# 40 CFR 91.426 - Dilute emission sampling calculations.

§ 91.426 Dilute emission sampling calculations.
(a) The final reported emission test results must be computed by use of the following formula:
Where:
Awm=Weighted mass emission level (HC, CO, CO2, or NOX) for a test [g/kW-hr].
Wi=Average mass flow rate of an emission from a test engine during mode i [g/hr].
WFi = Weighting factor for each mode i as defined in § 91.410(a).
Pi = Gross average power generated during mode i [kW] calculated from the following equation (power for the idle mode shall always be zero for this calculation):
speed = average engine speed measured during mode i [rev./minute]
torque = average engine torque measured during mode i [N-m]
KHi = Humidity correction factor for mode i. This correction factor only affects calculations for NOX and is equal to one for all other emissions. KHi is also equal to one for all two-stroke engines.
(b) The mass flow rate (Wi) of an emission for mode i is determined from the following equation:
Where:
Qi = Volumetric flow rate of the dilute exhaust through the CVS at standard conditions [m3/hr at STP].
D = Density of a specific emission (DHC, DCO, DCO2, DNOx) in the exhaust [g/m3].
DFi = Dilution factor of the dilute exhaust during mode i.
CDi = Concentration of the emission (HC, CO, NOX) in the dilute exhaust extracted from the CVS during mode i [ppm].
CBi = Concentration of the emission (HC, CO, NOX) in the background sample during mode i [ppm].
STP = Standard temperature and pressure. All volumetric calculations made for the equations in this section are to be corrected to a standard temperature of 20 °C and 101.3 kPa.
(c) Densities for emissions that are to be measured for this test procedure are:
DHC = 576.8 g/m3
DNOX = 1912 g/m3
DCO = 1164 g/m3
DCO2 = 1829 g/m3
(1) The value of DHC above is calculated based on the assumption that the fuel used has a carbon to hydrogen ratio of 1:1.85. For other fuels, DHC can be calculated from the following formula:
Where:
MHC = Molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule [g/mole].
RSTP = Ideal gas constant for a gas at STP = 0.024065 [m3-mole].
(2) The idealized molecular weight of the exhaust hydrocarbons, ie., the molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule, MHC can be calculated from the following formula:
Where:
MC = Molecular weight of carbon = 12.01 [g/mole].
MH = Molecular weight of hydrogen = 1.008 [g/mole].
α = Hydrogen to carbon ratio of the test fuel.
(3) The value of DNOx above assumes that NOX in entirely in the form of NO2.
(d) The dilution factor (DF) is the ratio of the volumetric flow rate of the background air to that of the raw engine exhaust. The following formula is used to determine DF:
Where:
CDHC = Concentration of HC in the dilute sample [ppm].
CDCO = Concentration of CO in the dilute sample [ppm].
CDCO2 = Concentration of CO2 in the dilute sample [ppm].
(e) The humidity correction factor KH is an adjustment made to the measured NOX. This corrects for the sensitivity that a spark-ignition engine has to the humidity of its combustion air. The following formula is used to determine KH for NOX calculations:
Where:
H = Absolute humidity of the engine intake air [grams of water per kilogram of dry air].
(f) The absolute humidity of the engine intake air H is calculated using the following formula:
Where:
Pdew = Saturated vapor pressure at the dew point temperature [kPa].
Pb = Barometric pressure [kPa].
(g) The fuel mass flow rate Fi can be either measured or calculated using the following formula:
Where:
Mf = Mass of fuel consumed by the engine during the mode [g].
T = Duration of the sampling period [hr].
(h) The mass of fuel consumed during the mode sampling period, MFUEL can be calculated from the following equation:
Where:
GS = Mass of carbon measured during the mode sampling period [g].
R2 = The fuel carbon weight fraction, which is the mass of carbon in fuel per mass of fuel [g/g].
(i) The grams of carbon measured during the mode GS can be calculated from the following equation:
Where:
HCmass = mass of hydrocarbon emissions for the mode sampling period [g].
COmass = mass of carbon monoxide emissions for the mode sampling period [g].
CO2mass = mass of carbon dioxide emissions for the mode sampling period [g].
α = The atomic hydrogen to carbon ratio of the fuel.
Beta! The text on the eCFR tab represents the unofficial eCFR text at ecfr.gov.
§ 91.426 Dilute emission sampling calculations.

(a) The final reported emission test results must be computed by use of the following formula:

Where:
Awm = Weighted mass emission level (HC, CO, CO2, or NOX) for a test [g/kW-hr].
Wi = Average mass flow rate of an emission from a test engine during mode i [g/hr].
WFi = Weighting factor for each mode i as defined in § 91.410(a).
Pi = Gross average power generated during mode i [kW] calculated from the following equation (power for the idle mode shall always be zero for this calculation):
speed = average engine speed measured during mode i [rev./minute]
torque = average engine torque measured during mode i [N-m]
KHi = Humidity correction factor for mode i. This correction factor only affects calculations for NOX and is equal to one for all other emissions. KHi is also equal to one for all two-stroke engines.

(b) The mass flow rate (Wi) of an emission for mode i is determined from the following equation:

Where:
Qi = Volumetric flow rate of the dilute exhaust through the CVS at standard conditions [m 3/hr at STP].
D = Density of a specific emission (DHC, DCO, DCO2, DNOx) in the exhaust [g/m 3].
DFi = Dilution factor of the dilute exhaust during mode i.
CDi = Concentration of the emission (HC, CO, NOX) in the dilute exhaust extracted from the CVS during mode i [ppm].
CBi = Concentration of the emission (HC, CO, NOX) in the background sample during mode i [ppm].
STP = Standard temperature and pressure. All volumetric calculations made for the equations in this section are to be corrected to a standard temperature of 20 °C and 101.3 kPa.

(c) Densities for emissions that are to be measured for this test procedure are:

DHC = 576.8 g/m 3
DNOX = 1912 g/m 3
DCO = 1164 g/m 3
DCO2 = 1829 g/m 3

(1) The value of DHC above is calculated based on the assumption that the fuel used has a carbon to hydrogen ratio of 1:1.85. For other fuels, DHC can be calculated from the following formula:

Where:
MHC = Molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule [g/mole].
RSTP = Ideal gas constant for a gas at STP = 0.024065 [m 3-mole].

(2) The idealized molecular weight of the exhaust hydrocarbons, ie., the molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule, MHC can be calculated from the following formula:

Where:
MC = Molecular weight of carbon = 12.01 [g/mole].
MH = Molecular weight of hydrogen = 1.008 [g/mole].
α = Hydrogen to carbon ratio of the test fuel.

(3) The value of DNOx above assumes that NOX in entirely in the form of NO2.

(d) The dilution factor (DF) is the ratio of the volumetric flow rate of the background air to that of the raw engine exhaust. The following formula is used to determine DF:

Where:
CDHC = Concentration of HC in the dilute sample [ppm].
CDCO = Concentration of CO in the dilute sample [ppm].
CDCO2 = Concentration of CO2 in the dilute sample [ppm].

(e) The humidity correction factor KH is an adjustment made to the measured NOX. This corrects for the sensitivity that a spark-ignition engine has to the humidity of its combustion air. The following formula is used to determine KH for NOX calculations:

Where:
H = Absolute humidity of the engine intake air [grams of water per kilogram of dry air].

(f) The absolute humidity of the engine intake air H is calculated using the following formula:

Where:
Pdew = Saturated vapor pressure at the dew point temperature [kPa].
Pb = Barometric pressure [kPa].

(g) The fuel mass flow rate Fi can be either measured or calculated using the following formula:

Where:
Mf = Mass of fuel consumed by the engine during the mode [g].
T = Duration of the sampling period [hr].

(h) The mass of fuel consumed during the mode sampling period, MFUEL can be calculated from the following equation:

Where:
GS = Mass of carbon measured during the mode sampling period [g].
R2 = The fuel carbon weight fraction, which is the mass of carbon in fuel per mass of fuel [g/g].

(i) The grams of carbon measured during the mode GS can be calculated from the following equation:

Where:
HCmass = mass of hydrocarbon emissions for the mode sampling period [g].
COmass = mass of carbon monoxide emissions for the mode sampling period [g].
CO2mass = mass of carbon dioxide emissions for the mode sampling period [g].
α = The atomic hydrogen to carbon ratio of the fuel.