WLTP Annex 4, Road load Calculation

1. WLTP-DTP-LabProcICE-191 WLTP Annex 4, Road load Calculation BMW, EG-63, 15.02.2013 C. Lueginger proposal for calculating the road load

2. WLTP Annex 4, Road load Calculation Introduction, Motivation Motivation: In order to get a representative and repeatable CO2-value for an individual vehicle, many measurements are necessary. Measurements are expensive and inaccurate. Proposal: Measure only absolute worst- and best-case. Calculate as much as possible. Details are shown here. Introduction: It is possible - within a certain range - to calculate the influence of aerodynamic, rolling resistance and mass in a simple way. This calculation is not more inaccurate than a measurement (equipment, tolerances!). WLTP Annex 4, Road load calculation, BMW, EG-63, 15.02.2013

3. WLTP Annex 4, Road load Calculation Step 1, Measurement Thisis an examplewithbiggervaluesforillustration! • absolute best case: • lowest weight • best aerodynamics • best tyre (lowest rolling resistance) • Result: • F0F1F2bc • massbc • CO2-value • absolute worst case: • highest weight • worst aerodynamics • worst tyre (worst rolling resistance) • Result: • F0F1F2wc • masswc • CO2-value „Measure best- and worst case anddetermineinfluenceof optional equipment.“ WLTP Annex 4, Road load calculation, BMW, EG-63, 15.02.2013

4. WLTP Annex 4, Road load Calculation Step 2, PrepAration and Normalization Thisis an examplewithbiggervaluesforillustration! ΔF0F1F2 = F0F1F2wc - F0F1F2bc Δm = masswc - massbc Approximatingfrom F01F1F2 to F0 and F2 has a verylittleerror, ifyouhaveonlytheinfluenceoftheseparameters (linear regression). Remove linear coefficient: ΔF0F1F2  ΔF0 ΔF2 rollingresistance / weight aerodynamics inertia „Divide Road loadintosingleinfluences und normalizeitwithdatafrom optional equipment.“ WLTP Annex 4, Road load calculation, BMW, EG-63, 15.02.2013

5. WLTP Annex 4, Road load Calculation Step 3, Calculating an individual value of a vehicle Thisis an examplewithbiggervaluesforillustration! • Thiscalculationprovidesmorerepresentative CO2-values (including RR) but reducingmeasurementsatthe same time. • Calculationcanbemoreprecisethanmeasurements. • If CO2-range getstoo large, measuringof intermediate pointscouldbe a solution. • Worst-case apporach: Calculation will also work, ifinfluencesaresetto worst-case. E.g. leaving out aerodynamicsortakingthe worst RR. WLTP Annex 4, Road load calculation, BMW, EG-63, 15.02.2013

6. WLTP Annex 4, Road load Calculation Proposal • The road load coefficients f0, f1 and f2 for an individual vehicle within in a vehicle family is determined through interpolation of • measured data of selected vehicle using tyre out of highest rolling resistance class and equipped with selectable options with highest aerodynamic drag (measured at TMH) and • measured data of selected vehicle using tyre out of lowest rolling resistance class and equipped with selectable options with lowest aerodynamic drag (measured at TML). • f0ind = interpolation of f0max - f0min (based on RR difference of classes and individual vehicle test mass) • f1ind = (f1max + f1min ) /2 or regression to eliminate f1 and add it to f0 and f2 • f2ind = interpolation of f2max - f 2min (based on manufacturer data of aerodynamic drag of selected options) • If the road load of a vehicle is tested only at TMH, the rolling resistance has to be derived from data at TMH. • If the manufacturer does not provide aerodynamic data of selected options, f2 from the vehicle with highest aerodynamic drag shall be used. WLTP Annex 4, Road load calculation, BMW, EG-63, 15.02.2013