Document ID: chunk:federal_register_of_legislation:F2024L00447:reg:0:p52
Version: federal_register_of_legislation:F2024L00447
Segment Type: reg
Provision Reference: reg 0 (pt 52/57)
Character Range: 236126–239231

spatial resolution

              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, characterized 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 hcorr(t) as:

              where:

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

hcorr(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 at 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]

4.3.2. Additional data smoothing
              The 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 (see Figure A10/1). The first smoothing run shall be applied as follows:

              where:

roadgrade,1(d)  —  smoothed road grade at the discrete way point under consideration after the first smoothing run [m/m]

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

hint,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]

da              —  reference way point at d(0) [m]

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

The second smoothing run shall be applied as follows:

              where:

roadgrade,2(d)  —  smoothed road grade at the discrete way point under consideration after the second smoothing run [m/m]

hint,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]

da              —  reference way point at d(0) [m]

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

    Figure A10/1
    Illustration of the procedure to smooth the interpolated altitude signals

              4.3.3. Calculation of the final result

              The positive cumulative elevation gain of a total trip shall be calculated by integrating all positive interpolated and smoothed road grades, i.e., roadgrade,2(d). The result should be normalized by the total test