# 40 CFR 86.1342-90 - Calculations; exhaust emissions.

§ 86.1342-90 Calculations; exhaust emissions.
(a) The final reported transient emission test results should be computed by using the following formula:
Where:
(1) AWM = Weighted mass emission level (HC, CO, CO2. or NOX) in grams per brake horsepower-hour and, if appropriate, the weighted mass total hydrocarbon equivalent, in grams per brake horsepower-hour.
(2) gC = Mass emission level in grams or grams carbon mass equivalent, measured during the cold start test.
(3) gH = Mass emission level in grams or grams carbon mass equivalent, measured during the hot start test.
(4) BHP − hrC = Total brake horsepower-hour (brake horsepower integrated over time) for the cold start test.
(5) BHP-hrH = Total brake horsepower-hour (brake horsepower integrated over time) for the hot start test.
(b) The mass of each pollutant for the cold start test and the hot start test for bag measurements and diesel continuously heated sampling system measurements is determined from the following equations:
(1) Hydrocarbon mass:
HCmass = Vmix × DensityHC × (HCconc/106)
(2) Oxides of nitrogen mass:
NOxmass = Vmix × DensityNO2 × KH × (NOxconc/106)
(3) Carbon monoxide mass:
COmass = Vmix × DensityCO × (COconc/106)
(4) Carbon dioxide mass:
CO2mass = Vmix × Density CO2 × (CO2conc/102)
(5) Methanol mass:
CH3OHmass = Vmix × Density CH3OH × (CH3OHconc/106)
(6) Formaldehyde mass:
HCHOmass = Vmix × DensityHCHO × (HCHOconc/106)
(7) Total hydrocarbon equivalent mass:
(i)
(c) The mass of each pollutant for the cold start test and the hot start test for flow compensated sample systems is determined from the following equations:
(d) Meaning of symbols:
(1)
(i) HCmass = Hydrocarbon emissions, in grams per test phase.
(ii) DensityHC = Density of hydrocarbons = 16.33 g/ft3 (0.5768 kg/m3) for gasoline and the gasoline fraction of methanol-fuel, and may be used for petroleum and the petroleum fraction of methanol diesel fuel if desired, 16.42 g/ft3 (0.5800 kg/m3) for #l petroleum diesel fuel and 16.27 g/ft3 (0.5746 kg/m3) for #2 diesel, assuming an average carbon to hydrogen ratio of 1:1.85 for gasoline, 1:1.93 for #1 petroleum diesel fuel and 1:1.80 for #2 petroleum diesel fuel at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
(iii)
(A) HCconc = Hydrocarbon concentration of the dilute exhaust sample corrected for background, in ppm carbon equivalent (i.e., equivalent propane × 3).
(B) HCconc = HCe − HCd(1 − (1/DF))
Where:
(iv)
(A) HCe = Hydrocarbon concentration of the dilute exhaust bag sample or, for diesel continuous heated sampling systems, average hydrocarbon concentration of the dilute exhaust sample as determined from the integrated HC traces, in ppm carbon equivalent. For flow compensated systems (HCe)i is the instantaneous concentration.
(B) For petroleum-fueled engines, HCe is the FID measurement.
(C) For methanol-fueled engines:
HCe = FID HCe − (r)CCH3OHe
(v) FID HCe = Concentration of hydrocarbon plus methanol in dilute exhaust as measured by the FID, ppm carbon equivalent.
(vi) r = FID response to methanol.
(vii) CCH3OHe = Concentration of methanol in dilute exhaust as determined from the dilute exhaust methanol sample, ppm carbon.
(viii)
(A) HCd = Hydrocarbon concentration of the dilution air as measured, in ppm carbon equivalent.
(B) HCd = FID HCd − (r)CCH3OHd
(ix) FID HCd = Concentration of hydrocarbon plus methanol in dilution air as measured by the FID, ppm carbon equivalent.
(x) CCH3OHd = Concentration of methanol in dilution air as determined from dilution air methanol sample in ppm carbon.
(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/m3), assuming they are in the form of nitrogen dioxide, at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
(iii)
(A) NOxconc = Oxides of nitrogen concentration of the dilute exhaust sample corrected for background, in ppm.
(B) NOxconc = NOxe − NOxd [1 − (1/DF)]
Where:
(iv) NOxe = Oxides of nitrogen concentration of the dilute exhaust bag sample as measured, in ppm. For flow compensated sample systems (NOxe)i is the instantaneous concentration.
(v) NOxd = Oxides of nitrogen concentration of the dilution air as measured, in ppm.
(3)
(i) COmass = Carbon monoxide emissions, grams per test phase.
(ii) DensityCO = Density of carbon monoxide is 32.97 g/ft3 (1.164 kg/m3), at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
(iii)
(A) COconc = Carbon monoxide concentration of the dilute exhaust sample corrected for background, water vapor, and CO2 extraction, ppm.
(B) COconc = COe − COd[1 − (1/DF)]
Where:
(iv) COe = Carbon monoxide concentration of the dilute exhaust bag sample volume corrected for water vapor and carbon dioxide extraction, in ppm. For flow compensated sample systems (COe)i is the instantaneous concentration.
(v)
(A) COe = (1 − 0.01925CO2. − 0.000323R)COem for gasoline and petroleum diesel fuel, with hydrogen to carbon ratio of 1.85:1.
(B) COe = [1 − (0.01 0.005HCR) CO2. − 0.000323R] COem for methanol fuel, where HCR is hydrogen to carbon ratio as measured for the fuel used.
Where:
(vi) COem = Carbon monoxide concentration of the dilute exhaust sample as measured, in ppm.
(vii)
(A) CO2. = Carbon dioxide concentration of the dilute exhaust bag sample, in percent, if measured. For flow compensated sample systems, (CO2.)i is the instantaneous concentration. For cases where exhaust sampling of CO2 is not performed, the following approximation is permitted:
(B)
Where:
(C) α = Average carbon to hydrogen ratio, as specified by the Administrator.
(D) M′ = Fuel mass consumed during the test cycle.
(E) R = Relative humidity of the dilution air, percent.
(viii)
(A) COd = Carbon monoxide concentration of the dilution air corrected for water vapor extraction, in ppm.
(B) COd = (1 − 0.000323R)COdm.
Where:
(ix) COdm = Carbon monoxide concentration of the dilution air sample as measured, in ppm.
Note:
If a CO instrument which meets the criteria specified in § 86.1311 is used and the conditioning column has been deleted, COem must be substituted directly for COe, and COdm must be substituted directly for COd.
(4)
(i) CO2mass = Carbon dioxide emissions, in grams per test phase.
(ii) Density CO2 = Density of carbon dioxide is 51.81 g/ft3 (1.830 kg/m3), at 68 °F (20 °C) and 760 mm Hg (101.3 kPa) pressure.
(iii) CO2conc = Carbon dioxide concentration of the dilute exhaust sample corrected for background, in percent.
(iv) CO2mass = CO2. − CO2.[1 − (1/DF)].
Where:
(v) CO2. = Carbon dioxide concentration of the dilution air as measured, in percent.
(5)
(i) CH3OHmass = Methanol emissions corrected for background, in grams per test phase.
(ii) DensityCH3OH = Density of methanol is 37.71 g/ft3 (1.332 kg/m3), at 68 °F (20 °C) and 760 mm Hg (101.3kPa) pressure.
(iii)
(A) CH3OHconc = Methanol concentration of the dilute exhaust corrected for background, in ppm.
(B) CH3OHconc = CCH3OHe − CCH3OHd [1 − (1/DF)].
Where:
(iv)
(A) CCH3OHe = Methanol concentration in the dilute exhaust, in ppm.
(B)
(v)
(A) CCH3OHd = Methanol concentration in the dilution air, in ppm.
(B)
(vi) CCH3OHR = Concentration of methanol in standard sample for calibration of GC, µg/ml.
(vii) ACH3OHR = GC peak area of standard sample.
(viii) TEM = Temperature of methanol sample withdrawn from dilute exhaust, °R.
(ix) TDM = Temperature of methanol sample withdrawn from dilution air, °R.
(x) PB = Barometric pressure during test, mm Hg.
(xi) VEM = Volume of methanol sample withdrawn from dilute exhaust, ft3.
(xii) VDM = Volume of methanol sample withdrawn from dilution air, ft3.
(xiii) AS = GC peak area of sample drawn from dilute exhaust.
(xiv) AD = GC peak area of sample drawn from dilution air.
(xv) AVS = Volume of absorbing reagent (deionized water) in impinger through which methanol sample from dilute exhaust is drawn, ml.
(xvi) AVD = Volume of absorbing reagent (deionized water) in impinger through which methanol sample from dilution air is drawn, ml.
(xvii) 1 = first impinger.
(xviii) 2 = second impinger.
(6)
(i) HCHOmass = Formaldehyde emissions corrected for background, grams per test phase.
(ii) DensityHCHO = Density of formaldehyde is 35.36 g/ft3 (1.249 kg/m3), at 68 °F (20 °C) and 760 mmHg (101.3 kPa) pressure.
(iii)
(A) HCHOconc = Formaldehyde concentration of the dilute exhaust corrected for background, ppm.
(B) HCHOconc = CHCHOe − CHCHOd [1 − (1/DF)].
Where:
(iv)
(A) CHCHOe = Formaldehyde concentration in dilute exhaust, ppm.
(B)
(v)
(A) CHCHOd = Formaldehyde concentration in dilution air, ppm.
(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)
(A) Q = Ratio of molecular weights of formaldehyde to its DNPH derivative.
(B) Q = 0.1429.
(ix) TEF = Temperature of formaldehyde sample withdrawn from dilute exhaust, °R.
(x) VSE = Volume of formaldehyde sample withdrawn from dilute exhaust, ft3.
(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.
(xiii) VAA = Volume of sampling solution for dilution air formaldehyde sample, ml.
(xiv) TDF = Temperature of formaldehyde sample withdrawn from dilution air, °R.
(xv) VSA=Volume of formaldehyde sample withdrawn from dilution air, ft3.
(7)
(i) DF=13.4/[CO2. (HCe COe)10−4] for petroleum-fueled vehicles, or DF=13.4/CO2.
for methanol-fueled vehicles, where fuel composition is CX Hy Oz as measured for the fuel used.
(8)
(i) KH = Humidity correction factor.
(ii) For gasoline-fueled and methanol-fueled diesel engines: KH = 1/[1 − 0.0047 (H − 75)] (or for SI units, KH = 1/[1 − 0.0329(H − 10.71)]).
(iii) For petroleum-fueled and methanol-fueled diesel engines: KH = 1/[1 − 0.0026 (H − 75)] (or for SI units = 1/[1 − 0.0182 (H − 10.71)]).
Where:
(iv)
(A) H = Absolute humidity of the engine intake air in grains (grams) of water per pound (kilogram) of dry air.
(B) (1) H = [(43.478)Ri × Pd]/[PB − (Pd × Ri/100)]
(2) For SI units,
H = [(6.211)Ri × Pd]/[PB − (Pd × Ri/100)]
(C) Ri = Relative humidity of the engine intake air, percent.
(D) Pd = Saturated vapor pressure, in mm Hg (kPa) at the engine intake air dry bulb temperature.
(E) PB = Barometric pressure, in mm Hg (kPa).
(9)
(i) Vmix = Total dilute exhaust volume in cubic feet per test phase corrected to standard conditions (528 °R) (293 °K) and 760 mm Hg (101.3 kPa).
(ii) (Vmix)i = Instantaneous dilute exhaust volumetric flow rate (for compensated flow systems), ft3/sec.
(iii) T = Time interval (seconds) between samples in flow compensated systems.
(iv) T = Total sampling time (seconds).
(v) For PDP-CVS:
(A)
(B) For SI units,
Where:
(vi) Vo = Volume of gas pumped by the positive displacement pump, in cubic feet (cubic meters) per revolution. This volume is dependent on the pressure differential across the positive displacement pump.
(vii) N = Number of revolutions of the positive displacement pump during the test phase while samples are being collected.
(viii) PB = Barometric pressure, mm Hg (kPa).
(ix) P4 = Pressure depression below atmospheric measured at the inlet to the positive displacement pump, in mm Hg (kPa) (during an idle mode).
(x) Tp = Average temperature of dilute exhaust entering positive displacement pump during test, °R (°K).
(e) Sample calculation of mass values of exhaust emissions:
(1) Assume the following test results for a gasoline engine:
Cold start cycle test results Hot start cycle test results
Vmix 6924 ft 3 6873 ft3.
R 30.2 percent 30.2 percent.
Ri 30.2 percent 30.2 percent.
PB 735 mm Hq 735 mm Hg.
Pd 22.676 mm Hq 22.676 mm Hq.
HCe 132.07 ppm C equiv 86.13 ppm C equiv.
NOxe 7.86 ppm 10.98 ppm.
COem 171.22 ppm 114.28 ppm.
CO2. 0.178 percent 0.381 percent.
HCd 3.60 ppm C equiv 8.70 ppm C equiv.
NOd 0.0 ppm 0.10 ppm.
COdm 0.89 ppm 0.89 ppm.
C02. 0.0 percent 0.038 percent.
BHP-hr 0.259 0.347.
Then:
(2) Cold Start Test:
(i) H
= [(43.478)(30.2)(22.676)]/[735−
(22.676)(30.2)/100]
= 41 grains of water per pound of dry air.
(ii) KH = 1/[1−0.0047(41-75)] = 0.862
(iii) COe
= [1−0.01925(.178)−
0.000323(30.2)]171.22
= 169.0 ppm
(iv) COd=[1−0.000323(30.2)] 0.89=
0.881 ppm
(v) DF
= 13.4/[.178 (132.07 169.0)(10−4)]
= 64.390
(vi) HCconc
= 132.07−3.6[1−(1/64.390)]
= 128.5 ppm
(vii) HCmass
= 6924(16.33)(128.5/106)
= 14.53 grams
(viii) NOxconc
= 7.86−0.0[1−(1/64.390)]
= 7.86 ppm
(ix) NOxmass
= 6924(54.16)(.862)(7.86/106)
= 2.54 grams
(x) COconc
= 169.0−.881[1−(1/64.390)]
= 168.0 ppm
(xi) COmass
= 6924(32.97)(168.0/106)
= 38.35 grams
(xii) CO2conc=.178−0[1−1/64.390)]=
0.178%
(xiii) CO2mass=6924(51.81)(.178/100)=639
grams
(3) Hot start test: Similar calculations result in the following:
(i) HCmass = 8.72 grams
(ii) NOxmass = 3.49 grams
(iii) COmass = 25.70 grams
(iv) CO2mass = 1226 grams
(4) Weighted mass emission results:
(i) HCwm = 1/7(14.53) 6/7(8.72)/1/7(0.259) 6/7(0.347) = 28.6 grams/BHP−hr
(ii) NOXwm = 1/7(2.54) 6/7(3.49)/1/7(0.259) 6/7(0.347) = 10.0 grams/BHP−hr
(iii) COwm = 1/7(38.35) 6/7(25.70)/1/7(0.259) 6/7(0.347) = 82.2 grams/BHP−hr
(iv) CO2wm = 1/7(639) 6/7(1226)/1/7(0.259) 6/7(0.347) = 3415 grams/BHP−hr
(f) The final reported brake-specific fuel consumption (BSFC) shall be computed by use of the following formula:
Where:
(1) BSFC = brake-specific fuel consumption in pounds of fuel per brake horsepower-hour (lbs/BHP-hr).
(2) MC = mass of fuel, in lbs, used by the engine during the cold start test.
(3) MH = mass of fuel, in lbs, used by the engine during the hot start test.
(4) BHP-hrC = total brake horsepower-hours (brake horsepower integrated with respect to time) for the cold start test.
(5) BHP-hrH = total brake horsepower-hours (brake horsepower integrated with respect to time) for the hot start test.
(g)
(1) The mass of fuel for the cold start and hot start test is determined from mass fuel flow measurements made during the tests, or from the following equation:
M = (Gs/R2)(1/453.6)
(2) Meaning of symbols:
(i) M = Mass of fuel, in lbs, used by the engine during the cold or hot start test.
(ii) Gs = Grams of carbon measured during the cold or hot start test:
Where:
(iii) HCmass = Hydrocarbon emissions, in grams, for cold or hot start test.
(iv) COmass = Carbon monoxide emissions, in grams, for cold or hot start test.
(v) CO2mass = Carbon dioxide emissions, in grams, for cold or hot start test.
(vi) α = The atomic hydrogen to carbon ratio of the fuel.
(vii)
(A) R2 = The grams of carbon in the fuel per gram of fuel.
(B) R2 = 12.011/[12.011 α(1.008)]
(h) Sample calculation of brake-specific fuel consumption:
(1) Assume the following test results:
Cold start cycle test results Hot start cycle test results
BHP-hr 6.945 7.078
α 1.85 1.85
HCmass (grams) 37.08 28.82
COmass (grams) 357.69 350.33
C02mass (grams) 5,419.62 5,361.32
Then:
(i) Gs for cold start test = [12.011/(12.011 (1.008)(1.85))](37.08) 0.429(357.69) 0.273(5419.62) = 1665.10 grams
(ii) Gs for hot start test = [12.011/(12.011 (1.008)(1.85))](28.82) 0.429(350.33) 0.273(5361.32) = 1638.88 grams
(iii) R2 = 12.011/[12.011 (1.008)1.85] = 0.866
(iv)
(A) Mc = (1665.10/.866)(1/453.6) = 4.24 lbs (calculated), or
(B) = 4.24 lbs (directly measured).
(v)
(A) MH = (1638.88/.866)(1/453.6) = 4.17 lbs (calculated), or
(B) = 4.17 lbs (directly measured).
(2) Brake-specific fuel consumption results:
BSFC (1/7)(4.24) =(6/7)(4.17)/(1/7)(6.945) (6/7)(7.078) = 0.592 lbs of fuel/BHP−hr
(i) For dilute sampling systems which require conversion of as-measured dry concentrations to wet concentrations, the following equation shall be used for any combination of bagged, continuous, or fuel mass-approximated sample measurements (except for CO measurements made through conditioning columns, as explained in paragraph (d)(3) of this section):
Wet concentration = Kw × dry concentration.
Where:
(1)
(i) For English units,
Kw = 1−(α/200) × CO2.(′)−((1.608 × H)/(7000 1.608 × H))
See paragraph (d)(1) of this section for α values.
(ii) For SI units,
Kw = 1−(α/200) × CO2.(′)−((1.608 × H)/(1000 1.608 × H))
See paragraph (d)(1) of this section for α values.
(2) CO2.(′) = either CO2. or CO2.′ as applicable.
(3)
(i) H = Absolute humidity of the CVS dilution air, in grains (grams) of water per lb (kg) of dry air.
(ii) For English units,
H ′ = [(43.478)Ri′ × Pd′]/[PB−(Pd′ × Ri′/100)]
(iii) For SI units,
H′ = [(6.211)Ri′ × Pd′]/[PB−(Pd′ × Ri′/100)]
(4) Ri = Relative humidity of the CVS dilution air, in percent.
(5) Pd = Saturated vapor pressure, in mm Hg (kPa) at the ambient dry bulb temperature of the CVS dilution air.
(6) PB = Barometric pressure, mm Hg (kPa).
[54 FR 14605, Apr. 11, 1989, as amended at 62 FR 47135, Sept. 5, 1997]
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Title 40 published on 2015-07-01

The following are ALL rules, proposed rules, and notices (chronologically) published in the Federal Register relating to 40 CFR Part 86 after this date.

• 2015-09-08; vol. 80 # 173 - Tuesday, September 8, 2015
1. 80 FR 53756 - Greenhouse Gas Emissions and Fuel Efficiency Standards for Medium- and Heavy-Duty Engines and Vehicles—Phase 2; Extension of Comment Period
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DEPARTMENT OF TRANSPORTATION, ENVIRONMENTAL PROTECTION AGENCY, National Highway Traffic Safety Administration
Proposed rule; extension of comment period.
The comment period for the proposed rule published July 13, 2015 (80 FR 40139) is extended. Written comments for both documents must be received on or before October 1, 2015.
40 CFR Parts 9, 22, 85, 86, 600, 1033, 1036, 1037, 1039, 1042, 1065, 1066, and 1068