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Diesel Engine Fuel Consumption Calculation


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.


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.

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
Topic revision: r3 - 08 Dec 2015, MatthesRieke
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