Appendix 7a F1

This Appendix describes the calculation procedures to verify the trip dynamics by determining the excess or absence of dynamics during urban, rural and motorway driving.

Dynamic parameters like acceleration, (v · a_pos) or RPA shall be determined with a speed signal of an accuracy of 0,1 % for all speed values above 3 km/h and a sampling frequency of 1 Hz. This accuracy requirement is generally fulfilled by distance calibrated signals obtained from a wheel (rotational) speed sensor. Otherwise, acceleration shall be determined with an accuracy of 0,01 m/s² and a sampling frequency of 1 Hz. In this case the separate speed signal, in (v · a_pos), shall have an accuracy of at least 0,1 km/h.

The correct speed trace builds the basis for further calculations and binning as described in paragraph 3.1.2 and 3.1.3.

The following calculations shall be performed over the whole time based speed trace (1 Hz resolution) from second 1 to second t_t (last second).

The distance increment per data sample shall be calculated as follows:

where:

The acceleration shall be calculated as follows:

where:

The product of vehicle speed per acceleration shall be calculated as follows:

where:

After the calculation of a_i and (v · a)_i, the values v_i, d_i, a_i and (v · a)_i shall be ranked in ascending order of the vehicle speed.

All datasets with v_i ≤ 60 km/h belong to the ‘urban’ speed bin, all datasets with 60 km/h < v_i ≤ 90 km/h belong to the ‘rural’ speed bin and all datasets with v_i > 90 km/h belong to the ‘motorway’ speed bin.

For N2 category vehicles that are equipped with a device limiting vehicle speed to 90 km/h, all datasets with v_i ≤ 60 km/h belong to the ‘urban’ speed bin, all datasets with 60 km/h < v_i ≤ 80 km/h belong to the ‘rural’ speed bin and all datasets with v_i > 80 km/h belong to the ‘motorway’ speed bin.

The number of datasets with acceleration values a_i > 0,1 m/s² shall be greater or equal to 100 in each speed bin.

For each speed bin the average vehicle speed ${\bar{v}}_k$ shall be calculated as follows:

${\bar{v}}_k=\left({\sum }_i{v}_{\mathrm{i,k}}\right)∕N_k$, i = 1 to N_k, k= u, r, m

Where:

N_k is the total number of samples of the urban, rural, and motorway shares.

The 95^th percentile of the $v\times a_{\mathrm{pos}}$ values shall be calculated as follows:

The ${\left(v\times a\right)}_{\mathrm{i,k}}$ values in each speed bin shall be ranked in ascending order for all datasets with $a_{\mathrm{i,k}}>\mathrm{0,1 m}∕s^2$$a_{\mathrm{i,k}}\ge \mathrm{0,1 m}∕s^2$ and the total number of these samples M_k shall be determined.

Percentile values are then assigned to the ${\left(v\times a_{\mathrm{pos}}\right)}_{\mathrm{i,k}}$ values with $a_{\mathrm{i,k}}\ge \mathrm{0,1 m}∕s^2$ as follows:

The lowest $v\times a_{\mathrm{pos}}$ value gets the percentile 1/M_k, the second lowest 2/M_k, the third lowest 3/M_k and the highest value $M_k∕M_k=\mathrm{100 \%.}$

${\left(v\times a_{\mathrm{pos}}\right)}_{k^{-}}\left[95\right]$ is the ${\left(v\times a_{\mathrm{pos}}\right)}_{\mathrm{j,k}}$ value, with $j∕M_k=\mathrm{95 \%.}$ If $j∕M_k=\mathrm{95 \%.}$ cannot be met, ${\left(v\times a_{\mathrm{pos}}\right)}_{k^{-}}\left[95\right]$ shall be calculated by linear interpolation between consecutive samples j and j+1 with $j∕M_k<\mathrm{95 \%}$ and $\left(j+1\right)∕M_k>\mathrm{95 \%}$.

The relative positive acceleration per speed bin shall be calculated as follows:

where:

If ${\bar{v}}_k\le \mathrm{74,6km}∕h$

and

is fulfilled, the trip is invalid.

If ${\bar{v}}_k>\mathrm{74,6km}∕h$ and ${\left(v\times a_{\mathrm{pos}}\right)}_{k^{-}}\left[95\right]>\left(\mathrm{0,0742}\times {\bar{v}}_k+\mathrm{18,966}\right)$ is fulfilled, the trip is invalid.

F2Upon the request of the manufacturer, and only for those N1 or N2 vehicles where the vehicle power-to-mass ratio is less than or equal to 44 W/kg then:

If ${\bar{v}}_k\le \mathrm{74,6\; km}∕h$

and

is fulfilled, the trip is invalid.

If ${\bar{v}}_k>\mathrm{74,6\; km}∕h$

and

is fulfilled, the trip is invalid.

To calculate the power-to-mass ratio, the following values shall be used:

• the mass which corresponds to the actual test mass of the vehicle including the drivers and the PEMS equipment (kg);

• the maximum rated engine power as declared by the manufacturer (W).

If ${\bar{v}}_k\le \mathrm{94,05\; km}∕h$ and ${\mathrm{RPA}}_k<\left(-\mathrm{0,0016}\times {\bar{v}}_k+\mathrm{0,1755}\right)$ is fulfilled, the trip is invalid.

If ${\bar{v}}_k>\mathrm{94,05\; km}∕h$ and RPA_k < 0,025 is fulfilled, the trip is invalid.