Av MPG Readout vs Calculated

[Jackpine]

Jim - This is a pretty old subject, but I can tell it's still confusing people. I've just done a bit of research and I'll try to clarify some points (but not all of them)!

First, it would be nice if the Gryphon used a simple "Miles Driven/Fuel Used" calculation for Avg Economy, but it doesn't. The reason is that the truck has no "Fuel Used" sensor or even a simple "Flowmeter". Forget the gas gauge, we all know it's set up to really just warn us if we're close to empty. Instead, the fuel economy calculations seem to depend on an "inferred" value that the PCM determines by looking at the MAF sensor values: http://forum.gopowerhungry.com/63-post7.html

This method of determining fuel used has at least two inaccuracies and maybe more:

1. The MAF sensor is not particularly accurate - it's just a heated wire that is cooled by the action of airflow which alters its electrical resistance. Inaccuracies are then corrected by input from the O2 sensors allowing the PCM to increase/decrease the injector delivery as needed to maintain proper A/F ratio in "closed loop" operation.
2. As Bill said in the cited post, the inferred value of fuel delivered was based on the ideal A/F ratio for "real gasoline", and E10 gas causes the engine to operate at a richer A/F ratio. E85 requires a VERY rich mixture.
3. The inferred value for fuel used may not account for additional enriching during "open loop" (hard acceleration or cold engine).
4. Any accumulated "flow" calculation is inherently less accurate than a corresponding measurement of total volume.

Now, I can't find where Bill told me this, but here's how the "Avg Economy" is calculated. The "Inst Econ" value is sampled each second. These are then averaged using this formula:
((Current Avg Econ x Sample Count) + Current Inst Econ Reading) / (Sample Count + 1)

Clearly, if the "Avg Econ" has recently been reset, the "Sample Count" will be small and each new "Inst Econ" value will have a fairly significant impact.

Once the sample count reaches 100,000 (at one sample per second this is around four full tankfuls assuming normal fuel consumption), the Sample Count is held constant at 100,000 and each new Inst Econ value should have a fairly low effect (you continually multiply by 100,000 and divide by 100,001).

So, to provide a sense of how this works out - assume the current "Avg Econ" is 15.5 MPG and you stop at a stoplight where the Inst Econ drops to zero. This is what you will see for Avg Econ in the next second:

1. Sample Count = 10: ((15.5 x 10) + 0) / 11 = 14.091 (10 seconds after reset)
2. Sample Count = 100: ((15.5 x 100) + 0) / 101 = 15.347 (1 minute, 40 seconds after reset)
3. Sample Count = 1000: ((15.5 x 1000) + 0) / 1001 = 15.484 (16.67 minutes after reset)
4. Sample Count - 25,000: ((15.5 x 25000) + 0) / 25001 = 15.4994 (6.94 hours, 451 miles at 65 mph and about 30 gallons used)
5. Sample count = 100,000: ((15.5 x 100000) + 0) / 100001 = 15.4998 (27.78 hours of samples)

And, if you sit at that stoplight, this is what you'll see at the end of each second stopped:

Samples = 10: 14.0909, 12.9167, 11.9231, 11.0714, 10.3333, 9.6875, 9.1176, 8.6111, 8.1579, 7.7500
Samples = 100: 15.3465, 15.1961, 15.0485, 14.9038, 14.7619, 14.6226, 14.4860, 14.3519, 14.2202, 14.0909
Samples = 1000: 15.4845, 15.4691, 15.4536, 15.4382, 15.4229, 15.4076, 15.3923, 15.3770, 15.3617, 15.3465
Samples = 25000: 15.4994, 15.4988, 15.4981, 15.4975, 15.4969, 15.4963, 15.4957, 15.4950, 15.4944, 15.4938
Samples = 100000: 15.4998, 15.4997, 15.4995, 15.4994, 15.4992, 15.4991, 15.4989, 15.4988, 15.4986, 15.4985

You can see that to get a true Average MPG value, you do NOT want to reset at each fillup.

There's one more problem with this method of calculation though. It's an average of discrete "snapshot" values, rather than a single calculation of distance/fuel. And, it gives each value identical "weight". It's a bit like the error you get by calculating an "average of averages", where each average may have used a different sample size. Still, without a sensor for real fuel consumption, I don't see an alternative.

- Jack