WLTP ANNEX 4, ROAD LOAD CALCULATION Proposal for calculating the road load of individual vehicles C.…

WLTP ANNEX 4, ROAD LOAD CALCULATIONProposal for calculating the road load of individual vehicles

C. Lueginger, BMW; A. Feucht, Audi

14.03.2013

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 CalculationIntroduction, Motivation

WLTP Annex 4, Road load calculation, BMW / Audi, 14.03.2013

Motivation:• In order to get a representative and repeatable CO2-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 CalculationStep 1, Measurement


best case:• lowest weight• best aerodynamics• best tyre (lowest

rolling resistance)Result:• driving resistance

coefficients F0F1F2bc

• CO2-values (low, mid, high, e-high)

0100200300400500600700

0 50 100

driv

ing

resi

stan

ce [N

]

vehicle speed [km/h]

worst case:• highest weight• worst aerodynamics• worst tyre (highes

rolling resistance)Result:• driving resistance

coefficients F0F1F2wc

• CO2-values (low, mid, high, e-high)

„Measure best- and worst case and determine influence of optional equipment.“

Optional equipment: Weight Aerodynamics Tyres(ISO-measurement)18“ tyres + 10 kg 18“ tyres 0.044 m² (cw*A) 16“ 8.2 kg/t (Label C)design package + 5 kg design

package0.011 m² (cw*A) 17“ 9.2 kg/t (Label E)

glass roof + 15 kg … 18“ 10.0 kg/t (Label E)massageseat + 60 kg 19“ 11.7 kg/t (Label F)…Sumofdifference: 150 kg 0.066 m² (cw*A) 3.5 kg/t

This is an example with bigger values for illustration!

WLTP Annex 4, Road load CalculationStep 2, Mathematical fitting of difference


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 = (F0wc - F0bc ) + (F1wc – F1bc ) * v + (F2wc – F2bc ) * v2

rolling resistance / weight aerodynamics inertia

Total Resistance F [N] : F0 + F1 *v + F2 * v2 + m * a

with F0 = RR * m * g + F0rest and F2= rair / 2 * cd * ADriving Resistance Acceleration Resistance

ΔFacc = (masswc – massbc) * a

wc bc difference approx.

F0 [N] 193.8 132.3 61.5 61.5

F1 [N/(km/h)] 0.292 0.293 -0.001 X

F2 [N/(km/h)^2] 0.0301 0.02736 0.00279 0.00278

weight

worst case 1703 kg

best case 1553 kg

Δm 150 kg

WLTP Annex 4, Road load CalculationStep 2, Preparation and Scaling, Part 2

WLTP Annex 4, Road load calculation, BMW / Audi, 14.03.2013„Calculate CO2-scaling factor for each parameter.“

Input: aero weight and RR inertia

Range: 0.066 m² cw*A 150 kg and 3.5 kg/t 150 kg

Scaling factor Sa Sr Si

CO2-Range:(divide by cycle

energy)

117 g/km

normalizationF2=0.0027

8

100 g/km

normalization

F0=61.5

Input: aero weight and RR inertia

physical difference of optional equipment

Y g CO2/kmper Δcw*A

X g CO2/kmper ΔµRR*mass / per Δmass*µRR

Z g CO2/kmper kg

Scaling: Calculate cycle energy to compensate for vehicle resistance:E = (driving resistance + acceleration resistance ) * distanceThis can be done for the whole cycle or the 4 parts separately

E bc E wcDE a DE weight, RR DE inertia

WLTP Annex 4, Road load CalculationStep 3, Calculating the individual value of a vehicle


• This calculation provides more representative CO2-values (including RR) and reduces the number of measurements at the same time.

• Calculation can be more precise than measurements.• If the CO2-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.

Option weight and RR aerodynamics difference approx.kg / RR m² (cw*A) kg 61.5

design package + 5 kg + 0.011 + 5 X

18“ tyres + 10 kg / + 1.80 kg/t + 0.044 + 10 0.00278

glass roof + 15 kg - + 15massage seats + 60 kg - + 60 kgSum: +90 kg / +1.8 kg/t + 0,055 + 90kg ΔCO2 + 5.4 g/km + 2.6 g/km + 2.1 g/kmCO2-Label: 100 g/km + 10.1 g/km 110.1 g/km

This is an example with bigger values for illustration!

WLTP Annex 4, Road load CalculationProposal


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).

• F0F1F2ind = F0F1F2bc + DF0ind + DF2ind with

DF0ind = interpolation of F0max – F0min (based on RR difference and individual vehicle test mass) DF2ind = interpolation of F2max – F2min (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 CalculationJustification und Summary


• With individual road load, the CO2-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.• CO2-effect of each option can be communicated to the customer

Validation necessary?

Documents

WLTP ANNEX 4, ROAD LOAD CALCULATION Proposal for calculating the road load of individual vehicles C.…