40 CFR §86.144-94
Verified against eCFR.gov as of June 20, 2026View official text on eCFR.gov ↗
The final reported test results shall be computed by use of the following formula:
- (a)For light-duty vehicles and light duty trucks:
- (1)YWM = Weighted mass emissions of each pollutant, i.e., THC, CO, THCE, NMHC, NMHCE, CH4, NOX, or CO2, in grams per vehicle mile.
- (2)Yct = Mass emissions as calculated from the “transient” phase of the cold start test, in grams per test phase.
- (3)Yht = Mass emissions as calculated from the “transient” phase of the hot start test, in grams per test phase.
- (4)Ys = Mass emissions as calculated from the “stabilized” phase of the cold start test, in grams per test phase.
- (5)Dct = The measured driving distance from the “transient” phase of the cold start test, in miles.
- (6)Dht = The measured distance from the “transient” phase of the hot start test, in miles.
- (7)Ds = The measured driving distance from the “stabilized” phase of the cold start test, in miles.
- (b)The mass of each pollutant for each phase of both the cold start test and the hot start test is determined from the following:
- (c)Meaning of symbols:
- (1)
- (i)HCmass = Total hydrocarbon emissions, in grams per test phase.
- (ii)DensityHC = Density of total hydrocarbon.
- (A)For gasoline-fuel, diesel-fuel and methanol fuel; DensityHC = 16.33 g/ft 3−carbon atom (0.5768 kg/m 3−carbon atom), assuming an average carbon to hydrogen ratio of 1:1.85, at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (B)For natural gas and liquefied petroleum gas-fuel; DensityHC = 1.1771 (12.011 + H/C (1.008)) g/ft 3−carbon atom (0.04157(12.011 + H/C (1.008))kg/m 3−carbon atom), where H/C is the hydrogen to carbon ratio of the hydrocarbon components of the test fuel, at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (iii)
- (iv)
- (v)FID HCe = Concentration of total hydrocarbon plus methanol in dilute exhaust as measured by the FID, ppm carbon equivalent.
- (vi)r = FID response to methanol.
- (vii)CCH 3OHe = Concentration of methanol in dilute exhaust as determined from the dilute exhaust methanol sample in ppm carbon. For vehicles not fueled with methanol, CCH 3OHe equals zero.
- (viii)
- (ix)FID HCd = Concentration of total hydrocarbon plus methanol in dilution air as measured by the FID, ppm carbon equivalent.
- (x)CCH 3OHd = Concentration of methanol in dilution air as determined from dilution air methanol sample in ppm carbon. For vehicles not fueled with methanol, CCH 3OHd equals zero.
- (2)
- (i)NOxmass = Oxides of nitrogen emissions, in grams per test phase.
- (ii)DensityNO2 = Density of oxides of nitrogen is 54.16 g/ft3 (1.913 kg/m 3) assuming they are in the form of nitrogen dioxide, at 68 °F (20 °C) and 760 mm Hg (101.3kPa) pressure.
- (iii)
- (iv)NOxe = Oxides of nitrogen concentration of the dilute exhaust sample as measured, in ppm.
- (v)NOxd = Oxides of nitrogen concentration of the dilution air as measured, in ppm.
- (3)
- (i)COmass = Carbon monoxide emissions, in grams per test phase.
- (ii)DensityCO = Density of carbon monoxide is 32.97 g/ft 3 (1.164 kg/m3), at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (iii)
- (iv)
- (A)COe = Carbon monoxide concentration of the dilute exhaust volume corrected for water vapor and carbon dioxide extraction, in ppm.
- (B)COe = (1 − 0.01925CO2e-0.000323R)COem for petroleum fuel with hydrogen to carbon ratio of 1.85:1.
- (C)COe = [1−(0.01 + 0.005HCR) CO2e−0.000323R]COem for methanol-fuel or natural gas-fuel or liquefied petroleum gas-fuel, where HCR is hydrogen-to-carbon ratio as measured for the fuel used.
- (v)COem = Carbon monoxide concentration of the dilute exhaust sample as measured, in ppm.
- (vi)CO2e = Carbon dioxide concentration of the dilute exhaust sample, in percent.
- (vii)R = Relative humidity of the dilution air, in percent (see § 86.142(n)).
- (viii)
- (ix)COdm = Carbon monoxide concentration of the dilution air sample as measured, in ppm.
- (4)
- (5)
- (i)CH3OHmass = Methanol emissions corrected for background, in grams per test phase.
- (ii)DensityCH3OH = Density of methanol is 37.71 g/ft 3-carbon atom (1.332 kg/m 3-carbon atom), at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (iii)
- (iv)
- (v)
- (vi)TEM = Temperature of methanol sample withdrawn from dilute exhaust, °R.
- (vii)TDM = Temperature of methanol sample withdrawn from dilution air, °R.
- (viii)PB = Barometric pressure during test, mm Hg.
- (ix)VEM = Volume of methanol sample withdrawn from dilute exhaust, ft 3.
- (x)VDM = Volume of methanol sample withdrawn from dilution air, ft 3.
- (xi)CS = GC concentration of sample drawn from dilute exhaust, µg/ml.
- (xii)CD = GC concentration of sample drawn from dilution air, µg/ml.
- (xiii)AVS = Volume of absorbing reagent (deionized water) in impinger through which methanol sample from dilute exhaust is drawn, ml.
- (6)
- (i)HCHOmass = Formaldehyde emissions corrected for background, in grams per test phase.
- (ii)DensityHCHO = Density of formaldehyde is 35.36 g/ft 3- carbon atom (1.249 kg/m 3-carbon atom), at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (iii)
- (iv)
- (v)
- (vi)CFDE = Concentration of DNPH derivative of formaldehyde from dilute exhaust sample in sampling solution, µg/ml.
- (vii)VAE = Volume of sampling solution for dilute exhaust formaldehyde sample, ml.
- (viii)
- (ix)TEF = Temperature of formaldehyde sample withdrawn from dilute exhaust, °R.
- (x)VSE = Volume of formaldehyde sample withdrawn from dilute exhaust, ft 3.
- (xi)PB = Barometric pressure during test, mm Hg.
- (xii)CFDA = Concentration of DNPH derivative of formaldehyde from dilution air sample in sampling solution, µg/ml.
- (7)
- (i)DF = 13.4/[CO2e + (HCe + COe) 10−4] for petroleum-fueled vehicles.
- (ii)For methanol-fueled vehicles, where fuel composition is CXHyOz as measured, or calculated, for the fuel used:
- (iii)
- (iv)
- (v)
- (vi)Ra = Relative humidity of the ambient air, percent.
- (vii)Pd = Saturated vapor pressure, mm Hg (kPa) at the ambient dry bulb temperature.
- (viii)PB = Barometric pressure, mm Hg (kPa).
- (ix)
- (x)Vo = Volume of gas pumped by the positive displacement pump, in cubic feet (m 3) per revolution. This volume is dependent on the pressure differential across the positive displacement pump.
- (xi)N = Number of revolutions of the positive displacement pump during the test phase while samples are being collected.
- (xii)PB = Barometric pressure, mm Hg (kPa).
- (8)
- (i)NMHCconc = HCconc − (rCH4 × CH4conc).
- (ii)DensityNMHC = The density of non-methane hydrocarbon.
- (A)For gasoline-fuel and diesel-fuel; DensityNMHC = 16.33 g/ft 3-carbon atom (0.5768 kg/m 3-carbon atom), assuming an average carbon to hydrogen ratio of 1:1.85 at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (B)For natural gas and liquefied petroleum gas fuel; DensityNMHC = 1.1771(12.011 + H/C(1.008))g/ft 3-carbon atom (0.04157(12.011 + H/C(1.008))kg/m 3-carbon atom), where H/C is the hydrogen to carbon ratio of the non-methane hydrocarbon components of the test fuel, at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
- (iii)
- (iv)CH4e = Methane exhaust bag concentration in ppm carbon equivalent.
- (v)CH4d = Methane concentration of the dilution air in ppm carbon equivalent.
- (vi)rCH4 = HC FID response to methane as measured in § 86.121(d).
- (9)
- (10)
- (1)
- (d)For petroleum-fueled vehicles, example calculation of mass values of exhaust emissions using positive displacement pump:
- (1)For the “transient” phase of the cold start test assume the following: Vo = 0.29344 ft 3rev; N = 10,485; R = 48.0 pct; Ra = 48.2 percent; PB = 762 mm Hg; Pd = 22.225 mm Hg; P4 = 70 mm Hg; Tp = 570 °R; HCe = 105.8 ppm, carbon equivalent; NOxe = 11.2 ppm; COem = 306.6 ppm; CO2e = 1.43 percent; CH4e = 10.74 ppm; HCd = 12.1 ppm; NOxd = 0.8 ppm; COdm = 15.3 ppm; CO2d = 0.032 percent; CH4d = 2.20 ppm; Dct = 3.598 miles.
- (i)Vmix = (0.29344)(10,485)(762-70)(528)/(760)(570) = 2595.0 ft 3 per test phase.
- (ii)H = (43.478)(48.2)(22.225)/762 − (22.225)(48.2/100) = 62 grains of water per pound of dry air.
- (iii)KH = 1/[1 − 0.0047(62-75)] = 0.9424.
- (iv)COe = [1-0.01925(1.43) − 0.000323(48)](306.6) = 293.4 ppm.
- (v)COd = [1 − 0.000323(48)](15.3) = 15.1 ppm.
- (vi)DF = 13.4/[1.43 + 10−4(105.8 + 293.4)] = 9.116.
- (vii)HCconc = 105.8-12.1(1 − 1/9.116) = 95.03 ppm.
- (viii)HCmass = (2595)(16.33)(95.03/1,000,000) = 4.027 grams per test phase.
- (ix)NOxconc = 11.2 − 0.8(1 − 1/9.116) = 10.49 ppm.
- (x)NOxmass = (2595)(54.16)(10.49/1,000,000)(0.9424) = 1.389 grams per test phase.
- (xi)COconc = 293.4 − 15.1(1 − 1/9.116) = 280.0 ppm.
- (xii)COmass = (2595)(32.97)(280/1,000,000) = 23.96 grams per test phase.
- (2)For the stabilized portion of the cold start test assume that similar calculations resulted in the following:
- (3)For the “transient” portion of the hot start test assume that similar calculations resulted in the following:
- (4)Weighted mass emission results:
- (i)HCwm = 0.43[(4.027 + 0.62)/(3.598 + 3.902)] + 0.57[(0.51 + 0.62)/(3.598 + 3.902)] = 0.352 gram per vehicle mile.
- (ii)NOxwm = 0.43[(1.389 + 1.27)/(3.598 + 3.902)] + 0.57[(1.38 + 1.27)/(3.598 + 3.902)] = 0.354 gram per vehicle mile.
- (iii)COwm = 0.43[(23.96 + 5.98)/(3.598 + 3.902)] + 0.57[(5.01 + 5.98)/(3.598 + 3.902)] = 2.55 grams per vehicle mile.
- (iv)CO2wm = 0.43[(1886 + 2346)/(3.598 + 3.902) + 0.57[(1758 + 2346)/(3.598 + 3.902)] = 555 gram per vehicle mile.
- (v)NMHCwm = 0.43[(3.655 + 0.50)/(3.598 + 3.902)] + 0.57[(0.44 + 0.50)/(3.598 + 3.902)] = 0.310 gram per vehicle mile.
- (1)For the “transient” phase of the cold start test assume the following: Vo = 0.29344 ft 3rev; N = 10,485; R = 48.0 pct; Ra = 48.2 percent; PB = 762 mm Hg; Pd = 22.225 mm Hg; P4 = 70 mm Hg; Tp = 570 °R; HCe = 105.8 ppm, carbon equivalent; NOxe = 11.2 ppm; COem = 306.6 ppm; CO2e = 1.43 percent; CH4e = 10.74 ppm; HCd = 12.1 ppm; NOxd = 0.8 ppm; COdm = 15.3 ppm; CO2d = 0.032 percent; CH4d = 2.20 ppm; Dct = 3.598 miles.
- (e)For methanol-fueled vehicles with measured fuel composition of CH3.487 O0.763, example calculation of exhaust emissions using positive displacement pump:
- (1)For the “transient” phase of the cold start test assume the following: V0 = 0.29344 ft 3 rev; N = 25,801; R = 37.5 pct; Ra = 37.5 percent; PB = 725.42 mm Hg; Pd = 22.02 mm Hg; P4 = 70 mm Hg; Tp 570 deg.R; FID HCe = 14.65 ppm, carbon equivalent; r = 0.788; TEM = 527.67 deg.R; VEM = 0.2818 ft 3; CS1 = 7.101; AVS1 = 15.0 ml; CS2 = 0.256; AVS2 = 15.0 ml; TDM = 527.67 deg.R; VDM = 1.1389 ft 3; CD1 = 0.439; AVD1 = 15.0 ml; CD2 = 0.0; AVD2 = 15.0 ml; CFDE = 8.970 µg/ml; VAE = 5.0 ml; Q = 0.1429; TEF = 527.67 deg.R; VSE = 0.2857 ft 3; CFDA = 0.39 µg/ml; VAA = 5.0 ml; TDF = 527.67 deg.R; VSA = 1.1043 ft 3; NOX. = 5.273 ppm; COem = 98.8 ppm; CO2e = 0.469 pct; CH4e = 2.825 ppm; FID HCd = 2.771 ppm; NOX. = 0.146 ppm; COdm = 1.195 ppm; CO2d = 0.039 percent; CH4d = 2.019 ppm; Dct = 3.583 miles.
- (i)Vmix = (0.29344)(25,801)(725.42-70)(528)/(760)(570) = 6048.1.0 ft 3 per test phase.
- (ii)H = (43.478)(37.5)(22.02)/[725.42-(22.02 × 37.5/100)] = 50 grains of water per pound of dry air.
- (iii)KH = 1/[1−0.0047(50−75)] = 0.8951.
- (iv)COe = [1-(0.01 + 0.005 × 3.487) × 0.469)−0.000323(37.5)) × 98.8 = 96.332 ppm.
- (v)COd = (1−0.000323(37.5)) × 1.195 = 1.181 ppm.
- (vi)CCH3OHe = (3.813 × 10−2)(527.67)[(7.101)(15.0) + (0.256)(15.0)]/(725.42)(0.2818) = 10.86 ppm.
- (vii)HCe = 14.65−(0.788)(10.86) = 6.092.
- (viii)DF = 100(1/[1 + (3.487/2) + 3.76(1 + (3.487/4) − (0.763/2))])/0.469 + (6.092 + 96.332 + 10.86 + 0.664)(10−4) = 24.939.
- (ix)CCH3OHd = (3.813 × 10−2)(527.67)[(0.439)(15.0) + (0.0)(15.0)]/(725.42)(1.1389) = 0.16 ppm.
- (x)CH3OHconc = 10.86−0.16(1-1/24.939) = 10.71 ppm.
- (xi)CH3OHmass = 6048.1 × 37.71 × (10.71/1,000,000) = 2.44 grams per test phase.
- (xii)HCconc = [14.65 − (0.788)(10.86)] − [2.771 − (0.788)(0.16)] (1-1/24.94) = 3.553 ppm.
- (xiii)HCmass = (6048.1)(16.33)(3.553/1,000,000) = 0.35 grams per test phase.
- (xiv)CHCHOe = 4.069 × 10−2(8.970)(5.0)(0.1429)(527.67)/(0.2857)(725.42) = 0.664 ppm.
- (xv)CHCHOd = 4.069 × 10−2(0.39)(5.0)(0.1429)(527.67)/(1.1043)(725.42) = 0.0075 ppm.
- (xvi)HCHOconc = 0.664-0.0075(1-1/24.939) = 0.6568 ppm.
- (xvii)HCHOmass = (6048.1)(35.36)(0.6568/1,000,000) = 0.1405 grams per test phase.
- (xviii)THCE = 0.35 + (13.8756/32.042)(2.44) + (13.8756/ 30.0262)(0.1405) = 1.47 grams per test phase.
- (xix)NOXconc = 5.273−(0.146)(1-1/24.939) = 5.13 ppm.
- (xx)NOXmass = (6048.1)(54.16)(5.13/1,000,000)(0.8951) = 1.505 grams per test phase.
- (xix)NOXconc = 5.273−(0.146)(1-1/24.939) = 5.13 ppm.
- (xviii)THCE = 0.35 + (13.8756/32.042)(2.44) + (13.8756/ 30.0262)(0.1405) = 1.47 grams per test phase.
- (xvii)HCHOmass = (6048.1)(35.36)(0.6568/1,000,000) = 0.1405 grams per test phase.
- (xvi)HCHOconc = 0.664-0.0075(1-1/24.939) = 0.6568 ppm.
- (xv)CHCHOd = 4.069 × 10−2(0.39)(5.0)(0.1429)(527.67)/(1.1043)(725.42) = 0.0075 ppm.
- (xiv)CHCHOe = 4.069 × 10−2(8.970)(5.0)(0.1429)(527.67)/(0.2857)(725.42) = 0.664 ppm.
- (xiii)HCmass = (6048.1)(16.33)(3.553/1,000,000) = 0.35 grams per test phase.
- (2)For the stabilized portion of the cold start test assume that similar calculations resulted in the following:
- (3)For the “transient” portion of the hot start test assume that similar calculations resulted in the following:
- (4)Weighted emission results:
- (i)THCEwm = (0.43) × (1.473 + 0.143)/(3.583 + 3.854) + (0.57) × (0.488 + 0.143)/(3.577 + 3.854) = 0.142 grams as carbon equivalent per mile.
- (ii)NOxwm = (0.43) × (1.505 + 0.979)/(3.583 + 3.854) + (0.57) × (1.505 + 0.979)/3.577 + 3.854) = 0.344 grams per mile.
- (iii)COwm = (0.43) × (18.983 + 0.365)/(3.583 = 3.854) + (0.57) × (3.696 + 0.365)/(3.577 + 3.854) = 1.43 grams per mile.
- (iv)CO2wm = (0.43) × (1353 + 1467)/(3.583 + 3.854) + (0.57) × (1179 + 1467)/(3.577 + 3.854) = 366 grams per mile.
- (v)NMHCEwm = (0.43) × (1.386 + 0.113)/(3.583 + 3.854) + (0.57) × (0.426 = 0.113)/(3.577 + 3.854) = 0.128 grams per mile.
- (1)For the “transient” phase of the cold start test assume the following: V0 = 0.29344 ft 3 rev; N = 25,801; R = 37.5 pct; Ra = 37.5 percent; PB = 725.42 mm Hg; Pd = 22.02 mm Hg; P4 = 70 mm Hg; Tp 570 deg.R; FID HCe = 14.65 ppm, carbon equivalent; r = 0.788; TEM = 527.67 deg.R; VEM = 0.2818 ft 3; CS1 = 7.101; AVS1 = 15.0 ml; CS2 = 0.256; AVS2 = 15.0 ml; TDM = 527.67 deg.R; VDM = 1.1389 ft 3; CD1 = 0.439; AVD1 = 15.0 ml; CD2 = 0.0; AVD2 = 15.0 ml; CFDE = 8.970 µg/ml; VAE = 5.0 ml; Q = 0.1429; TEF = 527.67 deg.R; VSE = 0.2857 ft 3; CFDA = 0.39 µg/ml; VAA = 5.0 ml; TDF = 527.67 deg.R; VSA = 1.1043 ft 3; NOX. = 5.273 ppm; COem = 98.8 ppm; CO2e = 0.469 pct; CH4e = 2.825 ppm; FID HCd = 2.771 ppm; NOX. = 0.146 ppm; COdm = 1.195 ppm; CO2d = 0.039 percent; CH4d = 2.019 ppm; Dct = 3.583 miles.