Appendix 2 – Road Load Matrix Family

Appendix 2 – Road Load Matrix Family

The objective is to deliver realistic road load values for low-volume vehicles, in particular for large vans, under reduced test burden but without opening a loophole for unwanted application. The IG indicated a conservative approach as the guiding principle when developing the Road Load Matrix Family method. Although the Road Load Matrix Family is built on physical laws, a safety margin should prevent the new method delivers profitable values compared to standard methods (coast down, torque meter, wind tunnel) and should provide an incentive to use, if possible, these standard methods.

The basic principle of the Road Load Matrix Family is only one generic road load measurement, and extrapolation⁵⁰ of the outcome of this measurement to derive the settings of vehicle H and L for chassis dynamometer tests. This is in contrast to the standard road load determination methods, which always use two measurements at the extremes for vehicle H and L.

For the Road Load Matrix Family it was decided that the method should not be applicable for high-volume main stream vehicles. This was achieved by setting an objective criteria by means of a minimum limit to the technically permissible maximum laden mass of 3000 kg. The scope of vehicles within the GTR itself is limited to a technically permissible maximum laden mass of 3,500 kg.

The safety margin implemented in the Road Load Matrix Family method is ensured by the following two elements:

1. 
   Estimated worst C_d
   An important principle of the Road Load Matrix Family method is the selection of a representative test vehicle. On the one hand the test vehicle should be as representative as possible for the vehicle family (estimated average mass of optional equipment, representative body shape) in order to keep the actual average production vehicle as close as possible to the measured test vehicle. On the other hand the aerodynamic parameters are not considered in the extrapolation of the road load values to vehicle H and L, therefore the representative body of the test vehicle should have a configuration with the estimated worst-case C_d value (e.g by installing external body options such as spoilers and roofrails, and by selecting the least aerodynamic wheel rims).
   
2. 
   Correlation factors: The road load values for vehicles H and L are calculated from the value of the tested vehicle by extrapolation. To establish a safety margin conservative correlation factors are introduced. In this appendix a correlation factor is defined as the value to which the dominant vehicle parameters are assumed to correlate with the road load. The correlation factor has a value between 0 and 1. To ensure a safety margin for upward and downward extrapolation, the correlation factors are different in both directions.
   

Conservative correlation factors were introduced in order to derive road load values of each individual vehicle and vehicles H and L that are very likely to be higher than the actual values if they had been measured. The correlation factors are based on:

1. 
   The best available scientific knowledge of the dependency of road load values to vehicle parameters. Besides C_d, for which the worst case approach is chosen, the dominant parameters are test mass (TM), tyre rolling resistance (RR) and frontal area (A_f). These parameters are selected as parameters in the correlation formulas.
   
2. 
   Observed real world correlations. Only a very limited number of measurements was available to the Task Force, indicating a direct correlation of typically 85-90% on the selected vehicle parameters.
   
3. 
   The determination of the conservative correlation factors was based on the following assumptions and scientific evidence⁵¹:
   

1. 
   the parameters selected to be included in the correlation are a selection of the main influences. By assuming they together account for all of the road load influences, consequently their impact will overrepresented.
   
2. 
   total rolling resistance is a combination of tyre and the drivetrain losses. Drivetrain resistances are only slightly vehicle mass dependent. Typically drivetrain losses make up for 10%-20% of the total f₀ coefficient. The share is typically lower for vehicle H than for vehicle L.
   An EC study yielded 14% of drivetrain losses for a front wheel drive vehicle with manual transmission. Larger effects for automatic transmissions and all-wheel drive can be expected.
   
3. 
   remaining unexplained effects occur. The separation between rolling resistance and air drag is not as straightforward as the f₀ and f₂ equations suggest. In the standard coast down method this is overcome by the introduction of f₁. Yet in the Road Load Matrix Family method, f₁ is set to 0.
   

4. 
   The outer envelope of observed correlation is considered to be the conservative approach, implying a higher correlation factor for calculation of road load values towards vehicle H and a lower correlation factor towards vehicle L. This is shown in Figure . The further away from the measured road load on the test vehicle, the higher the extrapolated road load will be above the actual road load value.
   

Figure : Upward and downward extrapolation for the road load matrix family

The safety margin for the selected correlation factors was calculated based on a (limited) database of road load measurements of heavy LCV’s, which was provided by ACEA⁵¹. This was done to verify if the correlation factors would lead to comparable safety margins for vehicle L and H. These LCV’s have CO₂ emissions in the order of 260 to 300 g/km. The absolute and relative safety margins for the selected correlation factors are indicated in the table below for a typical example vehicle:

1. 
   Safety margin is the calculated road load values of vehicle H or L minus the measured road load values for the vehicles in the database, expressed in resulting delta CO₂-figures.
   
2. 
   X_up is the correlation factor for the calculation of the road load values of vehicle H
   
3. 
   X_down is the correlation factor for the calculation of the road load values of vehicle L
   

By extrapolation of the road load to vehicle L and H, the target road loads for measuring these vehicles at the chassis dynamometer can be found. The test vehicle is tested at the vehicle L and the vehicle H road loads, and the CO₂ results are used to draw an interpolation line for CO₂ against cycle energy. For any of the other vehicles in the RLMF, the cycle energy will be calculated from the extrapolated road load, and then the CO₂ follows from the interpolation method. Note that the CO₂ interpolation line does not have the kinked shape of red line in Figure .

The effect of the safety margin on the resulting CO₂ value by a higher calculated road load is graphically represented in Figure . For the middle vehicle, the road load is measured, hence there is no difference. However, both vehicle L and H have received a higher CO₂ value because of their higher road loads.

Figure : Graphical representation of the effect of the safety margin on CO₂

Whereas the family range of the standard road load family is 35% of the cycle energy demand of vehicle H_R, no direct limitation for the Road Load Matrix Family was proposed. This limitation was not deemed necessary since:

1. 
   The scope of application is limited to vehicles with a technically permissible maximum laden mass above 3 tons
   
2. 
   A representative vehicle (with worst-case aerodynamic drag) is used as a basis for the road load determination
   
3. 
   The built in safety margin ensures that the difference to the actual road load worsens for vehicles further away from the tested vehicle.
   

In addition to the determination of the road load for individual vehicles, the road load matrix family approach is also extended to the CO₂ determination in order to reduce the test burden and to avoid wind tunnel measurements for vehicles falling in the scope of the RLMF.

The vehicles within a RLMF for which CO₂ interpolation is applied have to fulfill the same criteria as for the Interpolation Family of normal passenger vehicles. However, the RLMF is not limited to a 30g/km CO₂-range. The larger the range of CO₂ the RLMF, the wider the safety margin of the road load will be and as a consequence also for the CO₂.



Figure 42: Link between safety margin on Road Load and CO₂

The CO₂ measurements for vehicle L and H are performed on a chassis dyno using the road loads of the RLMF calculation. These measured CO₂ values are used for the interpolation of individual CO₂ values based on the individual cycle energy, which is an output of the RLMF calculation. This method is similar to what is already described in the GTR on the CO₂ interpolation for normal passenger cars, and is illustrated in Figure .

It is also possible to reduce the safety margin by performing additional coast down measurements between the representative vehicle and the vehicles L and/or H. With the resulting cycle energies and using the CO₂ measurements for vehicle L and H, the CO₂-value for an individual vehicle can then be calculated more precisely.