Annex II

Annex IIIA to Regulation (EC) No 692/2008 is amended as follows:

1. (1)

   point 2.1 is replaced by the following:

   ‘2.1

   Not-to-exceed emission limits

   Throughout the normal life of a vehicle type approved according to Regulation (EC) No 715/2007, its emissions determined in accordance with the requirements of this Annex and emitted at any possible RDE test performed in accordance with the requirements of this Annex, shall not be higher than the following not-to-exceed (NTE) values:

   NTE_pollutant = CF_pollutant × TF(p ₁,…, p_n ) × EURO-6

   where EURO-6 is the applicable Euro 6 emission limit laid down in Table 2 of Annex I to Regulation (EC) No 715/2007.’;

2. (2)

   the following points 2.1.1, 2.1.2 and 2.1.3 are inserted:

   ‘2.1.1

   Final conformity factors

   The conformity factor CF_pollutant for the respective pollutant is specified as follows:

   CO emissions shall be measured and recorded at RDE tests.
   Pollutant	Mass of oxides of nitrogen (NOx)	Number of particles (PN)	Mass of carbon monoxide (CO)f1	Mass of total hydrocarbons (THC)	Combined mass of total hydrocarbons and oxides of nitrogen (THC + NOx)
   CFpollutant	1 + margin with margin = 0,5	to be determined	—	—	—

   “margin” is a parameter taking into account the additional measurement uncertainties introduced by the PEMS equipment, which are subject to an annual review and shall be revised as a result of the improved quality of the PEMS procedure or technical progress.

   2.1.2

   Temporary conformity factors

   By way of exception to the provisions of point 2.1.1, during a period of 5 years and 4 months following the dates specified in Article 10(4) and (5) of Regulation (EC) No 715/2007 and upon request of the manufacturer, the following temporary conformity factors may apply:

   CO emissions shall be measured and recorded at RDE tests.
   Pollutant	Mass of oxides of nitrogen (NOx)	Number of particles (PN)	Mass of carbon monoxide (CO)f2	Mass of total hydrocarbons (THC)	Combined mass of total hydrocarbons and oxides of nitrogen (THC + NOx)
   CFpollutant	2,1	to be determined	—	—	—

   The application of temporary conformity factors shall be recorded in the certificate of conformity of the vehicle.

   2.1.3

   Transfer functions

   The transfer function TF(p1,…, p_n ) referred to in point 2.1 is set to 1 for the entire range of parameters p_i (i = 1,…,n).

   If the transfer function TF(p ₁,…, p_n ) is amended, this shall be done in a manner which is not detrimental to the environmental impact and the effectiveness of the RDE test procedures. In particular the following condition shall hold:

   ∫ TF (p1,…, pn) * Q (p1,…, pn) dp = ∫ Q (p1,…, pn) dp

   Where:

   • dp represents the integral over the entire space of the parameters p_i (i = 1,…,n)

   • Q(p₁,…, p_n), is the probability density of an event corresponding to the parameters p_i (i = 1,…,n) in real driving.’;

3. (3)

   the following point 3.1.0 is inserted:

   ‘3.1.0

   The requirements of point 2.1 shall be fulfilled for the urban part and the complete PEMS trip. Upon the choice of the manufacturer the conditions of at least one of the two points below shall be fulfilled:

   1. 3.1.0.1

      M_gas,d,t ≤ NTE_pollutant and M_gas,d,u ≤ NTE_pollutant with the definitions of point 2.1 of this Annex and points 6.1 and 6.3 of Appendix 5 and the setting gas = pollutant.

   2. 3.1.0.2

      M_w,gas,d ≤ NTE_pollutant and M_w,gas,d,U ≤ NTE_pollutant with the definitions of point 2.1 of this Annex and point 3.9 of Appendix 6 and the setting gas = pollutant.’;

4. (4)

   point 5.3 is deleted;

5. (5)

   point 5.4 is replaced by the following:

   ‘5.4.

   Dynamic conditions

   The dynamic conditions encompass the effect of road grade, head wind and driving dynamics (accelerations, decelerations) and auxiliary systems upon energy consumption and emissions of the test vehicle. The verification of the normality of dynamic conditions shall be done after the test is completed, using the recorded PEMS data. This verification shall be conducted in two steps:

   1. 5.4.1

      The overall excess or insufficiency of driving dynamics during the trip shall be checked using the methods described in Appendix 7a to this Annex.

   2. 5.4.2

      If the trip results as valid following the verifications according to point 5.4.1, the methods for verifying the normality of the dynamic conditions and laid down in Appendices 5 and 6 to this Annex must be applied. Each method includes a reference for dynamic conditions, ranges around the reference and the minimum coverage requirements to achieve a valid test.’;

6. (6)

   point 6.8 is replaced by the following:

   ‘6.8

   The average speed (including stops) of the urban driving part of the trip should be between 15 and 40 km/h. Stop periods, defined as vehicle speed of less than 1 km/h, shall account for 6-30 % of the time duration of urban operation. Urban operation shall contain several stop periods of 10 s or longer. If a stop period lasts more than 180 s, the emission events during the 180 s following such an excessively long stop period shall be excluded from the evaluation.’;

7. (7)

   in point 6.11, the following sentence is added:

   ‘In addition, the proportional cumulative positive altitude gain shall be less than 1 200 m/100km) and be determined according to Appendix 7b.’;

8. (8)

   point 9.5 is replaced by the following:

   ‘9.5.

   If during a particular time interval the ambient conditions are extended in accordance with point 5.2, the emissions during this particular time interval, calculated according to Appendix 4, shall be divided by a value of 1,6 before being evaluated for compliance with the requirements of this Annex.’;

9. (9)

   Appendix 1 is amended as follows:

   1. (a)

      in point 3.4.6, the following sentence is added:

      ‘It is permitted to power any safety-related illumination of fixtures and installations of PEMS components outside of the vehicle's cabin by the vehicle's battery.’;

   2. (b)

      in point 4.5, the following sentence is added:

      ‘To minimise analyser drift, one should conduct the zero and span calibration of analysers at an ambient temperature that resembles, as closely as possible, the temperature experienced by the test equipment during the RDE trip.’;

10. (10)

    in Appendix 2, footnote 2 to Table 4 in point 8 is replaced by the following:

    ‘(²)

    This general requirement applies to the speed sensor only; if vehicle speed is used to determine parameters like acceleration, the product of speed and positive acceleration, or RPA, the speed signal shall have an accuracy of 0,1 % above 3 km/h and a sampling frequency of 1 Hz. This accuracy requirement can be met by using the signal of a wheel rotational speed sensor.’;

11. (11)

    in Appendix 6 point 2 the following definition is deleted:

    a_i

    ‘Actual acceleration in time step i, if not other defined in an equation:

    $a_i=\frac{\left(v_{i+1}-v_i\right)}{\mathrm{3,6}\times \left(t_{i+1}-t_i\right)}$ , [m/s²]’;

12. (12)

    in Appendix 6 point 2 the following definitions are inserted:

    ${\bar{m}}_{\mathrm{gas,U}}$

    ‘Weighted emission value of an exhaust gas component ‘gas’ for the subsample of all seconds i with v_i < 60 km/h, g/s

    M_w,gas,d,U

    Weighted distance-specific emissions for the exhaust gas component ‘gas’ for the subsample of all seconds i with v_i < 60 km/h, g/km

    ${\bar{v}}_U$

    Weighted vehicle speed in the wheel power class j, km/h’;

13. (13)

    in Appendix 6 point 3.1 the first paragraph is replaced by the following text:

    ‘The actual wheel power P_r,i shall be the total power to overcome air resistance, rolling resistance, road gradients, longitudinal inertia of the vehicle and rotational inertia of the wheels.’;

14. (14)

    in Appendix 6 point 3.2 is replaced by the following text:

    ‘3.2

    Classification of the moving averages to urban, rural and motorway

    The standard power frequencies are defined for urban driving and for the total trip (see paragraph 3.4) and a separate evaluation of the emissions shall be made for the total trip and for the urban part. The three second moving averages calculated according to paragraph 3.3 shall therefore be allocated later to urban and extra-urban driving conditions according to the velocity signal (v_i) from the actual second i as outlined in Table 1-1.

    Table 1-1

    Speed ranges for the allocation of test data to urban, rural and motorway conditions in the power binning method

    	Urban	Rural	Motorway
    vi [km/h]	0 to ≤ 60	> 60 to ≤ 90	> 90

    ’

15. (15)

    in Appendix 6 point 3.9 is replaced by the following text:

    ‘3.9.

    Calculation of the weighted distance-specific emission value

    The time-based weighted averages of the emissions in the test shall be converted into distance-based emissions once for the urban data set and once for the total data set as follows:

    • For the total trip: $M_{\mathrm{w,gas,d}}=1000\times \frac{{\bar{m}}_{\mathrm{gas}}\times 3600}{\bar{v}}$

    • For the urban part of the trip: $M_{\mathrm{w,gas,d,U}}=1000\times \frac{{\bar{m}}_{\mathrm{gas,U}}\times 3600}{{\bar{v}}_U}$

    Using these formulas, weighted averages shall be calculated for the following pollutants for the total trip and for the urban part of the trip:

    M_w,NOx,d

    weighted NO_x test result in [mg/km]

    M_w,NOx,d,U

    weighted NO_x test result in [mg/km]

    M_w,CO,d

    weighted CO test result in [mg/km]

    M_w,CO,d,U

    weighted CO test result in [mg/km]’;

16. (16)

    the following Appendices 7a and 7b are inserted:

    Appendix 7a

    Verification of overall trip dynamics

    1.

    INTRODUCTION

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

    2.

    SYMBOLS

    RPA

    relative positive acceleration

    ‘acceleration resolution a_res ’

    minimum acceleration > 0 measured in m/s²

    T4253H

    compound data smoother

    ‘positive acceleration a_pos ’

    acceleration [m/s²] greater than 0,1 m/s²

    Index (i) refers to the time step

    Index (j) refers to the time step of positive acceleration datasets

    Index (k) refers to the category (t = total, u = urban, r = rural, m = motorway)

    Δ

    difference

    >

    larger

    ≥

    larger or equal

    %

    per cent

    <

    smaller

    ≤

    smaller or equal

    a

    acceleration [m/s²]

    a_i

    acceleration in time step i [m/s²]

    a_pos

    positive acceleration greater than 0,1 m/s² [m/s²]

    a_pos,i,k

    positive acceleration greater than 0,1 m/s² in time step i considering the urban, rural and motorway shares [m/s²]

    a_res

    acceleration resolution [m/s²]

    d_i

    distance covered in time step i [m]

    d_i,k

    distance covered in time step i considering the urban, rural and motorway shares [m]

    M_k

    number of samples for urban, rural and motorway shares with positive acceleration greater than 0,1 m/s²

    N_k

    total number of samples for the urban, rural and motorway shares and the complete trip

    RPA_k

    relative positive acceleration for urban, rural and motorway shares [m/s² or kWs/(kg × km)]

    t_k

    duration of the urban, rural and motorway shares and the complete trip [s]

    v

    vehicle speed [km/h]

    v_i

    actual vehicle speed in time step i [km/h]

    v_i,k

    actual vehicle speed in time step i considering the urban, rural and motorway shares [km/h]

    (v · a)_i

    actual vehicle speed per acceleration in time step i [m²/s³ or W/kg]

    (v · a_pos)_j,k

    actual vehicle speed per positive acceleration greater than 0,1 m/s² in time step j considering the urban, rural and motorway shares [m²/s³ or W/kg].

    (v · a_pos)_k _[95]

    95th percentile of the product of vehicle speed per positive acceleration greater than 0,1 m/s² for urban, rural and motorway shares [m²/s³ or W/kg]

    ${\bar{v}}_k$

    average vehicle speed for urban, rural and motorway shares [km/h]

    3.

    TRIP INDICATORS

    3.1.

    Calculations

    3.1.1.

    Data pre-processing

    Dynamic parameters like acceleration, v · a_pos or RPA shall be determined with a speed signal of an accuracy of 0,1 % above 3 km/h and a sampling frequency of 1 Hz. This accuracy requirement is generally fulfilled by wheel (rotational) speed signals.

    The speed trace shall be checked for faulty or implausible sections. The vehicle speed trace of such sections is characterised by steps, jumps, terraced speed traces or missing values. Short faulty sections shall be corrected, for example by data interpolation or benchmarking against a secondary speed signal. Alternatively, short trips containing faulty sections could be excluded from the subsequent data analysis. In a second step the acceleration values shall be ranked in ascending order, in order to determine the acceleration resolution a_res = (minimum acceleration value > 0).

    If a_res ≤ 0,01 m/s ², the vehicle speed measurement is accurate enough.

    If 0,01 < a_res ≤ r_max m/s², smoothing by using a T4253 Hanning filter.

    If a_res > r_max m/s², the trip is invalid.

    The T4253 Hanning filter performs the following calculations: The smoother starts with a running median of 4, which is centred by a running median of 2. It then re-smoothes these values by applying a running median of 5, a running median of 3, and Hanning (running weighted averages). Residuals are computed by subtracting the smoothed series from the original series. This whole process is then repeated on the computed residuals. Finally, the smoothed residuals are computed by subtracting the smoothed values obtained the first time through the process.

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

    3.1.2.

    Calculation of distance, acceleration and v · a

    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:

    d_i = v_i /3,6, i = 1 to N_t

    Where:

    • d_i is the distance covered in time step i [m]

    • v _i is the actual vehicle speed in time step i [km/h]

    • N _t is the total number of samples

    The acceleration shall be calculated as follows:

    a_i = (v _{i + 1} – v _{i – 1})/(2 · 3,6), i = 1 to N_t

    Where:

    a_i is the acceleration in time step i [m/s²]. For i = 1: v_{i – 1} = 0, for i = N_t : v_{i + 1} = 0.

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

    (v · a)_i = v_i · a_i /3,6, i = 1 to N_t

    Where:

    (v · a)_i is the product of the actual vehicle speed per acceleration in time step i [m²/s³ or W/kg].

    3.1.3.

    Binning of the results

    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.

    The number of datasets with acceleration values a_i > 0,1 m/s² shall be bigger or equal to 150 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.

    3.1.4.

    Calculation of v · a_pos_[95] per speed bin

    The 95th percentile of the v · a_pos values shall be calculated as follows:

    The (v · a)_i,k values in each speed bin shall be ranked in ascending order for all datasets with a_i,k ≥ 0,1 m/s ² and the total number of these samples M_k shall be determined.

    Percentile values are then assigned to the (v · a_pos)_j,k values with a_i,k ≥ 0,1 m/s ² as follows:

    The lowest v · a_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 =100 %.

    (v · a_pos)_k _[95] is the (v · a_pos)_j,k value, with j/M_k = 95 %. If j/M_k = 95 % cannot be met, (v · a_pos)_k _[95] shall be calculated by linear interpolation between consecutive samples j and j + 1 with j/M_k < 95 % and (j + 1)/M_k > 95 %.

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

    RPA_k = Σ _j (Δt · (v · a_pos ) _j,k )/Σ _id_i,k , j = 1 to M_k,i = 1 to N_k,k = u,r,m

    Where:

    RPA_k is the relative positive acceleration for urban, rural and motorway shares in [m/s² or kWs/(kg*km)]

    Δt

    time difference equal to 1 second

    M_k

    the sample number for urban, rural and motorway shares with positive acceleration

    N_k

    the total sample number for urban, rural and motorway shares.

    4.

    VERIFICATION OF TRIP VALIDITY

    4.1.1.

    Verification of v*a_{pos_[95]} per speed bin (with v in [km/h])

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

    and

    $${\left(v\times a_{\mathrm{pos}}\right)}_k\_\left[95\right]>\left(\mathrm{0,136}\times {\bar{v}}_k+\mathrm{14,44}\right)$$

    is fulfilled, the trip is invalid.

    If ${\bar{v}}_k>\mathrm{74,6}\mathrm{km}∕h$ 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.

    4.1.2.

    Verification of RPA per speed bin

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

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

    Appendix 7b

    Procedure to determine the cumulative positive elevation gain of a trip

    1.

    INTRODUCTION

    This Appendix describes the procedure to determine the cumulative elevation gain of an RDE trip.

    2.

    SYMBOLS

    d(0)

    distance at the start of a trip [m]

    d

    cumulative distance travelled at the discrete way point under consideration [m]

    d₀

    cumulative distance travelled until the measurement directly before the respective way point d [m]

    d₁

    cumulative distance travelled until the measurement directly after the respective way point d [m]

    d_a

    reference way point at d(0) [m]

    d_e

    cumulative distance travelled until the last discrete way point [m]

    d_i

    instantaneous distance [m]

    d_tot

    total test distance [m]

    h(0)

    vehicle altitude after the screening and principle verification of data quality at the start of a trip [m above sea level]

    h(t)

    vehicle altitude after the screening and principle verification of data quality at point t [m above sea level]

    h(d)

    vehicle altitude at the way point d [m above sea level]

    h(t-1)

    vehicle altitude after the screening and principle verification of data quality at point t-1 [m above sea level]

    h_corr(0)

    corrected altitude directly before the respective way point d [m above sea level]

    h_corr(1)

    corrected altitude directly after the respective way point d [m above sea level]

    h_corr(t)

    corrected instantaneous vehicle altitude at data point t [m above sea level]

    h_corr(t-1)

    corrected instantaneous vehicle altitude at data point t-1 [m above sea level]

    h_GPS,i

    instantaneous vehicle altitude measured with GPS [m above sea level]

    h_GPS(t)

    vehicle altitude measured with GPS at data point t [m above sea level]

    h_int(d)

    interpolated altitude at the discrete way point under consideration d [m above sea level]

    h_int,sm,1(d)

    smoothed interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]

    h_map(t)

    vehicle altitude based on topographic map at data point t [m above sea level]

    Hz

    hertz

    km/h

    kilometre per hour

    m

    metre

    road_grade,1(d)

    smoothed road grade at the discrete way point under consideration d after the first smoothing run [m/m]

    road_grade,2(d)

    smoothed road grade at the discrete way point under consideration d after the second smoothing run [m/m]

    sin

    trigonometric sine function

    t

    time passed since test start [s]

    t₀

    time passed at the measurement directly located before the respective way point d [s]

    v_i

    instantaneous vehicle speed [km/h]

    v(t)

    vehicle speed of data point t [km/h].

    3.

    GENERAL REQUIREMENTS

    The cumulative positive elevation gain of an RDE trip shall be determined based on three parameters: the instantaneous vehicle altitude h_GPS,i [m above sea level] as measured with the GPS, the instantaneous vehicle speed v_i [km/h] recorded at a frequency of 1 Hz and the corresponding time t [s] that has passed since test start.

    4.

    CALCULATION OF CUMULATIVE POSITIVE ELEVATION GAIN

    4.1.

    General

    The cumulative positive elevation gain of an RDE trip shall be calculated as a three-step procedure, consisting of: (i) the screening and principle verification of data quality; (ii) the correction of instantaneous vehicle altitude data; and (iii) the calculation of the cumulative positive elevation gain.

    4.2.

    Screening and principle verification of data quality

    The instantaneous vehicle speed data shall be checked for completeness. Correcting for missing data is permitted if gaps remain within the requirements specified in Point 7 of Appendix 4; else, the test results shall be voided. The instantaneous altitude data shall be checked for completeness. Data gaps shall be completed by data interpolation. The correctness of interpolated data shall be verified by a topographic map. It is recommended to correct interpolated data if the following condition applies:

    |h_GPS(t) – h_map(t)| > 40 m

    The altitude correction shall be applied so that:

    h(t) = h_map(t)

    where:

    h(t)

    vehicle altitude after the screening and principle verification of data quality at data point t [m above sea level]

    h_GPS(t)

    vehicle altitude measured with GPS at data point t [m above sea level]

    h_map(t)

    vehicle altitude based on topographic map at data point t [m above sea level].

    4.3.

    Correction of instantaneous vehicle altitude data

    The altitude h(0) at the start of a trip at d(0) shall be obtained by GPS and verified for correctness with information from a topographic map. The deviation shall not be larger than 40 m. Any instantaneous altitude data h(t) shall be corrected if the following condition applies:

    |h(t) – h(t – 1)| > (v(t)/3,6 * sin45°)

    The altitude correction shall be applied so that:

    h_corr(t) = h_corr (t-1)

    where:

    h(t)

    vehicle altitude after the screening and principle verification of data quality at data point t [m above sea level]

    h(t-1)

    vehicle altitude after the screening and principle verification of data quality at data point t-1 [m above sea level]

    v(t)

    vehicle speed of data point t [km/h]

    h_corr(t)

    corrected instantaneous vehicle altitude at data point t [m above sea level]

    h_corr(t-1)

    corrected instantaneous vehicle altitude at data point t-1 [m above sea level].

    Upon the completion of the correction procedure, a valid set of altitude data is established. This data set shall be used for the final calculation of the cumulative positive elevation gain as described in point 4.4.

    4.4.

    Final calculation of the cumulative positive elevation gain

    4.4.1.

    Establishment of a uniform spatial resolution

    The total distance d_tot [m] covered by a trip shall be determined as sum of the instantaneous distances d_i . The instantaneous distance d_i shall be determined as:

    $$d_i=\frac{v_i}{\mathrm{3,6}}$$

    Where:

    d_i

    instantaneous distance [m]

    v_i

    instantaneous vehicle speed [km/h]

    The cumulative elevation gain shall be calculated from data of a constant spatial resolution of 1 m starting with the first measurement at the start of a trip d(0). The discrete data points at a resolution of 1 m are referred to as way points, characterised by a specific distance value d (e.g., 0, 1, 2, 3 m…) and their corresponding altitude h(d) [m above sea level].

    The altitude of each discrete way point d shall be calculated through interpolation of the instantaneous altitude h_corr(t) as:

    $$h_{\mathrm{int}}\left(d\right)=h_{\mathrm{corr}}\left(0\right)+\frac{h_{\mathrm{corr}}\left(1\right)-h_{\mathrm{corr}}\left(0\right)}{d_1-d_0}\times \left(d-d_0\right)$$

    Where:

    h_int(d)

    interpolated altitude at the discrete way point under consideration d [m above sea level]

    h_corr(0)

    corrected altitude directly before the respective way point d [m above sea level]

    hcorr(1)

    corrected altitude directly after the respective way point d [m above sea level]

    d

    cumulative distance travelled until the discrete way point under consideration d [m]

    d₀

    cumulative distance travelled until the measurement located directly before the respective way point d [m]

    d₁

    cumulative distance travelled until the measurement located directly after the respective way point d [m].

    4.4.2.

    Additional data smoothing

    The altitude data obtained for each discrete way point shall be smoothed by applying a two-step procedure; d_a and d_e denote the first and last data point respectively (Figure 1). The first smoothing run shall be applied as follows:

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(d\right)=\frac{h_{\mathrm{int}}\left(d+200m\right)-h_{\mathrm{int}}\left(d_a\right)}{\left(d+200m\right)}$ for d ≤ 200 m

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(d\right)=\frac{h_{\mathrm{int}}\left(d+200m\right)-h_{\mathrm{int}}\left(d-200m\right)}{\left(d+200m\right)-\left(d-200m\right)}$ for 200 m < d < (d_e – 200 m)

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(d\right)=\frac{h_{\mathrm{int}}\left(d_e\right)-h_{\mathrm{int}}\left(d-200m\right)}{d_e-\left(d-200m\right)}$ for d ≥ (d_e – 200 m)

    h _int,sm,1(d) = h _int,sm,1(d – 1 m) + road _grade,1(d), d = d_a + 1 to d_e

    h _int,sm,1(d_a ) = h_int (d_a ) + road _grade,1(d_a )

    Where:

    road_grade,1(d)

    smoothed road grade at the discrete way point under consideration after the first smoothing run [m/m]

    h_int(d)

    interpolated altitude at the discrete way point under consideration d [m above sea level]

    h_int,sm,1(d)

    smoothed interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]

    d

    cumulative distance travelled at the discrete way point under consideration [m]

    d_a

    reference way point at a distance of zero metres [m]

    d_e

    cumulative distance travelled until the last discrete way point [m].

    The second smoothing run shall be applied as follows:

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(d\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(d+200m\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(d_a\right)}{\left(d+200m\right)}$ for d ≤ 200 m

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(d\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(d+200m\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(d-200m\right)}{\left(d+200m\right)-\left(d-200m\right)}$ for 200 m < d < (d_e – 200 m)

    ${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(d\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(d_e\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(d-200m\right)}{d_e-\left(d-200m\right)}$ for d ≥ (d_e – 200 m)

    Where:

    road_grade,2(d)

    smoothed road grade at the discrete way point under consideration after the second smoothing run [m/m]

    h_int,sm,1(d)

    smoothed interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]

    d

    cumulative distance travelled at the discrete way point under consideration [m]

    d_a

    reference way point at a distance of zero metres [m]

    d_e

    cumulative distance travelled until the last discrete way point [m].

    Figure 1

    Illustration of the procedure to smooth the interpolated altitude signals

    

    4.4.3.

    Calculation of the final result

    The positive cumulative elevation gain of a trip shall be calculated by integrating all positive interpolated and smoothed road grades, i.e. road_grade,2(d). The result should be normalised by the total test distance d_tot and expressed in meters of cumulative elevation gain per 100 kilometres of distance.

    5.

    NUMERICAL EXAMPLE

    Tables 1 and 2 show the steps performed in order to calculate the positive elevation gain on the basis of data recorded during an on-road test performed with PEMS. For the sake of brevity an extract of 800 m and 160 s is presented here.

    5.1.

    Screening and principle verification of data quality

    The screening and principle verification of data quality consists of two steps. First, the completeness of vehicle speed data is checked. No data gaps related to vehicle speed are detected in the present data sample (see Table 1). Second, the altitude data are checked for completeness; in the data sample, altitude data related to seconds 2 and 3 are missing. The gaps are filled by interpolating the GPS signal. In addition, the GPS altitude is verified by a topographic map; this verification includes the altitude h(0) at the start of the trip. Altitude data related to seconds 112-114 are corrected on the basis of the topographic map to satisfy the following condition:

    h_GPS(t) – h_map(t) < – 40 m

    As result of the applied data verification, the data in the fifth column h(t) are obtained.

    5.2.

    Correction of instantaneous vehicle altitude data

    As a next step, the altitude data h(t) of seconds 1 to 4, 111 to 112 and 159 to 160 are corrected assuming the altitude values of seconds 0, 110 and 158 respectively since the following condition applies:

    |h(t) – h(t – 1)| > (v(t)/3,6 * sin45°)

    As result of the applied data correction, the data in the sixth column h_corr(t) are obtained. The effect of the applied verification and correction steps on the altitude data is depicted in Figure 2.

    5.3.

    Calculation of the cumulative positive elevation gain

    5.3.1.

    Establishment of a uniform spatial resolution

    The instantaneous distance d_i is calculated by dividing the instantaneous vehicle speed measured in km/h by 3,6 (Column 7 in Table 1). Recalculating the altitude data to obtain a uniform spatial resolution of 1 m yields the discrete way points d (Column 1 in Table 2) and their corresponding altitude values h_int(d) (Column 7 in Table 2). The altitude of each discrete way point d is calculated through interpolation of the measured instantaneous altitude h_corr as:

    $$h_{\mathrm{int}}\left(0\right)=\mathrm{120,3}+\frac{\mathrm{120,3}-\mathrm{120,3}}{\mathrm{0,1}-\mathrm{0,0}}\times \left(0-0\right)=\mathrm{120,3000}$$ $$h_{\mathrm{int}}\left(520\right)=\mathrm{132,5}+\frac{\mathrm{132,6}-\mathrm{132,5}}{\mathrm{523,6}-\mathrm{519,9}}\times \left(520-\mathrm{519,9}\right)=\mathrm{132,5027}$$

    5.3.2.

    Additional data smoothing

    In Table 2, the first and last discrete way points are: d_a  = 0 m and d_e  = 799 m, respectively. The altitude data of each discrete way point is smoothed by applying a two-step procedure. The first smoothing run consists of:

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(0\right)=\frac{h_{\mathrm{int}}\left(200m\right)-h_{\mathrm{int}}\left(0\right)}{\left(0+200m\right)}=\frac{\mathrm{120,9682}-\mathrm{120,3000}}{200}=\mathrm{0,0033}$$

    chosen to demonstrate the smoothing for d ≤ 200 m

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(320\right)=\frac{h_{\mathrm{int}}\left(520\right)-h_{\mathrm{int}}\left(120\right)}{\left(520\right)-\left(120\right)}=\frac{\mathrm{132,5027}-\mathrm{121,9808}}{400}=\mathrm{0,0288}$$

    chosen to demonstrate the smoothing for 200 m < d < (599 m)

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,1}}\left(720\right)=\frac{h_{\mathrm{int}}\left(799\right)-h_{\mathrm{int}}\left(520\right)}{799-\left(520\right)}=\frac{\mathrm{121,2000}-\mathrm{132,5027}}{279}=-\mathrm{0,0405}$$

    chosen to demonstrate the smoothing for d ≥ (599 m)

    The smoothed and interpolated altitude is calculated as:

    h _int,sm,1(0) = h_int (0) + road _grade,1(0) = 120,3 + 0,0033 ≈ 120,3033 m

    h _int,sm,1(799) = h _int,sm,1(798) + road _grade,1(799) = 121,2550 – 0,0220 = 121,2330 m

    Second smoothing run:

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(0\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(200\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(0\right)}{\left(200\right)}=\frac{\mathrm{119,9618}-\mathrm{120,3033}}{\left(200\right)}=-\mathrm{0,0017}$$

    chosen to demonstrate the smoothing for d ≤ 200 m

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(320\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(520\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(120\right)}{\left(520\right)-\left(120\right)}=\frac{\mathrm{123,6809}-\mathrm{120,1843}}{400}=\mathrm{0,0087}$$

    chosen to demonstrate the smoothing for 200 m < d < (599 m)

    $${\mathrm{road}}_{\mathrm{grade}\mathrm{,2}}\left(720\right)=\frac{h_{\mathrm{int,sm}\mathrm{,1}}\left(799\right)-h_{\mathrm{int,sm}\mathrm{,1}}\left(520\right)}{799-\left(520\right)}=\frac{\mathrm{121,2330}-\mathrm{123,6809}}{279}=-\mathrm{0,0088}$$

    chosen to demonstrate the smoothing for d ≥ (599 m)

    5.3.3.

    Calculation of the final result

    The positive cumulative elevation gain of a trip is calculated by integrating all positive interpolated and smoothed road grades, i.e. road_grade,2(d). For the presented example the total covered distance was d_tot  = 139,7 km and all positive interpolated and smoothed road grades were of 516 m. Therefore a positive cumulative elevation gain of 516 × 100/139,7 = 370 m/100 km was achieved.

    Table 1

    Correction of instantaneous vehicle altitude data

    - denotes data gaps
    Time t [s]	v(t) [km/h]	hGPS(t) [m]	hmap(t) [m]	h(t) [m]	hcorr(t) [m]	di [m]	Cum. d [m]
    0	0,00	122,7	129,0	122,7	122,7	0,0	0,0
    1	0,00	122,8	129,0	122,8	122,7	0,0	0,0
    2	0,00	-	129,1	123,6	122,7	0,0	0,0
    3	0,00	-	129,2	124,3	122,7	0,0	0,0
    4	0,00	125,1	129,0	125,1	122,7	0,0	0,0
    …	…	…	…	…	…	…	…
    18	0,00	120,2	129,4	120,2	120,2	0,0	0,0
    19	0,32	120,2	129,4	120,2	120,2	0,1	0,1
    …	…	…	…	…	…	…	…
    37	24,31	120,9	132,7	120,9	120,9	6,8	117,9
    38	28,18	121,2	133,0	121,2	121,2	7,8	125,7
    …	…	…	…	…	…	…	…
    46	13,52	121,4	131,9	121,4	121,4	3,8	193,4
    47	38,48	120,7	131,5	120,7	120,7	10,7	204,1
    …	…	…	…	…	…	…	…
    56	42,67	119,8	125,2	119,8	119,8	11,9	308,4
    57	41,70	119,7	124,8	119,7	119,7	11,6	320,0
    …	…	…	…	…	…	…	…
    110	10,95	125,2	132,2	125,2	125,2	3,0	509,0
    111	11,75	100,8	132,3	100,8	125,2	3,3	512,2
    112	13,52	0,0	132,4	132,4	125,2	3,8	516,0
    113	14,01	0,0	132,5	132,5	132,5	3,9	519,9
    114	13,36	24,30	132,6	132,6	132,6	3,7	523,6
    …	…	…	…	…	…	…
    149	39,93	123,6	129,6	123,6	123,6	11,1	719,2
    150	39,61	123,4	129,5	123,4	123,4	11,0	730,2
    …	…	…	…	…	…	…
    157	14,81	121,3	126,1	121,3	121,3	4,1	792,1
    158	14,19	121,2	126,2	121,2	121,2	3,9	796,1
    159	10,00	128,5	126,1	128,5	121,2	2,8	798,8
    160	4,10	130,6	126,0	130,6	121,2	1,2	800,0

    Table 2

    Calculation of road grade

    d[m]	t0 [s]	d0 [m]	d1 [m]	h0 [m]	h1 [m]	hint(d) [m]	roadgrade,1(d) [m/m]	hint,sm,1(d) [m]	roadgrade,2(d) [m/m]
    0	18	0,0	0,1	120,3	120,4	120,3	0,0035	120,3	– 0,0015
    …	…	…	…	…	…	…	…	…	…
    120	37	117,9	125,7	120,9	121,2	121,0	– 0,0019	120,2	0,0035
    …	…	…	…	…	…	…	…	…	…
    200	46	193,4	204,1	121,4	120,7	121,0	– 0,0040	120,0	0,0051
    …	…	…	…	…	…	…	…	…	…
    320	56	308,4	320,0	119,8	119,7	119,7	0,0288	121,4	0,0088
    …	…	…	…	…	…	…	…	…	…
    520	113	519,9	523,6	132,5	132,6	132,5	0,0097	123,7	0,0037
    …	…	…	…	…	…	…	…	…	…
    720	149	719,2	730,2	123,6	123,4	123,6	– 0,0405	122,9	– 0,0086
    …	…	…	…	…	…	…	…	…	…
    798	158	796,1	798,8	121,2	121,2	121,2	– 0,0219	121,3	– 0,0151
    799	159	798,8	800,0	121,2	121,2	121,2	– 0,0220	121,3	– 0,0152

    Figure 2

    The effect of data verification and correction — The altitude profile measured by GPS h_GPS(t), the altitude profile provided by the topographic map h_map(t), the altitude profile obtained after the screening and principle verification of data quality h(t) and the correction hcorr(t) of data listed in Table 1

    

    Figure 3

    Comparison between the corrected altitude profile h_corr(t) and the smoothed and interpolated altitude h_int,sm,1

    

    Table 2

    Calculation of the positive elevation gain

    d[m]	t0 [s]	d0 [m]	d1 [m]	h0 [m]	h1 [m]	hint(d) [m]	roadgrade,1(d) [m/m]	hint,sm,1(d) [m]	roadgrade,2(d) [m/m]
    0	18	0,0	0,1	120,3	120,4	120,3	0,0035	120,3	– 0,0015
    …	…	…	…	…	…	…	…	…	…
    120	37	117,9	125,7	120,9	121,2	121,0	– 0,0019	120,2	0,0035
    …	…	…	…	…	…	…	…	…	…
    200	46	193,4	204,1	121,4	120,7	121,0	– 0,0040	120,0	0,0051
    …	…	…	…	…	…	…	…	…	…
    320	56	308,4	320,0	119,8	119,7	119,7	0,0288	121,4	0,0088
    …	…	…	…	…	…	…	…	…	…
    520	113	519,9	523,6	132,5	132,6	132,5	0,0097	123,7	0,0037
    …	…	…	…	…	…	…	…	…	…
    720	149	719,2	730,2	123,6	123,4	123,6	– 0,0405	122,9	– 0,0086
    …	…	…	…	…	…	…	…	…	…
    798	158	796,1	798,8	121,2	121,2	121,2	– 0,0219	121,3	– 0,0151
    799	159	798,8	800,0	121,2	121,2	121,2	– 0,0220	121,3	– 0,0152