Efficient driving for a 1,000 mile tank

You are of course welcome. But there is more.

I have been running a dashcam test in parallel. When I get home, I'll export the "*.kml" files and upload them to one of my summary reports. Unlike Consumer Reports and others, I'm a great believer in sharing everything associated with this experiment. Better engineers, scientists, and empiricists are not afraid of sharing their raw data and analysis.

Here is the gas receipt after adding one gallon and driving about four miles:

I am pretty sure this was a 'short fill' marathon. I should have gotten another hundred or so miles to 'dry tank' but there is no need to repeat the experiment. Once the lessons are learned, time to look for new puzzles.

Bob Wilson

 

The 'zip' file contains a folder with Google Earch "kml" files showing what I did on Sunday. They show my driving speeds and routes but not what you see in the cabin. They can help in the "route planning."

I have some movies showing the cabin displays but they are too large to post here. So this morning before work, I started working on how to share. I should have something up in a day or so but here is the protocol in text:

STATE: coldstart

1. Set car to "Energy Display"
2. Accelerate to 26-27 mph and set Cruise Control
3. Drive car normally while it warms up - takes ~5 minutes or 2 miles or when engine coolant reaches 70C

STATE: in "D" and cruise control set 26-27 mph

1. Drive car to avoid being a "rolling road block" . . . the hardest part . . . involves route and time of day choices.
2. "Energy Display" shows current into traction battery -> shift into "N"

STATE: in "N" and speed above cruise set speed, 26-27 mph

1. Drive car to avoid being a "rolling road block"
2. If speed becomes excessive or 46 mph, shift into "D" and light braking to moderate speed
3. If speed approaches set speed, 26-27 mph -> shift into "D" and "Resume" cruise control

STATE: approaching a hard stop or stop-light

1. Shift into "D" and no one following, early, lightly brake to ~15 mph
2. Shift into "N" approaching stop light
3. If you must stop, shift into "D" and come to a complete stop

Just make sure each trip takes an hour so you need a place to 'do laps.'

GOOD LUCK!
Bob Wilson

 

Ok, this is how efficient driving works (Cliff notes at the end) :

SET CRUISE CONTROL SPEED AND SHIFTER IN "D" WITH ENERGY FLOW DISPLAY

Once set, the speed will stay within 1 mph of the set speed, feet on the floorboard:​

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The Prius will automatically send power to the wheels and excess power to the traction battery. In this case part of the power is also going via the electrical path to the wheels:​

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The engine is running at maximum efficiency and excess energy is banked in the traction battery. Ordinary cars including diesels can not do this because as their engines produce less power, the engine mechanical drag significantly reduces the efficiency. Idling diesel or gas engines are the least efficient ways to burn fuel.​

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If the load is a little less, the engine will continue to run at maximum efficiency with power to the wheels and some excess power to the traction battery:​

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Again, maximum engine efficiency at cruise control set speed and excess power is banked.​

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Here the car has turned off the engine so the traction battery is using the previously, banked energy to sustain the speed:​

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Remember, this excess energy was generated with the engine running at maximum efficiency.​

WATCH FOR ENERGY COMING FROM WHEELS TO TRACTION BATTERY:

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This must be on for about 1/4 second before shifting into "N" after the engine stops.​

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Here is the actual shift:​

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SHIFTED INTO "N" PRESERVING KINETIC AND USING POTENTIAL ENERGY

Monitor speed and reduce by shifting into "D" to say within speed limit or back to "N" to preserve speed:​

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WHEN SPEED DECAYS TO CRUISE CONTROL SET SPEED

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• Shift into "D"
• Pause 1/4 second
• "Resume" cruise control, lift stalk 1/4 second

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
The goal of efficient driving is the engine always operates at peak, efficiency. The car will 'bank' the excess energy in the traction battery or in the potential energy going up a grade. Cruise control will handle speed control and all the technical details are handled by the Prius computers. But what goes up must come down.

On a downgrade, assuming the speed limit is higher than the cruise control set speed, let the car turn off the engine, shift into "N" and gravity will maintain speed. If the grade is steep enough that the speed approaches the speed limit, shift into "D" and bank the extra potential energy back in the traction battery. If it is still about to exceed the speed limit, light braking while in "D" will bank more energy in the battery. On a well chosen route, the feet remain on the floor.

When the downgrade finally levels out, go back to "D" and cruise control "resume". Any excess energy in the traction battery will sustain the kinetic energy. Then the car will turn on and efficiently run the engine and until the next downgrade.
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
For pilots, engineers, science students, and scientists, the Prius has these sources of motive energy:

• kinetic - 100% efficient - increasing kinetic energy means higher speeds which increases drag energy losses. Not a good tradeoff. Try to keep speeds a low as possible to minimize drag energy losses. But preservation of kinetic energy is a win-win. In driving, look for routes with a minimum of hard stops and maximum of YIELD intersections including right turn YIELD. Approach a red stoplight at an early, slowed speed, say half of the cruise control set speed, to give the light a chance to turn green and preserve that part of the kinetic energy.
• potential - 100% efficient - using potential energy to sustain speed within the speed limit range minimizes drag energy losses. Excellent source if the route includes long, shallow, slopes.
• traction battery - ~80% round trip efficiency, it works more as an energy bank for excess engine power. Do to round-trip, energy losses, avoid if potential energy or kinetic energy can be used. It is a unique capability of the Prius.
• engine - ~35-38% efficient - converts gasoline energy into motive power with excess energy banked in potential, traction battery energy, and sustaining kinetic energy (aka., cruise control managed speed.)

* * * * * * * Cliff notes version * * * * *

• Set cruise control for 26-27 mph and monitor energy display
• When wheels alone are charging battery, shift into "N"
• When speed reaches cruise control set speed: shift into "D", and then cruise control "resume"

Bob Wilson

 

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Bob Wilson

 

With power to the Garmin GPS now shared with the dashcam, I've been able to check the calibration:

• 100.4 miles (GPS) / 100.0 miles (indicated) -> 100.4% distance correction factor
• 1,004.8 miles (GPS) ~92.2 MPG

I wanted to make sure as I knew my tires and odometer were within 1%. It is nice to know the odometer was reading low.

Bob Wilson

 

Potential energy is from changing the altitude. It is stored when the car drives up a grade and returned when the car rolls down a grade and independent of battery power. It has 100% round-trip efficiency minus drag.

Kinetic energy is the energy from changing the velocity. It is stored when the car accelerates and returned when the car coasts down with just drag slowing down the car. It is independent of traction battery and potential energy. It too is 100% efficient minus drag.

Battery energy is saved by charging, typically 90% efficient. Battery discharge typically has 90% efficiency. It is independent of potential energy, the altitude change. Round trip, 81% efficient minus drag.

Drag is typically represented by the EPA as a 2nd order, polynomial as a function of speed:

• A + B*v + C*v*v
  • A - lbs
  • B - lbs/mph
  • C - lbs/mph**2

Since drag is a squared function of velocity, it is important to minimize speed which is why cruise control is used. The only time velocity increases is when the car is rolling in "N" down a shallow grade and the rate of potential energy loss is greater than the drag . . . typically adding 5 mph to the 26-27 mph cruise control speed.

Bob Wilson

 

It took 45 hours of sitting and watching the traffic and the displays including the Scangauge. In effect, meditating on the energy flows. Then I noticed:

• 0.20 gal/hr - fuel flow to engine when in no-load, idle
• ~0.60 gal/hr - minimum fuel flow when engine running up to ~1.20 when climbing a grade

There appears to be a 'forbidden' zone between 0.20-to-0.60 gal/hr . . . why?

Regardless of cause, the effect is to put the engine in a higher efficiency, operating point. The mechanical drag that vampires some the engine thermodynamic efficiency is diluted by the higher power setting. But what to do with the excess power . . . bank it in the traction battery.

It was the curious gap between 0.20-to-0.60 gal/hr. that 'turned on the light.' It is analogous to how making each trip last 60 minutes diluted the 5 minutes of initial warm-up, ~30-35 MPG, with 55 minutes of 99.9 MPG. Do the partial fractions:

• 30*5 = 150 mpg-minutes for 5 minutes
• 100*55 = 5500 mpg-minutes for 55 minutes
• 5650 mpg-minutes / 60 = ~94.2 MPG ... pretty close to the 91.8-92.2 MPG

We are used to thinking of engine thermodynamic efficiency as driven by Carnot's law and that is true IF we ignore the engine mechanical drag. But the engine mechanical drag exists and turning over the engine puts a load so all of the idle fuel flow is being spent to overcome this drag. When you envision engine mechanical drag as a brake, you begin to see the internal energy flow due to mechanical drag. But increase the engine power even a little and the mechanical drag becomes a small fraction of engine power . . . the excess goes out of the shaft.

In the case of our Prius, this excess power, the power generated at a fuel flow of 0.60 gal/hr and higher, can go into potential energy, climbing a slope, or into the traction battery, or any ratio of the two. Just I did not see 0.25-0.55 gal/hr or anything between 0.20-to-0.60 gal/hr. Either the engine was off and the car sustained velocity from either the traction battery charge or any available potential energy descending a grade OR the engine was running 0.60-1.20 gal/hr and providing power to the front wheels and traction battery including ascending grades.

Bob Wilson

 

This is not easy stuff to master. When I was an engineering student many decades ago, we learned that many problems that were intractable doing a forces analysis became much simpler and provided equally useful solution with an energy flow analysis. In math it is the equivalent of transforming impossible to deal with problems into a different format that can be resolved and then transforming the result back into the original. Sorry, I don't remember the exact terms, just the processes involved.

I'll try to work up some PowerPoint charts (aka., today's version of a blackboard) and see if I can make it clearer.

Bob Wilson

 

I

It is not an rpm gap, it is a fuel consumption gap that is difficult to notice . . .

I'll address it in the charts.

Bob Wilson

 

The answer lies in the 'operating line' in a BSFC chart. Frank did a really nice graph about a month ago of actual measurements. I'll have to check my home resources to find the exact chart but the essence is this:

1. Initially, the ICE rpm stays constant but the torque varies as the operating line ascends vertically.
   • Torque is increasing which means power out (and fuel consumption) is increasing but the ICE rpm remains constant.
2. There is a 'knee' when the ICE rpm heads to the right (increasing ICE rpm) about a 20-25 degree angle as rpm increases and torque increases marginally.

We normally work in the higher power regions where ICE rpm is somewhat (NOT LINEAR) proportional to the power out. But these are regions outside of slower, urban speed power regions.

Bob Wilson