10.11.2022
4.3.2.5.2.
EN
Official Journal of the European Union
L 290/283
Mechanical drag modelling Mechanical drag consisting of separate components representing tyre Dtyre and front and rear axle frictional losses Df and Dr (including transmission losses) shall be modelled as a three-term polynomial as a function of vehicle speed v as in the equation below: Dmech = Am + Bm v + Cm v2 where Am, Bm, and Cm are determined in the data analysis using the least squares method.
These constants reflect the combined driveline and tyre drag.
In the case that the tested vehicle is the representative vehicle of a road load matrix family, the coefficient Bm shall be set to zero and the coefficients Am and Cm shall be recalculated with a least squares regression analysis.
4.3.2.5.3.
Aerodynamic drag modelling The aerodynamic drag coefficient CD(Y) shall be modelled as a five-term polynomial as a function of yaw angle Y as in the equation below: CD(Y) = a0 + a1Y + a2Y2 + a3Y3 + a4Y4 a0 to a4 are constant coefficients whose values are determined in the data analysis.
The aerodynamic drag shall be determined by combining the drag coefficient with the vehicle’s frontal area Af and the relative wind velocity vr.
Daero ¼
Daero ¼ 4.3.2.5.4.
Ê1Ì 2
Ê1Ì 2
Ü ρ Ü Af Ü v2r Ü CD ðYÞ
Ü ρ Ü Af Ü v2r ða0 þ a1 Y þ a2 Y2 þ a3 Y3 þ a4 Y4 Þ
Final equation of motion Through substitution, the final form of the equation of motion becomes:
Äme 4.3.2.6.
Í Î Ê 1Ì dv dh ¼ Am þ B m v þ Cm v 2 þ Ü ρ Ü Af Ü v2r Ü ða0 þ a1 Y þ a2 Y2 þ a3 Y3 þ a4 Y4 Þ þ ðm Ü g Ü Þ dt 2 ds
Data reduction A three-term equation shall be generated to describe the road load force as a function of velocity, F = A + Bv + Cv2, corrected to standard ambient temperature and pressure conditions, and in still air.
The method for this analysis process is described in paragraphs 4.3.2.6.1. to 4.3.2.6.10. inclusive of this annex.
4.3.2.6.1.
Determining calibration coefficients If not previously determined, calibration factors to correct for vehicle blockage shall be determined for relative wind speed and yaw angle.
Vehicle speed v, relative wind velocity vr and yaw Y measurements during the warm-up phase of the test procedure shall be recorded.
Paired runs in alternate directions on the test track at a constant velocity of 80 km/h shall be performed, and the arithmetic average values of v, vr and Y for each run shall be determined.
Calibration factors that minimize the total errors in head and cross winds over all the run pairs, i.e. the sum of (headi – headi+1)2, etc., shall be selected where headi and headi+1 refer to wind speed and wind direction from the paired test runs in opposing directions during the vehicle warm-up/stabilization prior to testing.