Division 2 ANNEX III SHALL BE AMENDED AS FOLLOWS:

the following section shall be added:

“3.

CALIBRATION OF THE CVS SYSTEM

3.1.

General

The CVS system shall be calibrated by using an accurate flowmeter and means to change operating conditions.

The flow through the system shall be measured at different flow operating settings, and the control parameters of the system shall be measured and related to the flow.

Various type of flowmeters may be used, e.g. calibrated venturi, calibrated laminar flowmeter, calibrated turbinemeter.

3.2.

Calibration of the Positive Displacement Pump (PDP)

All the parameters related to the pump shall be simultaneously measured along with the parameters related to a calibration venturi which is connected in series with the pump. The calculated flow rate (in m³/min at pump inlet, absolute pressure and temperature) shall be plotted against a correlation function which is the value of a specific combination of pump parameters. The linear equation which relates the pump flow and the correlation function shall be determined. If a CVS has a multiple speed drive, the calibration shall be performed for each range used.

Temperature stability shall be maintained during calibration.

Leaks in all the connections and ducting between the calibration venturi and the CVS pump shall be maintained lower than 0,3% of the lowest flow point (highest restriction and lowest PDP speed point).

3.2.1.

Data Analysis

The air flowrate (Q_s) at each restriction setting (minimum 6 settings) shall be calculated in standard m³/min from the flowmeter data using the manufacturer's prescribed method. The air flow rate shall then be converted to pump flow (V₀) in m³/rev at absolute pump inlet temperature and pressure as follows:

$$V_0=\frac{Q_s}{n}x\frac{T}{273}x\frac{\mathrm{101.3}}{p_A}$$

where,

Q_s

air flow rate at standard conditions (101,3 kPa, 273 K) (m³/s)

T

temperature at pump inlet (K)

p_A

absolute pressure at pump inlet (p_B- p₁) (kPa)

n

pump speed (rev/s)

To account for the interaction of pressure variations at the pump and the pump slip rate, the correlation function (X₀) between pump speed, pressure differential from pump inlet to pump outlet and absolute pump outlet pressure shall be calculated as follows:

$$X0=\frac{1}{n}x\sqrt{\frac{\Delta p_p}{p_A}}$$

where,

Δp _p

pressure differential from pump inlet to pump outlet (kPa)

p_A

absolute outlet pressure at pump outlet (kPa)

A linear least-square fit shall be performed to generate the calibration equation as follows:

$$V_0=D_0-mx\left(X_0\right)$$

D₀ and m are the intercept and slope constants, respectively, describing the regression lines.

For a CVS system with multiple speeds, the calibration curves generated for the different pump flow ranges shall be approximately parallel, and the intercept values (D₀) shall increase as the pump flow range decreases.

The values calculated by the equation shall be within ± 0,5% of the measured value of V₀. Values of m will vary from one pump to another. Particulate influx over time will cause the pump slip to decrease, as reflected by lower values for m. Therefore, calibration shall be performed at pump start-up, after major maintenance, and if the total system verification (section 3.5) indicates a change in the slip rate.

3.3.

Calibration of the Critical Flow Venturi (CFV)

Calibration of the CFV is based upon the flow equation for a critical venturi. Gas flow is a function of inlet pressure and temperature, as shown below:

$$Q_s=\frac{K_{v}x{p}_A}{\sqrt{T}}$$

where,

K_v

calibration coefficient

p_A

absolute pressure at venturi inlet (kPa)

T

temperature at venturi inlet (K)

3.3.1.

Data Analysis

The air flow rate (Q_s) at each restriction setting (minimum 8 settings) shall be calculated in standard m³/min from the flowmeter data using the manufacturer's prescribed method. The calibration coefficient shall be calculated from the calibration data for each setting as follows:

$$K_v=\frac{Q_{s}x\sqrt{T}}{p_A}$$

where,

Q_s

air flow rate at standard conditions (101,3 kPa, 273 K) (m³/s)

T

temperature at the venturi inlet (K)

p_A

absolute pressure at venturi inlet (kPa)

To determine the range of critical flow, K_v shall be plotted as a function of venturi inlet pressure. For critical (choked) flow, K_v will have a relatively constant value. As pressure decreases (vacuum increases), the venturi becomes unchoked and K_v decreases, which indicates that the CFV is operated outside the permissible range.

For a minimum of eight points in the region of critical flow, the average K_V and the standard deviation shall be calculated. The standard deviation shall not exceed ± 0,3% of the average K_V

3.4.

Calibration of the Subsonic Venturi (SSV)

Calibration of the SSV is based upon the flow equation for a subsonic venturi. Gas flow is a function of inlet pressure and temperature, pressure drop between the SSV inlet and throat, as shown below:

$$Q_{\mathrm{SSV}}=A_0{d}^2{C}_d{P}_A\sqrt{\left[\frac{1}{T}\left(r^{\mathrm{1.4286}}-r^{\mathrm{1.7143}}\right)\left(\frac{1}{\mathrm{1-}{ß}^4{r}^{\mathrm{1.4286}}}\right)\right]}$$

where,

A₀

collection of constants and units conversions

= 0,006111 in SI units $\left(\frac{m^3}{\min }\right)\left(\frac{K^{\frac{1}{2}}}{\mathrm{kPa}}\right)\left(\frac{1}{{\mathrm{mm}}^2}\right)$

d

diameter of the SSV throat (m)

C_d

discharge coefficient of the SSV

P_A

absolute pressure at venturi inlet (kPa)

T

temperature at the venturi inlet (K)

r

ratio of the SSV throat to inlet absolute, static pressure = $\mathrm{1\; -}\frac{\Delta P}{P_A}$

ß

ratio of the SSV throat diameter, d, to the inlet pipe inner diameter = $\frac{d}{D}$

3.4.1.

Data Analysis

The air flow rate (Q_SSV) at each flow setting (minimum 16 settings) shall be calculated in standard m³/min from the flowmeter data using the manufacturer's prescribed method. The discharge coefficient shall be calculated from the calibration data for each setting as follows:

$$C_d=\frac{Q_{\mathrm{SSV}}}{A_0{d}^2{P}_A\sqrt{\left[\frac{1}{T}\left(r^{\mathrm{1.4286}}-r^{\mathrm{1.71743}}\right)\left(\frac{1}{\mathrm{1-}{ß}^4{r}^{\mathrm{1.4286}}}\right)\right]}}$$

where,

Q_SSV

air flow rate at standard conditions (101,3 kPa, 273 K), m³/s

T

temperature at the venturi inlet, K

d

diameter of the SSV throat, m

r

ratio of the SSV throat to inlet absolute, static pressure = $\mathrm{1\; -}\frac{\Delta P}{P_A}$

ß

ratio of the SSV throat diameter, d, to the inlet pipe inner diameter = $\frac{d}{D}$

To determine the range of subsonic flow, C_d shall be plotted as a function of Reynolds number, at the SSV throat. The Re at the SSV throat is calculated with the following formula:

$$\mathrm{Re\; =}{A}_1\frac{Q_{\mathrm{SSV}}}{\mathrm{d\mu }}$$

where,

A₁

a collection of constants and units conversions

$$\mathrm{=\; 25,55152}\left(\frac{1}{m^3}\right)\left(\frac{\min }{s}\right)\left(\frac{\mathrm{mm}}{m}\right)$$

Q_SSV

air flow rate at standard conditions (101,3 kPa, 273 K) (m³/s)

d

diameter of the SSV throat (m)

μ

absolute or dynamic viscosity of the gas, calculated with the following formula:

$$\mu =\frac{{\mathrm{bT}}^{\mathrm{3/2}}}{S+T}=\frac{{\mathrm{bT}}^{\mathrm{1/2}}}{\mathrm{1+}\frac{S}{T}}\mathrm{kg/m-s}$$

where:

b

empirical constant = ${\mathrm{1,458\; ·\; 10}}^6\frac{\mathrm{kg}}{{\mathrm{msK}}^{\frac{1}{2}}}$

S

empirical constant = 110,4 K

Because Q_SSV is an input to the Re formula, the calculations must be started with an initial guess for Q_SSV or C_d of the calibration venturi, and repeated until Q_SSV converges. The convergence method must be accurate to 0,1% or better.

For a minimum of sixteen points in the subsonic flow region, the calculated values of C_d from the resulting calibration curve fit equation must be within ± 0,5% of the measured C_d for each calibration point.

3.5.

Total System Verification

The total accuracy of the CVS sampling system and analytical system shall be determined by introducing a known mass of a pollutant gas into the system while it is being operated in the normal manner. The pollutant is analysed, and the mass calculated according to Annex III, Appendix 3, section 2.4.1 except in the case of propane where a factor of 0,000472 is used in place of 0,000479 for HC. Either of the following two techniques shall be used.

3.5.1.

Metering with a Critical Flow Orifice

A known quantity of pure gas (propane) shall be fed into the CVS system through a calibrated critical orifice. If the inlet pressure is high enough, the flow rate, which is adjusted by means of the critical flow orifice, is independent of the orifice outlet pressure (critical flow). The CVS system shall be operated as in a normal exhaust emission test for about 5 to 10 minutes. A gas sample shall be analysed with the usual equipment (sampling bag or integrating method), and the mass of the gas calculated. The mass so determined shall be within ± 3% of the known mass of the gas injected.

3.5.2.

Metering by Means of a Gravimetric Technique

The weight of a small cylinder filled with propane shall be determined with a precision of ± 0,01 g. For about 5 to 10 minutes, the CVS system shall be operated as in a normal exhaust emission test, while carbon monoxide or propane is injected into the system. The quantity of pure gas discharged shall be determined by means of differential weighing. A gas sample shall be analysed with the usual equipment (sampling bag or integrating method), and the mass of the gas calculated. The mass so determined shall be within ± 3% of the known mass of the gas injected.”

Appendix 3 shall be amended as follows:

1. (a)

   The following title for this Appendix shall be inserted: "DATA EVALUATION AND CALCULATIONS"

2. (b)

   the title of section 1 shall read "DATA EVALUATION AND CALCULATIONS - NRSC TEST"

3. (c)

   section 1.2 shall be replaced by the following:

   “1.2

   Participate emissions

   For the evaluation of the particulates, the total sample masses (MSAM,i) through the filters shall be recorded for each mode. The filters shall be returned to the weighing chamber and conditioned for at least one hour, but not more than 80 hours, and then weighed. The gross weight of the filters shall be recorded and the tare weight (see section 3.1, Annex III) subtracted. The particulate mass (Mf for single filter method; Mf,i for the multiple filter method) is the sum of the particulate masses collected on the primary and back-up filters. If background correction is to be applied, the dilution air mass (MDIL) through the filters and the particulate mass (Md) shall be recorded. If more than one measurement was made, the quotient Md/MDIL must be calculated for each single measurement and the values averaged.”

4. (d)

   section 1.3.1 shall be replaced by the following:

   “1.3.1.

   Determination of the exhaust gas flow

   The exhaust gas flow rate (G_EXHW,) shall be determined for each mode according to Annex III, Appendix 1, sections 1.2.1 to 1.2.3.

   When using a full flow dilution system, the total dilute exhaust gas flow rate (G_TOTW,) shall be determined for each mode according to Annex III, Appendix 1, section 1.2.4.”

5. (e)

   sections 1.3.2 -1.4.6 shall be replaced by the following:

   “1.3.2.

   Dry/wet correction (G_EXHW,) shall be determined for each mode according to Annex III, Appendix 1, sections 1.2.1 to 1.2.3.

   When applying G_EXHW the measured concentration shall be converted to a wet basis according to the following formulae, if not already measured on a wet basis:

   conc (wet) = k_w × conc (dry)

   For the raw exhaust gas:

   $$K_{W,r\mathrm{,1}}=\left(\frac{1}{\mathrm{1\; +\; 1,88\; \times \; 0,005\; \times }\left(\%\mathrm{CO}[\mathrm{dry}\mathrm{]\; +\; \%}{\mathrm{CO}}_2[\mathrm{dry}]\right)+K_{w2}}\right)$$

   For the diluted gas:

   $$K_{W,e\mathrm{,1}}=\left(\mathrm{1\; -}\frac{\mathrm{1,88\; \times }{\mathrm{CO}}_2\mathrm{\%(}\mathrm{wet})}{200}\right)-K_{W1}$$

   or:

   $$K_{W,e\mathrm{,1}}=\left(\frac{\mathrm{1\; -}{K}_{W1}}{\mathrm{1+}\frac{\mathrm{1,88\; \times }{\mathrm{CO}}_2\mathrm{\%(}\mathrm{dry})}{200}}\right)$$

   For the dilution air:

   $$k_{W,d}\mathrm{=\; 1\; -}{k}_{W1}$$

   $$k_{W1}=\frac{\mathrm{1,608\; \times }\left[H_d\times \left(\mathrm{1\; -\; 1\; /}\mathrm{DF}\right)+H_a\times \left(\mathrm{1\; /}\mathrm{DF}\right)\right]}{\mathrm{1000\; +\; 1,608\; \times }\left[H_d\times \left(\mathrm{1\; -\; 1\; /}\mathrm{DF}\right)+H_a\times \left(\mathrm{1\; /}\mathrm{DF}\right)\right]}$$

   $$H_d=\frac{\mathrm{6,22\; \times }{R}_d\times p_d}{p_B-p_d\times R_d{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   For the intake air (if different from the dilution air):

   $$k_{\mathrm{W,a}}\mathrm{=\; 1\; -}{k}_{W2}$$

   $$k_{W2}=\frac{\mathrm{1,608\; \times }{H}_a}{\mathrm{1000\; +}\left(\mathrm{1,608\; \times }{H}_a\right)}$$

   $$H_a=\frac{\mathrm{6,22\; \times }{R}_a\times p_a}{p_B-p_a\times R_a{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   where:

   H_a

   absolute humidity of the intake air (g water per kg dry air)

   H_d

   absolute humidity of the dilution air (g water per kg dry air)

   R_d

   relative humidity of the dilution air (%)

   R_a

   relative humidity of the intake air (%)

   p_d

   saturation vapour pressure of the dilution air (kPa)

   p_a

   saturation vapour pressure of the intake air (kPa)

   p_B

   total barometric pressure (kPa).

   NOTE: H _a and H _d may be derived from relative humidity measurement, as described above, or from dewpoint measurement, vapour pressure measurement or dry/wet bulb measurement using the generally accepted formulae.

   1.3.3.

   Humidity correction for NOx

   As the NOx emission depends on ambient air conditions, the NO_x concentration shall be corrected for ambient air temperature and humidity by the factors K_H given in the following formula:

   $$k_H=\frac{1}{\mathrm{1\; -\; 0,0182\; \times }\left(H_a\mathrm{-\; 10,71}\right)\mathrm{+\; 0,0045\; \times }\left(T_a\mathrm{-\; 298}\right)}$$

   where:

   T _a

   temperatures of the air in (K)

   H_a

   humidity of the intake air (g water per kg dry air):

   $$H_a=\frac{\mathrm{6,220\; \times }{R}_a\times p_a}{p_B-p_a\times R_a{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   where:

   R_a

   relative humidity of the intake air (%)

   p_a

   saturation vapour pressure of the intake air (kPa)

   p_B

   total barometric pressure (kPa).

   NOTE: H _a may be derived from relative humidity measurement, as described above, or from dewpoint measurement, vapour pressure measurement or dry/wet bulb measurement using the generally accepted formulae.

   1.3.4.

   Calculation of emission mass flow rates

   The emission mass flow rates for each mode shall be calculated as follows:

   1. (a)

      For the raw exhaust gas^f8:

      $${\mathrm{Gas}}_{\mathrm{mass}}{\mathrm{=\; u\; \times \; conc\; \times \; G}}_{\mathrm{EXHW}}$$
   2. (b)

      For the dilute exhaust gas:

      $${\mathrm{Gas}}_{\mathrm{mass}}{\mathrm{=\; u\; \times \; conc}}_c{\mathrm{\times \; G}}_{\mathrm{TOTW}}$$

      where:

      conc_c is the background corrected concentration

      $${\mathrm{conc}}_c=\mathrm{conc}-{\mathrm{conc}}_d\times \left(\mathrm{1-}\left(\mathrm{1\; /}\mathrm{DF}\right)\right)$$ $$\mathrm{DF}\mathrm{=\; 13,4/}\left({\mathrm{conc}}_{{\mathrm{CO}}_2}+\left({\mathrm{conc}}_{\mathrm{CO}}+{\mathrm{conc}}_{\mathrm{HC}}\right){\mathrm{\times \; 10}}^{\mathrm{-4}}\right)$$

      or:

      DF=13,4/concCO₂

      The coefficients u - wet shall be used according to Table 4:

      Table 4. Values of the coefficients u - wet for various exhaust components

      Gas	u	conc
      NOx	0,001587	ppm
      CO	0,000966	ppm
      HC	0,000479	ppm
      CO2	15,19	percent

      The density of HC is based upon an average carbon to hydrogen ratio of 1:1,85.

   1.3.5.

   Calculation of the specific emissions

   The specific emission (g/kWh) shall be calculated for all individual components in the following way:

   $$\mathrm{Individual\; gas}=\frac{\underset{i\mathrm{=\; 1}}{\overset{n}{\Sigma }}{\mathrm{Gas}}_{{\mathrm{mass}}_i}\times {\mathrm{WF}}_i}{\underset{i\mathrm{=\; 1}}{\overset{n}{\Sigma }}{P}_i\times {\mathrm{WF}}_i}$$

   where P_i = P_m,i + P_AE,i.

   The weighting factors and the number of modes (n) used in the above calculation are according to Annex III, section 3.7.1.

   1.4.

   Calculation of the particulate emission

   The particulate emission shall be calculated in the following way:

   1.4.1.

   Humidity correction factor for particulates

   As the particulate emission of diesel engines depends on ambient air conditions, the particulate mass flow rate shall be corrected for ambient air humidity with the factor K_p given in the following formula:

   $$K_p\mathrm{=\; 1/}\left(\mathrm{1\; +\; 0,0133\; \times }\left(H_a\mathrm{-\; 10,71}\right)\right)$$

   where:

   H_a

   humidity of the intake air, gram of water per kg dry air

   $$H_a=\frac{\mathrm{6,220\; \times }{R}_a\times p_a}{p_B-p_a\times R_a{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   where:

   R_a

   relative humidity of the intake air (%)

   p_a

   saturation vapour pressure of the intake air (kPa)

   p_B

   total barometric pressure (kPa)

   NOTE: H _a may be derived from relative humidity measurement, as described above, or from dewpoint measurement, vapour pressure measurement or dry/wet bulb measurement using the generally accepted formulae

   1.4.2.

   Partial flow dilution system

   The final reported test results of the particulate emission shall be derived through the following steps. Since various types of dilution rate control may be used, different calculation methods for equivalent diluted exhaust gas mass flow rate G_EDF apply. All calculations shall be based upon the average values of the individual modes (i) during the sampling period.

   1.4.2.1.

   Isokinetic systems

   $$G_{\mathrm{EDFW,i}}{\mathrm{=\; G}}_{\mathrm{EXHW,i}}{\mathrm{\times \; q}}_i$$

   $$q_i=\frac{G_{\mathrm{DILW,i}}+\left(G_{\mathrm{EXHW,i}}\times r\right)}{\left(G_{\mathrm{EXHW,i}}\times r\right)}$$

   where r corresponds to the ratio of the cross sectional areas of the isokinetic probe A_p and exhaust pipe A_T:

   $$r=\frac{A_p}{A_T}$$

   1.4.2.2.

   Systems with measurement of CO₂ or NO_x concentration

   $$G_{\mathrm{EDFW,i}}{\mathrm{=\; G}}_{\mathrm{EXHW,i}}{\mathrm{\times \; q}}_i$$

   $$q_i=\frac{{\mathrm{Conc}}_{\mathrm{E,i}}-{\mathrm{Conc}}_{\mathrm{A,i}}}{{\mathrm{Conc}}_{\mathrm{D,i}}-{\mathrm{Conc}}_{\mathrm{A,i}}}$$

   where:

   Conc_E

   wet concentration of the tracer gas in raw exhaust

   Conc_D

   wet concentration of the tracer gas in the diluted exhaust

   Conc_A

   wet concentration of the tracer gas in the dilution air

   Concentrations measured on a dry basis shall be converted to a wet basis according to section 1.3.2..

   1.4.2.3.

   Systems with CO2 measurement and carbon balance method

   $$G_{\mathrm{EDFW,i}}=\frac{\mathrm{206,6\; \times }{G}_{\mathrm{FUEL,i}}}{{\mathrm{CO}}_{2\mathrm{D,i}}-{\mathrm{CO}}_{2\mathrm{A,i}}}$$

   where:

   CO_2D

   CO₂ concentration of the diluted exhaust

   CO_2A

   CO₂ concentration of the dilution air

   (concentrations in volume % on wet basis)

   This equation is based upon the carbon balance assumption (carbon atoms supplied to the engine are emitted as CO₂) and derived through the following steps:

   $$G_{\mathrm{EDFW,i}}{\mathrm{=\; G}}_{\mathrm{EXHW,i}}{\mathrm{\times \; q}}_i$$

   and:

   $$q_i=\frac{\mathrm{206,6\; \times }{G}_{\mathrm{FUEL,i}}}{G_{\mathrm{EXHW,i}}\times \left({\mathrm{CO}}_{2\mathrm{D,i}}-{\mathrm{CO}}_{2\mathrm{A,i}}\right)}$$

   1.4.2.4.

   Systems with flow measurement

   $$G_{\mathrm{EDFW,i}}{\mathrm{=\; G}}_{\mathrm{EXHW,i}}{\mathrm{\times \; q}}_i$$

   $$q_i=\frac{G_{\mathrm{TOTW,i}}}{\left(G_{\mathrm{TOTW,i}}-G_{\mathrm{DILW,i}}\right)}$$

   1.4.3.

   Full flow dilution system

   The final reported test results of the particulate emission shall be derived through the following steps.

   All calculations shall be based upon the average values of the individual modes (i) during the sampling period.

   $$G_{\mathrm{EDFW,i}}{\mathrm{=\; G}}_{\mathrm{TOTW,i}}$$

   1.4.4.

   Calculation of the particulate mass flow rate

   The particulate mass flow rate shall be calculated as follows:

   For the single filter method:

   $${\mathrm{PT}}_{\mathrm{mass}}=\frac{M_f}{M_{\mathrm{SAM}}}\times \frac{{\left(G_{\mathrm{EDFW}}\right)}_{\mathrm{aver}}}{1000}$$

   where:

   (G_EDFW)_aver over the test cycle shall be determined by summation of the average values of the individual modes during the sampling period:

   $${\left(G_{\mathrm{EDFW}}\right)}_{\mathrm{aver}}\underset{i\mathrm{=\; 1}}{\overset{n}{\mathrm{=\; \Sigma }}}{G}_{\mathrm{EDFW,i}}\times {\mathrm{WF}}_i$$

   $$M_{\mathrm{SAM}}\underset{i\mathrm{=\; 1}}{\overset{n}{\mathrm{=\; \Sigma }}}{M}_{\mathrm{SAM,i}}$$

   where i = 1,... n

   For the multiple filter method:

   $${\mathrm{PT}}_{\mathrm{mass}}=\frac{M_{\mathrm{f,i}}}{M_{\mathrm{SAM,i}}}\times \frac{{\left(G_{\mathrm{EDFW,i}}\right)}_{\mathrm{aver}}}{1000}$$

   where i = 1,...n

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

   For single filter method:

   $${\mathrm{PT}}_{\mathrm{mass}}=\left[\frac{M_f}{M_{\mathrm{SAM}}}-\left(\frac{M_d}{M_{\mathrm{DIL}}}\times \left(\underset{i\mathrm{=\; 1}}{\overset{i=n}{\Sigma }}\left(\mathrm{1-}\frac{1}{{\mathrm{DF}}_i}\right)\times {\mathrm{WF}}_i\right)\right)\right]\times \frac{{\left(G_{\mathrm{EDFW}}\right)}_{\mathrm{aver}}}{1000}$$

   If more than one measurement is made, (M_d/M_DIL) shall be replaced with (M_d/M_DIL)_aver

   $$\mathrm{DF}\mathrm{=\; 13,4/}\left({\mathrm{concCO}}_2+\left(\mathrm{concCO}+\mathrm{concHC}\right){\mathrm{\times \; 10}}^{\mathrm{-4}}\right)$$

   or:

   DF = 13,4/concCO₂

   For multiple filter method:

   $${\mathrm{PT}}_{\mathrm{mass,i}}=\left[\frac{M_{\mathrm{f,i}}}{M_{\mathrm{SAM,i}}}-\left(\frac{M_d}{M_{\mathrm{DIL}}}\times \left(\mathrm{1\; -}\frac{1}{{\mathrm{DF}}_i}\right)\right)\right]\times \left[\frac{G_{\mathrm{EDFW,i}}}{1000}\right]$$

   If more than one measurement is made, (M_d/M_DIL) shall be replaced with (M_d/M_DIL)_aver

   $$\mathrm{DF}\mathrm{=\; 13,4/}\left({\mathrm{concCO}}_2+\left(\mathrm{concCO}+\mathrm{concHC}\right){\mathrm{\times \; 10}}^{\mathrm{-4}}\right)$$

   or:

   DF=13,4/concCO₂

   1.4.5.

   Calculation of the specific emissions

   The specific emission of particulates PT (g/kWh) shall be calculated in the following way^f9:

   For the single filter method:

   $$\mathrm{PT}=\frac{{\mathrm{PT}}_{\mathrm{mass}}}{\underset{i\mathrm{=\; 1}}{\overset{n}{\Sigma }}{P}_i\times {\mathrm{WF}}_i}$$

   For the multiple filter method:

   $$\mathrm{PT}=\frac{\underset{i\mathrm{=\; 1}}{\overset{n}{\Sigma }}{\mathrm{PT}}_{\mathrm{mass,i}}\times {\mathrm{WF}}_i}{\underset{i\mathrm{=\; 1}}{\overset{n}{\Sigma }}{P}_i\times {\mathrm{WF}}_i}$$

   1.4.6.

   Effective weighting factor

   For the single filter method, the effective weighting factor WF_E,i for each mode shall be calculated in the following way:

   $${\mathrm{WF}}_{\mathrm{E,i}}=\frac{M_{\mathrm{SAM,i}}\times {\left(G_{\mathrm{EDFW}}\right)}_{\mathrm{aver}}}{M_{\mathrm{SAM}}\times \left(G_{\mathrm{EDFW,i}}\right)}$$

   where i = 1,... n.

   The value of the effective weighting factors shall be within ± 0,005 (absolute value) of the weighting factors listed in Annex III, section 3.7.1.”

6. (f)

   The following section shall be inserted:

   “2.

   DATA EVALUATION AND CALCULATIONS (NRTC TEST)

   The two following measurement principles that can be used for the evaluation of pollutant emissions over the NRTC cycle are described in this section:

   • the gaseous components are measured in the raw exhaust gas on a real time basis, and the particulates are determined using a partial flow dilution system;

   • the gaseous components and the particulates are determined using a full flow dilution system (CVS system).

   2.1.

   Calculation of gaseous emissions in the raw exhaust gas and of the particulate emissions with a partial flow dilution system

   2.1.1.

   Introduction

   The instantaneous concentration signals of the gaseous components are used for the calculation of the mass emissions by multiplication with the instantaneous exhaust mass flow rate. The exhaust mass flow rate may be measured directly, or calculated using the methods described in Annex III, Appendix 1, section 2.2.3 (intake air and fuel flow measurement, tracer method, intake air and air/fuel ratio measurement). Special attention shall be paid to the response times of the different instruments. These differences shall be accounted for by time aligning the signals.

   For particulates, the exhaust mass flow rate signals are used for controlling the partial flow dilution system to take a sample proportional to the exhaust mass flow rate. The quality of proportionality is checked by applying a regression analysis between sample and exhaust flow as described in Annex III, Appendix 1, section 2.4.

   2.1.2.

   Determination of the gaseous components

   2.1.2.1.

   Calculation of mass emission

   The mass of the pollutants M _gas (g/test) shall be determined by calculating the instantaneous mass emissions from the raw concentrations of the pollutants, the u values from Table 4 (see also Section 1.3.4) and the exhaust mass flow, aligned for the transformation time and integrating the instantaneous values over the cycle. Preferably, the concentrations should be measured on a wet basis. If measured on a dry basis, the dry/wet correction as described here below shall be applied to the instantaneous concentration values before any further calculation is done.

   Table 4. Values of the coefficients u - wet-for various exhaust components

   Gas	u	conc
   NOx	0,001587	ppm
   CO	0,000966	ppm
   HC	0,000479	ppm
   CO2	15,19	percent

   The density of HC is based upon an average carbon to hydrogen ratio of 1:1,85.

   The following formula shall be applied:

   $$M_{\mathrm{gas}}={\underset{i\mathrm{=\; 1}}{\overset{i=n}{\Sigma }}u\times {\mathrm{conc}}_i\times G_{\mathrm{EXHW,i}}\times \frac{1}{f}}_{\mathrm{(in/g/test)}}$$

   where

   u

   ratio between density of exhaust component and density of exhaust gas

   conc _i

   instantaneous concentration of the respective component in the raw exhaust gas (ppm)

   G _EXHW,i

   instantaneous exhaust mass flow (kg/s)

   f

   data sampling rate (Hz)

   n

   number of measurements

   For the calculation of NO_x, the humidity correction factor k _H, as described here below, shall be used.

   The instantaneously measured concentration shall be converted to a wet basis as described here below, if no1 already measured on a wet basis

   2.1.2.2.

   Dry/wet correction

   If the instantaneously measured concentration is measured on a dry basis, it shall be converted to a wet basis according to the following formulae:

   $${\mathrm{conc}}_{\mathrm{wet}}=k_w\times {\mathrm{conc}}_{\mathrm{dry}}$$

   where

   $$K_{\mathrm{W,r}\mathrm{,1}}=\left(\frac{1}{\mathrm{1\; +\; 1,88\; \times \; 0,005\; \times }\left({\mathrm{conc}}_{\mathrm{CO}}+{\mathrm{conc}}_{{\mathrm{CO}}_2}\right)+K_{W2}}\right)$$

   with

   $$K_{\mathrm{w2}}=\frac{\mathrm{1,608\; \times }{H}_a}{\mathrm{1000\; +}\left(\mathrm{1,608\; *}{H}_a\right)}$$

   where

   conc _CO2

   dry CO₂ concentration (%)

   conc _CO

   dry CO concentration (%)

   H _a

   intake air humidity, (g water per kg dry air)

   $$H_a=\frac{\mathrm{6,220\; \times }{R}_a\times p_a}{p_B-p_a\times R_a{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   R_a

   relative humidity of the intake air (%)

   p_a

   saturation vapour pressure of the intake air (kPa)

   p_B

   total barometric pressure (kPa)

   NOTE: H _a may be derived from relative humidity measurement, as described above, or from dewpoint measurement, vapour pressure measurement or dry/wet bulb measurement using the generally accepted formulae.

   2.1.2.3.

   NOx correction for humidity and temperature

   As the NO_x emission depends on ambient air conditions, the NO_x concentration shall be corrected for humidity and ambient air temperature with the factors given in the following formula:

   $$k_H=\frac{1}{\mathrm{1\; -\; 0,0182\; \times }\left(H_a\mathrm{-\; 10,71}\right)\mathrm{+\; 0,0045\; \times }\left(T_a\mathrm{-\; 298}\right)}$$

   with:

   T _a

   temperature of the intake air, K

   H _a

   humidity of the intake air,g water per kg dry air

   $$H_a=\frac{\mathrm{6,220\; \times }{R}_a\times p_a}{p_B-p_a\times R_a{\mathrm{\times \; 10}}^{\mathrm{-2}}}$$

   where:

   R_a

   relative humidity of the intake air (%)

   p_a

   saturation vapour pressure of the intake air ( kPa)

   p_B

   total barometric pressure (kPa)

   NOTE: H _a may be derived from relative humidity measurement, as described above, or from dewpoint measurement, vapour pressure measurement or dry/wet bulb measurement using the generally accepted formulae.

   2.1.2.4.

   Calculation of the specific emissions

   The specific emissions (g/kWh) shall be calculated for each individual component in the following way:

   Individual gas = M _gas /W _act

   where

   W _act

   actual cycle work as determined in Annex III Section 4.6.2 (kWh)

   2.1.3.

   Particulate determination

   2.1.3.1.

   Calculation of mass emission

   The mass of particulates M _PT (g/test) shall be calculated by either of the following methods:

   1. (a)
      $$M_{\mathrm{PT}}=\frac{M_f}{M_{\mathrm{SAM}}}\times \frac{M_{\mathrm{EDFW}}}{1000}$$

      where

      M _f

   2. particulate mass sampled over the cycle (mg)

   M_SAM

   3. mass of diluted exhaust gas passing the particulate collection filters (kg)

   M _EDFW

   4. mass of equivalent diluted exhaust gas over the cycle (kg)

   The total mass of equivalent diluted exhaust gas mass over the cycle shall be determined as follows:

   $$M_{\mathrm{EDFW}}\underset{i\mathrm{=\; 1}}{\overset{i=n}{\mathrm{=\; \Sigma }}}{G}_{\mathrm{EDFW}\mathrm{,i}}\times \frac{1}{f}$$ $$G_{\mathrm{EDFW,i}}=G_{\mathrm{EXHW,i}}\times q_i$$ $$q_i=\frac{G_{\mathrm{TOTW,i}}}{\left(G_{\mathrm{TOTW,i}}-G_{\mathrm{DILW,i}}\right)}$$

   where

   G _EDFW,i

   5. instantaneous equivalent diluted exhaust mass flow rate (kg/s)

   G _EXHW,i

   6. instantaneous exhaust mass flow rate (kg/s)

   q _i

   7. instantaneous dilution ratio

   G _TOTW,I

   8. instantaneous diluted exhaust mass flow rate through dilution tunnel (kg/s)

   G _DILW,i

   9. instantaneous dilution air mass flow rate (kg/s)

   f

   10. data sampling rate (Hz)

   n

   11. number of measurements

7. (b)
   $$M_{\mathrm{PT}}=\frac{M_f}{r_s\mathrm{x\; 1000}}$$

   where

   M _f

8. particulate mass sampled over the cycle (mg)

r _s

9. average sample ratio over the test cycle

where

$$r_s=\frac{M_{\mathrm{SE}}}{M_{\mathrm{EXHW}}}\times \frac{M_{\mathrm{SAM}}}{M_{\mathrm{TOTW}}}$$ M _SE

10. sampled exhaust mass over the cycle (kg)

M _EXHW

11. total exhaust mass flow over the cycle (kg)

M _SAM

12. mass of diluted exhaust gas passing the particulate collection filters (kg)

M _TOTW

13. mass of diluted exhaust gas passing the dilution tunnel (kg)

NOTE: In case of the total sampling type system, M _SAM and M _TOTW are identical.