{
  "url": "https://openlegislation.uk/eu-regulation-2017-1151/annex-IIIA/appendix-7b",
  "json_url": "https://openlegislation.uk/eu-regulation-2017-1151/annex-IIIA/appendix-7b.json",
  "legislation": "eur/2017/1151",
  "legislation_title": "Commission Regulation (EU) 2017/1151 of 1 June 2017 supplementing Regulation (EC) No 715/2007 of the European Parliament and of the Council on type-approval of motor vehicles with respect to emissions from light passenger and commercial vehicles (Euro 5 and Euro 6) and on access to vehicle repair and maintenance information, amending Directive 2007/46/EC of the European Parliament and of the Council, Commission Regulation (EC) No 692/2008 and Commission Regulation (EU) No 1230/2012 and repealing Commission Regulation (EC) No 692/2008 (Text with EEA relevance)",
  "legislation_url": "https://openlegislation.uk/eu-regulation-2017-1151",
  "path": "annex/IIIA/appendix/7b",
  "kind": "appendix",
  "number": "7b",
  "heading": null,
  "text": "Procedure to determine the cumulative positive elevation gain of a PEMS trip\n1.\nINTRODUCTION\nThis Appendix describes the procedure to determine the cumulative elevation gain of a PEMS trip.\n2.\nSYMBOLS, PARAMETERS AND UNITS\nd(0)distance at the start of a trip [m]\ndcumulative distance travelled at the discrete way point under consideration [m]\nd0cumulative distance travelled until the measurement directly before the respective way point d [m]\nd1cumulative distance travelled until the measurement directly after the respective way point d [m]\ndareference way point at d(0) [m]\ndecumulative distance travelled until the last discrete way point [m]\ndiinstantaneous distance [m]\ndtottotal test distance [m]\nh(0)vehicle altitude after the screening and principle verification of data quality at the start of a trip [m above sea level]\nh(t)vehicle altitude after the screening and principle verification of data quality at point t [m above sea level]\nh(d)vehicle altitude at the way point d [m above sea level]\nh(t-1)vehicle altitude after the screening and principle verification of data quality at point t-1 [m above sea level]\nhcorr(0)corrected altitude directly before the respective way point d [m above sea level]\nhcorr(1)corrected altitude directly after the respective way point d [m above sea level]\nhcorr(t)corrected instantaneous vehicle altitude at data point t [m above sea level]\nhcorr(t-1)corrected instantaneous vehicle altitude at data point t-1 [m above sea level]\nhGPS,iinstantaneous vehicle altitude measured with GPS [m above sea level]\nhGPS(t)vehicle altitude measured with GPS at data point t [m above sea level]\nhint(d)interpolated altitude at the discrete way point under consideration d [m above sea level]\nhint,sm,1(d)smoothed and interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]\nhmap(t)vehicle altitude based on topographic map at data point t [m above sea level]\nHzhertz\nkm/hkilometer per hour\nmmeter\nroadgrade,1(d)smoothed road grade at the discrete way point under consideration d after the first smoothing run [m/m]\nroadgrade,2(d)smoothed road grade at the discrete way point under consideration d after the second smoothing run [m/m]\nsintrigonometric sine function\nttime passed since test start [s]\nt0time passed at the measurement directly located before the respective way point d [s]\nviinstantaneous vehicle speed [km/h]\nv(t)vehicle speed at a data point t [km/h]\n3.\nGENERAL REQUIREMENTS\nThe cumulative positive elevation gain of a RDE trip shall be determined based on three parameters: the instantaneous vehicle altitude hGPS,i [m above sea level] as measured with the GPS, the instantaneous vehicle speed vi [km/h] recorded at a frequency of 1 Hz and the corresponding time t [s] that has passed since test start.\n4.\nCALCULATION OF CUMULATIVE POSITIVE ELEVATION GAIN\n4.1.\nGeneral\nThe cumulative positive elevation gain of a 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.\n4.2.\nScreening and principle verification of data quality\nThe 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:\nhGPSt− hmapt>40mThe altitude correction shall be applied so that:\nht= hmaptwhere:\nh(t)vehicle altitude after the screening and principle verification of data quality at data point t [m above sea level]\nhGPS(t)vehicle altitude measured with GPS at data point t [m above sea level]\nhmap(t)vehicle altitude based on topographic map at data point t [m above sea level]\n4.3.\nCorrection of instantaneous vehicle altitude data\nThe 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:\nht− ht− 1>vt∕ 3,6× sin45°The altitude correction shall be applied so that:\nhcorrt= hcorrt− 1where:\nh(t)vehicle altitude after the screening and principle verification of data quality at data point t [m above sea level]\nh(t-1)vehicle altitude after the screening and principle verification of data quality at data point t-1 [m above sea level]\nv(t)vehicle speed of data point t [km/h]\nhcorr(t)corrected instantaneous vehicle altitude at data point t [m above sea level]\nhcorr(t-1)corrected instantaneous vehicle altitude at data point t-1 [m above sea level]\nUpon the completion of the correction procedure, a valid set of altitude data is established. This data set shall be used for the calculation of the cumulative positive elevation gain as described in Point 13.4.\n4.4.\nFinal calculation of the cumulative positive elevation gain\n4.4.1.\nEstablishment of a uniform spatial resolution\nThe total distance dtot [m] covered by a trip shall be determined as sum of the instantaneous distances di. The instantaneous distance di shall be determined as:\ndi=vi3,6Where:\ndiinstantaneous distance [m]\nviinstantaneous vehicle speed [km/h]\nThe 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, characterized by a specific distance value d (e.g., 0, 1, 2, 3 m…) and their corresponding altitude h(d) [m above sea level].\nThe altitude of each discrete way point d shall be calculated through interpolation of the instantaneous altitude hcorr (t) as:\nhintd=hcorr0+hcorr1− hcorr0d1− d0×d− d0Where:\nhint(d)interpolated altitude at the discrete way point under consideration d [m above sea level]\nhcorr(0)corrected altitude directly before the respective way point d [m above sea level]\nhcorr(1)corrected altitude directly after the respective way point d [m above sea level]\ndcumulative distance traveled until the discrete way point under consideration d [m]\nd0cumulative distance travelled until the measurement located directly before the respective way point d [m]\nd1cumulative distance travelled until the measurement located directly after the respective way point d [m]\n4.4.2.\nAdditional data smoothing\nThe altitude data obtained for each discrete way point shall be smoothed by applying a two-step procedure; da and de denote the first and last data point respectively (Figure 1). The first smoothing run shall be applied as follows:\nroadgrade,1d=hintd+ 200m− hintdad+ 200m for d≤ 200mroadgrade,1d=hintd+ 200m− hintd− 200md+ 200m−d− 200m for 200m< d<de− 200mroadgrade,1d=hintde− hintd− 200mde−d− 200m for d≥de− 200mhint,sm,1d=hint,sm,1d− 1m+ roadgrade,1d, d= da+ 1 to dehint,sm,1da=hintda+ roadgrade,1daWhere:\nroadgrade,1(d)smoothed road grade at the discrete way point under consideration after the first smoothing run [m/m]\nhint(d)interpolated altitude at the discrete way point under consideration d [m above sea level]\nhint,sm,1(d)smoothed interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]\ndcumulative distance travelled at the discrete way point under consideration [m]\ndareference way point at a distance of zero meters [m]\ndecumulative distance travelled until the last discrete way point [m]\nThe second smoothing run shall be applied as follows:\nroadgrade,2d=hint,sm,1d+ 200m− hint,sm,1dad+ 200m for d≤ 200mroadgrade,2d=hint,sm,1d+ 200m− hint,sm,1d− 200md+ 200m−d− 200m for 200m< d<de− 200mroadgrade,2d=hint,sm,1de− hint,sm,1d− 200mde−d− 200m for d≥de− 200mWhere:\nroadgrade,2(d)smoothed road grade at the discrete way point under consideration after the second smoothing run [m/m]\nhint,sm,1(d)smoothed interpolated altitude, after the first smoothing run at the discrete way point under consideration d [m above sea level]\ndcumulative distance travelled at the discrete way point under consideration [m]\ndareference way point at a distance of zero meters [m]\ndecumulative distance travelled until the last discrete way point [m]\nFigure 1\nIllustration of the procedure to smooth the interpolated altitude signals\n4.4.3.\nCalculation of the final result\nThe positive cumulative elevation gain of a total trip shall be calculated by integrating all positive interpolated and smoothed road grades, i.e. road grade,2(d). The result should be normalized by the total test distance dtot and expressed in metres of cumulative elevation gain per one hundred kilometres of distance.\nThe positive cumulative elevation gain of the urban part of a trip shall then be calculated based on the vehicle speed over each discrete way point:\nvw = 1 / (tw,i – tw,i – 1) · 602 / 1 000\nWhere:\nvw - waypoint vehicle speed [km/h]\nAll datasets with vw =< 60 km/h belong to the urban part of the trip.\nIntegrate all of the positive interpolated and smoothed road grades that correspond to urban datasets.\nIntegrate the number of 1m waypoints which correspond to urban datasets and divide by 1 000 to calculate urban test distance d urban [km].\nThe positive cumulative elevation gain of the urban part of trip shall then be calculated by dividing the urban elevation gain by the urban test distance, and expressed in metres of cumulative elevation gain per one hundred kilometres of distance.\n5.\nNUMERICAL EXAMPLE\nTables 1 and 2 show how 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 800m and 160s is presented here.\n5.1.\nScreening and principle verification of data quality\nThe 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:\nhGPSt− hmapt<− 40mAs result of the applied data verification, the data in the fifth column h(t) are obtained.\n5.2.\nCorrection of instantaneous vehicle altitude data\nAs 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 for the altitude data in these time periods the following condition applies:\nht− ht− 1>vt∕ 3,6× sin45°As result of the applied data correction, the data in the sixth column hcorr(t) are obtained. The effect of the applied verification and correction steps on the altitude data is depicted in Figure 2.\n5.3.\nCalculation of the cumulative positive elevation gain\n5.3.1.\nEstablishment of a uniform spatial resolution\nThe instantaneous distance di 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 hint(d) (Column 7 in Table 2). The altitude of each discrete way point d is calculated through interpolation of the measured instantaneous altitude hcorr as:\nhint0=120,3+120,3− 120,30,1− 0,0×0− 0= 120,3000hint520=132,5+132,6− 132,5523,6− 519,9×520− 519,9= 132,50275.3.2.\nAdditional data smoothing\nIn Table 2, the first and last discrete way points are: da=0m and de=799m, respectively. The altitude data of each discrete way point is smoothed by applying a two steps procedure. The first smoothing run consists of:\nroadgrade,10=hint200m− hint00+ 200m=120,9682− 120,3000200= 0,0033chosen to demonstrate the smoothing for d ≤ 200m\nroadgrade,1320=hint520− hint120520−120=132,5027− 121,0400= 0,0288chosen to demonstrate the smoothing for 200m < d < (599m)\nroadgrade,1720=hint799− hint520799−520=121,2000− 132,5027279=− 0,0405chosen to demonstrate the smoothing for d ≥ (599m)\nThe smoothed and interpolated altitude is calculated as:\nhint,sm,10=hint0+ roadgrade,10= 120,3+ 0,0033≈ 120,3033mhint,sm,1799=hint,sm,1798+ roadgrade,1799= 121,2550− 0,0220= 121,2330mSecond smoothing run:\nroadgrade,20=hint,sm,1200− hint,sm,10200=119,9618− 120,3033200=− 0,0017chosen to demonstrate the smoothing for d ≤ 200m\nroadgrade,2320=hint,sm,1520− hint,sm,1120520−120=123,6809− 120,1843400= 0,0087chosen to demonstrate the smoothing for 200m < d < (599)\nroadgrade,2720=hint,sm,1799− hint,sm,1520799−520=121,2330− 123,6809279=− 0,0088chosen to demonstrate the smoothing for d ≥ (599m)\n5.3.3.\nCalculation of the final result\nThe positive cumulative elevation gain of a trip is calculated by integrating all positive interpolated and smoothed road grades, i.e. values in the column roadgrade,2(d) in Table 2. For the entire data set the total covered distance was dtot= 139,7 km and all positive interpolated and smoothed road grades were of 516m. Therefore the positive cumulative elevation gain reached 516*100/139,7=370m/100km.\nTable 1\nCorrection of instantaneous vehicle altitude data\n— denotes data gaps\nTimet [s]\nv(t)[km/h]\nhGPS(t)[m]\nhmap(t)[m]\nh(t)[m]\nhcorr(t)[m]\ndi[m]\nCum. d[m]\n0\n0,00\n122,7\n129,0\n122,7\n122,7\n0,0\n0,0\n1\n0,00\n122,8\n129,0\n122,8\n122,7\n0,0\n0,0\n2\n0,00\n—\n129,1\n123,6\n122,7\n0,0\n0,0\n3\n0,00\n—\n129,2\n124,3\n122,7\n0,0\n0,0\n4\n0,00\n125,1\n129,0\n125,1\n122,7\n0,0\n0,0\n…\n…\n…\n…\n…\n…\n…\n…\n18\n0,00\n120,2\n129,4\n120,2\n120,2\n0,0\n0,0\n19\n0,32\n120,2\n129,4\n120,2\n120,2\n0,1\n0,1\n…\n…\n…\n…\n…\n…\n…\n…\n37\n24,31\n120,9\n132,7\n120,9\n120,9\n6,8\n117,9\n38\n28,18\n121,2\n133,0\n121,2\n121,2\n7,8\n125,7\n…\n…\n…\n…\n…\n…\n…\n…\n46\n13,52\n121,4\n131,9\n121,4\n121,4\n3,8\n193,4\n47\n38,48\n120,7\n131,5\n120,7\n120,7\n10,7\n204,1\n…\n…\n…\n…\n…\n…\n…\n…\n56\n42,67\n119,8\n125,2\n119,8\n119,8\n11,9\n308,4\n57\n41,70\n119,7\n124,8\n119,7\n119,7\n11,6\n320,0\n…\n…\n…\n…\n…\n…\n…\n…\n110\n10,95\n125,2\n132,2\n125,2\n125,2\n3,0\n509,0\n111\n11,75\n100,8\n132,3\n100,8\n125,2\n3,3\n512,2\n112\n13,52\n0,0\n132,4\n132,4\n125,2\n3,8\n516,0\n113\n14,01\n0,0\n132,5\n132,5\n132,5\n3,9\n519,9\n114\n13,36\n24,30\n132,6\n132,6\n132,6\n3,7\n523,6\n…\n…\n…\n…\n…\n…\n…\n149\n39,93\n123,6\n129,6\n123,6\n123,6\n11,1\n719,2\n150\n39,61\n123,4\n129,5\n123,4\n123,4\n11,0\n730,2\n…\n…\n…\n…\n…\n…\n…\n157\n14,81\n121,3\n126,1\n121,3\n121,3\n4,1\n792,1\n158\n14,19\n121,2\n126,2\n121,2\n121,2\n3,9\n796,1\n159\n10,00\n128,5\n126,1\n128,5\n121,2\n2,8\n798,8\n160\n4,10\n130,6\n126,0\n130,6\n121,2\n1,2\n800,0\nTable 2\nCalculation of road grade\nd[m]\nt0[s]\nd0[m]\nd1[m]\nh0[m]\nh1[m]\nhint(d)[m]\nroadgrade,1(d)[m/m]\nhint,sm,1(d)[m]\nroadgrade,2(d)[m/m]\n0\n18\n0,0\n0,1\n120,3\n120,4\n120,3\n0,0035\n120,3\n– 0,0015\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n120\n37\n117,9\n125,7\n120,9\n121,2\n121,0\n– 0,0019\n120,2\n0,0035\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n200\n46\n193,4\n204,1\n121,4\n120,7\n121,0\n– 0,0040\n120,0\n0,0051\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n320\n56\n308,4\n320,0\n119,8\n119,7\n119,7\n0,0288\n121,4\n0,0088\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n520\n113\n519,9\n523,6\n132,5\n132,6\n132,5\n0,0097\n123,7\n0,0037\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n720\n149\n719,2\n730,2\n123,6\n123,4\n123,6\n– 0,0405\n122,9\n– 0,0086\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n798\n158\n796,1\n798,8\n121,2\n121,2\n121,2\n– 0,0219\n121,3\n– 0,0151\n799\n159\n798,8\n800,0\n121,2\n121,2\n121,2\n– 0,0220\n121,3\n– 0,0152\nFigure 2\nThe effect of data verification and correction - The altitude profile measured by GPS hGPS(t), the altitude profile provided by the topographic map hmap(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\nFigure 3\nComparison between the corrected altitude profile hcorr(t) and the smoothed and interpolated altitude hint,sm,1\nTable 3\nCalculation of the positive elevation gain\nd[m]\nt0[s]\nd0[m]\nd1[m]\nh0[m]\nh1[m]\nhint(d)[m]\nroadgrade,1(d)[m/m]\nhint,sm,1(d)[m]\nroadgrade,2(d)[m/m]\n0\n18\n0,0\n0,1\n120,3\n120,4\n120,3\n0,0035\n120,3\n– 0,0015\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n120\n37\n117,9\n125,7\n120,9\n121,2\n121,0\n– 0,0019\n120,2\n0,0035\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n200\n46\n193,4\n204,1\n121,4\n120,7\n121,0\n– 0,0040\n120,0\n0,0051\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n320\n56\n308,4\n320,0\n119,8\n119,7\n119,7\n0,0288\n121,4\n0,0088\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n520\n113\n519,9\n523,6\n132,5\n132,6\n132,5\n0,0097\n123,7\n0,0037\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n720\n149\n719,2\n730,2\n123,6\n123,4\n123,6\n– 0,0405\n122,9\n– 0,0086\n…\n…\n…\n…\n…\n…\n…\n…\n…\n…\n798\n158\n796,1\n798,8\n121,2\n121,2\n121,2\n– 0,0219\n121,3\n– 0,0151\n799\n159\n798,8\n800,0\n121,2\n121,2\n121,2\n– 0,0220\n121,3\n– 0,0152",
  "extent": "E+W+S+N.I.",
  "status": null,
  "version": "current",
  "annotations": [
    {
      "type": "F",
      "label": "F1",
      "text": "Substituted by Commission Regulation (EU) 2018/1832 of 5 November 2018 amending Directive 2007/46/EC of the European Parliament and of the Council, Commission Regulation (EC) No 692/2008 and Commission Regulation (EU) 2017/1151 for the purpose of improving the emission type approval tests and procedures for light passenger and commercial vehicles, including those for in-service conformity and real-driving emissions and introducing devices for monitoring the consumption of fuel and electric energy (Text with EEA relevance)."
    }
  ],
  "outstanding_effects": [],
  "provenance": {
    "source": "legislation.gov.uk",
    "source_url": "https://www.legislation.gov.uk/eur/2017/1151/annex/IIIA/appendix/7b",
    "retrieved_at": "2026-11-01T14:44:48.753743+00:00"
  },
  "licence": "Open Government Licence v3.0",
  "licence_url": "https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/",
  "attribution": "Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives."
}