calculated vs. computer MPG - Please post your results

Thanks much for posting this thread. I bought my 2010 Prius I in June and have been tracking my actual vs computer MPG results regularly since I've driven the car. I live in Vermont and travel a lot on different road types and conditions (dirt, secondary, interstate). I typically drive with the EcoMode on, whether I'm driving city or highway. Keep in mind that Vermont is a hilly state and my efficiency varies depending on where I'm driving (variance ~ 4 mpg across 10 fill ups).

I've been disappointed in how the computer has overestimated my efficiency. Here are my stats after about 10 different fill ups and tracking:

Actual calculated average MPG: 52.1
Computer generated MPG: 56.7
Average difference: 4.5

Does anyone wonder whether this difference we're seeing is due to the way the Prius computer estimates efficiency based on a time-weighted average rather than a distance-weighted average? This is the first Prius I've owned so I don't know if this has always been the way efficiency has been estimated in generations I and II, but it seems to me that this might explain the difference.

Consider the example below with a total travel time of 60 minutes and travel distance of 40 miles for simplicity:

I drive for 30 minutes in the city at an avg speed of 20 mph (10 miles) and achieve a computed efficiency of 60 mpg. I then drive for 30 minutes on the highway at an avg speed of 60 mph (30 miles) with a computed efficiency of 40 mpg. Because the Prius computer estimates efficiency on a time-weighted basis, my average efficiency for the trip would be 50 mpg on the computer, calculated like this:
((30min*60mpg)+(30min*40mpg))/60min = 50mpg

However, to me, this time-weighted estimation seems flawed because it is not based on an efficiency weighted by distance - which should be the actual efficiency we want to calculate when we divide the total distance traveled between fill ups by the gallons of gas consumed.

If we calculated efficiency in this example with a distance-weighed method, we would actually get a lower value of 45 mpg. The 5 mpg difference is right about what many are reporting between computer and actual efficiency. The math for the distance weighted efficiency goes like this:
((10miles*60mpg)+(30miles*40mpg))/40miles = 45mpg

With this logic I would suspect that people who predominately drive in the city would see a greater discrepancy between actual vs computer MPG than those who drive predominately on the highway.

 

Yes, many have wondered. No, it would make no sense for it to be done like this. And it can be mathematically proven that it isn't.

First, you have to give the Toyota engineers a little credit for being able to understand the correct math and, if they took any shortcuts that it would be a true shortcut. Software-wise it makes no sense to do anything other than to collect distance units and fuel units. Each of these is going to be some small increment, such as a wheel rotation or fuel injected to a cyclinder. Once you are accumulating these, over time, it saves you nothing to do anything like a time-weighted average.

Besides, to prove this, you can just be in EV mode, drive a few feet, then stop, wait for the time-histogram to click over, drive a few more feet and repeat...you'll get lots of 100 mpg bars. Now drive normally and you'll see that those 100 mpg segments did not bias the overall mpg by much at all as a proper calculation would.

The actual reasons as to why the reported mpg iseems to be generally better than the actual pump calculated mpg is probably due to several factors, such as inaccuracy in the fuel consumption measurements and a marketing desire to not underestimate.

3PriusMike

 

Could some of the apparent differences be due to the way the car is filled up, and therefore, how one accurately determines how much gas was really used?

For example, do most people estimate the gas used based on how much goes into the tank when the pump first clicks off, of do they continue to add gas after the initial trip of the gas pump? I know that when a gas pump trips off can vary significantly from station to station, or how far the nozzle is inserted into the fillup hole, etc. If i continue to add after the pump trips off, I can ofen get another 1/4-12 gallon of gas into the tank. So, the question I'm asking is - How accurately do we really know how much gas was used? If I start out with what I think was a full tank of gas, and then fill it up a week latter, with say, 8 gallons of gas, how do I know for sure that I used 8 gallons of gas in that week? Maybe I did not fill it up to exactly the same point as when I started out the week? How do I know accurately to what level I've filled it up each time I go for gas? I don't think I do know with any accuracy greater than +/- 1/4-1/2 gallon. If I fill up until the pumps clicks off, and it says I put in 8 gallons...does that mean I used 8 gallons in a weeks worth of driving? I don't think it does, at least with any accuracy.

I think the only way I know, with any precision, how much gas I really used is to start with an empty tank of gas, and then add a known quantity of gas and run it until empty. That way, the pump and the manner in which the tank is filled back up again is taken out of the equation.

By the way, I'm pretty sure the computer monitors the gas used based on a mass flow meter (monitoring gas flowing through the fuel injectors), and usually, these mass flow meters are very accurate. Back in the days of carborated cars, these types of measurments were quite prone to error...but with fuel injector systems, with mass flow meters, I'd bet money that they are fairly accurate.

 

Another way may be to keep a record of the amount of fuel added over a long distance and many fill ups. The errors will be smaller compared to the total and should tend to cancel each other out. I checked mine over a 3300 mile distance and came up with a 4.5% to 5% error with the displayed mileage being the higher. I think if it were a difference in gas pumps or the amount of in the tank when full the errors would be both ways but everyone who has checked has discovered this same 4% to 5% error always with the display reading higher.

I agree that the fuel flow to the injectors measured by the car will be very accurate, I also know the mileage measured by the odometer is pretty close. I think the only logical conclusion is that this "error" was introduced deliberately by Toyota to try to convince it's customers that the car gets better mileage than it really does. I guess what bothers me the most about this is that Toyota management thinks we are to dumb to notice!

 

I'm not sure Toyota would risk it's good reputation, by trying to fudge the numbers upwards by a measily 4%-5%?? If it was proven beyond a shadow of a doubt, by careful independent studies, that showed Toyota skewd the results, I think that could do big damage to their reputaion in the hybrid market. They already have a winner, so, I'm not sure it would make good business sense to mess with what they already have - for what, 4% to 5% difference?

But I do agree with you that looking at the average number of gallons filled up over a long period, should average out the error that I referred to.

But here's what I do know for fact - over the past month of driving 1200+ miles, I averge between 55MPG and 61MPG, no matter whether I use calculated numbers, or the computer. That's better than the EPA number of 50MPG, so I figure I'm ahead, and not behind what the sticker said. That's really the bottom line for me. I might be upset if I was expecting 50MPG, and I got lower numbers...but that's not the case...at least for me it isn't. Just the opposite - I get better numbers than expected. Maybe we've become greedy?

As a side note, and based on what I read on the computer - the best mileage (for me) is obtained when I'm driving at low to moderate speeds (under 60 mph). As per the manual - once i obtain driving speed on the highway I commute, I take my foot off the gas peddle for a second, and then ever so gently re-engage the gas. Assuming i don't have any significant load (such as going up a hill or trying to accelerate), the electric motor does most of the work mantaining speed. At that point, my MPG's begin to climb steadily.

 

Starting Labor Day, September 7, my wife and I drove from Tucson, Arizona to the Blue Ridge Parkway in Virginia, and back, returning September 22. We drove just over 5,200 miles at freeway speeds and up numerous mountains and hills, with enough luggage, snacks, and things to drink to last us 16 days weighing us down. The average mpg showing on the Prius computer was 54.5. When I calculated our actual mpg after totaling all our gas receipts, it was 54.46. We were very favorably impressed both by our mileage results and the accuracy of our on-board computer!opcorn:

 

I hope I'm wrong about Toyota deliberately fudging the displayed numbers but no one has a better answer at this time. Toyota is a very large bureaucratic organization and this was most likely a marketing decision not an engineering decision. A couple of interesting posts by Ken1784, numbers 63 and 124 of this thread. Apparently other manufacturers, VW for one, have done the same thing with no repercussions. I predict it won't get fixed and Toyota will never comment on it.

I'm not complaining about the mileage, I am doing better than the EPA average also, at least most of the time.

 

Just a quick comment...
The key speed is 46 mph.
http://priuschat.com/forums/gen-iii-2010-prius-main-forum/62635-46-mph-new-threshold-stealth.html
Above and below that speed, Prius acts completely different animal.

Ken@Japan

 

Welcome to PriusChat! Thank you for your post.

How did you determine these averages?

Why do you believe Toyota's calculations are made this way? First of all, it isn't a calculation of anything, but simply a series of mathematical actions. I think you've understood this, but I'm curious why you believe Toyota would make such mistakes.

What would the MPG calculation look like if, instead of driving anywhere for the second 30 minutes, you simply sat in your car? You may say that the mileage for the second 30 minutes is zero, because you traveled 0 miles, so that the only information that mattered would be from the first 30 minutes. But this cannot be the case. You could have sat in the car with the engine running the whole time (therefore using gasoline) or with the engine off (not using any gasoline).

The only calculations that have value are ones measuring the miles and dividing that number by the total gallons used. (See below.)

This is an interesting way of describing the calculation for mileage for the event you described. You need to take the miles and divide it by the total gallons used. You determine the gallons used during each measured event.

For this reason, I'd be a bit more comfortable describing it as this:
40 miles/((10 miles/60mpg)+(30 miles/40mpg) or
40 miles/((1/6 gal) + (3/4 gal)) ==> 40 miles/((4/24 gal) + (18/24 gal)) ==> 40 miles/(22/24 gal) ==> 43.6 mpg

 

Yes, a priori's calculation is correct. There is only ONE way to calculate mileage and that is miles driven divided by gallons used. I'm certain that's how the Prius computer calculates mileage, except that it slightly (5% or so) under measures the amount of fuel used.

 

In taking the time to read back through this entire thread, I realize there's a lot of discussion on HOW the Prius computer estimates efficiency. Although I didn't see any discussion of how incremental efficiency is averaged over time/distance (perhaps I missed this as you indicate). Clearly it would have to begin with an estimation of fuel used over distance traveled - this is not difficult to understand. However, it would seem to me that the time or distance resolution (or increment) with which the computer collects and then sums/averages these efficiency units would matter. Perhaps my naivete on this front led me to jump to the (incorrect) assumption that each bar on the histogram was averaged the length of a trip to estimate the average efficiency.

Yeah... sure I'd love to give the Toyota engineers more credit. After all, they've designed an incredible vehicle that I truly love to drive. But... like most people who have posted in this thread, it strikes me as really odd that they didn't get efficiency estimation right with the computer. Whether intentional or not, this is not a trivial mistake. I think it's really too bad that this is the case, since I suspect that most Prius owners bought the car because of it's efficiency, and now we're stuck with a computer that doesn't really work.

 

wwo
Sounds good ！

 

It is pretty simple. Distance is measured, say in wheel rotations. Fuel in injected drops. Then mpg = d/f *k, where k converts from those units into mpg. When you reset a trip odometer both counters are set to zero and increment over time. Every so often the math is done and that trip mpg is shown (assuming the display is set to show it). Completely seperately, each time you start the car time-based algorithm takes a snapshot of the two values at time 0, then at 1 min, 2 min etc.

To display any bar a simple subtraction finds the fuel consumed during that time period and the distance traveled during that time, calc the mpg and display. Perhaps it stores the mpg for each time period after that or just keeps the raw values -- doesn't matter. The point is that keeping one master set of incrementing d and f values is the obvious way it could/should work and the time-based samples are derived from them, not the other way around.

The fact that there are now two independent trip odometers and thus two mpg's going at once is a minor addition to my theory above.

Yes, I wish that the displayed value was closer than 5% to the pump-measured method...if in fact they are that far apart as it seems they might be. But I seriously doubt the reason is an incorrect digital algorithm. It is just so easy to do it right for anyone who has worked on real-time measurement software. This isn't rocket science...and for the record I was the chief software engineer on a real-time experiment control computer on the Space Shuttle.

Remember, the pump bias is to overreport fuel used (by up to the legal requirement of 0.5%), plus some fuel evaporates. The bias in the car is to underreport fuel used (for marketing). Distance traveled (since we're not using GPS), has errors due to tire wear and probably a few other things.

3PriusMike

 

Ken,

I don't know what the stealth number is, but I do know there is a "sweet spot", where my mileage is high. For me, under my driving road conditions, that seems to be between 30-50 mph, so it does jive with your number.

 

I think this is the answer -

I did some checking around with other manufacturers/cars, and all seem to report the same, ie, the calcualted fuel economy is always lower than that displayed by the car's computer. Some of the same reasons, as discussed here, were also discussed for BMW and Ford automobiles. The one that makes the most sense to me, besides not being able to accurately determine how much gas was used from your fillup number, mentions that the in the calculated mode, gas is consumed during idling, or when the car is not in motion. Now, with hybrid cars, the engine usually (but not always) shuts down when stopped/idling...but, if the battery needs to be re-charged, the gas engine will come on consuming gas. It would appear (?) that the car computer does not factor in gas that is consumed when the car is not in motion (ie, 0 MPG, while standing still). This is fine so long as the gas engine does not turn on during the period when the car is standing still...but if it does, it looks like this small amount of consumed gas is NOT factored into the total amount of gas consumed. If this is what is happening, then the calculated number will always be lower than that displayed by the computer - so this is not just a Toyota error....but is endemic to how most computers software calculates the efficiency when the car is not moving.

 

I appreciate the research you've done on this, particularly in showing that most other manufacturers also have a similar issue. (Whether they also have a 5% overstatement is unknown.)

The fact is, though, that gasoline used while the car is idling is part of the calculation. I have seen the numbers drop dramatically while sitting in the car while the ICE is running.

 

How does the computer handle the fact that no miles have been driven while you're sitting there?

Lets say you are sitting at a traffic light and the engine comes on cosuming X amount of gas for a minute. If I try to average this MPG (for this 1 minute) with the MPG averaged over my trip to this point, what number do I put in for the MPG while I'm standing still? If should be zero, since I'm not moving....so what number does the computer use?

 

The MPG when stopped in non-hybrids is ZERO, because the car is moving zero miles while burning fuel to keep the engine running. In hybrids like the Prius, the battery keeps the gas engine (ICE) off until the charge is near depletion, then if you persist with the car turned on and stopped, the ICE turns on automatically and burn fuel to generate charge to the battery delivering 0 MPG for that period of time!

 

Which is exactly my point with regards to the discrepency between the computer and calculated values for gas mileage (from fillup numbers). In some cases, the engine does turn on for short periods to recharge the battery. If it turns on while stopped, the computer estimates "0 MPG" during that period.

So, the question becomes - What is the algorithm to averge in this "0 MPG" during the period that the car is stationary, and the gas engine is running? 0 miles traveled, divided by 0.1 gallons of gas is still 0 MPG....0 miles traveled, divided by say 0.2 gallons of gas is still 0 MPG, etc.