How much does elevation climb and drop affect range?

[ℬête Noire]

Attached is a potential route leg. Missoula, MT to Lethbridge, AB. Net elevation across the leg is a drop of approximately 200'. A lot of the trip is along river valley bottom. However there is at least one pass that I've identified, at Summit, MT. It's elevation is 5338'. What's the rule of thumb on losses for up-down, assuming dry highway and mindful driving to avoid friction braking as best as possible?

Assuming a full charged fresh M3 LR, high summer months so hopefully no snow, does this leg look like it could be an issue?

 

[ChadS]

I haven't seen measurements for the Model 3 yet, but given its weight I would assume that it would cost about 7-8 miles of range for every 1,000 of elevation gain.

How much you get back coming down varies more, depending on grade, speed, regen selection, and if you brake. But as an average, you will usually get around 2/3 of those miles back.

 

[ℬête Noire]

It's that 2/3 efficiency number that I was looking for, thanks.

The first approximation of the extra work put in by the rise is pretty easy, assume 2 people and sundries brings vehicle weight to 2T: 2000kg * 9.8 * 650m = 12.74MJ = 3.54kWh

Assuming 240Wh/mile that's 14.8mi range loss, so approximately 5mi net loss after coming back down. Nice, now just need to check make sure there aren't any other serious humps on the route and that Summit truly is the summit (rather than say False Summit just down the road...yes, real name).

 

[gregincal]

300 miles across a mountain pass? I don't think that leg is doable. These resources are pretty good for checking out such things:

A Better Routeplanner
EV Trip Planner

 

[ThosEM]

I haven't done a lot of mountain driving myself, but some have reported that range is only affected by 5% or so between points at the same altitude, during real travels in the Alps or Rockies. But of course it depends on altitude gain/loss compared with total miles driven. Assuming 90% efficiency for both propulsion and regeneration, you'd expect to regain 80% of the extra energy put into altitude (over and above driving the same distance on the level), when coming back down. So 67% sounds cautiously conservative to me.

For a real given trip of X miles with an altitude gain/loss corresponding to Y miles at normal consumption, the fractional loss of range should be about 0.2Y/X. So if you're driving 100 miles with a 5000 ft. gain/loss (5*8 miles per ChadS), that's 0.2*40/100 or 8%.

All of which suggests that routes could be rated by the amount of vertical up/down as well as the net altitude change.

 

[ℬête Noire]

300 miles across a mountain pass? I don't think that leg is doable. These resources are pretty good for checking out such things:

A Better Routeplanner
EV Trip Planner

I used that first one, that spit that route out. Well actually it told me to skip Lethbridge and go straight up the side of the Rockies through Longview. ¯\_(ツ)_/¯ Stunning view on that drive but didn't pass my sanity check.

 

[SageBrush]

How much you get back coming down varies more, depending on grade, speed, regen selection, and if you brake. But as an average, you will usually get around 2/3 of those miles back.

Yep.

I drive on roads that are usually pretty empty or have a passing lane so I drive with energy conservation in mind: I let the climb bleed off speed as I approach the summit and then gain it back on the way down. On the flip side I let my speed go higher than usual on the descent. I come pretty close to the efficiency of level driving by limiting regen (and of course avoiding friction brakes.)

 

[ℬête Noire]

All of which suggests that routes could be rated by the amount of vertical up/down as well as the net altitude change.

Yeah, that route is net downhill headed North. I figure I'll take a shot and do an assessment, based of how close it cuts it, of whether I have to go all the way out to Vancouver/Seattle for the return trip.

 

[ℬête Noire]

Yep.

I drive on roads that are usually pretty empty or have a passing lane so I drive with energy conservation in mind: I let the climb bleed off speed as I approach the summit and then gain it back on the way down. I come pretty close to the efficiency of level driving by avoiding regen (and of course avoiding friction brakes.)

The thing with mountain passes is you climb so far, for so long that you can't really feather them like that. I'll just make sure not to accelerate up (EDIT:in the lay sense of speeding up, obviously in physics sense I'm always accelerating just to keep a constant speed), so I don't exasperate friction losses due to the slope under the wheels.

 

[SageBrush]

The thing with mountain passes is you climb so far, for so long that you can't really feather them like that. I'll just make sure not to accelerate up (EDIT:in the lay sense of speeding up, obviously in physics sense I'm always accelerating just to keep a constant speed), so I don't exasperate friction losses due to the slope under the wheels.

No doubt, some roads require brakes.
My driving is in the Rockies though, so the techniques mentioned work for a lot of situations. The limiter is more traffic than topography from my experience.

 

[gregincal]

I used that first one, that spit that route out. Well actually it told me to skip Lethbridge and go straight up the side of the Rockies through Longview. ¯\_(ツ)_/¯ Stunning view on that drive but didn't pass my sanity check.

What settings are you using? Using ABRP shows me the leg shown doesn't really work (OK, it's theoretically possible, but you have to drive slowly and leave with 100% and arrive with 8%, no thanks). I definitely recommend having arrival percentage set to 15%.

 

[ℬête Noire]

What settings are you using? Using ABRP shows me the leg shown doesn't really work (OK, it's theoretically possible, but you have to drive slowly and leave with 100% and arrive with 8%, no thanks). I definitely recommend having arrival percentage set to 15%.

"Ships aren't built to sit in the harbour." This isn't even close to the dodgiest leg of the route. Once I get to Calgary and start heading East I'm in real pioneer mode.

Not sure what I had it set before but now it's putting me through Fernie. Huh. ((P.S. They list the M3 80kWh, that's what I'm using there.))

Digging around looks like there is a 10kW destination charger in Kalispell. Maybe I'll plan around stopping there for the night, $100 room gets me the charger. That'd be a slam dunk to make it.

 

[SageBrush]

The thing with mountain passes is you climb so far, for so long that you can't really feather them like that. I'll just make sure not to accelerate up (EDIT:in the lay sense of speeding up, obviously in physics sense I'm always accelerating just to keep a constant speed), so I don't exasperate friction losses due to the slope under the wheels.

A little arithmetic shows that bleeding off speed from 70 mph down to 30 mph before a summit is about 0.18 kWh of KE. That is getting close to 1 mile extra range per occurrence.

 

[gregincal]

The 3 does not have 80kWh usable. According to EPA docs it has 78, but the 3 will display 0 miles remaining after using 73kWh.

Spending the night in Kalispell sounds like a great idea.

 

[ℬête Noire]

A little arithmetic shows that bleeding off speed from 70 mph down to 30 mph before a summit is about 0.18 kWh of KE. That is getting close to 1 mile extra range per occurrence.

Right, so you're very near 100% recovery on that rather than maybe 65% efficiency relying on regen, netting about 1/3mi range improvement per incident. That can certainly add up over a route with a lots of hills.

However a 70mph to 30mph speed drop translates to only about 45m (150ft) of elevation change, if my math is right. On say a 500m pass the benefit of feathering like that will get heavily diluted. Past the 45m mark the benefit of slowing down is really more about avoiding fighting higher wind resistance with less traction than normal, because of slope under the wheel.

 

[ℬête Noire]

The 3 does not have 80kWh usable. According to EPA docs it has 78, but the 3 will display 0 miles remaining after using 73kWh.

I have no idea what that site assumes for range, how they calculate it. Why the don't list it as the "M3, 310mi" I don't know....not that that number is exactly spot on either (seems like it's a lowball). It's quite possible they aren't actually using that '80kWh' in a literal sense. Or if they are it's just backwards from the range rating and it all works out in the end.

EDIT: FWIW I tried a P100D on 19" wheels, probably the closest range analogue they have listed, with 15% bottom buffer. It goes through that route SC to SC. Dropping to a 90D they throw a caution yellow on reaching Lethbridge (it's actually Fort McLeod).

Spending the night in Kalispell sounds like a great idea.

Last time I drove Houston -> Calgary I did it from pre-dawn of one day until near dusk of the next (33hrs of actual driving). Ironmanned it because I had a hard deadline, for a lease return, that was a poor fit with some other stuff I was committed to. Overnighted in Cheyenne. This trip I'll have a young passenger (father-daughter road trip!), so I expect it'll will require two overnights. Camp the first and hotel the 2nd seems reasonable, Kalispell is probably a great natural break.

 

[dgpcolorado]

Bear in mind that when tackling a pass, you need enough charge to get to the top before you can benefit from the gains on the downside. Case in point:

^ Denver Supercharger Station to Silverthorne Supercharger Station via the Eisenhower tunnel [11,158 ft (3,401 m)].

It's not necessarily how much energy you end up with at your destination it is how much you have left at the high point. This is something of an extreme example, however.

One more thing that I've discussed elsewhere, but will mention here, is that when traveling at high altitude you tend to go farther than trip planners calculate, other things (temperature, weather, speed) being equal. That's because even though the trip planners adjust for elevation gain and loss, they tend to assume a density altitude at sea level. Since the air density is significantly lower at high altitude — meaning fewer air molecules to push out of the way — I find that I get better range than the trip planners (including Tesla's) project when driving at high altitude.

The OP's proposed trip isn't at particularly high altitude but it likely will get a bit of a benefit from being at 3000 feet and above.

FWIW.

 

[dgpcolorado]

An elevation plot of the Missoula to Fort MacLeod trip leg:

 

[ℬête Noire]

Since the air density is significantly lower at high altitude — meaning fewer air molecules to push out of the way — I find that I get better range than the trip planners (including Tesla's) project when driving at high altitude.

Hehe, like you read my mind. I've been trying to find hard numbers for this effect, to see what kind of percentage it might work out to be. I know it's enough that track & field records that are based on highly anaerobic activity get an asterisk when set at high altitudes with as little as 1000m elevation above sea level.

EDIT: SWEET ELEVATION CHART! Thank you very much.

 

[dgpcolorado]

Hehe, like you read my mind. I've been trying to find hard numbers for this effect, to see what kind of percentage it might work out to be. I know it's enough that track & field records that are based on highly anaerobic activity get an asterisk when set at high altitudes with as little as 1000m elevation above sea level.

EDIT: SWEET ELEVATION CHART! Thank you very much.

Here are some tools you can use to get a rough idea of how air density decreases with altitude:

Air - Altitude, Density and Specific Volume

It isn't quite as simple as it seems since air temperature generally decreases as altitude increases — referred to as the "lapse rate" (from my pilot training) — and a lower temperature slightly increases air density. Overall, however, the higher you go the less dense the air, which means decreased drag. This can be quite significant at highway speeds.