Document ID: chunk:federal_register_of_legislation:F2023C00229:reg:9:p7
Version: federal_register_of_legislation:F2023C00229
Segment Type: reg
Provision Reference: reg 9 (pt 7/71)
Character Range: 226048–229290

The value is only valid for the reference fuel specified in Annex IV.

5.3.                            Full flow dilution system

              The reported test results of the particulate emission shall be determined through the following steps. All calculations shall be based upon the average values of the individual modes during the sampling period.

5.4.                            Calculation of the particulate mass flow rate

              The particulate mass flow rate shall be calculated as follows:
         where

              determined over the test cycle by summation of the average values of the individual modes during the sampling period.

         The particulate mass flow rate may be background corrected as follows:

         If more than one measurement is made,  shall be replaced with .

         for the individual modes

         or,

          for the individual modes.
or,
5.5.                            Calculation of the specific emission

              The particulate emission shall be calculated in the following way:

5.6.                            Effective weighting factor

              The effective weighting factor WFE,i for each mode shall be calculated in the following way:

              The value of the effective weighting factors shall be within ± 0,003 (± 0,005 for the idle mode) of the weighting factors listed in Section 2.7.1.

6.                                 CALCULATION OF THE SMOKE VALUES

6.1.                            Bessel algorithm

              The Bessel algorithm shall be used to compute the 1 s average values from the instantaneous smoke readings, converted in accordance with Section 6.3.1. The algorithm emulates a low pass second order filter, and its use requires iterative calculations to determine the coefficients. These coefficients are a function of the response time of the opacimeter system and the sampling rate. Therefore, Section 6.1.1 must be repeated whenever the system response time and/or sampling rate changes.

6.1.1.                        Calculation of filter response time and Bessel constants

              The required Bessel response time (tF) is a function of the physical and electrical response times of the opacimeter system, as specified in Annex III, Appendix 4, Section 5.2.4, and shall be calculated by the following equation:

              where:

              tp = physical response time, s
              te = electrical response time, s
              The calculations for estimating the filter cut-off frequency (fc) are based on a step input 0 to 1 in ≤ 0,01 s (see Annex VII). The response time is defined as the time between when the Bessel output reaches 10 % (t10) and when it reaches 90 % (t90) of this step function. This must be obtained by iterating on fc until t90-  t10≈tF. The first iteration for fc is given by the following formula:

              The Bessel constants E and K shall be calculated by 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 ×