WLTP ANNEX 4 AND 7, DELTA CD*A BMW, Christoph Lueginger, Thomas Schütz ALTERNATIVE DETERMINATION METHODS WLTP-10-21e

At the request of the manufacturer and with the agreement of the type approval authority an equivalent method (e.g. simulation) can be used for the determination under the following restrictions: (a) The alternative determination method fulfils at least an accuracy of m² (c d *A f ); (b) The method shall be used only for that kind of aerodynamic influencing parts (e.g. wheels, body shapes, cooling system,...), for that equivalency was demonstrated. (c) In advance evidence of equivalency has to be shown to the authority for each road load family and has to be based on wind tunnel measurements. (d) If the influence of an option is more than [100]% bigger than the option, with which the evidence was given, it shall not be determined with the alternative method. Page 2 WLTP ANNEX 4 AND 7, ALTERNATIVE DELTA CD*AF PROPOSAL FOR ALTERNATIVE CD*AF DETERMINATION Proposal:  Allow for other determination methods (e.g. simulation), in a very restricted an guided way. Justification:  The difference between very similar options (e.g. same rim on different bodystyles) may be in the order of the measurement tolerance of c d *A f. In this case we could reduce unnecessary effort (wind tunnel measurements are very costly and time consuming), while at the same time providing more accurate data on the influence of options or body shapes.  Measurement will remain the basic principle anyway! WLTP Annex 4 and 7, alternative cd*A determination, BMW,

Page 3 WLTP ANNEX 4 AND 7, ALTERNATIVE DELTA CD*AF CD*AF TOLERANCE  The accuracy for aerodynamic options and body shapes will be anyway defined more clearly by that proposal within the drafting taskforce.  OEM is responsible for correct Delta cd*A, however it is determined. WLTP Annex 4 and 7, alternative cd*A determination, BMW, New proposed text within Annex 7: Aerodynamic drag of an individual vehicle The aerodynamic drag shall be measured for the drag influencing options and body shapes at a wind tunnel fulfilling the requirements of paragraph 3.2. of Annex 4 verified by the responsible authority. [Alternative cd*Af] Δ(c d *A f ) LH (m²) is the difference of the aerodynamic drag of the test vehicle H compared to the test vehicle L and shall be recorded. Δ(c d *A f ) ind (m²) is the difference in aerodynamic drag between an individual vehicle and the test vehicle L, due to options and body shapes on the vehicle that differ from those of the test vehicle L. These aerodynamic drag differences shall be determined with an accuracy of m² (c d *A f ). Δ(c d *A f ) may be calculated according to the following equation maintaining the accuracy of m² also for the sum of options and body shapes:

Page 4 WLTP ANNEX 4 AND 7, ALTERNATIVE DELTA CD*AF SIMULATION CRITERIA History:  Out of the IWG meeting in Pune there was a request on giving simulation criteria. Simulation criteria for aerodynamics (CFD simulation): General simulation properties Three dimensional simulation involving friction. Direct simulation or modeling of turbulence via at least one-equation model (e.g. Spalart Almaras). Navier-Stokes or Lattice-Boltzmann based methods are allowed. Numerical solution needs to be evaluated over an averaging interval in which c d *A f may not exceed [5/1000]. Model accuracy Ground movement shall be modeled (either as an infinite belt or a five-belt or one belt). Wheel rotation shall be modeled. The cordial deviation of surface elements may not exceed [0.1] mm. The volume deficit between full CAD geometry and the discretized simulation model may not exceed [tbd] %. List of software vendors / products: EXA: PowerFLOW; OpenCFD: OpenFoam; Adapco: CCM+; Ansys: Fluent; Ansys: CFX WLTP Annex 4 and 7, alternative cd*A determination, BMW,

Page 5 WLTP ANNEX 4 AND 7, ALTERNATIVE DELTA CD*AF CONCLUSION AND RECOMMENDATION Conclusion:  Writing down simulation criteria is possible, but accuracy criteria is stricter anyway and is therefore sufficient.  Restrictions due to:  road load family  measurement basis as the evidence  type of options restriction  accuracy requirement  limited range Proposal and recommendation of Annex 4 task force:  Discuss that proposal and shift the date for adoption to the next IWG. WLTP Annex 4 and 7, alternative cd*A determination, BMW,