WLTP ANNEX 4, ROAD LOAD CALCULATION Proposal for calculating the road load of individual vehicles C. Lueginger, BMW; A. Feucht, Audi WLTP-DTP-LabProcICE-202 (partly presented at DTP-13) Note: Proposal not yet finalized. It is an intermediate proposal which reflects the current state of discussions in the Drafting Task Force and outlines the general concept.

WLTP Annex 4, Road load Calculation Introduction, Motivation WLTP Annex 4, Road load calculation, BMW / Audi, Motivation: In order to get a representative and repeatable CO 2 -value for an individual vehicle, many measurements are necessary. Measurements are expensive and object to measurement inaccuracies Proposal: Measure only worst- and best-case. Calculate the individual car. Details are shown here. Introduction: It is possible to calculate the influence of aerodynamics, rolling resistance and mass. This calculation is at least as accurate as a measurement (equipment, tolerances).

WLTP Annex 4, Road load Calculation Step 1, Measurement WLTP Annex 4, Road load calculation, BMW / Audi, best case: lowest weight best aerodynamics best tyre (lowest rolling resistance) Result: driving resistance coefficients F0F1F2 bc CO 2 -values (low, mid, high, e-high) worst case: highest weight worst aerodynamics worst tyre (highes rolling resistance) Result: driving resistance coefficients F0F1F2 wc CO 2 -values (low, mid, high, e-high) „Measure best- and worst case and determine influence of optional equipment.“ This is an example with bigger values for illustration!

WLTP Annex 4, Road load Calculation Step 2, Mathematical fitting of difference WLTP Annex 4, Road load calculation, BMW / Audi, Remove linear coefficient by least square fit since physical influence of difference (tyre, mass and aero) only affects F0 and F2 ΔF0F1F2  ΔF0* ΔF2* Remove linear coefficient by least square fit since physical influence of difference (tyre, mass and aero) only affects F0 and F2 ΔF0F1F2  ΔF0* ΔF2* „Divide Road load into single influences.“ ΔF0F1F2 = (F0 wc - F0 bc ) + (F1 wc – F1 bc ) * v + (F2 wc – F2 bc ) * v 2 rolling resistance / weight aerodynamics inertia Total Resistance F [N] : F0 + F1 *v + F2 * v 2 + m * a with F0 = RR * m * g + F0 rest and F2=  air  / 2 * cd * A Driving ResistanceAcceleration Resistance ΔFacc = (mass wc – mass bc ) * a wcbcdifferenceapprox. F0 [N] F1 [N/(km/h)] X F2 [N/(km/h)^2] weight worst case1703 kg best case1553 kg ΔmΔm150 kg

WLTP Annex 4, Road load Calculation Step 2, Preparation and Scaling, Part 2 WLTP Annex 4, Road load calculation, BMW / Audi, „Calculate CO 2 -scaling factor for each parameter.“ Input:aeroweight and RRinertia Range:0.066 m² c w *A150 kg and 3.5 kg/t150 kg Scaling factorSaSrSi CO 2 -Range: (divide by cycle energy) 117 g/km normalization F2= g/km normalization F0=61.5 Input:aeroweight and RRinertia physical difference of optional equipment Y g CO2/km per Δc w *A X g CO2/km per Δµ RR *mass / per Δmass*µ RR Z g CO2/km per kg Scaling: Calculate cycle energy to compensate for vehicle resistance: E = (driving resistance + acceleration resistance ) * distance This can be done for the whole cycle or the 4 parts separately E bc E wc  E a  E weight, RR  E inertia

WLTP Annex 4, Road load Calculation Step 3, Calculating the individual value of a vehicle WLTP Annex 4, Road load calculation, BMW / Audi, This calculation provides more representative CO 2 -values (including RR) and reduces the number of measurements at the same time. Calculation can be more precise than measurements. If the CO 2 -range gets too large, measuring of intermediate points could be a solution and/or the 4 parts (low, mid, high, extra-high) can be interpolated separately. Worst-case approach: Calculation will also work, if influences are set to worst-case. E.g. leaving out aerodynamics or taking the worst RR. Optionweight and RRaerodynamicsdifferenceapprox. kg / RRm² (c w *A)kg 61.5 design package+ 5 kg X 18“ tyres+ 10 kg / kg/t glass roof+ 15 kg-+ 15 massage seats+ 60 kg- Sum:+90 kg / +1.8 kg/t + 0, kg ΔCO g/km g/km+ 2.1 g/km CO2-Label: 100 g/km g/km  g/km This is an example with bigger values for illustration!

WLTP Annex 4, Road load Calculation Proposal WLTP Annex 4, Road load calculation, BMW / Audi, 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 tyres 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 tyres out of lowest rolling resistance class and equipped with selectable options with lowest aerodynamic drag (measured at TML). F0F1F2 ind = F0F1F2 bc +  F0 ind +  F2 ind with  F0 ind = interpolation of F0 max – F0 min (based on RR difference and individual vehicle test mass)  F2 ind = interpolation of F2 max – F2 min (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 Justification und Summary WLTP Annex 4, Road load calculation, BMW / Audi, With individual road load, the CO 2 -value of an individual vehicle can be checked (e.g. COP). Less test burden due to fewer measurements. Calculation is at least as accurate as measuring. Worst-case approach is always possible. Calculation is done by traceable formulas, only basic physics are used. CO 2 -effect of each option can be communicated to the customer Validation necessary?