We're getting to the same place but I'm starting earlier in the process by working directly from acceleration to get the distance.

 

chestr — Don't forget that the averaging must be done with respect to the volume of fuel used (gallons) in order to derive the trip-average FE from the instantaneous FE — not w.r.t distance; not w.r.t time. When you sit idling (instantaneous FE = 0 mpg) you are still accumulating gallons of fuel used ("dG" in the integral), and so this still contributes to the averaging process. You imply that this isn't so, but it is. The contribution of idling episodes happens to be zero, of course, because the instantaneous FE is zero when idling. The integral correctly handles this averaging process to get the trip-average FE. Idling pulls the trip-average FE down because of these zero contributions. But you need to know the fuel usage to compute this integral, and that's why, as I said, computing trip-average FE from instantaneous FE isn't feasible. But computing trip-average FC from instantaneous FC is feasible.

Stan

 

for those confused about why time is not a factor in these equations :

time is a factor, but it cancels out of the equation.

This is the same reason that the mass of an object does not affect how fast it falls to the ground.

 

Perhaps another example will help in understanding what I've been saying. I'll choose US units, and will work out the trip-average FE in mpg from the instantaneous mpg readings. Suppose that a "trip" consists of the following three segments in sequence:

1. Idling at 0 mpg for 0.1 gallons
2. Driving at 20 mpg for 0.4 gallons (speed and/or time taken irrelevant)
3. Driving at 40 mpg for 1.0 gallons (speed and/or time taken irrelevant)

[Of course, it would not actually be possible to drive such a course in practice — one's instantaneous mpg reading can't jump straight from 0 -> 20 -> 40 mpg without going through the values in between as the car accelerates. This is just a simplified thought experiment for instructional purposes. The integral expression that I gave for the general case handles the most general situation, where the mpg reading varies in any way whatsoever as the car is driven.]

Then the volume-weighted average value of the mpg gives the trip-average FE as:

trip-average FE = volume-weighted average of the instantaneous FE
= (0 x 0.1 + 20 x 0.4 + 40 x 1.0) / (0.1 + 0.4 + 1.0)
= 48/1.5
= 32 mpg

You can easily see that this is indeed the correct answer, by noting that the individual distances covered are:

1. 0 miles
2. 8 miles
3. 40 miles

totalling 48 miles, with total fuel usage of 1.5 gallons. This gives a trip average FE = 48/1.5 = 32 mpg as above.

Notice that in neither of these two calculations did time, speed, or acceleration come into play — they really are irrelevant to the issue! You can play around with them if you wish, but this is quite unnecessary. The trouble with trip-average FE is that, in order to compute it you need to have both the instantaneous mpg readout (given by the FE gauge) and the running fuel usage information in gallons. The latter isn't conveniently available, and so this isn't feasible, as I have said repeatedly. On the other hand, to compute trip-average FC in L/100 km, one must compute a distance-weighted average of the instantaneous FC, and to do so one only needs to have available both the instantaneous L/100 km readout (given by the FC gauge) and the running distance covered as the car is driven. The latter is available, either by looking out the window or by looking at the odometer/trip indicator. This is quite feasible.


Stan

 

I appreciate all the comments made so far. I was most concerned about fuel used in an acceleration of o to 45 mph. Does time affect the amount of fuel used? I understand full throttle is wasteful. I would like to know more.

Thanks!


Bill

 

Since it's inconvenient to measure the distance traveled while accelerating it's difficult to calculate mpg directly. In calculating mpg, time only enters into the equation indirectly. It's just the easiest value to measure to evaluate two accelerations. Acceleration for a time gives velocity. Velocity for a time gives distance.

It would be interesting to do some semi scientific testing at a track & develop some real numbers. My personal preference is to get up to 40mph quickly to maximize cruising mpg distance.

 

My method is, from a standing start moderately accelerating up to 35 over about 1000 feet. Then putting on the cruise. After about 20 seconds then slowly accelerate up to 45 and put on the cruise again.

This method has helped me reach my best gas mileage so far.

 

UTAlumnus — You say: "Since it's inconvenient to measure the distance traveled while accelerating it's difficult to calculate mpg directly." I disagree with this statement. To compute trip-average FE (in mpg say) one does not average with respect to distance, but rather with respect to the volume of fuel used. [This is because FE has the distance in the numerator, and the volume in the denominator. The averaging (integration) is with respect to the denominator variable.] This is not easy to do because, although you do have an instantaneous-FE mpg gauge, you don't have a fuel volume indicator in the TCH.

Distance averaging is correct only for trip-average FC (in L/100 km say). [This is because FC has the volume in the numerator, and the distance in the denominator. Again, the averaging (integration) is with respect to the denominator variable.] This can be easily approximated by looking out the window at the distance covered at each instantaneous-FC L/100 km gauge value (or by watching the trip indicator readout).

Stan

 

Stanley:
I have found that brisk acceleration is the best approach also, but the best I find is to manage the battery to the upper blue level and avoid keeping it in the green. I do this by intentionally putting it into EV mode. I noted on a long distance trip last month where I got 40 MPG the system did this on its own. I would think that this would not be a logical technique, but it seems to work. What are your thoughts?

Chuck

 

I try to accelerate normally at 20 mpg. I let it level off at whatever speed. Then accelerate more if need to get to the desired speed.

Any long hill climbing, I try to keep it at 20 mpg using the cruise. There are those few steep hills where it will drop to about 16 mpg. Nothing I can do about that, crawl I guess.