Diesel Engine Fuel Consumption Calculation

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Introduction

Calculating the fuel consumption for a diesel engine car requires more complex algorithms, taking the lambda/O2 probe measurements into account. Not every car provides lambda probe values over OBD-II, hence consumption calculation is currently only supported for a subset of diesel cars.

Parameters

The following parameters are required for estimating fuel consumption:

Parameter	Abbrevation	unit	provided by
Intake air pressure	IAP	kPa	OBD-II
Intake air temperature	IAT	°C	OBD-II
Mass air flow	MAF	kg/s	OBD-II
Vehicle speed	Speed	km/h	OBD-II
O2 lambda equivalence ratio	O2 EQ	(ratio)	OBD-II / statistics
minimum required air for diesel = 14.5	MRAD		constant
diesel fuel density = ~ 0.83	DFD	kg/l	constant
mass fuel flow = MAF * 3600 / (O2 EQ * MRAD)	MFF	kg/h	on-the-fly calc
volumetric fuel flow = MFF * DFD	VFF	l/h	on-the-fly calc
Fuel consumption = VFF * 100 / Speed	FC	l/100km	on-the-fly calc

Fuel Consumption

The app calculates the current (distinct) fuel consumption as volmetric fuel flow (l/h) for each measurement point. It is assumed that there is no fuel consumption at all for Lambda Voltage values > 1.1V. The transformation to l/100km is done after finishing a track route:

Fuel consumption = average(VFF) * total_duration / total_distance * 100

• total_duration provided as hours
• total_distance as kilometres

O2 Lambda Equivalence Ratio

We have observed that O2 lambda ER data provided via OBD-II is often capped at a value of 2.0. Thus the formula breaks as the actual value is likely to exceed that threshold. The app uses the derived lambda ER formula if it observes a OBD lambda ER value > 1.97.

Using statistic methods it is possible to create a regression function using the O2 lambda voltage which is also provided when O2 lambda ER is available. The result is a function of the form

• f(x) = a / ( b - c * x )

• where x is the Lambda Voltage value

The coefficients might vary across different cars and engines. This has to be evaluated. For a VW Passat B6 2.0l TDI we have calculated the following coefficients from a given track:

• f(x) = 0.23478 / ( 0.218911 - 0.18415 * x )

Calcuating the Regression function (DEPRECATED)

The regression function is assumed static for all cars at the moment. The following is kept for the sake of completness:

In order to get a fealing on how such a regression function varies across different cars, a first step would be to calculate a similar function for

• different tracks of the same car
• different cars

and compare the coefficients.

Attached find an example excel sheet with a trend line calculation for the regression function.

• LambdaVoltagER-Function.xls: LambdaVoltagER-Function.xls

Required steps in Excel:

• Filter data using "O2 Lambda Voltage ER <= 0.98"
• create an XY diagram (x = Voltage, y = Voltage ER)
• create a 3-degree polynomic trend line (e.g. see Office help or this turorial for details) and display its formula in the diagram
  • set the intercept to 1