Shouldn't FE go up faster than it goes down.

[John Sparks]

Okay I consider myself a fairly intelligent person but the one thing that I truly suck at is mathematics.

 

What I don't understand is this: say I drive .5 miles in EV then .5 with the ICE, then another half EV.

 

In the middle of this scenario when the ICE is on the mileage drops rapidly understandable but, when switching back to EV it's much slower to go back up. This of course is the case, the mileage levels off but still you loose mileage faster than you gain it.

 

I know this is how it is but my mathematics deficient brain doesn't completely understand it. When in EV mode the car is using no fuel at all. Infinity mileage and when the engine comes on it is not the complete opposite. You are achieving mileage. Whether it be 20 mpg or 40 mpg.

 

This confuses me. Getting unlimited mileage should bring up overall mileage opposed to the ICE bringing it down faster while it is indeed getting mileage out of the gas.

 

Am I making any sense here? I know there's nothing that can be done but, it bugs me cause to my small brain it doesn't make any sense. If anyone can explain it, please do.

 

Thanks. :)

[plus 3 golfer]

It may appear that way but it depends on when you take the snapshot of the FE.  A small change to a small number all else being the same results in a larger % change than the same small change to a large number.  Think of it as fuel used not infinite mpg. FE = Miles / Fuel used.  Dividing by zero has no meaning because any number (X) multiplied by zero = zero.  So in the formula FE = Miles / 0 or Miles = 0*FE = zero. Thus, the FE is not infinite but undefined for pure EV operation. So, it depends on the gallons of fuel used when the snapshot is taken and then change in gallons of fuel whether running in EV or ICE as to the effect on FE. 

 

Here's a curve that might help explain it.  The FE curve is a hyperbola such that when the total fuel used is a very small number (towards zero on the X axis, one will see large changes in FE (Y axis) for changes in fuel used.  But if the fuel used is a larger number for the same miles (towards the right on the X axis), then for the same small change in fuel, there will be a small change in FE.    So, it matters where one is one the curve when one takes a snapshot of their FE.  But it really doesn't matter whether one drives in ICE first or last as long as the distance and fuel used is the same.  It's the total miles / total fuel used.  Hope this helps.  Maybe someone can explain it better.

 

 

[fbov]

And in 25 words or less...

It's about how you spend your time. You spend a lot of time moving, and very little time using fuel, so fuel acts more quickly!

 

Make sense?

 

Your example is a 1.5 mile drive with ICE on for 0.5 miles. The ICE effect must occur in 1/3 the time, so it happens 3x faster.

 

Frnak

[plus 3 golfer]

Yep makes sense but hard to visualize. :) Here's the same curve above with a simple example for 2 legs: first virtually all EV for a mile and then ICE for a mile.  Now add a third mile of virtually all EV at 200 mpg to the example.  

 

What's the change in FE after 2 miles from mile 1? shown on graph at 150 MPG decrease 

What's the average FE after 3 miles? (3 miles / 0.045 gallons) = 66.7 MPG

What's the change in FE from mile 2 to mile 3?  66.7- 50 = 16.7 MPG increase

 

What is material is the fuel burned whether ICE runs, EV propels the car, you go up a long grade or down a long grade. So, two legs at 200 MPG + one leg at 28.7 mpg is only 66.7 MPG not the simple average of the 3 legs (428.7/3) = 142.9 MPG.  Even if you burned zero fuel in the EV legs, the average MPG = 3 miles / 0.035 gallons = 85.7 MPG up from the 66.7 but not anywhere near the 142.9 simple average of the legs.

 

 

Edited March 18, 2014 by Plus 3 Golfer

[HPRifleman]

The further you go, the more miles driven/fuel used the mileage meter has recorded. With more data it takes longer to change the average mileage number.

 

For example, right after you reset the mileage meter it displays numbers based on very little data so there is a lot of variance. As you travel further there is more data to make a more stable average.

Edited March 19, 2014 by HPRifleman

[John Sparks]

Thanks guys! :)

 

I understand that the more miles averaged in means that overall fuel economy is going to be less affected. I also understand that it ultimately boils down to fuel used for miles driven. It just always seems that regardless you always loose mileage faster than you gain.

 

I wonder if you could do a controlled test with same terrain, wind, load, etc, what the results would be.

 

I guess considering the conditions that make the engine come on, around here it usually has to do with going up a hill but not always, could be the largest factor. It just confuses me how sometimes when I turn off the car I have a high EV percentage and my mileage is not as good as times when the EV use is less but then sometimes it is. I guess that leads back to load on the engine, etc.

 

Like I said I consider myself fairly intelligent but this probably makes me sound like an idiot.

[fbov]

No, John, it makes you sound like someone trying to figure something out.

 

There are two patterns I see, that other have discussed:

- high MPG is correlated with high EV mileage fraction - the more you drive EV, the better the MPG.

- High EV fraction is correlated with high ICE fuel consumption

 

The first is obvious; use less fuel by not running the ICE, which is what uses fuel.

 

The second isn't... and it gets right back to load on the engine, as you suspect.  The guys getting high mileage, get very poor mileage when using ICE - they get the most energy out of ICE when it's on, but only use it sparingly. Here's a comparison from lasst September, when it was warm enough to make the comparison...

- rural route

47.1 MPG and 68% EV, but 15.4 MPG when ICE is running

- expressway

41.9 MPG and 33% EV, but 27.9 MPG when ICE is running

 

It's clearly better to run 2/3 EV than 1/3, even if the engine's using nearly twice the fuel/mile when you do!

 

BTW,  ICE-running MPG is

- (total miles/MPG) = fuel used

- (total miles - EV miles) = miles when ICE is running

- ICE MPG = (miles with ICE running / fuel used)

 

Have fun,

Frank

[SnowStorm]

It could be just an issue of initial conditions.  Look at the following graphs where we start with different initial conditions for SOC and whether ICE is ON or OFF.  The modeling assumes a long term average of 50 MPG and the ICE running 50% of the time (1 mile per cycle).

 

Here we start with a "full" battery and the ICE OFF.  Indicated MPG will be "infinite" (999.9 if it shows at all) until ICE turns ON and MPG drops like a rock to 50 MPG.  Then it goes to 74 and back down to 50.  Each cycle drops more than it goes up because the long term average must settle "down" to 50 MPG.  Dark blue is SOC and Magenta is MPG.

 

Now we start with an "empty" battery and the ICE ON.  Indicated MPG is steady at 25 until ICE turns OFF and MPG rises to 50 MPG.  Then it drops to 37 and goes back up to 50.  Each cycle rises more than it drops because the long term average must settle "up" to 50 MPG.  In this case you could say "FE goes up faster than it goes down".  It all depends on the initial conditions.

 

Not surprisingly, if you start with SOC at 50% (ICE On in this case), the graph centers around the long term average.

 

All of which goes to show why its best to start (and if possible end) all comparisons with SOC at 50%.  Things work out a little nicer.

But if you're trying for the 600 mile/tank club, start with a full battery (jus' don't tell Jus! :secret: )!

[salsaguy]

This is why using "average" is a bad measurement/statistic ssometimes since extreme values (high or low) have a big impact on it, whereas using median does not. But it's what we use here in the USA so we live with it. Don't worry just be happy to be getting 38-48 mph in your cmax compared to your previous cars mpg ;) 

[John Sparks]

Thanks again guys.

 

Interesting graphs SnowStorm. Kind of goes back to what Frank was saying. It all comes down to load / conditions.

 

Salesguy, I guess you refereeing to how in metric it's measured L/100 Km? Honestly mpg avg is easier for me but then again I'm not a custom to using the metric system. BTW my last car got 46-53 mpg depending on the time if year. :)

 

I'm expecting to get better out of my Cmax but I'm am concerned with the gauge to gas pump discrepancy. I have seen where others have used a gps to track miles, etc. and their figures have came out slighty better than the car so the jury is still out on that for me.

[plus 3 golfer]

John, I think you are still missing the point.   It's where you start (take the snapshot of the FE) not about the load / conditions as changes in load / conditions needs to be held constant in "testing".  All that is being varied is the starting point.  SnowStorm's curves are simply the application of the basic FE curves in my posts above and show that if one starts with high FE, the FE decrease is greater as you fall to approach the average.  Start with a low FE and the increase is not as great (compared to the decrease) as you approach the average.  Look at the curve in the 4th post.  If you start with EV and then run ICE, FE drops 150 mpg.  If you start with ICE and the go to EV, FE increases by only 21.4 mpg.  Carry this alternating ICE, EV out and one approaches the average FE over time (SnowStorm's curves).   Adding in other conditions, doesn't change this fundamental principle.   I think this should answer your questions:

 

"Shouldn't FE go up faster than it goes down" and  "This confuses me. Getting unlimited mileage should bring up overall mileage opposed to the ICE bringing it down faster while it is indeed getting mileage out of the gas." 

 

As far as the metric - using "L/100km, it doesn't matter.  The principle is the same.  Don't really know what salsaguy is referring to.

Edited March 19, 2014 by Plus 3 Golfer

[plus 3 golfer]

I have one more thought as to why it may be difficult to see why operating ICE decreases EV FE more than operating EV increases ICE FE (which is substance of the OP).  Most of us have driven non-hybrid cars and see FE ranges in say the 30 - 40 mpg range.  In this 30-40 mpg range, it will be difficult to see any difference in magnitude of FE change between 1) starting with high FE then low FE compared to 2) starting with low FE, then high FE.  In other words, going from 40 mpg to 30 mpg in successive miles will yield about an average of 34.3 mpg overall or close to the simple average of 35 mpg.  

 

Below is my graph from above with two straight lines added to illustrate this.  The straight green line represents what the FE curve would have to look like for the there to be the same magnitude of change going from high FE (200 mpg) to low FE (28.7 mpg) or low FE to high FE.  As one can see, the green line is very far away from the FE curve indicating that the relationship between MPG and fuel used is not linear.  Hence the simple average of 200 mpg and 28.6 mpg or 114.3 mpg is quite a bit more than the actual FE of 50 mpg.   

 

Now, looking at a typical non-hybrid vehicle range of FE of  say 30 - 40 mpg, the orange-dashed straight line is virtually the same as the FE curve in that 30 - 40 mpg range.   This means that the magnitude of increasing or decreasing FE will be virtually the same.  The FE curve is virtually linear in this region and hence one sees a very linear relationship between FE and fuel used.  I can then see how one might think that a high FE leg  (for example, EV operation in a hybrid)  should have a large effect on increasing overall FE.  But it won't because such EV operation is at one extreme of the FE curve. 

 

So, with the hybrid we need to rethink what we saw in the past with non-hybrid vehicles and recognize this non-linear relationship between FE and fuel used for hybrid operation and how it affects overall FE.    

 

Edited March 19, 2014 by Plus 3 Golfer

[anilruia]

Assuming that you are averaging fuel economy achieved over equal distances, using MPG, the average is the harmonic mean, vs with using GPM (or L/100k) it is the arithmetic mean.

So, if you achieved 20MPG using ICE and 80MPG using EV, your average will be 32MPG - so much closer to the lower number.

The same fuel efficiency, you got 5G/100M using ICE and 1.25G/100M using EV, the average is 3.125G/100M which seems much more intuitive.

That is the problem with using MPG for measurements as it inflates the distance when you get to higher MPG and compresses lower MPG together.

[plus 3 golfer]

Yes, the metric system simply uses the rate of fuel per unit distance and thus one can use the simple average for equal distances.   This may be what salsaguy was referring to above. But I have no idea why he brought up the median. So, in the metric system pure EV FE = 0 L/100 km where in the mpg system full EV mpg is not defined. 

 

Also, for those interested, to get the harmonic mean one takes the reciprocal of the average of sum of the reciprocal mpg = (1/((1/20)+(1/80))/2) = 32 mpg.  In my graph above, the average FE = 1/((1/200)+(1/28.6))/2) = 50 mpg.  It's a little hard intuitively to compute average FE over equal distances in the mpg system. :)

[fbov]

Assuming that you are averaging fuel economy achieved over equal distances, using MPG, the average is the harmonic mean, vs with using GPM (or L/100k) it is the arithmetic mean.

So, if you achieved 20MPG using ICE and 80MPG using EV, your average will be 32MPG - so much closer to the lower number.

ONLY if the ICE and EV data were for equal length segments... you've got the math right, but you've given each equal weight, and that's a very rare occurance. The curves look like this for your example.

 

In fact, anyone who tries to average the actual MPGs is in for a rude awakening, as EV doesn't use fuel, so mileage in EV is infinite (aka the inverse fo zero). I've used your values for the chart.

 

HAve fun,

Frank

[anilruia]

Well, even if you assume you got 20MPG with ICE for 100miles and infinite MPG with EV for 100 miles, that would still average out to 40MPG, much lower than what you would intuitively expect given that you are averaging with infinity on one side.

[John Sparks]

Well, even if you assume you got 20MPG with ICE for 100miles and infinite MPG with EV for 100 miles, that would still average out to 40MPG, much lower than what you would intuitively expect given that you are averaging with infinity on one side.

 

Okay for some reason this is what clicked. You drive 100 miles you've used 5 gallons, you drive 100 more in EV, you've still used 5 gallons. It goes back to what plus 3 golfer said. It's all about fuel used. Honestly it still doesn't seem right, but like he said you cannot assign a value to EV, technically it should be infinity but it doesn't work that way.

[Noah Harbinger]

Yes, the metric system simply uses the rate of fuel per unit distance and thus one can use the simple average for equal distances. 

 

Just being a nit-picker, but there's nothing inherently metric about quantity per distance.  Gallons per 100 miles makes just as much sense, for these purposes, as liters per 100km.