Which acceleration from 0 mph has the highest MPG?

Thanks! That was what I was looking for.

I do find that there is some speed-dependency in the HSI, where higher vehicle speeds shift the scale on the HSI, e.g., higher revs or kW would be at the edge of the ECO zone at 50 mph but well into the PWR zone at 25 mph.

I also find when climbing a 7%-ish grade from 25mph to highway speeds that staying below 2500 rpm seems to get slightly higher fuel economy; but isn't too far off until 3000 rpm.

 

Thanks, here is the BSFC chart I was remembering:

Thanks Toyota!

There is a broad range of rpm, ~1,400 - ~3,200, that stays in the area of peak engine efficiency. Closer to the center avoids excursions outside of the peak efficiency area.

Bob Wilson

 

I drive in very hilly terrain in high traffic density ( traffic light density is about one traffic light signal every 0.5 kilometers or 1/3 of a mile) where traffic jams are frequent. I found that ECO mode tended to frequently cause the battery level to drop below three bars in my daily commute (15.8 miles, +55 traffic lights) - this caused the Prius ICE to automatically recharge the HV battery which cause the Prius MPG to drop. Switching to PWR or normal mode helps reduce the drain on the HV battery - but switching to the ICE at a lower speed during acceleration - has almost eliminated the drain on the HV battery levels and boosted the Prius' overall MPG.

The optimization of MPG on the Prius as well as other cars is to make the most efficient use of the momentum generated by the acceleration. The heavier the car the more costly braking is when the car must comes to a complete stop and loses all of its momentum. The 3rd generation Prius is a fairly heavy car so braking is expensive wrt to fuel efficiency. However, if a Prius doesn't have to brake then its MPG jumps up. For example, during the summer, I time-shifted my 15.8 mile commute to when the traffic lights are all turned off which allowed me do greatly reduced the need to apply the Prius' brakes -- my Prius' MPG (as measured by a ScangaugeII AVG Xgauge) jumped from 65 mpg to +80 mpg per trip ( I've did this several times to meet the PriusChat 800 mile on one gas tank challenge). Every time the Prius has to brakes it loses momentum generated by the acceleration and this causes its overall MPG to drop. The Prius' regenerative braking recaptures some of the energy during the braking process but not all - the Prius' regenerative braking only recaptures about 10% to 50% of the braking energy. The most important hypermiling technique one learns is to maximize MPG is to minimize the amount of braking required. No matter how efficient the acceleration - the amount of braking either by the driver or the on board computer will cause the Prius' MPG to drop. The Prius is more difficult to hypermile than a regular car because the Prius has extra modes where it will automatically brake when the driver is not applying the brakes and when the car is not in cruise control - a driver seeking to optimize a Prius' overall fuel efficiency has to be aware of this.

In addition, as Bob Wilson has previously charted for us on PriusChat, as the Prius' speed goes over 25 mph its overall MPG will start to drop -- regardless of how efficient its acceleration was.


There is a Wayne Gerdes-Hobbit method of accelerating with a ScangaugeII - accelerations events are limited by LOAD (LOD) Xgauge so that 70 <= LOD <= 80. The Gasoline used per hour (GPH) can vary greatly based on whether the Prius is going uphill (+1.4) , going on an approximately flat part of road (1-.8) , or going downhill (<.6) when the LOD is fixed at 75. Simply put - it is more efficient to accelerate when going downhill and less efficient to accelerate when going uphill. This phenomena is called gravity assist [1].

[1] Gravity assist - Wikipedia, the free encyclopedia

 

I think this is because it's taking into account the efficiency of the total system, not just the engine. The engine can only deliver a fixed amount of torque directly to the drive wheels, so as it revs higher it's spinning MG1 faster to generate electricity to provide more torque via MG2.

It seems to me that the HSI is an indication of how much torque is being supplied to the drive wheels. In the ECO area, the engine is supplying most of the torque and not much electricity is being generated. In the PWR region and above, the MG1 -> MG2 path becomes a significant source of torque, which is less efficient due to electrical losses. At low speed, the engine doesn't need to rev fast to spin up MG1, so the HSI fills very quickly.

Have you ever noticed that if you hold the HSI in a steady position, the speedometer changes at a very steady rate across a wide speed range?

 

There's a hill behind our place, the main drag climbs it, with a lot of jogs and switchbacks. There's also a power line that goes straight up the hill, with a steep path, frequented by folks looking for cardiac workout.

That was our goal, but to reach the start of that path you need to walk up the first stretch of the hill-climbing road. Walking along you see the denizens from up the hill taking on that road in their cars, with straining engines. It really drives it home: hill climbing with a ton or two of steel is hard work.

 

Obviously it's easier to accelerate going downhill, but efficiency isn't the same as ease. Efficiency is useful energy delivered, divided by energy consumed. Accelerating downhill sometimes requires zero energy, in which case efficiency is zero, or undefined.

 

Right. That's why, I believe, best overall efficiency occurs at a lower engine speed when the car speed is slow than when the car speed is higher. The HSI takes that into account.

 

That does make sense, I should look at the MG1/MG2 torques at different speeds and throttle inputs.

 

A roller coaster and a soapbox derby racer are two examples of vehicles that rely only on gravitational forces to create acceleration, speed, momentum, and work (distance x mass). Any vehicle (with or without an engine) will have less work to do as long as the vehicle is working in the direction of gravity. A powered vehicle's energy efficiency is basically the same after 45 minutes of warming up - but the cost of warming up from a cold start climbs as the driving temperature drops below 60 degrees Fahrenheit- the bigger the engine the higher the cost of warming up. If one uses a engine block heater the cost of warming up mitigated the ICE cold start cost but the Prius does not normally come with an EBH. An ICE running efficiently does not translated to high MPG if the vehicle remains parked. A Vehicle's ICE energy efficiency is necessary for high MPG but it is not the only contributing factor to High MPG. High MPG also depends on the transmission, wheels/tires, and the driving environment. The driving environoment is a bit tricky part of this equation. Aerodynamic drag can be lessen by a tail wind ( wind moving from the rear to the front of a vehicle) when the vehicle is moving forward. With no wind, as the Prius goes over 25 mph aerodynamic drag eats away at its efficiency as Bob has charted out. In addition, if the roads are not smooth or dry - then as rolling resistance increases the Prius' energy efficiency drops. Driving with snow tires or with chains on the tires will increase road traction in the snow but it lower a Prius' MPG.

With respect to experimenting with the Prius fuel efficiency - the DOE tested the Prius on the ICE efficiency already -- they had data logging OBDII-laptop monitor to get real time rpm/fuel usage data. Initially I tried to use RPM on my Scangauge II to get the best MPG but then realize that low RPM doesn't equate to the best use of power. A low GPH doesn't always equate to the best MPG either. The answer I found was this - - conserving the vehicles momentum so it doesn't have to stop and getting the most distance for every ounce of gas burns is what increases MPG. Smaller more aerodynamically efficient, lighter weight vehicles tend to get the best MPG.

 

Either of these two rules of thumb work fine:

1. rpm between 1500 - 3000
2. instant MPG = MPH, or within about 20% of equality

 

Thats some serious testing Lexel, good stuff and thanks for taking the time to get those results and posting.

Can someone translate Lexels Method from KPH to MPH…

Thanks

 

MPH ~= KPH / 1.6

Bob Wilson

 

Nice! Some other bits of data that you could glean from your measurements (though additional data could improve the accuracy):

Charging the battery is about 27% efficient. (A gallon of gas has ~120 MJ of energy, which is about 31.7 MJ/liter. Taking the nominal battery voltage of 273.6V times 30712 Amp-seconds yields ~8.4 MJ. 8.4/31.7 ~= 27%)

According to some articles that discuss the next-generation Prius, the current generation ICE has 38.5% thermal efficiency. If the battery charging were happening at that peak point of efficiency, then the efficiency of the planetary gears, motor, and charging the battery would only be about 70%. On the other hand, the best thermal efficiency might be at a slightly higher-power point, which could reduce the lifespan of the battery, so they may sacrifice some engine efficiency there for battery reliability. I'm not sure I've seen what the transmission efficiency is, but 90-something percent is probably not a bad guess. I'd bet that the efficiency of the MG and charging is probably at least 80%, maybe even close to 90%.

 

Tables make the data a little clearer

	Km/h	mph	power
1	0-20	0-12.5	EV
2	20-30	12.5-19	1/2 to full ECO
3	30-50	19-31.25	low PWR

​

• ~29 Km/h (18 mph) - peak mileage speed (my benchmarks from 2003 Prius)
• low PWR - ~3,200 rpm, the peak, cooled, EGR value measured via miniVCI

This profile shows the change in speed is roughly proportional to the change in power. The lowest speed range is in the battery region and the highest speed range at the peak engine efficiency. Without going into the math, the vehicle kinetic energy looks to be proportional to the power setting. Begging the question, what about higher speeds? . . . "low PWR" is the best range. FYI, the car is fairly brisk at this speed, certainly adequate for Huntsville AL urban driving.

Bob Wilson

ps. The following table tags make it easy:​

"table=head" enclosed in "[]" - starts a table with the next line the column headers
"," or "|" separate columns with each line being a row
"/table" ends the table enclosed in "[]"​

 

Good god.
I love this place, and I love you guys...

But sometimes you all are a little heavy on the charts, graphs and scientific analysis.

IMO just accelerate safely, but aggressively, get up to speed and then let off.