Most EV miles on one charge?

Don't forget to specify a speed when when giving Wh/mile needed to move the car. Highway speeds require considerable more energy/mile than slow rolls in neutral.

 

It will always be the same delta, about ~40Wh/mile less for a 0.75% slope.

 

True, but if you do a round trip on the same route, gain and loss will cancel out pretty much. But there are still some variations that will affect the going to and coming back trips such as wind or traffic or temperature difference. Of course, if your one-way distance is far longer than the EV range, then it won't work.

I tweaked the map app a little bit. I got the final distance to shorten by half a mile, but the profile is now almost perfectly symmetrical.

 

40 miles round trip uphill/downhill will use far more energy than 40 miles on level ground.

 

Yes, I know. Someone else's 40miles on EV is not comparable to my EV miles. But that's not the point I am making. If you want to compare the difference in EV range for two different occasions. It may be the same car, could be different cars of the same model year or different times of the year, or even different drivers, comparing the round trips of the same route will give a better handle on the variations. My point is that by comparing the round trip for the commuting distance of 35.4miles, my 2021 PP is doing a better job on the EV range than the 2017 PP did a few years ago.

 

Only for steeps that require some significant braking on descent. For shallow slopes, and steeps short enough to just roll with it, there needn't be much of any difference, should there? My non-plugin Gen3 does wonders in mild such conditions.

OP certainly isn't taking 250 Wh/mile when going 44 miles. That would be an 11 kWh battery, which a Prime simply doesn't have. Considering how much of the battery is normally used, it seems 145-160 Wh/mile is more reasonable.

I'm seeing the Prime with a curb weight of at least 3365 lbs, so figure at least 3500 lbs with driver. With that weight, I'm figuring a gravitational potential difference of 52 Wh/mile, at the wheels. Then since the vehicle is less than 100% efficient at converting battery electric energy to mechanical wheel energy, shouldn't that represent 55-60-ish Wh saved at the battery?

The 250 Wh/mile is the EPA rating on the Monroney Sticker, after fudge factors and adjustments to approximate what real world drivers should expect. In the detailed test details, I think I'm reading raw test measurements of 162.62 Wh/mile on the City test (ave speed 21.2 mph, max speed 56.7, 23 full stops), 194.665 Wh/mile on the Highway test (ave speed 48.3, max speed 60) for the 2021 Prime. If one does a steady lower speed test, similar to a slower highway test or a stopless city test, Wh/mile should be even lower.

Put into neutral, the car may not start rolling by itself on that 0.75% slope. But if anything gives it an initial push to move, are you sure it will stop rolling by itself? I'm not certain enough to confidently stand in front of it.

 

If you have to give it more "gas" to go up the hill and/or use the brake pedal on the way down it will be less efficient than cruising the same distance on flat ground.

It's irrelevant for calculating the difference due to potential energy.

I think incorporating the efficiency is too complex for this discussion. We would have to have a good understanding of the rolling resistance of the tires, the speed of the vehicle, the angle of the slope, and the specific efficiency of the drivetrain given those particular variables.

After ~2,000 miles in the 2021, I am averaging 169 Wh/mile which is cumulative of all driving conditions (uphill, downhill, highway, city). Perhaps coincidentally, that's what I averaged in the Leaf too. It's likely not as good as could be had with the car since I live on a hill and require relatively enormous amounts of power to return home.

There is a long drive I make occasionally that just exceeds my EV range and only involves a couple of hundred feet worth of elevation change. On that drive I can get just a tad over 40 miles.

It may keep rolling, or may not. I'm not sure a 3/4-inch elevation difference between the rear and front wheels is enough to overcome the friction losses and tire rolling resistance, but I haven't performed that experiment.

 

"Giving it more gas" to go uphill doesn't necessary cost anything if you can recover it all coasting or gliding downhill without braking. It depends on the specifics of the hills.

A regular Gen3 Prius has a nearly flat engine efficiency curve over a very wide power range (significantly wider than Gen2), so the uphill side of the mountain is nearly irrelevant for a fairly reasonable range of slopes, so long as the engine can keep operation to near-peak efficiency. (See BSFC charts posted elsewhere for appropriate RPM bounds.) So hill traveling efficiency is determined mostly by the downhill slopes and distances, and whether or not the driver can reasonably coast or glide nearly all of it (e.g. shallow slopes, and steeper segments short enough to not need any braking), vs needing to apply energy-wasting brakes (e.g. steeper longer slopes) to prevent excess speeds.

A G4 Prime shouldn't have backslid on this.

Irrelevant comment applied to wrong context.

Are you agreeing, disagreeing, or distracting from the 52 Wh/mile on an 0.75% slope as I figured, vs. ~40 you claimed?

... so we can dispense with your earlier 250 Wh/mile claim?

I.e. 146 Wh/mile.

 

You can't recover it all. You'd have a perpetual motion machine if you could.

If that were true, when and where you use EV would be largely irrelevant to overall efficiency. This isn't borne out by experimentation. Using HV for uphill and EV for downhill and level travel yields significantly better overall MPG than the reverse.

Yes, if you use 3,500 lbs it's 52 Wh/mi on a 0.75% slope. I just did a back of the napkin calculation based on 3,000 lbs.

No. The two numbers have no relationship to one another. 250 Wh/mile is the EPA rating. It's not a claim. It's a fact.

 

You misapply the First Law. I'm not saying to regenerate anything and stuff it back to where it came from. I used "recover" in a different sense.

That isn't how that figure was introduced into this thread.

The unadjusted EPA test results file clearly shows that the car can be moved with significantly lower energy per unit distance.

 

It cannot be recovered in any sense. There's no way to travel up a grade and then coast down using the same net energy as traveling the same distance on flat land at the same speed(s). Anything otherwise would be to suggest that somehow the Prius is able to elevate itself with 100% efficiency.

Say you have the following conditions:

• Your Prius Prime and you're able to get 150 Wh/mile on flat level ground in no wind conditions.
• A 1,000-foot grade 5 miles each direction (~3.8%)

Driving the 5 miles up the grade will require 750 Wh plus the extra power needed to lift the 3,500 lb Prius 1,000 feet. The potential energy of a 1,000-foot elevation gradient for a 3,500 lb object is ~1318 Wh. It will take more energy than that to elevate your Prius because it isn't 100% efficient converting electrical energy stored in the battery into motive power. For the purposes of this experiment, let's say it's 90% efficient. That means the Prius will need 1,318 Wh / 0.9 = 1,464 Wh to climb 1,000 feet in addition to the 750 Wh it needs to travel those 5 miles. It's like vector addition.



Now for the purposes of the experiment we'll assume you can coast down the descent without using any energy from the battery at all. Total trip energy is 750 Wh + 1464 Wh = 2,214 Wh, or 221.4 Wh/mile. That is significantly worse than the 150 Wh/mile traveling the same distance on level ground, and that's at 90% efficiency which I doubt.

Somebody's going to suggest regen, so we can address the case where the slope is sufficient to allow not only coasting, but regen. Remember that pushing the car 5 miles takes 750 Wh. We'll assume for the experiment that there are no losses when realizing gravitational energy, so the 5-mile downhill trip only consumes 750 Wh * 0.9 = 675 Wh to get the car rolling and keep it rolling against friction and wind resistance. That leaves 643 Wh of potential energy to recover by regen. If regen is 75% efficient you will recover ~482 Wh. The net trip energy will be 750 Wh + 1464 Wh - 482 Wh = 1,732 Wh. The 10-mile level trip still requires 13% less energy than going over the hill.

Nobody claimed otherwise. I simply said if you get 250 Wh/mile on level ground you'd get 250 Wh/mile minus the potential energy difference in elevation traveling downhill at the same speed.

 

Your mis-assertion doesn't make the mis-application true.

Your 3.8% slope example very clearly violates the conditions I described earlier. My experience is that the car rolls downhill too fast on that much slope, thus requiring some form of braking:

"So hill traveling efficiency is determined mostly by the downhill slopes and distances, and whether or not the driver can reasonably coast or glide nearly all of it (e.g. shallow slopes, and steeper segments short enough to not need any braking), vs needing to apply energy-wasting brakes (e.g. steeper longer slopes) to prevent excess speeds."

I do this on slopes less than approximately 2%, though the useful threshold should also be speed dependent, for the same reason that energy per distance on flat ground is also a function of speed.

Re-figuring your image around that constraint, the energy cost of your climb no longer exceeds the horizontal distance energy if the slope is 1.94% or less, which dovetails very nicely with my approximately 2% slope estimate for which this can work.

That is, unless you also try to claim that a Prius cannot glide down a 1.94% slope without applying additional motive power.

 

The slope is irrelevant. You cannot recapture 100% of the energy used to climb a hill by rolling down the hill. It's impossible no matter what the slope. To do so requires zero losses to friction, zero losses to wind resistance, and 100% efficiency in converting electricity from the battery to motive power.

Nothing is free, in physics or in anything else. You cannot do more work with the same energy. Lifting a car one billionth of a millimeter and setting it down still requires more energy than not doing so. There's no way around it.

 

You have gone silly. I'm not claiming any better kinetic <--> gravity energy 'conversion' efficiency in mountain driving or rolling hills than an ordinary pendulum gets as it swings back and forth. And we don't classify pendulums as physically impossible perpetual motion machines.

My basic claim had been that, on friendly terrain in which the descent doesn't require any form of braking, a decently skilled driver can get essentially the same MPG as on a flat road. Not all mountain or rolling hilly roads, or even most of them, meet the needed conditions. But some do!

Let me now broaden that claim: on the select friendliest possible mountain roads, one can actually get better MPG than on a flat level road on the valley floor. This is in part due to the thinner air at higher altitude (less air drag and more efficient gasoline engine operation). And in part to better opportunities for terrain-coordinated Pulse & Glide (P&G). P&G is an HV-mode fuel saving hypermiling method that is generally too crowd-unfriendly to be practiced in traffic on flat roads, but can be seamlessly fit to some mountain conditions without being unfriendly.

For thinner air at higher altitude, note that in the example in post #32, air pressure and density at the top of the hill is 4% less than at the bottom. Air drag, the greatest mechanical energy loss mechanism in modern cars at highway speed, is thus reduced 4% at the hilltop, or an average of about 2% over the whole hill, compared to the flat road at the bottom. This 2% gain is greater than the kinetic<--> gravity 'pendulum conversion' loss. And this applies in both EV and HV modes. It will save about 1.5 to 2 Wh/mile over this full hill course.

P&G works best in a Prius when the ICE can stop spinning in the Glide phase, saving coarsely 1500 Watts of parasitic drain. Gen2 and Gen3 are limited to 40-something mph for this best case (some smaller savings still available at higher speed), but regular Gen4s can go above 60 mph, and Prime up to 84. For the example hill in post #32, the 5 mile downslope (5 minutes at 60 mph) will save 125 Wh, or average 12.5 Wh/mile over the whole 10 mile hill course, compared to the valley road. But I have previously stated that the 3.8% slope is too steep for preserving MPG due to the need for energy-wasting braking. So cut this slope down to under 2%. Then it may become too shallow to fully Glide all the way, so some occasional pulses may need to be added, amount depending on slope specifics. An 80% downhill Glide duty cycle will still save 10 Wh/mile. Offset this slightly because the ICE won't climb the hill at exactly the same point on its BSFC chart as it can run the flat valley road, but this engine's efficiency plateau is broad and flat enough that the car can still retain most of that Glide savings.

Some rolling hills are nearly ideal for terrain-coordinated P&G. No noticeable extra fuel cost over a net-zero-elevation route despite thousands of feet of gross climbing. My very best Gen3 round trip MPGs are on such routes.

There are some more smaller possible savings items in the mountains too, if one wishes to continue the discussion.

 

The only silly thing in this conversation is the idea that you can drive a vehicle n miles up and down gentle slopes using the same energy as driving the same vehicle n miles on flat road. It's not possible. I can't convince you that it takes more energy to push a Prius n miles and lift it y feet and lower it down again than it does to push it n miles without any lifting. I don't know what to tell you if you won't accept that. You're arguing that you can raise and lower the car using zero energy. I want to see somebody lift a Prius, even one inch, and lower it back down to the ground using zero energy - even zero net energy.

 

It is possible. Don't try to break the First Law. Look for other paths, for things that can be trimmed to get a bit closer to the First Law ideals without breaking it. But that means looking for other paths, not simply asserting there are none and refusing to even look.

How about a B747, climbing from sea level to 40,000 feet vs 2000 feet? The air is 80% thinner up there, drastically reducing drag, much more than offsetting the cost of the climb. Different paths with different losses.

The Prius can't climb as high, so can't get a similar drag reduction and fuel savings as a commercial airliner, but it can get a non-zero savings.

You completely misrepresent my claims. The trip still requires a significant amount of fuel. I'm describing how to reduce that fuel under certain carefully selected circumstances and path choice, not eliminate it.

Gasoline engines are notoriously inefficient. There are ways to operate them for noticeably improved energy conversion, just go into any hypermiling forum to learn some of the details. Some of these methods are linked with particular path choices.

Irrelevant to the issue at hand. A vertical drop follows an infinite slope, which I have very specifically excluded because it uses energy-wasting braking on the descent. Look instead for using that vertical inch to move that car at least four feet forward.

You seem stuck in a box with blinders, indirectly claiming that the fuel cost of moving a vehicle between two points is a fixed, immutable constant, not a basket of variables that can shifted around and optimized. This is then an excuse to not even consider any possible alternatives to reduce the still considerable wastage.

Step out of that box, and take off those blinders. Take a road trip from LA to, across, and back from the Rocky Mountain high plateaus, and watch your MPG compared to the same distance at sea level. Mine gets better up there in Colorado, even before descending home. Then degrades after I return to near sea level.

 

I'm not going to get into the physics debate, but I will say I do get surprisingly good efficiency in the mountains. Probably because it's essentially extreme pulse and glide, plus the average speeds are low when not on the highway. For example, I can go from my house to Rocky Mountain National Park and back, about 100 miles round trip, on 1 charge and around 1 gallon of gas (if the car reports mpg accurately). I live at around 5,100 feet and the point where I usually turn around is at 10,800 feet.

My record for EV range is starting at the top of Mount Evans (14,200 feet) with 1% battery remaining. From there I drove about 60 miles to somewhere in Denver (5,200 feet), all in EV mode. So that's 60 miles on 0.06kWh if you don't count the potential energy of starting at the top of a mountain. I hit a high of around 80% charge near Idaho Springs on the way down. It took a lot of gas to get up to the summit of course. I think I averaged 30 mpg on the way up.

Both of those drives have low average speed, 25-45mph for much of the way down. At highway speed it takes more power into the battery to maintain speed on the same grade, and it quickly gets beyond what the battery can accept. I don't remember the specifics, but the battery can take something like 12-15kW regen almost indefinitely as long as the temperature is reasonable and the state of charge is low, but at 18-20kW it will only allow that for a couple minutes. It tops out at 40kW, but that is only allowed for maybe 10 seconds.

EV efficiency seems to drop off sharply above around 50% power, so climbing hills in EV mode is probably not ideal. Or in other words from 0-50% power it almost doesn't matter how you accelerate. But from 50% to full throttle there seems to be a pretty significant drop in efficiency. HV mode remains remarkably efficient going up sustained climbs, although I wonder if it's less efficient at very low speeds because of the way the transmission works?

 

These sorts of trips would be interesting to better break down, if the Prime would give sufficiently detailed reports on each mode. Which I understand that it does not.

My own manual transmission Forester (EPA 28 highway, 24 combined) gets 36 mpg going up and down I-70 in western Colorado (e.g. Utah border to Aspen and back) in winter easier than it can get 33 mpg here in western Washington any time of year. Since some of that is from reduced Otto-cycle pumping loss at high altitude, and Prius's Atkinsonized engine has improvements to reduce pumping loss even at sea level, it probably won't see as much gain from the higher elevation.

 

Please explain for me using physics and showing your calculations how you can move a Prius over a hill using no more energy than moving it the same distance on level ground.

Aren't you the one arguing that it's going to require the same amount of fuel energy to make either trip with different variables (i.e., hills vs flat terrain)?