How does this change whether you need a fairly accurate value for the distance?

We've got a fuel volume indicator. What we need is fuel flow. If we had good numbers for fuel flow at a given instantaneous mpg reading, we wouldn't even need distance since what we're comparing is the fuel burned for a given acceleration to a speed. Just a stopwatch (flow is volume/time).

 

UTAlumnus — You don't need distance at all for computing trip-FE from instantaneous-FE in mpg. You also don't want fuel flow rate (gal/h), which involves time, but rather just the fuel volume used (gal) since the beginning of the trip (which is the time integral of the fuel flow rate). The car's fuel gauge isn't useful for showing moment by moment changes in the fuel remaining in the tank since it isn't sensitive enough. ScanGauge can be set to read out the fuel used from the tank since the last startup, and from this you can compute the moment by moment fuel usage in gallons. Then to get the trip-average mpg, you need to average the instantaneous-mpg reading that your TCH's FE gauge gives you with respect to the gallons of fuel used at each of those varying instantaneous-mpg readings. My previous examples showed a simplified version of what needs to be done. You do not use the distance (miles) reading at all in order to compute trip-average FE in this way. To maximize trip-average FE in mpg, you want to drive so as to get the highest possible instantaneous-FE for the least number of gallons used at that instantaneous-FE, at all points along your trip. That's all there is to it! But how does one achieve this? That's the question. But mathematically, this is what one wants to achieve. I have been attempting to clarify what the objective is, and how to remove the indirect variables (time, distance, speed, acceleration, ... for FE) from misleading us about this.

Stan

 

Let me elaborate a bit. For trip-FE in mpg it's difficult to say very much that's both accurate and useful. For trip-FC in L/100 km, however, one can say a lot that's both accurate and useful. Since the averaging is of instantaneous-FC (in L/100 km) with respect to distance (in km), it's possible to conclude that:
To minimize trip-average FC in L/100 km, you want to drive so as to get the lowest possible instantaneous-FC for the greatest number of kilometers travelled at that instantaneous-FC, at all points along your trip.
Now, the relation between FE in mpg and FC in L/100 km is:
(FE in mpg) = 235.2 / (FC in L/100 km).
Thus, minimizing instantaneous-FC is equivalent to maximizing instantaneous-FE. It follows that it is correct to say:
To maximize trip-average FE in mpg, you want to drive so as to get the highest possible instantaneous-FE for the greatest number of miles travelled at that instantaneous-FE, at all points along your trip.
I said as much near the end of my post #7. There's no precise mathematical relationship that can be displayed between instantaneous-FE, distance travelled, and trip-average FE, but this generalized statement is correct, and is the best I can do. The advice is thus to drive the biggest distances (not times) at the highest instantaneous-mpg possible, or conversely, to drive the smallest possible distances (not times) at low instantaneous-mpg's.

Incidentally, the mathematical theorem relating average values to instantaneous values is called the Mean Value Theorem of the Integral Calculus.

Stan

 

Exactly.

Time and distance are directly related. The shortest time will give you the shortest distance required to accelerate to a given speed.

That's the one we've been swapping variables in like the ways to pronounce tomato. It's been too many years since Calculus classes for me to be able to name theories.

 

Only true if the acceleration is the same each time. I know that's being picky, but it does make a real difference in practice. When using time as a factor in your FC calculation, you also must consider acceleration. When using distance, you only need to consider... well, distance.

 

Exactly!

Stan

 

I'd like to look at this issue from another angle: how can we know that we are using the ICE near its most efficient range?

With just a little gas, most of the energy is going toward overcoming the engine's friction and other parasitic loads and so little is left to turn the wheels. So, the efficiency (energy supplied to the wheels and batteries vs. the amount of fuel consumed) is low. Thus "turtle mode" is almost like idling: litte motion for the gas consumed.

Conversely, at very high throttle, the exhaust gas is hotter, fuel may be burned less efficiently, and friction is higher (due to higher RPM), and so efficiency drops. Thus "jackrabbit mode" is also a waste of fuel.

Please note that engine efficiency is not the same thing as milage. Making a car more aerodynamic will improve its milage, but that has no effect on its engine or drive-train and so has no effect on the engine's efficiency.

I've seen charts here for the Prius that demonstrate a broad band of efficient engine operation. I assume the Camry engine has a similar efficient power band.

Assuming it does, how can we know that we are keeping the engine in that efficient range?

Is it good enough to accelerate briskly but not harshly? Or is something more precise needed? If more precision is needed, would a tach be enough to get close, or do we need to account for other variables?

I hope this gets us back to the spirit of the original question.

--Allen

 

True if you're trying to hit the same FE every time. Not if you're looking at which acceleration is more efficient. For any given acceleration, you will get the shortest distance from the one that results in the shortest time. If you have a reasonable idea what your acceleration was and how long you accelerated, you can calculate the distance traveled for that acceleration. This allows you to compare two accelerations. I.e. is it better to accelerate for a much longer time at acceleration 1 verses a shorter time at acceleration 2 to reach a given speed. Unless you go back with a tape measure, how are you going to get an accurate distance? If you calculate it based on time, all you need is a stopwatch. I know my distance estimation isn't up to getting a number close enough by looking out the window.

 

Some of those parasitic loads are rolling resistance and drag. Aerodynamics influence drag. Changing tire make/model changes rolling resistance. Changing these will change the overall engine efficiency because it changes the energy needed to rotate the tires.

 

Where did you see the info about hooking a laptop up to the prius? I would love to do that with my TCH as I'm a gadget geek and like things like that.

I am not asking so that it helps me improve mpg...just curious.

Honestly too, you get used to the new driving habits and it isn't so bad. It's actually more relaxing typically than the frantic gotta get there mentality. I'm not a tree hugger, but I know we have to conserve our resources because India and China won't. I'm doing my part and saving money, too. (not driving my 2007 Expedition EL if I don't need to saves a crap ton of money too) I have a lot of feelings about global warming and things like that. I guess when I put two and two together and realized that we are becoming a virus to this planet, I wanted to do what I could without living in a strat hut on gilligan's island to treat the planet with a bit more respect. I'm still an american, but that doesn't mean I need to act like an environmental slob and not care about what impact I have. Enough people don't care... Do what you think you need to do...all I'm saying is that we have one planet and treat it with respect when you can. We created the monsters of China and India and we'll pay that price too...but that's another discussion as it'll result in a rant.

Mark