gain in altitude" sounds very close to my empirical results - almost dead on for the first phase on my climb (mine was about 7.7miles per 1000 ft, your formula comes out to 7.625 miles per 1000 ft. Given environmental differences, that's close enough to be identical.

What accounts for the second, steeper part of my climb being more efficient, I don't quite understand, except perhaps the much lower speed, or perhaps the short distance resulted in a bigger rounding error (the "129" could have been 129.49, and the 110 could have been 109.51), so the loss would have been larger and thus closer to the formal's result.

But then again, from the base to the top, it came out to only 6.3 miles per 1000 ft.

At any rate - using your formula, which basically translates to 7.5 miles per 1000 ft climb seems safe.

shs| March 5, 2013The other aspect of driving in the mountains is that one is rarely going straight, but rather always turning, and when turning, the tires, especially the fronts, are scrubbing off energy, or braking. I wonder how significant is the energy loss associated with driving on winding roads. I Should have my car in a few weeks and maybe find out for myself, but in the meantime, what are your experiences?

wheatcraft| March 5, 2013@diego..: "What accounts for the second, steeper part of my climb being more efficient, I don't quite understand ..."

The reason for this is the Model S energy curve. This graph can be found here:

http://www.teslamotors.com/blog/model-s-efficiency-and-range

If you look at the graph, you can see that the max range for the MS is at about 22 mph, with the range being just over 450 miles at that speed.

derek| March 5, 2013Great numbers, guys. Thanks. That'll be useful for when trying to run it up to Tahoe. However, what a mixed bag of imperial and metric units! Winfried, wassup with that? Are you a displaced euro or Cannuck?

winfriedwilcke| March 5, 2013@diegopasadena - glad your results match the formula well. I

think that wheatcraft it the nail on the head with attributing the higher efficiency to the lower speed. The lower speed would strongly affect the E(flat ground) but not change the E(climb) part. See the range vs. speed charts which Tesla published to get a better handle on the E(flat ground) part of the formula.

@derek - guilty as charged with mixing units. I did the original physics calculation in metric units (naturally) but then felt compelled to translate into a handy formula for US drivers using non metric (ouch) units. Should have expressed H in feet to be consistent.