Document ID: chunk:federal_register_of_legislation:F2023C00229:reg:9:p8
Version: federal_register_of_legislation:F2023C00229
Segment Type: reg
Provision Reference: reg 9 (pt 8/71)
Character Range: 229005–231897

the following equations:

              where:

6.1.2.                        Calculation of the Bessel algorithm

              Using the values of E and K, the 1 s Bessel averaged response to a step input Si shall be calculated as  follows:

                      Yi = Yi- 1 + E × (Si + 2 × Si- 1 + Si- 2 – 4 × Yi- 2) + K × (Yi- 1 – Yi- 2)

              where:

              Si-2 = Si-1 = 0

              Si = 1

              Yi-2= Yi-1 = 0

              The times t10 and t90 shall be interpolated. The difference in time between t90 and t10 defines the response time tF for that value of fc. If this response time is not close enough to the required response time, iteration shall be continued until the actual response time is within 1 % of the required response as follows:

               ((t90 - t10) - tF) ≤ 0,01 × tF

6.2.                            Data evaluation

              The smoke measurement values shall be sampled with a minimum rate of 20 Hz.

6.3.                            Determination of smoke

6.3.1.                        Data conversion

              Since the basic measurement unit of all opacimeters is transmittance, the smoke values shall be converted from transmittance (τ) to the light absorption coefficient (k) as follows:

              and

              where:

              k = light absorption coefficient, m-1

              LA = effective optical path length, as submitted by instrument manufacturer, m N = opacity, %
              τ = transmittance, %

              The conversion shall be applied, before any further data processing is made.

6.3.2.                        Calculation of Bessel averaged smoke

              The proper cut-off frequency fc is the one that produces the required filter response time tF. Once this frequency has been determined through the iterative process of Section 6.1.1, the proper Bessel algorithm constants E and K shall be calculated. The Bessel algorithm shall then be applied to the instantaneous smoke trace (k-value), as described in Section 6.1.2:

                      Yi = Yi- 1 + E × (Si + 2 × Si- 1 + Si- 2 – 4 × Yi- 2) + K × (Yi- 1 – Yi- 2)

              The Bessel algorithm is recursive in nature. Thus, it needs some initial input values of Si-1 and Si-2 and initial output values Yi-1 and Yi-2 to get the algorithm started. These may be assumed to be 0.

              For each load step of the three speeds A, B and C, the maximum 1s value Ymax shall be selected from the individual Yi values of each smoke trace.

6.3.3.                        Final result

              The mean smoke values (SV) from each cycle (test speed) shall be calculated as follows: For test speed A: SVA = (Ymax1,A + Ymax2,A + Ymax3,A) / 3
              For test speed B: SVB = (Ymax1,B + Ymax2,B + Ymax3,B) / 3

              For test speed C: SVC = (Ymax1,C + Ymax2,C + Ymax3,C) / 3 where: