Subpart G - Calculations and Data Requirements

§1065.601 Overview.

(a) This subpart describes how to —-

(1) Use the signals recorded before, during, and after an emission test to calculate brake-specific emissions of each measured exhaust constituent.

§1065.602 Statistics.

(a) Overview. This section contains equations and example calculations for statistics that are specified in this part. In this section we use the letter “y” to denote a generic measured quantity, the superscript over-bar “^-” to denote an arithmetic mean, and the subscript “_ref” to denote the reference quantity being measured.

(b) Arithmetic mean. Calculate an arithmetic mean, y , as follows:

Example:

N = 3

y₁ = 10.60

y₂ = 11.91

y_N = y₃ = 11.09

y = 11.20

(c) Standard deviation. Calculate the standard deviation for a non-biased (e.g., N-1) sample, σ, as follows:

Example:

N = 3

y₁ = 10.60

y₂ = 11.91

y_N = y₃ = 11.09

y = 11.20

σ_y = 0.6619

(d) Root mean square. Calculate a root mean square, rms_y, as follows:

Example:

N = 3

y₁ = 10.60

y₂ = 11.91

y_N = y₃ = 11.09

rms_y = 11.21

(e) Accuracy. Determine accuracy as described in this paragraph (e). Make multiple measurements of a standard quantity to create a set of observed values, y , and compare each observed value to the known value of the standard quantity. The standard quantity may have a single known value, such as a gas standard, or a set of known values of negligible range, such as a known applied pressure produced by a calibration device during repeated applications. The known value of the standard quantity is represented by y_ref . If you use a standard quantity with a single value, y_ref would be constant. Calculate an accuracy value as follows:

Example:

y_ref = 1800.0

N = 3

y₁ = 1806.4

y₂ = 1803.1

y₃ = 1798.9

accuracy = 2.8

(f) t-test. Determine if your data passes a t-test by using the following equations and tables:

(1) For an unpaired t-test, calculate the t statistic and its number of degrees of freedom, v, as follows:

Example:

Y _ref = 1205.3

Y = 1123.8

σ_ref = 9.399

σ_y = 10.583

N_ref = 11

N = 7

t = 16.63

σ_ref = 9.399

σ_y = 10.583

N_ref = 11

N = 7

v = 11.76

(2) For a paired t-test, calculate the t statistic and its number of degrees of freedom, v, as follows, noting that the ε are the errors (e.g., differences) between each pair of y_ref and y :

Example 1:

ε = −0.12580

N = 16

σ_ε = 0.04837

t = 10.403

v = N−1

Example 2:

N = 16

v = 16−1

v = 15

(3) Use Table 1 of this section to compare t to the t_crit values tabulated versus the number of degrees of freedom. If t is less than t_crit, then t passes the t-test. The Microsoft Excel software has a TINV function that returns results equivalent results and may be used in place of Table 1, which follows:

(g) F-test. Calculate the F statistic as follows:

Example:

F = 1.268

(1) For a 90% confidence F-test, use the following table to compare F to the F_crit90 values tabulated versus (N−1) and (N_ref−1). If F is less than F_crit90, then F passes the F-test at 90% confidence.

(2) For a 95% confidence F-test, use the following table to compare F to the F_crit90 values tabulated versus (N−1) and (N_ref−1). If F is less than F_crit95, then F passes the F-test at 95% confidence.

(h) Slope. Calculate a least-squares regression slope, a_1y, using one of the following two methods:

(1) If the intercept floats, i.e., is not forced through zero:

Example:

N = 6000

y₁ = 2045.8

y = 1050.1

y_ref1 = 2045.0

y _ref = 1055.3

a_1y = 1.0110

(2) If the intercept is forced through zero, such as for verifying proportional sampling:

Example:

N = 6000

y₁ = 2045.8

y_ref1 = 2045.0

a_1y = 1.0110

(i) Intercept. For a floating intercept, calculate a least-squares regression intercept, a_0y, as follows:

Example:

y = 1050.1

a_1y = 1.0110

y _ref = 1055.3

a_0y = 1050.1 − (1.0110 · 1055.3)

a_0y = −16.8083

(j) Standard error of the estimate. Calculate a standard error of the estimate, SEE, using one of the following two methods:

(1) For a floating intercept:

Example:

N = 6000

y₁ = 2045.8

a_0y = −16.8083

a_1y = 1.0110

y_ref1 = 2045.0

SEE_y = 5.348

(2) If the intercept is forced through zero, such as for verifying proportional sampling:

Example:

N = 6000

y₁ = 2045.8

a_1y = 1.0110

y_ref1 = 2045.0

SEE_y = 5.347

(k) Coefficient of determination. Calculate a coefficient of determination, r_y², as follows:

Example:

N = 6000

y₁ = 2045.8

a_0y = −16.8083

a_1y = 1.0110

y_ref1 = 2045.0

y = 1480.5

(l) Flow-weighted mean concentration. In some sections of this part, you may need to calculate a flow-weighted mean concentration to determine the applicability of certain provisions. A flow-weighted mean is the mean of a quantity after it is weighted proportional to a corresponding flow rate. For example, if a gas concentration is measured continuously from the raw exhaust of an engine, its flow-weighted mean concentration is the sum of the products of each recorded concentration times its respective exhaust molar flow rate, divided by the sum of the recorded flow rate values. As another example, the bag concentration from a CVS system is the same as the flow-weighted mean concentration because the CVS system itself flow-weights the bag concentration. You might already expect a certain flow-weighted mean concentration of an emission at its standard based on previous testing with similar engines or testing with similar equipment and instruments. If you need to estimate your expected flow-weighted mean concentration of an emission at its standard, we recommend using the following examples as a guide for how to estimate the flow-weighted mean concentration expected at the standard. Note that these examples are not exact and that they contain assumptions that are not always valid. Use good engineering judgment to determine if you can use similar assumptions.

(1) To estimate the flow-weighted mean raw exhaust NO_X concentration from a turbocharged heavy-duty compression-ignition engine at a NO_X standard of 2.5 g/(kW·hr), you may do the following:

(i) Based on your engine design, approximate a map of maximum torque versus speed and use it with the applicable normalized duty cycle in the standard-setting part to generate a reference duty cycle as described in §1065.610. Calculate the total reference work, W_ref, as described in §1065.650. Divide the reference work by the duty cycle's time interval, Δt_dutycycle, to determine mean reference power, p _ref.

(ii) Based on your engine design, estimate maximum power, P_max, the design speed at maximum power, ƒ_nmax, the design maximum intake manifold boost pressure, P_inmax, and temperature, T_inmax. Also, estimate a mean fraction of power that is lost due to friction andpumping, P_frict. Use this information along with the engine displacement volume, V_disp, an approximate volumetric efficiency, η_V, and the number of engine strokes per power stroke (two-stroke or four-stroke), N_stroke, to estimate the maximum raw exhaust molar flow rate, n _exhmax.

(iii) Use your estimated values as described in the following example calculation:

Example:

e_NOX = 2.5 g/(kW·hr)

W_ref = 11.883 kW·hr

M_NOX = 46.0055 g/mol = 46.0055·10−⁶ g/μmol

Δt_dutycycle = 20 min = 1200 s

P _ref = 35.65 kW

P _frict = 15%

P_max = 125 kW

p_max = 300 kPa = 300000 Pa

V_disp = 3.0 l = 0.0030 m³/r

f_nmax = 2800 r/min = 46.67 r/s

N_stroke = 4

η_V = 0.9

R = 8.314472 J/(mol·K)

T_max = 348.15 K

(2) To estimate the flow-weighted mean NMHC concentration in a CVS from a naturally aspirated nonroad spark-ignition engine at an NMHC standard of 0.5 g/(kW·hr), you may do the following:

(i) Based on your engine design, approximate a map of maximum torque versus speed and use it with the applicable normalized duty cycle in the standard-setting part to generate a reference duty cycle as described in §1065.610. Calculate the total reference work, W_ref, as described in §1065.650.

(ii) Multiply your CVS total molar flow rate by the time interval of the duty cycle, Δt_dutycycle. The result is the total diluted exhaust flow of the n_dexh.

(iii) Use your estimated values as described in the following example calculation:

Example:

e_NMHC = 1.5 g/(kW·hr)

W_ref = 5.389 kW·hr

M_NMHC = 13.875389 g/mol = 13.875389·10−⁶ g/μmol

n _dexh = 6.021 mol/s

Δt_dutycycle = 30 min = 1800 s

X _NMHC = 53.8 µmol/mol

(m) Median. Determine median, M , as described in this paragraph (m). Arrange the data points in the data set in increasing order where the smallest value is ranked 1, the second-smallest value is ranked 2, etc.

(1) For even numbers of data points:

(i) Determine the rank of the data point whose value is used to determine the median as follows:

Eq. 1065.602-18

Where:

i = an indexing variable that represents the rank of the data point whose value is used to determine the median.

N = the number of data points in the set.

Example:

N = 4

y₁ = 41.515

y₂ = 41.780

y₃ = 41.861

y₄ = 41.902

i = 2

i = 2

(ii) Determine the median as the average of the data point i and the data point i + 1 as follows:

Example:

[70 FR 40516, July 13, 2005, as amended at 73 FR 37324, June 30, 2008; 75 FR 23044, Apr. 30, 2010; 76 FR 57452, Sept. 15, 2011; 79 FR 23779, Apr. 28, 2014; 81 FR 74170, Oct. 25, 2016; 86 FR 34548, Jun. 29, 2021; 87 FR 65865, Oct. 26, 2022; 89 FR 29807, Apr. 22, 2024]

§1065.610 Duty cycle generation.

This section describes how to generate duty cycles that are specific to your engine, based on the normalized duty cycles in the standard-setting part. During an emission test, use a duty cycle that is specific to your engine to command engine speed, torque, and power, as applicable, using an engine dynamometer and an engine operator demand. Paragraphs (a) and (b) of this section describe how to “normalize” your engine's map to determine the maximum test speed or torque for your engine. The rest of this section describes how to use these values to “denormalize” the duty cycles in the standard-setting parts, which are all published on a normalized basis. Thus, the term “normalized” in paragraphs (a) and (b) of this section refers to different values than it does in the rest of the section.

(a) Maximum test speed, ƒ . For variable-speed engines, determine ƒ _ntest from the torque and power maps, generated according to §1065.510, as follows:

(1) Determine a measured value for ƒ _ntest as follows:

(i) Determine maximum power, P_max, from the engine map generated according to §1065.510 and calculate the value for power equal to 98% of P_max.

(ii) Determine the lowest and highest engine speeds corresponding to 98% of P_max, using linear interpolation, and no extrapolation, as appropriate.

(iii) Determine the engine speed corresponding to maximum power, f_nPmax, by calculating the average of the two speed values from paragraph (a)(1)(ii) of this section. If there is only one speed where power is equal to 98% of P_max, take f_nPmax as the speed at which P_max occurs.

(iv) Transform the map into a normalized power-versus-speed map by dividing power terms by P_max and dividing speed terms by f_nPmax. Use the following equation to calculate a quantity representing the sum of squares from the normalized map:

Where:

i = an indexing variable that represents one recorded value of an engine map.

f_nnorm = an engine speed normalized by dividing it by f_nPmax.

P_norm = an engine power normalized by dividing it by P_max.

(v) Determine the maximum value for the sum of the squares from the map and multiply that value by 0.98.

(vi) Determine the lowest and highest engine speeds corresponding to the value calculated in paragraph (a)(1)(v) of this section, using linear interpolation as appropriate. Calculate f_ntest as the average of these two speed values. If there is only one speed corresponding to the value calculated in paragraph (a)(1)(v) of this section, take f_ntest as the speed where the maximum of the sum of the squares occurs.

(vii) The following example illustrates a calculation of f_ntest:

P_max = 230.0

(f_n1 = 2360, P₁ = 222.5, f_nnorm1 = 1.002, P_norm1 = 0.9675)

(f_n2 = 2364, P₂ = 226.8, f_nnorm2 = 1.004, P_norm2 = 0.9859)

(f_n3 = 2369, P₃ = 228.6, f_nnorm3 = 1.006, P_norm3 = 0.9940)

(f_n4 = 2374, P₄ = 218.7, f_nnorm4 = 1.008, P_norm4 = 0.9508)

Sum of squares = (1.002 ² + 0.9675 ²) = 1.94

Sum of squares = (1.004 ² + 0.9859 ²) = 1.98

Sum of squares = (1.006 ² + 0.9940 ²) = 2.00

Sum of squares = (1.008 ² + 0.9508 ²) = 1.92

(2) For engines with a high-speed governor that will be subject to a reference duty cycle that specifies normalized speeds greater than 100%, calculate an alternate maximum test speed, f_ntest,alt, as specified in this paragraph (a)(2). If f_ntest,alt is less than the measured maximum test speed, f_ntest, determined in paragraph (a)(1) of this section, replace f_ntest with f_ntest,alt. In this case, f_ntest,alt becomes the “maximum test speed” for that engine for all duty cycles. Note that §1065.510 allows you to apply an optional declared maximum test speed to the final measured maximum test speed determined as an outcome of the comparison between f_ntest, and f_ntest,alt in this paragraph (a)(2). Determine f_ntest,alt as follows:

Where:

f_ntest,alt = alternate maximum test speed

f_nhi,idle = warm high-idle speed

f_nidle = warm idle speed

% speed_max = maximum normalized speed from duty cycle

Example:

f_nhi,idle = 2200 r/min

f_nidle = 800 r/min

f_ntest,alt = 2133 r/min

(3) Transform normalized speeds to reference speeds according to paragraph (c) of this section by using the measured maximum test speed determined according to paragraphs (a)(1) and (2) of this section—or use your declared maximum test speed, as allowed in §1065.510.

(b) Maximum test torque,T . For constant-speed engines, determine T_test from the torque and power-versus-speed maps, generated according to §1065.510, as follows:

(1) For constant speed engines mapped using the methods in §1065.510(d)(5)(i) or (ii), determine a measured value for T_test as follows:

(i) Determine maximum power, P_max, from the engine map generated according to §1065.510 and calculate the value for power equal to 98% of P_max.

(ii) Determine the lowest and highest engine speeds corresponding to 98% of P_max, using linear interpolation, and no extrapolation, as appropriate.

(iii) Determine the engine speed corresponding to maximum power, f_nPmax, by calculating the average of the two speed values from paragraph (a)(1)(ii) of this section. If there is only one speed where power is equal to 98% of P_max, take f_nPmax as the speed at which P_max occurs.

(iv) Transform the map into a normalized power-versus-speed map by dividing power terms by P_max and dividing speed terms by f_nPmax. Use Eq. 1065.610-1 to calculate a quantity representing the sum of squares from the normalized map.

(v) Determine the maximum value for the sum of the squares from the map and multiply that value by 0.98.

(vi) Determine the lowest and highest engine speeds corresponding to the value calculated in paragraph (a)(1)(v) of this section, using linear interpolation as appropriate. Calculate f_ntest as the average of these two speed values. If there is only one speed corresponding to the value calculated in paragraph (a)(1)(v) of this section, take f_ntest as the speed where the maximum of the sum of the squares occurs.

(vii) The measured T_test is the mapped torque at f_ntest.

(2) For constant speed engines using the two-point mapping method in §1065.510(d)(5)(iii), you may follow paragraph (a)(1) of this section to determine the measured T_test , or you may use the measured torque of the second point as the measured T_test directly.

(3) Transform normalized torques to reference torques according to paragraph (d) of this section by using the measured maximum test torque determined according to paragraph (b)(1) or (2) of this section—or use your declared maximum test torque, as allowed in §1065.510.

(c) Generating reference speed values from normalized duty cycle speeds. Transform normalized speed values to reference values as follows:

(1) % speed. If your normalized duty cycle specifies % speed values, use your warm idle speed and your maximum test speed to transform the duty cycle, as follows:

Example:

% speed = 85% = 0.85

f_ntest = 2364 r/min

f_nidle = 650 r/min

f_nref = 0.85 (2364−650) + 650

f_nref = 2107 r/min

(2) A, B, C, and D speeds. If your normalized duty cycle specifies speeds as A, B, C, or D values, use your power-versus-speed curve to determine the lowest speed below maximum power at which 50% of maximum power occurs. Denote this value as n_lo. Take n_lo to be warm idle speed if all power points at speeds below the maximum power speed are higher than 50% of maximum power. Also determine the highest speed above maximum power at which 70% of maximum power occurs. Denote this value as n_hi. If all power points at speeds above the maximum power speed are higher than 70% of maximum power, take n_hi to be the declared maximum safe engine speed or the declared maximum representative engine speed, whichever is lower. Use n_hi and n_lo to calculate reference values for A, B, C, or D speeds as follows:

Example:

n_lo = 1005 r/min

n_hi = 2385 r/min

ƒ _nrefA = 0.25 · (2385 − 1005) + 1005

ƒ _nrefB = 0.50 · (2385 − 1005) + 1005

ƒ _nrefC = 0.75 · (2385 − 1005) + 1005

ƒ _nrefD = 0.15 · (2385 − 1005) + 1005

ƒ _nrefA = 1350 r/min

ƒ _nrefB = 1695 r/min

ƒ _nrefC = 2040 r/min

ƒ _nrefD = 1212 r/min

(3) Intermediate speed. Based on the map, determine maximum torque, T_max, and the corresponding speed, f_nTmax, calculated as the average of the lowest and highest speeds at which torque is equal to 98% of T_max. Use linear interpolation between points to determine the speeds where torque is equal to 98% of T_max. Identify your reference intermediate speed as one of the following values:

(i) f_nTmax if it is between (60 and 75) % of maximum test speed.

(ii) 60% of maximum test speed if f_nTmax is less than 60% of maximum test speed.

(iii) 75% of maximum test speed if f_nTmax is greater than 75% of maximum test speed.

(d) Generating reference torques from normalized duty-cycle torques. Transform normalized torques to reference torques using your map of maximum torque versus speed.

(1) Reference torque for variable-speed engines. For a given speed point, multiply the corresponding % torque by the maximum torque at that speed, according to your map. If your engine is subject to a reference duty cycle that specifies negative torque values (i.e., engine motoring), use negative torque for those motoring points (i.e., the motoring torque). If you map negative torque as allowed under §1065.510(c)(2) and the low-speed governor activates, resulting in positive torques, you may replace those positive motoring mapped torques with negative values between zero and the largest negative motoring torque. For both maximum and motoring torque maps, linearly interpolate mapped torque values to determine torque between mapped speeds. If the reference speed is below the minimum mapped speed (i.e., 95% of idle speed or 95% of lowest required speed, whichever is higher), use the mapped torque at the minimum mapped speed as the reference torque. The result is the reference torque for each speed point.

(2) Reference torque for constant-speed engines. Multiply a % torque value by your maximum test torque. The result is the reference torque for each point.

(3) Required deviations. We require the following deviations for variable-speed engines intended primarily for propulsion of a vehicle with an automatic or manual transmission where that engine is subject to a transient duty cycle that specifies points with normalized reference speed of 0% and normalized reference torque of 0% ( i.e., idle points). These deviations are intended to produce a more representative transient duty cycle for these applications. For steady-state duty cycles or transient duty cycles with no idle operation, the requirements in this paragraph (d)(3) do not apply. Idle points for steady-state duty cycles of such engines are to be run at conditions simulating neutral or park on the transmission. For manual transmissions, set CITT to zero, which results in warm-idle-in-drive speed and torque values being the same as warm-idle-in-neutral values. For the case of a manual transmission where the optional declared idle torque in §1065.510(f)(5)(iii) and the optional declared power in §1065.510(f)(6) are not declared (i.e., idle torque is zero), the required deviations in this paragraph (d)(3) have no impact and may be skipped.

(i) Determine the warm-idle-in-drive speed and torque values with the transmission in drive from the data collected during the engine mapping procedure in §1065.510. The warm-idle-in-drive torque is the sum of CITT and the torques representing loads from vehicle accessories. For example, the sum of the required declared CITT in §1065.510(f)(4), any optional declared torque in §1065.510(f)(5)(iii), and the torque on the primary output shaft from any optional declared power in §1065.510(f)(6).

(ii) Determine the warm-idle-in-neutral speed and torque values with the transmission in neutral from the data collected during the engine mapping procedure in §1065.510. The warm-idle-in-neutral torque is the sum of any optional declared torque in §1065.510(f)(5)(iii) and the torque on the primary output shaft from any optional declared power in §1065.510(f)(6) ( i.e., the sum of the torques representing loads from vehicle accessories).

(iii) Zero-percent speed for denormalization of non-idle points is the warm-idle-in-drive speed.

(iv) For motoring points, make no changes.

(v) If the cycle begins with an idle segment ( i.e., a set of one or more contiguous idle points), set the reference speed and torque values to the warm-idle-in-neutral values for this initial segment. This is to represent idle operation with the transmission in neutral or park at the start of the transient duty cycle, after the engine is started. If the initial idle segment is longer than 24 seconds, change the reference speed and torque values for the remaining idle points in the initial idle segment to the warm-idle-in-drive values ( i.e., change idle points corresponding to 25 seconds to the end of the initial idle segment to warm-idle-in-drive). This is to represent manually shifting the transmission to drive.

(vi) For all other idle segments, set the reference speed and torque values to the warm-idle-in-drive values. This is to represent the transmission operating in drive.

(vii) If the engine is intended primarily for automatic transmissions with a Neutral-When-Stationary feature that automatically shifts the transmission to neutral after the vehicle is stopped for a designated time and automatically shifts back to drive when the operator increases demand ( i.e., pushes the accelerator pedal), reprocess all idle segments. Change reference speed and torque values from the warm-idle-in-drive values to the warm-idle-in-neutral values for idle points in drive after the designated time.

(viii) For all nonidle nonmotoring points with normalized speed at or below zero percent and reference torque from zero to the warm-idle-in-drive torque value, set the reference torque to the warm-idle-in-drive torque value. This is to represent the transmission operating in drive.

(ix) For consecutive nonidle nonmotoring points that immediately follow and precede idle segments, with reference torque values from zero to the warm-idle-in-drive torque value, change their reference torques to the warm-idle-in-drive torque value. This is to represent the transmission operating in drive.

(x) For consecutive nonidle nonmotoring points that immediately follow and precede any point(s) that were modified in paragraph (d)(3)(viii) of this section, with reference torque values from zero to the warm-idle-in-drive torque value, change their reference torques to the warm-idle-in-drive torque value. This is to provide smooth torque transition around these points.

(4) Permissible deviations for any engine. If your engine does not operate below a certain minimum torque under normal in-use conditions, you may use a declared minimum torque as the reference value instead of any value denormalized to be less than the declared value. For example, if your engine is connected to a hydrostatic transmission and it has a minimum torque even when all the driven hydraulic actuators and motors are stationary and the engine is at idle, then you may use this declared minimum torque as a reference torque value instead of any reference torque value generated under paragraph (d)(1) or (2) of this section that is between zero and this declared minimum torque.

(e) Generating reference power values from normalized duty cycle powers. Transform normalized power values to reference speed and power values using your map of maximum power versus speed.

(1) First transform normalized speed values into reference speed values. For a given speed point, multiply the corresponding % power by the mapped power at maximum test speed, f_ntest, unless specified otherwise by the standard-setting part. The result is the reference power for each speed point, P_ref. Convert these reference powers to corresponding torques for operator demand and dynamometer control and for duty cycle validation per 1065.514. Use the reference speed associated with each reference power point for this conversion. As with cycles specified with % torque, linearly interpolate between these reference torque values generated from cycles with % power.

(2) Permissible deviations for any engine. If your engine does not operate below a certain power under normal in-use conditions, you may use a declared minimum power as the reference value instead of any value denormalized to be less than the declared value. For example, if your engine is directly connected to a propeller, it may have a minimum power called idle power. In this case, you may use this declared minimum power as a reference power value instead of any reference power value generated per paragraph (e)(1) of this section that is from zero to this declared minimum power.

[73 FR 37324, June 30, 2008, as amended at 73 FR 59330, Oct. 8, 2008; 75 FR 23045, Apr. 30, 2010; 76 FR 57453, Sept. 15, 2011; 78 FR 36398, June 17, 2013; 79 FR 23783, Apr. 28, 2014; 80 FR 9118, Feb. 19, 2015; 81 FR 74170, Oct. 25, 2016; 86 FR 34555, Jun. 29, 2021; 88 FR 4679, Jan. 24, 2023; 89 FR 29807, Apr. 22, 2024]

§1065.630 Local acceleration of gravity.

(a) The acceleration of Earth's gravity, a_g , varies depending on the test location. Determine a_g at your location by entering latitude, longitude, and elevation data into the U.S. National Oceanographic and Atmospheric Administration's surface gravity prediction website at https://geodesy.noaa.gov/cgi-bin/grav_pdx.prl.

(b) If the website specified in paragraph (a) of this section is unavailable, or the test location is outside of the continental United States, you may calculate a_g for your latitude as follows:

Where:

u = Degrees north or south latitude.

Example:

u = 45°

a_g = 9.7803267715 · (1 + 5.2790414 · 10⁻³ · sin ² (45) + 2.32718 · 10⁻⁵ · sin ⁴ (45) + 1.262 · 10⁻⁷ · sin ⁶ (45) + 7 · 10⁻¹⁰ · sin ⁸ (45)

a_g = 9.8061992026 m/s ²

[79 FR 23784, Apr. 28, 2014; 88 FR 4680, Jan. 24, 2023]

§1065.640 Flow meter calibration calculations.

This section describes the calculations for calibrating various flow meters. After you calibrate a flow meter using these calculations, use the calculations described in §1065.642 to calculate flow during an emission test. Paragraph (a) of this section first describes how to convert reference flow meter outputs for use in the calibration equations, which are presented on a molar basis. The remaining paragraphs describe the calibration calculations that are specific to certain types of flow meters.

(a) Reference meter conversions. The calibration equations in this section use molar flow rate, n _ref, as a reference quantity. If your reference meter outputs a flow rate in a different quantity, such as standard volume rate,V _stdref, actual volume rate,V _actref, or mass rate, m _ref, convert your reference meter output to a molar flow rate using the following equations, noting that while values for volume rate, mass rate, pressure, temperature, and molar mass may change during an emission test, you should ensure that they are as constant as practical for each individual set point during a flow meter calibration:

Where:

n _ref = reference molar flow rate.

V _stdref = reference volume flow rate corrected to a standard pressure and a standard temperature.

V _actref = reference volume flow rate at the actual pressure and temperature of the flow rate.

m _ref = reference mass flow.

p_std = standard pressure.

p_act = actual pressure of the flow rate.

T_std = standard temperature.

T_act = actual temperature of the flow rate.

R = molar gas constant.

M_mix = molar mass of the flow rate.

Example 1:

V _stdref = 1000.00 ft³/_min = 0.471948 m³/_s

p_std = 29.9213 in Hg @ 32 °F = 101.325 kPa = 101325 Pa = 101325 kg/(m·s²)

T_std = 68.0 °F = 293.15 K

R = 8.314472 J/(mol·K) = 8.314472 (m²·kg)/(s²·mol·K)

n _ref = 19.619 mol/s

Example 2:

m _ref = 17.2683 kg/min = 287.805 g/s

M_mix = 28.7805 g/mol

n _ref = 10.0000 mol/s

(b) PDP calibration calculations. Perform the following steps to calibrate a PDP flow meter:

(1) Calculate PDP volume pumped per revolution, V_rev, for each restrictor position from the mean values determined in §1065.340 as follows:

Where:

n ̇_ref = mean reference molar flow rate.

R = molar gas constant.

T ͞_in = mean temperature at the PDP inlet.

P ͞_in = mean static absolute pressure at the PDP inlet.

f ͞_nPDP = mean PDP speed.

Example:

n ̇_ref = 25.096 mol/s

R = 8.314472 J/(mol·K) = 8.314472 (m ²·kg)/(s ²·mol·K)

T ͞_in = 299.5 K

P ͞_in = 98.290 kPa = 98290 Pa = 98290 kg/(m·s ²)

f ͞_nPDP = 1205.1 r/min = 20.085 r/s

V_rev = 0.03166 m ³/r

(2) Calculate a PDP slip correction factor, K_s, for each restrictor position from the mean values determined in §1065.340 as follows:

Where:

f ͞_nPDP = mean PDP speed.

P ͞_out = mean static absolute pressure at the PDP outlet.

P ͞_in = mean static absolute pressure at the PDP inlet.

Example:

f ͞_nPDP = 1205.1 r/min = 20.085 r/s

P ͞_out = 100.103 kPa

P ͞_in = 98.290 kPa

K_s = 0.006700 s/r

(3) Perform a least-squares regression of V_rev, versus K_s, by calculating slope, a₁, and intercept, a₀, as described for a floating intercept in §1065.602.

(4) Repeat the procedure in paragraphs (b)(1) through (3) of this section for every speed that you run your PDP.

(5) The following table illustrates a range of typical values for different PDP speeds:

(6) For each speed at which you operate the PDP, use the appropriate regression equation from this paragraph (b) to calculate flow rate during emission testing as described in §1065.642.

(c) Venturi governing equations and permissible assumptions. This section describes the governing equations and permissible assumptions for calibrating a venturi and calculating flow using a venturi. Because a subsonic venturi (SSV) and a critical-flow venturi (CFV) both operate similarly, their governing equations are nearly the same, except for the equation describing their pressure ratio, r (i.e., r_SSV versus r_CFV). These governing equations assume one-dimensional isentropic inviscid flow of an ideal gas. Paragraph (c)(5) of this section describes other assumptions that may apply. If good engineering judgment dictates that you account for gas compressibility, you may either use an appropriate equation of state to determine values of Z as a function of measured pressure and temperature, or you may develop your own calibration equations based on good engineering judgment. Note that the equation for the flow coefficient, C_f, is based on the ideal gas assumption that the isentropic exponent, g, is equal to the ratio of specific heats, C_p/C_v. If good engineering judgment dictates using a real gas isentropic exponent, you may either use an appropriate equation of state to determine values of γ as a function of measured pressures and temperatures, or you may develop your own calibration equations based on good engineering judgment.

(1) Calculate molar flow rate, n ̇, as follows:

Where:

C_d = discharge coefficient, as determined in paragraph (c)(2) of this section.

C_f = flow coefficient, as determined in paragraph (c)(3) of this section.

A_t = venturi throat cross-sectional area.

p_in = venturi inlet absolute static pressure.

Z = compressibility factor.

M_mix = molar mass of gas mixture.

R = molar gas constant.

T_in = venturi inlet absolute temperature.

(2) Using the data collected in §1065.340, calculate C_d for each flow rate using the following equation:

Where:

n ̇_ref = a reference molar flow rate.

(3) Determine C_f using one of the following methods:

(i) For CFV flow meters only, determine C_fCFV from the following table based on your values for β and γ, using linear interpolation to find intermediate values:

(ii) For any CFV or SSV flow meter, you may use the following equation to calculate C_f for each flow rate:

Where:

g = isentropic exponent. For an ideal gas, this is the ratio of specific heats of the gas mixture, C_p/C_v.

r = pressure ratio, as determined in paragraph (c)(4) of this section.

b = ratio of venturi throat to inlet diameters.

(4) Calculate r as follows:

(i) For SSV systems only, calculate r_SSV using the following equation:

Where:

Δp_SSV = Differential static pressure; venturi inlet minus venturi throat.

(ii) For CFV systems only, calculate r_CFV iteratively using the following equation:

(5) You may apply any of the following simplifying assumptions or develop other values as appropriate for your test configuration, consistent with good engineering judgment:

(i) For raw exhaust, diluted exhaust, and dilution air, you may assume that the gas mixture behaves as an ideal gas: Z = 1.

(ii) For raw exhaust, you may assume g = 1.385.

(iii) For diluted exhaust and dilution air, you may assume g = 1.399.

(iv) For diluted exhaust and dilution air, you may assume the molar mass of the mixture, M_mix, is a function only of the amount of water in the dilution air or calibration air, as follows:

Where:

M_air = molar mass of dry air.

x_H2O = amount of H₂O in the dilution air or calibration air, determined as described in §1065.645.

M_H2O = molar mass of water.

Example:

M_air = 28.96559 g/mol

x_H2O = 0.0169 mol/mol

M_H2O = 18.01528 g/mol

M_mix = 28.96559 · (1- 0.0169) + 18.01528 · 0.0169

M_mix = 28.7805 g/mol

(v) For diluted exhaust and dilution air, you may assume a constant molar mass of the mixture, M_mix, for all calibration and all testing as long as your assumed molar mass differs no more than ±1% from the estimated minimum and maximum molar mass during calibration and testing.

You may assume this, using good engineering judgment, if you sufficiently control the amount of water in calibration air and in dilution air or if you remove sufficient water from both calibration air and dilution air. The following table gives examples of permissible ranges of dilution air dewpoint versus calibration air dewpoint:

(6) The following example illustrates the use of the governing equations to calculate C_d of an SSV flow meter at one reference flow meter value. Note that calculating C_d for a CFV flow meter would be similar, except that C_f would be determined from Table 2 of this section or calculated iteratively using values of b and g as described in paragraph (c)(2) of this section.

Example:

n ̇_ref = 57.625 mol/s

Z = 1

M_mix = 28.7805 g/mol = 0.0287805 kg/mol

R = 8.314472 J/(mol · K) = 8.314472 (m ² · kg)/(s ² · mol · K)

T_in = 298.15 K

A_t = 0.01824 m ²

p_in = 99.132 kPa = 99132.0 Pa = 99132 kg/(m·s ²)

g = 1.399

b = 0.8

Δp = 2.312 kPa

C_f = 0.274

C_d = 0.982

(d) SSV calibration. Perform the following steps to calibrate an SSV flow meter:

(1) Calculate the Reynolds number, Re^#, for each reference molar flow rate, n _ref, using the throat diameter of the venturi, d_t. Because the dynamic viscosity, µ, is needed to compute Re^#, you may use your own fluid viscosity model to determine µ for your calibration gas (usually air), using good engineering judgment. Alternatively, you may use the Sutherland three-coefficient viscosity model to approximate µ, as shown in the following sample calculation for Re^#:

Where, using the Sutherland three-coefficient viscosity model as captured in Table 4 of this section:

Where:

µ₀ = Sutherland reference viscosity.

T₀ = Sutherland reference temperature.

S = Sutherland constant.

Example:

µ₀ = 1.716·10⁻⁵ kg/(m·s)

T₀ = 273 K

S = 111 K

µ = 1.838·10^-5 kg/(m·s)

M_mix = 28.7805 g/mol = 0.0287805 kg/mol

n _ref = 57.625 mol/s

d_t = 152.4 mm = 0.1524 m

T_in = 298.15 K

Re^# = 7.538·10⁵

(2) Create an equation for C_d as a function of Re^#, using paired values of the two quantities. The equation may involve any mathematical expression, including a polynomial or a power series. The following equation is an example of a commonly used mathematical expression for relating C_d and Re^#:

(3) Perform a least-squares regression analysis to determine the best-fit coefficients for the equation and calculate SEE as described in §1065.602. When using Eq. 1065.640-12, treat C_d as y and the radical term as y_ref and use Eq. 1065.602-12 to calculate SEE. When using another mathematical expression, use the same approach to substitute that expression into the numerator of Eq. 1065.602-12 and replace the 2 in the denominator with the number of coefficients in the mathematical expression.

(4) If the equation meets the criterion of SEE ≤ 0.5% · C_dmax, you may use the equation for the corresponding range of Re^#, as described in §1065.642.

(5) If the equation does not meet the specified statistical criterion, you may use good engineering judgment to omit calibration data points; however you must use at least seven calibration data points to demonstrate that you meet the criterion. For example, this may involve narrowing the range of flow rates for a better curve fit.

(6) Take corrective action if the equation does not meet the specified statistical criterion even after omitting calibration data points. For example, select another mathematical expression for the C_d versus Re^# equation, check for leaks, or repeat the calibration process. If you must repeat the calibration process, we recommend applying tighter tolerances to measurements and allowing more time for flows to stabilize.

(7) Once you have an equation that meets the specified statistical criterion, you may use the equation only for the corresponding range of Re^#.

(e) CFV calibration. Some CFV flow meters consist of a single venturi and some consist of multiple venturis, where different combinations of venturis are used to meter different flow rates. For CFV flow meters that consist of multiple venturis, either calibrate each venturi independently to determine a separate discharge coefficient, C_d, for each venturi, or calibrate each combination of venturis as one venturi. In the case where you calibrate a combination of venturis, use the sum of the active venturi throat areas as A_t, the square root of the sum of the squares of the active venturi throat diameters as d_t, and the ratio of the venturi throat to inlet diameters as the ratio of the square root of the sum of the active venturi throat diameters (d_t) to the diameter of the common entrance to all the venturis. (D). To determine the C_d for a single venturi or a single combination of venturis, perform the following steps:

(1) Use the data collected at each calibration set point to calculate an individual C_d for each point using Eq. 1065.640-4.

(2) Calculate the mean and standard deviation of all the C_d values according to Eqs. 1065.602-1 and 1065.602-2.

(3) If the standard deviation of all the C_d values is less than or equal to 0.3% of the mean C_d, use the mean C_d in Eq. 1065.642-4, and use the CFV only up to the highest venturi pressure ratio, r, measured during calibration using the following equation:

Where:

Δp_CFV = Differential static pressure; venturi inlet minus venturi outlet.

(4) If the standard deviation of all the C_d values exceeds 0.3% of the mean C_d, omit the C_d value corresponding to the data point collected at the highest r measured during calibration.

(5) If the number of remaining data points is less than seven, take corrective action by checking your calibration data or repeating the calibration process. If you repeat the calibration process, we recommend checking for leaks, applying tighter tolerances to measurements and allowing more time for flows to stabilize.

(6) If the number of remaining C_d values is seven or greater, recalculate the mean and standard deviation of the remaining C_d values.

(7) If the standard deviation of the remaining C_d values is less than or equal to 0.3% of the mean of the remaining C_d, use that mean C_d in Eq. 1065.642-4, and use the CFV values only up to the highest r associated with the remaining C_d.

(8) If the standard deviation of the remaining C_d still exceeds 0.3% of the mean of the remaining C_d values, repeat the steps in paragraph (e)(4) through (8) of this section.

[79 FR 23785, Apr. 28, 2014, as amended at 81 FR 74172, Oct. 25, 2016; 86 FR 34556, Jun. 29, 2021]

§1065.642 PDP, SSV, and CFV molar flow rate calculations.

This section describes the equations for calculating molar flow rates from various flow meters. After you calibrate a flow meter according to §1065.640, use the calculations described in this section to calculate flow during an emission test.

(a) PDP molar flow rate.(1) Based on the speed at which you operate the PDP for a test interval, select the corresponding slope, a_1, and intercept, a_0, as calculated in §1065.640, to calculate PDP molar flow rate,, as follows:

Where:

f_nPDP = pump speed.

V_rev = PDP volume pumped per revolution, as determined in paragraph (a)(2) of this section.

p_in = static absolute pressure at the PDP inlet.

R = molar gas constant.

T_in = absolute temperature at the PDP inlet.

(2) Calculate V_rev using the following equation:

p_out = static absolute pressure at the PDP outlet.

Example:

a₁ = 0.8405 (m ³/s)

f_nPDP = 12.58 r/s

P_out = 99.950 kPa

P_in = 98.575 kPa = 98575 Pa = 98575 kg/(m·s ²)

a₀ = 0.056 (m ³/r)

R = 8.314472 J/(mol·K) = 8.314472 (m ²·kg)/(s ²·mol·K)

T_in = 323.5 K

n ̇ = 29.428 mol/s

(b) SSV molar flow rate. Calculate SSV molar flow rate, n , as follows:

Where:

C_d = discharge coefficient, as determined based on the C_d versus Re^# equation in §1065.640(d)(2).

C_f = flow coefficient, as determined in §1065.640(c)(3)(ii).

A_t = venturi throat cross-sectional area.

p_in = static absolute pressure at the venturi inlet.

Z = compressibility factor.

M_mix = molar mass of gas mixture.

R = molar gas constant.

T_in = absolute temperature at the venturi inlet.

Example:

A_t = 0.01824 m²

p_in = 99.132 kPa = 99132 Pa = 99132 kg/(m·s²)

Z = 1

M_mix = 28.7805 g/mol = 0.0287805 kg/mol

R = 8.314472 J/(mol·K) = 8.314472 (m²·kg)/(s²·mol·K)

T_in = 298.15 K

Re^# = 7.232·10⁵

γ = 1.399

β = 0.8

Δp = 2.312 kPa

Using Eq. 1065.640-7:

r_ssv = 0.997

Using Eq. 1065.640-6:

C_f = 0.274

Using Eq. 1065.640-5:

C_d = 0.990

n = 58.173 mol/s

(c) CFV molar flow rate. If you use multiple venturis and you calibrate each venturi independently to determine a separate discharge coefficient, C_d (or calibration coefficient, K_v), for each venturi, calculate the individual molar flow rates through each venturi and sum all their flow rates to determine CFV flow rate, n ̇. If you use multiple venturis and you calibrated venturis in combination, calculate n ̇ using the sum of the active venturi throat areas as A_t, the square root of the sum of the squares of the active venturi throat diameters as d_t, and the ratio of the venturi throat to inlet diameters as the ratio of the square root of the sum of the active venturi throat diameters (d_t) to the diameter of the common entrance to all the venturis (D).

(1) To calculate n through one venturi or one combination of venturis, use its respective mean C_d and other constants you determined according to §1065.640 and calculate n as follows:

Where:

C_f = flow coefficient, as determined in §1065.640(c)(3).

Example:

C_d = 0.985

C_f = 0.7219

A_t = 0.00456 m²

p_in = 98.836 kPa = 98836 Pa = 98836 kg/(m·s²)

Z = 1

M_mix = 28.7805 g/mol = 0.0287805 kg/mol

R = 8.314472 J/(mol·K) = 8.314472 (m²·kg)/(s²·mol·K)

T_in = 378.15 K

n = 33.690 mol/s

(2) To calculate the molar flow rate through one venturi or a combination of venturis, you may use its respective mean, K_v, and other constants you determined according to §1065.640 and calculate its molar flow rate n ̇ during an emission test. Note that if you follow the permissible ranges of dilution air dewpoint versus calibration air dewpoint in Table 3 of §1065.640, you may set M_mix-cal and M_mix equal to 1. Calculate n ̇ as follows:

Where:

V_stdref = volume flow rate of the standard at reference conditions of 293.15 K and 101.325 kPa.

T_in-cal = venturi inlet temperature during calibration.

P_in-cal = venturi inlet pressure during calibration.

M_mix-cal = molar mass of gas mixture used during calibration.

M_mix = molar mass of gas mixture during the emission test calculated using Eq. 1065.640-9.

Example:

V_stdref = 0.4895 m ³

T_in-cal = 302.52 K

P_in-cal = 99.654 kPa = 99654 Pa = 99654 kg/(m·s ²)

p_in = 98.836 kPa = 98836 Pa = 98836 kg/(m·s ²)

p_std = 101.325 kPa = 101325 Pa = 101325 kg/(m·s ²)

M_mix-cal = 28.9656 g/mol = 0.0289656 kg/mol

M_mix = 28.7805 g/mol = 0.0287805 kg/mol

T_in = 353.15 K

T_std = 293.15 K

R = 8.314472 J/(mol·K) = 8.314472 (m ²·kg)/(s ²·mol·K)

n ̇ = 16.457 mol/s

[81 FR 74177, Oct. 25, 2016; 86 FR 34557, Jun. 29, 2021]

§1065.643 Carbon balance error verification calculations.

This section describes how to calculate quantities used in the carbon balance error verification described in §1065.543. Paragraphs (a) through (c) of this section describe how to calculate the mass of carbon for a test interval from carbon-carrying fluid streams, intake air into the system, and exhaust emissions, respectively. Paragraph (d) of this section describes how to use these carbon masses to calculate four different quantities for evaluating carbon balance error. Use rectangular or trapezoidal integration methods to calculate masses and amounts over a test interval from continuously measured or calculated mass and molar flow rates.

(a) Fuel and other fluids. Determine the mass of fuel, DEF, and other carbon-carrying fluid streams, other than intake air, flowing into the system, m_fluidj, for each test interval. Note that §1065.543 allows you to omit all flows other than fuel. You may determine the mass of DEF based on ECM signals for DEF flow rate. You may determine fuel mass during field testing based on ECM signals for fuel flow rate. Calculate the mass of carbon from the combined carbon-carrying fluid streams flowing into the system as follows:

Where:

j = an indexing variable that represents one carbon-carrying fluid stream.

N = total number of carbon-carrying fluid streams into the system over the test interval.

w_C = carbon mass fraction of the carbon-carrying fluid stream as determined in §1065.655(d).

m_fluid = the mass of the carbon-carrying fluid stream determined over the test interval.

Example:

N = 2

w_Cfuel = 0.869

w_CDEF = 0.065

m_fuel = 1119.6 g

m_DEF = 36.8 g

m_Cfluid = 0.869·1119.6 + 0.065·36.8 = 975.3 g

(b) Intake air. Calculate the mass of carbon in the intake air, m_Cair, for each test interval using one of the methods in this paragraph (b). The methods are listed in order of preference. Use the first method where all the inputs are available for your test configuration. For methods that calculate m_Cair based on the amount of CO₂ per mole of intake air, we recommend measuring intake air concentration, but you may calculate x_CO2int using Eq. 1065.655-10 and letting x_CO2intdry = 375 µmol/mol.

(1) Calculate m_Cair, using the following equation if you measure intake air flow:

Where:

M_C = molar mass of carbon.

n_int = measured amount of intake air over the test interval.

x_CO2int = amount of intake air CO₂ per mole of intake air.

Example:

M_C = 12.0107 g/mol

n_int = 62862 mol

x_CO2int = 369 µmol/mol = 0.000369 mol/mol

m_Cair = 12.0107·62862·0.000369 = 278.6 g

(2) Calculate m_Cair, using the following equation if you measure or calculate raw exhaust flow and you calculate chemical balance terms:

Where:

M_C = molar mass of carbon.

n_exh = calculated or measured amount of raw exhaust over the test interval.

x_H2Oexh = amount of H₂O in exhaust per mole of exhaust.

x_CO2int = amount of intake air CO₂ per mole of intake air.

x_dil/exhdry = amount of excess air per mole of dry exhaust. Note that excess air and intake air have the same composition, so x_CO2dil = x_CO2int and x_H2Odil = x_H2Oint for the chemical balance calculation for raw exhaust.

x_int/exhdry = amount of intake air required to produce actual combustion products per mole of dry exhaust.

Example:

M_C = 12.0107 g/mol

n_exh = 62862 mol

x_H2Oexh = 0.034 mol/mol

x_CO2int = 369 µmol/mol = 0.000369 mol/mol

x_dil/exhdry = 0.570 mol/mol

x_int/exhdry = 0.465 mol/mol

m_Cair = 12.0107·62862·(1 − 0.034)·0.000369·(0.570 + 0.465) = 278.6 g

(3) Calculate m_Cair, using the following equation if you measure raw exhaust flow:

Where:

M_C = molar mass of carbon.

n_exh = measured amount of raw exhaust over the test interval.

x_CO2int = amount of intake air CO₂ per mole of intake air.

Example:

M_C = 12.0107 g/mol

n_exh = 62862 mol

x_CO2int = 369 µmol/mol = 0.000369 mol/mol

m_Cair = 12.0107·62862·0.000369 = 278.6 g

(4) Calculate m_Cair, using the following equation if you measure diluted exhaust flow and dilution air flow:

Where:

M_C = molar mass of carbon.

n_dexh = measured amount of diluted exhaust over the test interval as determined in §1065.642.

n_dil = measured amount of dilution air over the test interval as determined in §1065.667(b).

x_CO2int = amount of intake air CO₂ per mole of intake air.

Example:

M_C = 12.0107 g/mol

n_dexh = 942930 mol

n_dil = 880068 mol

x_CO2int = 369 µmol/mol = 0.000369 mol/mol

m_Cair = 12.0107·(942930 − 880068)·0.000369 = 278.6 g

(5) Determined m_Cair based on ECM signals for intake air flow as described in paragraph (b)(1) of this section.

(6) If you measure diluted exhaust, determine m_Cair as described in paragraph (b)(4) of this section using a calculated amount of dilution air over the test interval as determined in §1065.667(d) instead of the measured amount of dilution air.

(c) Exhaust emissions. Calculate the mass of carbon in exhaust emissions, m_Cexh, for each test interval as follows:

Where:

M_C = molar mass of carbon.

m_CO2 = mass of CO₂ over the test interval as determined in §1065.650(c).

M_CO2 = molar mass of carbon dioxide.

m_CO = mass of CO over the test interval as determined in §1065.650(c).

M_CO = molar mass of carbon monoxide.

m_THC = mass of THC over the test interval as determined in §1065.650(c).

M_THC = effective C₁ molar mass of total hydrocarbon as defined in §1065.1005(f)(2).

Example:

M_C = 12.0107 g/mol

m_CO2 = 4567 g

M_CO2 = 44.0095 g/mol

m_CO = 0.803 g

M_CO = 28.0101 g/mol

m_THC = 0.537 g

M_THC = 13.875389 g/mol

(d) Carbon balance error quantities. Calculate carbon balance error quantities as follows:

(1) Calculate carbon mass absolute error, ε_aC, for a test interval as follows:

Where:

m_Cexh = mass of carbon in exhaust emissions over the test interval as determined in paragraph (d) of this section.

m_Cfluid = mass of carbon in all the carbon-carrying fluid streams flowing into the system over the test interval as determined in paragraph (a) of this section.

m_Cair = mass of carbon in the intake air flowing into the system over the test interval as determined in paragraph (b) of this section.

Example:

m_Cexh = 1247.2 g

m_Cfluid = 975.3 g

m_Cair = 278.6 g

ε_aC = 1247.2 − 975.3 − 278.6

ε_aC = −6.7 g

(2) Calculate carbon mass rate absolute error, ε_aCrate, for a test interval as follows:

Where:

t = duration of the test interval.

Example:

ε_aC = −6.7 g

t = 1202.2 s = 0.3339 hr

ε_aCrate = −20.065 g/hr

(3) Calculate carbon mass relative error, ε_rC, for a test interval as follows:

Example:

ε_aC = −6.7 g

m_Cfluid = 975.3 g

m_Cair = 278.6 g

ε_rC = −0.0053

(4) Calculate composite carbon mass relative error, ε_rCcomp, for a duty cycle with multiple test intervals as follows:

(i) Calculate ε_rCcomp using the following equation:

Where:

i = an indexing variable that represents one test interval.

N = number of test intervals.

WF = weighting factor for the test interval as defined in the standard-setting part.

m_Cexh = mass of carbon in exhaust emissions over the test interval as determined in paragraph (c) of this section.

m_Cfluid = mass of carbon in all the carbon-carrying fluid streams that flowed into the system over the test interval as determined in paragraph (a) of this section.

m_Cair = mass of carbon in the intake air that flowed into the system over the test interval as determined in paragraph (b) of this section.

t = duration of the test interval. For duty cycles with multiple test intervals of a prescribed duration, such as cold-start and hot-start transient cycles, set t = 1 for all test intervals. For discrete-mode steady-state duty cycles with multiple test intervals of varying duration, set t equal to the actual duration of each test interval.

(ii) The following example illustrates calculation of ε_rCcomp, for cold-start and hot-start transient cycles:

N = 2

WF₁ = ¹/₇

WF₂ = ⁶/₇

m_Cexh1 = 1255.3 g

m_Cexh2 = 1247.2 g

m_Cfluid1 = 977.8 g

m_Cfluid2 = 975.3 g

m_Cair1 = 280.2 g

m_Cair2 = 278.6 g

ε_rCcomp = −0.0049

(iii) The following example illustrates calculation of ε_rCcomp for multiple test intervals with varying duration, such as discrete-mode steady-state duty cycles:

N = 2

WF₁ = 0.85

WF₂ = 0.15

m_Cexh1 = 2.873 g

m_Cexh2 = 0.125 g

m_Cfluid1 = 2.864 g

m_Cfluid2 = 0.095 g

m_Cair1 = 0.023 g

m_Cair2 = 0.024 g

t₁ = 123 s

t₂ = 306 s

ε_rCcomp = −0.0047

[86 FR 34557, Jun. 29, 2021; 87 FR 65865, Oct. 26, 2022; 88 FR 4680, Jan. 24, 2023]

§1065.644 Vacuum-decay leak rate.

This section describes how to calculate the leak rate of a vacuum-decay leak verification, which is described in §1065.345(e). Use the following equation to calculate the leak rate, , and compare it to the criterion specified in §1065.345(e):

Eq. 1065.644-1

Where:

V_vac = geometric volume of the vacuum-side of the sampling system.

R = molar gas constant.

p₂ = vacuum-side absolute pressure at time t _2.

T₂ = vacuum-side absolute temperature at time t _2.

p₁ = vacuum-side absolute pressure at time t _1.

T₁ = vacuum-side absolute temperature at time t _1.

t₂ = time at completion of vacuum-decay leak verification test.

t₁ = time at start of vacuum-decay leak verification test.

Example:

V_vac = 2.0000 L = 0.00200 m ³

R = 8.314472 J/(mol·K) = 8.314472 (m ² ·kg)/(s ² ·mol·K)

p₂ = 50.600 kPa = 50600 Pa = 50600 kg/(m·s ²)

T₂ = 293.15 K

p₁ = 25.300 kPa = 25300 Pa = 25300 kg/(m·s ²)

T₁ = 293.15 K

t₂ = 10:57:35 a.m.

t₁ = 10:56:25 a.m.

[79 FR 23795, Apr. 28, 2014; 89 FR 29808, Apr. 22, 2024]

§1065.645 Amount of water in an ideal gas.

This section describes how to determine the amount of water in an ideal gas, which you need for various performance verifications and emission calculations. Use the equation for the vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending on whether you measure dewpoint or relative humidity, perform one of the calculations in paragraph (b) or (c) of this section. Paragraph (d) of this section provides an equation for determining dewpoint from relative humidity and dry bulb temperature measurements. The equations for the vapor pressure of water as presented in this section are derived from equations in “Saturation Pressure of Water on the New Kelvin Temperature Scale” (Goff, J.A., Transactions American Society of Heating and Air-Conditioning Engineers, Vol. 63, No. 1607, pages 347-354). Note that the equations were originally published to derive vapor pressure in units of atmospheres and have been modified to derive results in units of kPa by converting the last term in each equation.

(a) Vapor pressure of water. Calculate the vapor pressure of water for a given saturation temperature condition, T_sat, as follows, or use good engineering judgment to use a different relationship of the vapor pressure of water to a given saturation temperature condition:

(1) For humidity measurements made at ambient temperatures from (0 to 100)°C, or for humidity measurements made over super-cooled water at ambient temperatures from (−50 to 0)°C, use the following equation:

(2) For humidity measurements over ice at ambient temperatures from (-100 to 0)°C, use the following equation:

(b) Dewpoint. If you measure humidity as a dewpoint, determine the amount of water in an ideal gas, x_H20, as follows:

Where:

x_H20 = amount of water in an ideal gas.

p_H20 = water vapor pressure at the measured dewpoint, T_sat = T_dew.

p_abs = wet static absolute pressure at the location of your dewpoint measurement.

Example:

:

p_abs = 99.980 kPa

T_sat = T_dew = 9.5°C

Using Eq. 1065.645-1,

p_H20 = 1.186581 kPa

x_H2O = 1.186581/99.980

x_H2O = 0.011868 mol/mol

(c) Relative humidity. If you measure humidity as a relative humidity, RH, determine the amount of water in an ideal gas, x_H2O, as follows:

Where:

x_H2O = amount of water in an ideal gas.

RH = relative humidity.

p_H2O = water vapor pressure at 100% relative humidity at the location of your relative humidity measurement, T_sat = T_amb.

p_abs = wet static absolute pressure at the location of your relative humidity measurement.

Example:

RH = 50.77% = 0.5077

p_abs = 99.980 kPa

T_sat = T_amb = 20°C

Using Eq. 1065.645-1,

p_H2O = 2.3371 kPa

x_H2O = (0.5077 · 2.3371)/99.980

x_H2O = 0.011868 mol/mol

(d) Dewpoint determination from relative humidity and dry bulb temperature. This paragraph (d) describes how to calculate dewpoint temperature from relative humidity, RH. This is based on “ITS-90 Formulations for Vapor Pressure, Frostpoint Temperature, Dewpoint Temperature, and Enhancement Factors in the Range −100 to + 100°C” (Hardy, B., The Proceedings of the Third International Symposium on Humidity & Moisture, Teddington, London, England, April 1998). Calculate p_H20sat as described in paragraph (a) of this section based on setting T_sat equal to T_amb. Calculate p_H20scaled by multiplying p_H20sat by RH. Calculate the dewpoint, T_dew, from p_H20 using the following equation:

Where:

ln(p_H2O) = the natural log of p_H2Oscaled, which is the water vapor pressure scaled to the relative humidity at the location of the relative humidity measurement, T_sat = T_amb

Example:

RH = 39.61% = 0.3961

T_{sat = Tamb} = 20.00°C = 293.15K

Using Eq. 1065.645-1,

p_H2Osat = 2.3371 kPa

p_H2Oscaled = (0.3961 · 2.3371) = 0.925717 kPa = 925.717 Pa

[73 FR 37327, June 30, 2008, as amended at 73 FR 59331, Oct. 8, 2008; 75 FR 23048, Apr. 30, 2010; 76 FR 57456, Sept. 15, 2011;79 FR 23796, Apr. 28, 2014; 81 FR 74179, Oct. 25, 2016]

§1065.650 Emission calculations.

(a) General. Calculate brake-specific emissions over each applicable duty cycle or test interval. For test intervals with zero work (or power), calculate the emission mass (or mass rate), but do not calculate brake-specific emissions. Unless specified otherwise, for the purposes of calculating and reporting emission mass (or mass rate), do not alter any negative values of measured or calculated quantities. You may truncate negative values in chemical balance quantities listed in §1065.655(c) to facilitate convergence. For duty cycles with multiple test intervals, refer to the standard-setting part for calculations you need to determine a composite result, such as a calculation that weights and sums the results of individual test intervals in a duty cycle. If the standard-setting part does not include those calculations, use the equations in paragraph (g) of this section. This section is written based on rectangular integration, where each indexed value (i.e., “ _i ”) represents (or approximates) the mean value of the parameter for its respective time interval, delta-t. You may also integrate continuous signals using trapezoidal integration consistent with good engineering judgment.

(b) Brake-specific emissions over a test interval. We specify three alternative ways to calculate brake-specific emissions over a test interval, as follows:

(1) For any testing, you may calculate the total mass of emissions, as described in paragraph (c) of this section, and divide it by the total work generated over the test interval, as described in paragraph (d) of this section, using the following equation:

Example:

m_NOx = 64.975 g

W = 25.783 kW · hr

e_NOx = 64.975/25.783

e_NOx = 2.520 g/(kW · hr)

(2) For discrete-mode steady-state testing, you may calculate the brake-specific emissions over a test interval using the ratio of emission mass rate to power, as described in paragraph (e) of this section, using the following equation:

(3) For field testing, you may calculate the ratio of total mass to total work, where these individual values are determined as described in paragraph (f) of this section. You may also use this approach for laboratory testing, consistent with good engineering judgment. Good engineering judgment dictates that this method not be used if there are any work flow paths described in §1065.210 that cross the system boundary, other than the primary output shaft (crankshaft). This is a special case in which you use a signal linearly proportional to raw exhaust molar flow rate to determine a value proportional to total emissions. You then use the same linearly proportional signal to determine total work using a chemical balance of fuel, DEF, intake air, and exhaust as described in §1065.655, plus information about your engine's brake-specific fuel consumption. Under this method, flow meters need not meet accuracy specifications, but they must meet the applicable linearity and repeatability specifications in subpart D or J of this part. The result is a brake-specific emission value calculated as follows:

Example:

m ̃ = 805.5 g

W ̃ = 52.102 kW · hr

e_CO = 805.5/52.102

e_CO = 2.520 g/(kW · hr)

(c) Total mass of emissions over a test interval. To calculate the total mass of an emission, multiply a concentration by its respective flow. For all systems, make preliminary calculations as described in paragraph (c)(1) of this section to correct concentrations. Next, use the method in paragraphs (c)(2) through (4) of this section that is appropriate for your system. Finally, if necessary, calculate the mass of NMHC as described in paragraph (c)(5) of this section for all systems. Calculate the total mass of emissions as follows:

(1) Concentration corrections. Perform the following sequence of preliminary calculations on recorded concentrations:

(i) Use good engineering judgment to time-align flow and concentration data to match transformation time, t₅₀, to within ±1 s.

(ii) Correct all gaseous emission analyzer concentration readings, including continuous readings, sample bag readings, and dilution air background readings, for drift as described in §1065.672. Note that you must omit this step where brake-specific emissions are calculated without the drift correction for performing the drift validation according to §1065.550(b). When applying the initial THC and CH ₄ contamination readings according to §1065.520(g), use the same values for both sets of calculations. You may also use as-measured values in the initial set of calculations and corrected values in the drift-corrected set of calculations as described in §1065.520(g)(7).

(iii) Correct all THC and CH₄ concentrations for initial contamination as described in §1065.660(a), including continuous readings, sample bags readings, and dilution air background readings.

(iv) Correct all concentrations measured on a “dry” basis to a “wet” basis, including dilution air background concentrations, as described in §1065.659.

(v) Calculate all NMHC and CH₄ concentrations, including dilution air background concentrations, as described in §1065.660.

(vi) For emission testing with an oxygenated fuel, calculate any HC concentrations, including dilution air background concentrations, as described in §1065.665. See subpart I of this part for testing with oxygenated fuels.

(vii) Correct all the NO_X concentrations, including dilution air background concentrations, for intake-air humidity as described in §1065.670.

(2) Continuous sampling. For continuous sampling, you must frequently record a continuously updated concentration signal. You may measure this concentration from a changing flow rate or a constant flow rate (including discrete-mode steady-state testing), as follows:

(i) Varying flow rate. If you continuously sample from a varying exhaust flow rate, time align and then multiply concentration measurements by the flow rate from which you extracted it. We consider the following to be examples of varying flows that require a continuous multiplication of concentration times molar flow rate: raw exhaust, exhaust diluted with a constant flow rate of dilution air, and CVS dilution with a CVS flow meter that does not have an upstream heat exchanger or electronic flow control. This multiplication results in the flow rate of the emission itself. Integrate the emission flow rate over a test interval to determine the total emission. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the mass of the emission, m. Calculate m for continuous sampling with variable flow using the following equations:

Where:

Example:

M_NMHC = 13.875389 g/mol

N = 1200

x_NMHC1 = 84.5 µmol/mol = 84.5 · 10 ⁻⁶ mol/mol

x_NMHC2 = 86.0 µmol/mol = 86.0 · 10 ⁻⁶ mol/mol

n _exh1 = 2.876 mol/s

n _exh2 = 2.224 mol/s

ƒ _record = 1 Hz

Using Eq. 1065.650-5,

Δ t = 1/1 = 1 s

m_NMHC = 13.875389 · (84.5 · 10 ⁻⁶ · 2.876 + 86.0 · 10 ⁻⁶ · 2.224 + . . . + x_NMHC1200 · n _exh) · 1

m_NMHC = 25.23 g

(ii) Constant flow rate. If you continuously sample from a constant exhaust flow rate, use the same emission calculations described in paragraph (c)(2)(i) of this section or calculate the mean or flow-weighted concentration recorded over the test interval and treat the mean as a batch sample, as described in paragraph (c)(3)(ii) of this section. We consider the following to be examples of constant exhaust flows: CVS diluted exhaust with a CVS flowmeter that has either an upstream heat exchanger, electronic flow control, or both.

(3) Batch sampling. For batch sampling, the concentration is a single value from a proportionally extracted batch sample (such as a bag, filter, impinger, or cartridge). In this case, multiply the mean concentration of the batch sample by the total flow from which the sample was extracted. You may calculate total flow by integrating a varying flow rate or by determining the mean of a constant flow rate, as follows:

(i) Varying flow rate. If you collect a batch sample from a varying exhaust flow rate, extract a sample proportional to the varying exhaust flow rate. We consider the following to be examples of varying flows that require proportional sampling: raw exhaust, exhaust diluted with a constant flow rate of dilution air, and CVS dilution with a CVS flow meter that does not have an upstream heat exchanger or electronic flow control. Integrate the flow rate over a test interval to determine the total flow from which you extracted the proportional sample. Multiply the mean concentration of the batch sample by the total flow from which the sample was extracted to determine the total emission. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the total emission mass, m. In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of exhaust, simply multiply it by the total flow. The result is the total mass of PM, m_PM. Calculate m for each constituent as follows:

(A) Calculate m for measuring gaseous emission constituents with sampling that results in a molar concentration, x , using the following equation:

Example:

M_NO = 46.0055 g/mol

N = 9000

x = 85.6 µmol/mol = 85.6 · 10 ⁻⁶ mol/mol

n _dexh1 = 25.534 mol/s

n _dexh2 = 26.950 mol/s

ƒ _record = 5 Hz

Using Eq. 1065.650-5:

Δ t = 1/5 = 0.2 s

m_NO 46.0055 · 85.6 · 10 ⁻⁶ · (25.534 + 26.950+ . . . +

n _exh9000) · 0.2

m_NO = 4.201 g

(B) Calculate m for sampling PM or any other analysis of a batch sample that yields a mass per mole of exhaust, M , using the following equation:

(ii) Proportional or constant flow rate. If you batch sample from a constant exhaust flow rate, extract a sample at a proportional or constant flow rate. We consider the following to be examples of constant exhaust flows: CVS diluted exhaust with a CVS flow meter that has either an upstream heat exchanger, electronic flow control, or both. Determine the mean molar flow rate from which you extracted the sample. Multiply the mean concentration of the batch sample by the mean molar flow rate of the exhaust from which the sample was extracted to determine the total emission and multiply the result by the time of the test interval. If the total emission is a molar quantity, convert this quantity to a mass by multiplying it by its molar mass, M. The result is the total emission mass, m. In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of exhaust, simply multiply it by the total flow, and the result is the total mass of PM, m_PM. Calculate m for each constituent as follows:

(A) Calculate m for measuring gaseous emission constituents with sampling that results in a molar concentration, x , using the following equation:

(B) Calculate m for sampling PM or any other analysis of a batch sample that yields a mass per mole of exhaust, M , using the following equation:

(C) The following example illustrates a calculation of m_PM :

M _PM = 144.0 µg/mol = 144.0 · 10 ⁻⁶ g/mol

n _dexh = 57.692 mol/s

Δ t = 1200 s

m_PM = 144.0 · 10 ⁻⁶ · 57.692 · 1200

m_PM = 9.9692 g

Example:

m_PMdil = 6.853 g

DR = 6:1

m_PM = 6.853 · 6

m_PM = 41.118 g

(4) Additional provisions for diluted exhaust sampling; continuous or batch. The following additional provisions apply for sampling emissions from diluted exhaust: (i) For sampling with a constant dilution ratio, DR, of diluted exhaust versus exhaust flow (e.g., secondary dilution for PM sampling), calculate m using the following equation:

(i) (i) For sampling with a constant dilution ratio, DR, of diluted exhaust versus exhaust flow (e.g., secondary dilution for PM sampling), calculate m using the following equation:

(ii) For continuous or batch sampling, you may measure background emissions in the dilution air. You may then subtract the measured background emissions, as described in § 1065.667.

(5) Mass of NMHC. Compare the corrected mass of NMHC to corrected mass of THC. If the corrected mass of NMHC is greater than 0.98 times the corrected mass of THC, take the corrected mass of NMHC to be 0.98 times the corrected mass of THC. If you omit the NMHC calculations as described in § 1065.660(b)(1), take the corrected mass of NMHC to be 0.98 times the corrected mass of THC.

(6) Mass of NMNEHC. Determine the mass of NMNEHC using one of the following methods:

(i) If the test fuel has less than 0.010 mol/mol of ethane and you omit the NMNEHC calculations as described in §1065.660(c)(1), take the corrected mass of NMNEHC to be 0.95 times the corrected mass of NMHC.

(ii) If the test fuel has at least 0.010 mol/mol of ethane and you omit the NMNEHC calculations as described in §1065.660(c)(1), take the corrected mass of NMNEHC to be 1.0 times the corrected mass of NMHC.

(d) Total work over a test interval. To calculate the total work from the engine over a test interval, add the total work from all the work paths described in §1065.210 that cross the system boundary including electrical energy/work, mechanical shaft work, and fluid pumping work. For all work paths, except the engine's primary output shaft (crankshaft), the total work for the path over the test interval is the integration of the net work flow rate (power) out of the system boundary. When energy/work flows into the system boundary, this work flow rate signal becomes negative; in this case, include these negative work rate values in the integration to calculate total work from that work path. Some work paths may result in a negative total work. Include negative total work values from any work path in the calculated total work from the engine rather than setting the values to zero. The rest of this paragraph (d) describes how to calculate total work from the engine's primary output shaft over a test interval. Before integrating power on the engine's primary output shaft, adjust the speed and torque data for the time alignment used in §1065.514(c). Any advance or delay used on the feedback signals for cycle validation must also be used for calculating work. Account for work of accessories according to §1065.110. Exclude any work during cranking and starting. Exclude work during actual motoring operation (negative feedback torques), unless the engine was connected to one or more energy storage devices. Examples of such energy storage devices include hybrid powertrain batteries and hydraulic accumulators, like the ones illustrated in Figure 1 of §1065.210. Exclude any work during reference zero-load idle periods (0% speed or idle speed with 0 N·m reference torque). Note, that there must be two consecutive reference zero load idle points to establish a period where the zero-load exclusion applies. Include work during idle points with simulated minimum torque such as Curb Idle Transmissions Torque (CITT) for automatic transmissions in “drive”. The work calculation method described in paragraphs (d)(1) though (7) of this section meets the requirements of this paragraph (d) using rectangular integration. You may use other logic that gives equivalent results. For example, you may use a trapezoidal integration method as described in paragraph (d)(8) of this section.

(1) Time align the recorded feedback speed and torque values by the amount used in §1065.514(c).

(2) Calculate shaft power at each point during the test interval by multiplying all the recorded feedback engine speeds by their respective feedback torques.

(3) Adjust (reduce) the shaft power values for accessories according to §1065.110.

(4) Set all power values during any cranking or starting period to zero. See §1065.525 for more information about engine cranking.

(5) Set all negative power values to zero, unless the engine was connected to one or more energy storage devices. If the engine was tested with an energy storage device, leave negative power values unaltered.

(6) Set all power values to zero during idle periods with a corresponding reference torque of 0 N · m.

(7) Integrate the resulting values for power over the test interval. Calculate total work as follows:

Where:

W = total work from the primary output shaft.

P = instantaneous power from the primary output shaft over an interval i.

Example:

N = 9000

ƒ _n1 = 1800.2 r/min

ƒ _n2 = 1805.8 r/min

T₁ = 177.23 N·m

T₂ = 175.00 N·m

C_rev = 2· π rad/r

C_t1 = 60 s/min

C_p = 1000 (N·m·rad/s)/kW

ƒ _record = 5 Hz

C_t2 = 3600 s/hr

P₁ = 33.41 kW

P₂ = 33.09 kW

Using Eq. 1065.650-5:

Δ t = 1/5 = 0.2 s

W = 16.875 kW·hr

(8) You may use a trapezoidal integration method instead of the rectangular integration described in this paragraph (d). To do this, you must integrate the fraction of work between points where the torque is positive. You may assume that speed and torque are linear between data points. You may not set negative values to zero before running the integration.

(e) Steady-state mass rate divided by power. To determine steady-state brake-specific emissions for a test interval as described in paragraph (b)(2) of this section, calculate the mean steady-state mass rate of the emission, m ̇̅, and the mean steady-state power, P ͞ as follows:

(1) To calculate, m , multiply its mean concentration, x , by its corresponding mean molar flow rate, n . If the result is a molar flow rate, convert this quantity to a mass rate by multiplying it by its molar mass, M. The result is the mean mass rate of the emission, m . In the case of PM emissions, where the mean PM concentration is already in units of mass per mole of exhaust, simply multiply it by the mean molar flow rate, n . The result is the mass rate of PM, m _PM . Calculate m using the following equation:

(2) To calculate an engine's mean steady-state total power, P , add the mean steady-state power from all the work paths described in §1065.210 that cross the system boundary including electrical power, mechanical shaft power, and fluid pumping power. For all work paths, except the engine's primary output shaft (crankshaft), the mean steady-state power over the test interval is the integration of the net work flow rate (power) out of the system boundary divided by the period of the test interval. When power flows into the system boundary, the power/work flow rate signal becomes negative; in this case, include these negative power/work rate values in the integration to calculate the mean power from that work path. Some work paths may result in a negative mean power. Include negative mean power values from any work path in the mean total power from the engine rather than setting these values to zero. The rest of this paragraph (e)(2) describes how to calculate the mean power from the engine's primary output shaft. Calculate P using Eq. 1065.650-13, noting that P , f _n , and T refer to mean power, mean rotational shaft frequency, and mean torque from the primary output shaft. Account for the power of simulated accessories according to §1065.110 (reducing the mean primary output shaft power or torque by the accessory power or torque). Set the power to zero during actual motoring operation (negative feedback torques), unless the engine was connected to one or more energy storage devices. Examples of such energy storage devices include hybrid powertrain batteries and hydraulic accumulators, like the ones denoted “Acc.” and “Batt.” as illustrated in Figure 1 of §1065.210. Set the power to zero for modes with a zero reference load (0 N·m reference torque or 0 kW reference power). Include power during idle modes with simulated minimum torque or power.

(3) Divide emission mass rate by power to calculate a brake-specific emission result as described in paragraph (b)(2) of this section.

(4) The following example shows how to calculate mass of emissions using mean mass rate and mean power:

M_CO = 28.0101 g/mol

x ͞_CO = 12.00 mmol/mol = 0.01200 mol/mol

n ̇̅ = 1.530 mol/s

f ͞_n = 3584.5 r/min = 375.37 rad/s

T ͞ = 121.50 N · m

m ̇̅ = 28.0101 · 0.01200 · 1.530

m ̇̅ = 0.514 g/s = 1850.4 g/hr

P ͞ = 121.5 · 375.37

P ͞ = 45607 W

P ͞ = 45.607 kW

e_CO = 1850.4/45.61

e_CO = 40.57 g/(kW · hr)

(f) Ratio of total mass of emissions to total work. To determine brake-specific emissions for a test interval as described in paragraph (b)(3) of this section, calculate a value proportional to the total mass of each emission. Divide each proportional value by a value that is similarly proportional to total work.

(1) Total mass. To determine a value proportional to the total mass of an emission, determine total mass as described in paragraph (c) of this section, except substitute for the molar flow rate, n , or the total flow, n, with a signal that is linearly proportional to molar flow rate, n , or linearly proportional to total flow, n , as follows:

(2) Total work. To calculate a value proportional to total work over a test interval, integrate a value that is proportional to power. Use information about the brake-specific fuel consumption of your engine, e_fuel, to convert a signal proportional to fuel flow rate to a signal proportional to power. To determine a signal proportional to fuel flow rate, divide a signal that is proportional to the mass rate of carbon products by the fraction of carbon in your fuel, w_C. You may use a measured w_C or you may use default values for a given fuel as described in §1065.655(e). Calculate the mass rate of carbon from the amount of carbon and water in the exhaust, which you determine with a chemical balance of fuel, DEF, intake air, and exhaust as described in §1065.655. In the chemical balance, you must use concentrations from the flow that generated the signal proportional to molar flow rate, n , in paragraph (e)(1) of this section. Calculate a value proportional to total work as follows:

Where:

(3) Brake-specific emissions. Divide the value proportional to total mass by the value proportional to total work to determine brake-specific emissions, as described in paragraph (b)(3) of this section.

(4) Example: The following example shows how to calculate mass of emissions using proportional values:

N = 3000

ƒ_record = 5 Hz

e_fuel = 285 g/(kW·hr)

w_fuel = 0.869 g/g

M_C = 12.0107 g/mol

n ̇₁ = 3.922 mol/s = 14119.2 mol/hr

x_Ccombdry1 = 91.634 mmol/mol = 0.091634 mol/mol

x_H2Oexh1 = 27.21 mmol/mol = 0.02721 mol/mol

Using Eq. 1065.650-5,

Δt = 0.2 s

W ̃ = 5.09 (kW·hr)

(g) Brake-specific emissions over a duty cycle with multiple test intervals. The standard-setting part may specify a duty cycle with multiple test intervals, such as with discrete-mode steady-state testing. Unless we specify otherwise, calculate composite brake-specific emissions over the duty cycle as described in this paragraph (g). If a measured mass (or mass rate) is negative, set it to zero for calculating composite brake-specific emissions, but leave it unchanged for drift validation. In the case of calculating composite brake-specific emissions relative to a combined emission standard (such as a NO_X + NMHC standard), change any negative mass (or mass rate) values to zero for a particular pollutant before combining the values for the different pollutants.

(1) Use the following equation to calculate composite brake-specific emissions for duty cycles with multiple test intervals all with prescribed durations, such as cold-start and hot-start transient cycles:

Where:

i = test interval number.

N = number of test intervals.

WF = weighting factor for the test interval as defined in the standard-setting part.

m = mass of emissions over the test interval as determined in paragraph (c) of this section.

W = total work from the engine over the test interval as determined in paragraph (d) of this section.

Example:

N = 2

WF₁ = 0.1428

WF₂ = 0.8572

m₁ = 70.125 g

m₂ = 64.975 g

W₁ = 25.783 kW·hr

W₂ = 25.783 kW·hr

e_NOxcomp = 2.548 g/kW·hr

(2) Calculate composite brake-specific emissions for duty cycles with multiple test intervals that allow use of varying duration, such as discrete-mode steady-state duty cycles, as follows:

(i) Use the following equation if you calculate brake-specific emissions over test intervals based on total mass and total work as described in paragraph (b)(1) of this section:

Where:

i = test interval number.

N = number of test intervals.

WF = weighting factor for the test interval as defined in the standard-setting part.

m = mass of emissions over the test interval as determined in paragraph (c) of this section.

W = total work from the engine over the test interval as determined in paragraph (d) of this section.

t = duration of the test interval.

Example:

N = 2

WF₁ = 0.85

WF₂ = 0.15

m₁ = 1.3753 g

m₂ = 0.4135 g

t₁ = 120 s

t₂ = 200 s

W₁ = 2.8375 kW · hr

W₂ = 0.0 kW · hr

e_NOxcomp = 0.5001 g/kW·hr

(ii) Use the following equation if you calculate brake-specific emissions over test intervals based on the ratio of mass rate to power as described in paragraph (b)(2) of this section:

Where:

i = test interval number.

N = number of test intervals.

WF = weighting factor for the test interval as defined in the standard-setting part.

m = mean steady-state mass rate of emissions over the test interval as determined in paragraph (e) of this section.

p = mean steady-state power over the test interval as described in paragraph (e) of this section.

Example:

N = 2

WF₁ = 0.85

WF₂ = 0.15

m ₁ = 2.25842 g/hr

m ₂ = 0.063443 g/hr

P ₁ = 4.5383 kW

P ₂ = 0.0 kW

e_NOxcomp = 0.5001 g/kW·hr

_eNOcomp = 0.5001 g/kW·hr

(h) Rounding. Round the final brake-specific emission values to be compared to the applicable standard only after all calculations are complete (including any drift correction, applicable deterioration factors, adjustment factors, and allowances) and the result is in g/(kW · hr) or units equivalent to the units of the standard, such as g/(hp · hr). See the definition of “Round” in §1065.1001.

[73 FR 37328, June 30, 2008, as amended at 73 FR 59332, Oct. 8, 2008; 75 FR 23048, Apr. 30, 2010; 76 FR 57457, Sept. 15, 2011;79 FR 23799, Apr. 28, 2014; 80 FR 9118, Feb. 19, 2015; 81 FR 74180, Oct. 25, 2016; 86 FR 34560, Jun. 29, 2021; 87 FR 65866, Oct. 26, 2022; 88 FR 4681, Jan. 24, 2023; 89 FR 29808, Apr. 22, 2024]

§1065.655 Carbon-based chemical balances of fuel, DEF, intake air, and exhaust.

(a) General. Chemical balances of fuel, intake air, and exhaust may be used to calculate flows, the amount of water in their flows, and the wet concentration of constituents in their flows. See §1065.520(f) for information about when to use this carbon-based chemical balance procedure. With one flow rate of either fuel, intake air, or exhaust, you may use chemical balances to determine the flows of the other two. For example, you may use chemical balances along with either intake air or fuel flow to determine raw exhaust flow. Note that chemical balance calculations allow measured values for the flow rate of diesel exhaust fluid for engines with urea-based selective catalytic reduction.

(b) Procedures that require chemical balances. We require chemical balances when you determine the following:

(1) A value proportional to total work, W ̃, when you choose to determine brake-specific emissions as described in §1065.650(f).

(2) Raw exhaust molar flow rate either from measured intake air molar flow rate or from fuel mass flow rate as described in paragraph (f) of this section.

(3) Raw exhaust molar flow rate from measured intake air molar flow rate and dilute exhaust molar flow rate, as described in paragraph (g) of this section.

(4) The amount of water in a raw or diluted exhaust flow, x_H2Oexh, when you do not measure the amount of water to correct for the amount of water removed by a sampling system. Note that you may not use the water measurement methods in §1065.257 to determine x_H2Oexh. Correct for removed water according to §1065.659.

(5) The calculated total dilution air flow when you do not measure dilution air flow to correct for background emissions as described in §1065.667(c) and (d).

(c) Chemical balance procedure. The calculations for a chemical balance involve a system of equations that require iteration. We recommend using a computer to solve this system of equations. You must guess the initial values of up to three quantities: the amount of water in the measured flow, x_H2Oexh, fraction of dilution air in diluted exhaust, x_dil/exh, and the amount of products on a C ₁ basis per dry mole of dry measured flow, x_Ccombdry. You may use time-weighted mean values of intake air humidity and dilution air humidity in the chemical balance; as long as your intake air and dilution air humidities remain within tolerances of ±0.0025 mol/mol of their respective mean values over the test interval. For each emission concentration, x, and amount of water, x_H2Oexh, you must determine their completely dry concentrations, x_dry and x_H2Oexhdry. You must also use your fuel mixture's atomic hydrogen-to-carbon ratio, α, oxygen-to-carbon ratio, β, sulfur-to-carbon ratio, γ, and nitrogen-to-carbon ratio, δ; you may optionally account for diesel exhaust fluid (or other fluids injected into the exhaust), if applicable. You may calculate α, β, γ, and δ based on measured fuel composition or based on measured fuel and diesel exhaust fluid (or other fluids injected into the exhaust) composition together, as described in paragraph (e) of this section. You may alternatively use any combination of default values and measured values as described in paragraph (e) of this section. Use the following steps to complete a chemical balance:

(1) Convert your measured concentrations such as, x_CO2meas, x_NOmeas, and x_H2Oint, to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: x_H2OxCO2meas, x_H2OxNOmeas, and x_H2Oint. If the amount of water present during a “wet” measurement is the same as the unknown amount of water in the exhaust flow, x_H2Oexh, iteratively solve for that value in the system of equations. If you measure only total NO_X and not NO and NO₂ separately, use good engineering judgment to estimate a split in your total NO_X concentration between NO and NO₂ for the chemical balances. For example, if you measure emissions from a stoichiometric spark-ignition engine, you may assume all NO_X is NO. For a compression-ignition engine, you may assume that your molar concentration of NO_X, x_NOx, is 75% NO and 25% NO₂. For NO₂ storage aftertreatment systems, you may assume x_NOx is 25% NO and 75% NO₂. Note that for calculating the mass of NO_X emissions, you must use the molar mass of NO₂ for the effective molar mass of all NO_X species, regardless of the actual NO₂ fraction of NO_X.

(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for x_H2Oexh, x_Ccombdry, and x_dil/exh. Use good engineering judgment to guess initial values for x_H2Oexh, x_Ccombdry, and x_dil/exh. We recommend guessing an initial amount of water that is about twice the amount of water in your intake or dilution air. We recommend guessing an initial value of x_Ccombdry as the sum of your measured CO₂, CO, and THC values. We also recommend guessing an initial x_dil/exh between 0.75 and 0.95, such as 0.8. Iterate values in the system of equations until the most recently updated guesses are all within ±1% of their respective most recently calculated values.

(3) Use the following symbols and subscripts in the equations for performing the chemical balance calculations in this paragraph (c):

(4) Use the following equations to iteratively solve for x_dil/exh, x_H2Oexh, and x_Ccombdry:

(5) The following example is a solution for x_dil/exh,x, x_H2Oexh, and x_Ccombdry using the equations in paragraph (c)(4) of this section:

a = 1.8

b = 0.05

g = 0.0003

d = 0.0001

(d) Carbon mass fraction of fuel. Determine carbon mass fraction of fuel, w_C, based on the fuel properties as determined in paragraph (e) of this section, optionally accounting for diesel exhaust fluid's contribution to α, β, γ, and δ, or other fluids injected into the exhaust, if applicable (for example, the engine is equipped with an emission control system that utilizes DEF). Calculate w_C using the following equation:

Where:

w_C = carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluids.

M_C = molar mass of carbon.

a = atomic hydrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids.

M_H = molar mass of hydrogen.

b = atomic oxygen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids.

M_O = molar mass of oxygen.

g = atomic sulfur-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids.

M_S = molar mass of sulfur.

d = atomic nitrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids.

M_N = molar mass of nitrogen.

Example:

a = 1.8

b = 0.05

g = 0.0003

d = 0.0001

M_C = 12.0107

M_H = 1.00794

M_O = 15.9994

M_S = 32.065

M_N = 14.0067

w_C = 0.8206

(e) Fuel and diesel exhaust fluid composition. Determine fuel and diesel exhaust fluid composition represented by α, β, γ, and δ as described in this paragraph (e). When using measured fuel or diesel exhaust fluid properties, you must determine values for α and β in all cases. If you determine compositions based on measured values and the default value listed in Table 2 of this section is zero, you may set γ and δ to zero; otherwise determine γ and δ (along with α and β) based on measured values. Determine elemental mass fractions and values for α, β, γ, and δ as follows:

(1) For liquid fuels, use the default values for α, β, γ, and δ in table 2 of this section or determine mass fractions of liquid fuels for calculation of α, β, γ, and δ as follows:

(i) Determine the carbon and hydrogen mass fractions according to ASTM D5291 (incorporated by reference, see §1065.1010). When using ASTM D5291 to determine carbon and hydrogen mass fractions of gasoline (with or without blended ethanol), use good engineering judgment to adapt the method as appropriate. This may include consulting with the instrument manufacturer on how to test high-volatility fuels. Allow the weight of volatile fuel samples to stabilize for 20 minutes before starting the analysis; if the weight still drifts after 20 minutes, prepare a new sample). Retest the sample if the carbon, hydrogen, oxygen, sulfur, and nitrogen mass fractions do not add up to a total mass of 100 ±0.5%; you may assume oxygen has a zero mass contribution for this specification for diesel fuel and neat (E0) gasoline. You may also assume that sulfur and nitrogen have a zero mass contribution for this specification for all fuels except residual fuel blends.

(ii) Determine oxygen mass fraction of gasoline (with or without blended ethanol) according to ASTM D5599 (incorporated by reference, see §1065.1010). For all other liquid fuels, determine the oxygen mass fraction using good engineering judgment.

(iii) Determine the nitrogen mass fraction according to ASTM D4629 or ASTM D5762 (incorporated by reference, see §1065.1010) for all liquid fuels. Select the correct method based on the expected nitrogen content.

(iv) Determine the sulfur mass fraction according to subpart H of this part.

(2) For gaseous fuels and diesel exhaust fluid, use the default values for α, β, γ, and δ in Table 2 of this section, or use good engineering judgment to determine those values based on measurement.

(3) For nonconstant fuel mixtures, you must account for the varying proportions of the different fuels. This paragraph (e)(3) generally applies for dual-fuel and flexible-fuel engines, but it also applies if diesel exhaust fluid is injected in a way that is not strictly proportional to fuel flow. Account for these varying concentrations either with a batch measurement that provides averaged values to represent the test interval, or by analyzing data from continuous mass rate measurements. Application of average values from a batch measurement generally applies to situations where one fluid is a minor component of the total fuel mixture, for example dual-fuel and flexible-fuel engines with diesel pilot injection, where the diesel pilot fuel mass is less than 5% of the total fuel mass and diesel exhaust fluid injection; consistent with good engineering judgment.

(4) Calculate α, β, γ, and δ as described in this paragraph (e)(4). If your fuel mixture contains fuels other than carbon-containing fuels, then calculate those fuels' mass fractions w_C , w_H , w_O , w_S , and w_N as described in §1065.656(d). Calculate α, β, γ, and δ using the following equations:

Eq. 1065.655-20

Eq. 1065.655-21

Eq. 1065.655-22

Eq. 1065.655-23

Where:

N = total number of fuels and injected fluids over the duty cycle.

j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.

m _j = the mass flow rate of the fuel or any injected fluid j. For applications using a single fuel and no DEF fluid, set this value to 1. For batch measurements, divide the total mass of fuel over the test interval duration to determine a mass rate.

w_Hmeas = hydrogen mass fraction of fuel or any injected fluid j.

w_Cmeas = carbon mass fraction of fuel or any injected fluid j.

w_Omeas = oxygen mass fraction of fuel or any injected fluid j.

w_Smeas = sulfur mass fraction of fuel or any injected fluid j.

w_Nmeas = nitrogen mass fraction of fuel or any injected fluid j.

Example:

N = 1

j = 1

m ₁ = 1

w_Hmeas1 = 0.1239

w_Cmeas1 = 0.8206

w_Omeas1 = 0.0547

w_Smeas1 = 0.00066

w_Nmeas1 = 0.000095

M_C = 12.0107 g/mol

M_H = 1.00794 g/mol

M_O = 15.9994 g/mol

M_S = 32.065 g/mol

M_N = 14.0067

(f) Calculated raw exhaust molar flow rate from measured intake air molar flow rate or fuel mass flow rate. You may calculate the raw exhaust molar flow rate from which you sampled emissions, n ̇_exh, based on the measured intake air molar flow rate, n ̇_int, or the measured fuel mass flow rate, m ̇_fuel, and the values calculated using the chemical balance in paragraph (c) of this section. The chemical balance must be based on raw exhaust gas concentrations. Solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record or n ̇_int or m ̇_fuel. For laboratory tests, calculating raw exhaust molar flow rate using measured fuel mass flow rate is valid only for steady-state testing. See §1065.915(d)(5)(iv) for application to field testing.

(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, you may calculate raw exhaust flow based on n ̇_int or m ̇_fuel using one of the following:

(i) You may measure flow rate through the crankcase vent and subtract it from the calculated exhaust flow.

(ii) You may estimate flow rate through the crankcase vent by engineering analysis as long as the uncertainty in your calculation does not adversely affect your ability to show that your engines comply with applicable emission standards.

(iii) You may assume your crankcase vent flow rate is zero.

(2) Intake air molar flow rate calculation. Calculate n ̇_exh based on n ̇_int using the following equation:

Where:

n ̇_exh = raw exhaust molar flow rate from which you measured emissions.

n ̇_int = intake air molar flow rate including humidity in intake air.

Example:

n ̇_int = 3.780 mol/s

x_int/exhdry = 0.69021 mol/mol

x_raw/exhdry = 1.10764 mol/mol

x_H20exhdry = 107.64 mmol/mol = 0.10764 mol/mol

(3) Fluid mass flow rate calculation. This calculation may be used only for steady-state laboratory testing. You may not use this calculation if the standard-setting part requires carbon balance error verification as described in §1065.543. See §1065.915(d)(5)(iv) for application to field testing. Calculate based on using the following equation:

Eq. 1065.655-25

Where:

n _exh = raw exhaust molar flow rate from which you measured emissions.

j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.

N = total number of fuels and injected fluids over the duty cycle.

m  j = the mass flow rate of the fuel or any injected fluid j.

w_C = carbon mass fraction of the fuel and any injected fluid j , as determined in paragraph (d) of this section.

Example:

N = 1

j = 1

m ₁ = 7.559 g/s

w_C1 = 0.869 g/g

M_C = 12.0107 g/mol

x_Ccombdry1 = 99.87 mmol/mol = 0.09987 mol/mol

x_H20exhdry1 = 107.64 mmol/mol = 0.10764 mol/mol

(g) Calculated raw exhaust molar flow rate from measured intake air molar flow rate, dilute exhaust molar flow rate, and dilute chemical balance. You may calculate the raw exhaust molar flow rate, n ̇_exh, based on the measured intake air molar flow rate, n ̇_int, the measured dilute exhaust molar flow rate, n ̇_dexh, and the values calculated using the chemical balance in paragraph (c) of this section. Note that the chemical balance must be based on dilute exhaust gas concentrations. For continuous-flow calculations, solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n ̇_int and n ̇_dexh. This calculated n ̇_exh may be used for the PM dilution ratio verification in §1065.546; the calculation of dilution air molar flow rate in the background correction in §1065.667; and the calculation of mass of emissions in §1065.650(c) for species that are measured in the raw exhaust.

(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, calculate raw exhaust flow as described in paragraph (e)(1) of this section.

(2) Dilute exhaust and intake air molar flow rate calculation. Calculate n ̇_exh as follows:

Example:

n ̇_int = 7.930 mol/s

x_raw/exhdry = 0.1544 mol/mol

x_int/exhdry = 0.1451 mol/mol

x_H20/exh = 32.46 mmol/mol = 0.03246 mol/mol

n ̇_dexh = 49.02 mol/s

n ̇_exh = (0.1544 − 0.1451) · (1 − 0.03246) · 49.02 + 7.930 = 0.4411 + 7.930 = 8.371 mol/s

[73 FR 37331, June 30, 2008, as amended at 73 FR 59334, Oct. 8, 2008; 75 FR 23051, Apr. 30, 2010; 76 FR 57458, Sept. 15, 2011; 79 FR 23799, Apr. 28, 2014; 81 FR 74182, Oct. 25, 2016; 86 FR 34563, Jun. 29, 2021; 87 FR 65866, Oct. 26, 2022; 88 FR 4684, Jan. 24, 2023; 89 FR 29808, Apr. 22, 2024]

§1065.656 Hydrogen-based chemical balances of fuel, DEF, intake air, and exhaust.

(a) General. Chemical balances of fuel, DEF, intake air, and exhaust may be used to calculate flows, the amount of water in their flows, and the wet concentration of constituents in their flows. See §1065.520(f) for information about when to use this hydrogen-based chemical balance procedure. With one flow rate of either fuel, intake air, or exhaust, you may use chemical balances to determine the flows of the other two. For example, you may use chemical balances along with either intake air or fuel flow to determine raw exhaust flow. Note that chemical balance calculations allow measured values for the flow rate of diesel exhaust fluid for engines with urea-based selective catalytic reduction.

(b) Procedures that require chemical balances. We require chemical balances when you determine the following:

(1) A value proportional to total work, when you choose to determine brake-specific emissions as described in §1065.650(f).

(2) Raw exhaust molar flow rate either from measured intake air molar flow rate or from fuel mass flow rate as described in paragraph (f) of this section.

(3) Raw exhaust molar flow rate from measured intake air molar flow rate and dilute exhaust molar flow rate as described in paragraph (g) of this section.

(4) The amount of water in a raw or diluted exhaust flow, x_H2Oexh , when you do not measure the amount of water to correct for the amount of water removed by a sampling system. Correct for removed water according to §1065.659.

(5) The calculated total dilution air flow when you do not measure dilution air flow to correct for background emissions as described in §1065.667(c) and (d).

(c) Chemical balance procedure. The calculations for a chemical balance involve a system of equations that require iteration. We recommend using a computer to solve this system of equations. You must guess the initial values of two of the following quantities: the amount of hydrogen in the measured flow, x_H2exhdry , the fraction of dilution air in diluted exhaust, x_dil/exhdry , and the amount of intake air required to produce actual combustion products per mole of dry exhaust, x_int/exhdry . You may use time-weighted mean values of intake air humidity and dilution air humidity in the chemical balance; as long as your intake air and dilution air humidities remain within tolerances of ±0.0025 mol/mol of their respective mean values over the test interval. For each emission concentration, x, and amount of water, x_H2Oexh , you must determine their completely dry concentrations, x_dry and x_H2Oexhdry . You must also use your fuel mixture's carbon mass fraction, w_C , hydrogen mass fraction, w_H , oxygen mass fraction, w_O , sulfur mass fraction, w_S , and nitrogen mass fraction, w_N ; you may optionally account for diesel exhaust fluid (or other fluids injected into the exhaust), if applicable. Calculate w_C , w _H , w_O , w _S , and w_N as described in paragraphs (d) and (e) of this section. You may alternatively use any combination of default values and measured values as described in paragraphs (d) and (e) of this section. Use the following steps to complete a chemical balance:

(1) Convert your measured concentrations such as x_H2meas , x _NH3meas , x_CO2meas , x_COmeas , x_THCmeas , x_O2meas , x_H2meas , x_NOmeas , x_NO2meas , and x_H2Oint , to dry concentrations by dividing them by one minus the amount of water present during their respective measurements; for example: x_H2Omeas , x_H2OxO2meas , x_H2OxNOmeas , and x_H2Oint . If the amount of water present during a “wet” measurement is the same as an unknown amount of water in the exhaust flow, x_H2Oexh , iteratively solve for that value in the system of equations. If you measure only total NO _X and not NO and NO ₂ separately, use good engineering judgment to estimate a split in your total NO _X concentration between NO and NO ₂ for the chemical balances. For example, if you measure emissions from a stoichiometric combustion engine, you may assume all NO _X is NO. For a lean-burn combustion engine, you may assume that your molar concentration of NO _X , x_NOx , is 75% NO and 25% NO ₂ . For NO ₂ storage aftertreatment systems, you may assume x_NOx is 25% NO and 75% NO _2. Note that for calculating the mass of NO _X emissions, you must use the molar mass of NO ₂ for the effective molar mass of all NO _X species, regardless of the actual NO ₂ fraction of NO _X .

(2) Enter the equations in paragraph (c)(5) of this section into a computer program to iteratively solve for x_H2exhdry , x_dil/exhdry , and x_int/exhdry . Use good engineering judgment to guess initial values for x_H2exhdry , x_dil/exhdry , and x_int/exhdry . We recommend guessing an initial amount of hydrogen of 0 mol/mol. We recommend guessing an initial x_int/exhdry of 1 mol/mol. We also recommend guessing an initial x_dil/exhdry of 0.8 mol/mol. Iterate values in the system of equations until the most recently updated guesses are all within ±1% or ±1 µmol/mol, whichever is larger, of their respective most recently calculated values.

(3) Use the following symbols and subscripts in the equations for performing the chemical balance calculations in this paragraph (c):

(4) Use the equations specified in this section to iteratively solve for x_int/exhdry , x_dil/exhdry , and x_H2exhdry . The following exceptions apply:

(i) For x_H2exhdry multiple equations are provided, see table 2 to paragraph (c)(6) of this section to determine for which cases the equations apply.

(ii) The calculation of x_O2exhdry is only required when x_O2meas is measured.

(iii) The calculation of x_NH3exhdry is only required for engines that use ammonia as fuel and engines that are subject to NH ₃ measurement under the standard setting part, for all other engines x_NH3exhdry may be set to zero.

(iv) The calculation of x_CO2exhdry is only required for engines that use carbon-containing fuels or fluids, either as single fuel or as part of the fuel mixture, and for engines that are subject to CO ₂ measurement under the standard setting part, for all other engines x_CO2exhdry may be set to a value that yields for x_Ccombdry a value of zero. (v) The calculation of x_COexhdry and x_THCexhdry is only required for engines that use carbon-containing fuels and for engines that are subject to CO and THC measurement under the standard setting part, for all other engines x_COexhdry and x_THCexhdry may be set to zero. (vi) The calculation of x_N2Oexhdry is only required for engines that are subject to N ₂ O measurement under the standard setting part, for all other engines x_N2Oexhdry may be set to zero.

(5) The chemical balance equations are as follows:

x _Ccombdry = x_co2exhdry + x_coexhdry + x_THCexhdry − x_co2dil · x_dil/exhdry − x_co2int · x_int/exhdry

Eq. 1065.656-1

Eq. 1065.656-2

Eq. 1065.656-3

Eq. 1065.656-4

Eq. 1065.656-5

Eq. 1065.656-6 (see table 2 of this section)

Eq. 1065.656-7 (see table 2 of this section)

Eq. 1065.656-8

Eq. 1065.656-9

Eq. 1065.656-10

Eq. 1065.656-11

Eq. 1065.656-12

Eq. 1065.656-13

Eq. 1065.656-14

Eq. 1065.656-15

Eq. 1065.656-16 (see table 2 of this section)

Eq. 1065.656-17

Eq. 1065.656-18

Eq. 1065.656-19

Eq. 1065.656-20

Eq. 1065.656-21

Eq. 1065.656-22

Eq. 1065.656-23

(6) Depending on your measurements, use the equations and guess the quantities specified in the following table:

(7) The following example is a solution for _{int/exhdry,dil/exhdry,} and _HOexhdry using the equations in paragraph (c)(5) of this section:

(d) Mass fractions of fuel. (1) For fuels other than carbon-containing fuels determine the mass fractions of fuel W_C , W_H , W_O , W_S , and W_N, based on the fuel properties as determined in paragraph (e) of this section. Calculate W_C , W_H , W_O , W_S , and W_N using the following equations:

Eq. 1065.656-24

Eq. 1065.656-25

Eq. 1065.656-26

Eq. 1065.656-27

Eq. 1065.656-28

Where:

w_C = carbon mass fraction of the fuel and any injected fluids.

w_H = hydrogen mass fraction of the fuel and any injected fluids.

w_O = oxygen mass fraction of the fuel and any injected fluids.

w_S = sulfur mass fraction of the fuel and any injected fluids.

w_N = nitrogen mass fraction of the fuel and any injected fluids.

τ = effective carbon content of the fuel and any injected fluids.

M_C = molar mass of carbon.

χ = effective hydrogen content of the fuel and any injected fluids.

M_H = molar mass of hydrogen.

ϕ = effective oxygen content of the fuel and any injected fluids.

M_O = molar mass of oxygen.

ξ = effective sulfur content of the fuel and any injected fluids.

M_S = molar mass of nitrogen.

ω = effective nitrogen content of the fuel and any injected fluids.

M_N = molar mass of nitrogen.

Example for NH fuel:

τ = 0

χ = 3

ϕ = 0

ξ = 0

ω = 1

M_C = 12.0107 g/mol

M_H = 1.00794 g/mol

M_O = 15.9994 g/mol

M_S = 32.065 g/mol

M_N = 14.0067 g/mol

w_C = 0 g/g

w_H = 0.1775530 g/g

w_O = 0 g/g

w_S = 0 g/g

w_N = 0.8224470 g/g

(2) For carbon-containing fuels and diesel exhaust fluid determine the mass fractions of fuel, W_C , W_H , W_O , W_S , and W_N , based on properties determined according to §1065.655(d). Calculate W_C , W_H , W_O , W_S , and W_N using the following equations:

Eq. 1065.656-29

Eq. 1065.656-30

Eq. 1065.656-31

Eq. 1065.656-32

Eq. 1065.656-33

Where:

w_C = carbon mass fraction of the fuel and any injected fluids.

w_H = hydrogen mass fraction of the fuel and any injected fluids.

w_O = oxygen mass fraction of the fuel and any injected fluids.

w_S = sulfur mass fraction of the fuel and any injected fluids.

w_N = nitrogen mass fraction of the fuel and any injected fluids.

M_C = molar mass of carbon.

α = atomic hydrogen-to-carbon ratio of the fuel and any injected fluids.

M_H = molar mass of hydrogen.

β = atomic oxygen-to-carbon ratio of the fuel and any injected fluids.

M_O = molar mass of oxygen.

γ = atomic sulfur-to-carbon ratio of the fuel and any injected fluids.

M_S = molar mass of sulfur.

δ = atomic nitrogen-to-carbon ratio of the fuel and any injected fluids.

M_N = molar mass of nitrogen.

Example:

α = 1.8

β = 0.05

γ = 0.0003

δ = 0.0001

M_C = 12.0107

M_H = 1.00794

M_O = 15.9994

M_S = 32.065

M_N = 14.0067

(3) For nonconstant fuel mixtures, you must account for the varying proportions of the different fuels. This paragraph (d)(3) generally applies for dual-fuel and flexible-fuel engines, but optionally it may also be applied if diesel exhaust fluid or other fluids injected into the exhaust are injected in a way that is not strictly proportional to fuel flow. Account for these varying concentrations either with a batch measurement that provides averaged values to represent the test interval, or by analyzing data from continuous mass rate measurements. Application of average values from a batch measurement generally applies to situations where one fluid is a minor component of the total fuel mixture; consistent with good engineering judgment. Calculate W_C , W_H , W_O , W_S , and W_N of the fuel mixture using the following equations:

Eq. 1065.656-34

Eq. 1065.656-35

Eq. 1065.656-36

Eq. 1065.656-37

Eq. 1065.656-38

Where:

w_C = carbon mass fraction of the mixture of test fuels and any injected fluids.

w_H = hydrogen mass fraction of the mixture of test fuels and any injected fluids.

w_O = oxygen mass fraction of the mixture of test fuels and any injected fluids.

w_S = sulfur mass fraction of the mixture of test fuels and any injected fluids.

w_N = nitrogen mass fraction of the mixture of test fuels and any injected fluids.

N = total number of fuels and injected fluids over the duty cycle.

j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.

m = the mass flow rate of the fuel or any injected fluid j. For batch measurements, divide the total mass of fuel over the test interval duration to determine a mass rate.

w_Cmeasj = carbon mass fraction of fuel or any injected fluid j.

w_Hmeasj = hydrogen mass fraction of fuel or any injected fluid j.

w_Omeasj = oxygen mass fraction of fuel or any injected fluid j.

w_Smeasj = sulfur mass fraction of fuel or any injected fluid j.

w_Nmeasj = nitrogen mass fraction of fuel or any injected fluid j.

Example for a mixture of diesel and NH₃fuel where diesel represents 15% of energy:

N = 2

m ₁ = 0.5352 g/s

m ₂ = 7.024 g/s

w_Cmeas1 = 0.820628 g/g

w_Hmeas1 = 0.123961 g/g

w_Omeas1 = 0.0546578 g/g

w_Smeas1 = 0.00065725 g/g

w_Nmeas1 = 0.0000957004 g/g

w_Cmeas2 = 0 g/g

w_Hmeas2 = 0.177553 g/g

w_Omeas2 = 0 g/g

w_Smeas2 = 0 g/g

w_Nmeas2 = 0.822447 g/g

w_C = 0.0581014 g/g

w_H = 0.1737586 g/g

w_O = 0.00386983 g/g

w_S = 0.0000465341 g/g

w_N = 0.76422359 g/g

(e) Fuel and diesel exhaust fluid composition. (1) For carbon-containing fuels and diesel exhaust fluid determine the composition represented by α, β, γ, and δ, as described in §1065.655(e).

(2) For fuels other than carbon-containing fuels use the default values for τ, χ, ϕ, ξ, and ω in table 3 to this section, or use good engineering judgment to determine those values based on measurement. If you determine compositions based on measured values and the default value listed in table 3 to this section is zero, you may set τ, ϕ, ξ, and ω to zero; otherwise determine τ, ϕ, ξ, and ω (along with χ) based on measured values.

(3) If your fuel mixture contains carbon-containing fuels and your testing requires fuel composition values referencing carbon, calculate α, β, γ, and δ for the fuel mixture as described in §1065.655(e)(4).

(4) Table 3 to this paragraph (e)(4) follows:

(f) Calculated raw exhaust molar flow rate from measured intake air molar flow rate or fuel mass flow rate. You may calculate the raw exhaust molar flow rate from which you sampled emissions, , based on the measured intake air molar flow rate, , or the measured fuel mass flow rate, , and the values calculated using the chemical balance in paragraph (c) of this section. The chemical balance must be based on raw exhaust gas concentrations. Solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record or . For laboratory tests, calculating raw exhaust molar flow rate using measured fuel mass flow rate is valid only for steady-state testing. See §1065.915(d)(5)(iv) for application to field testing.

(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, you may calculate raw exhaust flow based on or using one of the following:

(i) You may measure flow rate through the crankcase vent and subtract it from the calculated exhaust flow.

(ii) You may estimate flow rate through the crankcase vent by engineering analysis as long as the uncertainty in your calculation does not adversely affect your ability to show that your engines comply with applicable emission standards.

(iii) You may assume your crankcase vent flow rate is zero.

(2) Intake air molar flow rate calculation. Calculate n based on using the following equation:

Eq. 1065.656-39

Where:

n _exh = raw exhaust molar flow rate from which you measured emissions.

n _int = intake air molar flow rate including humidity in intake air.

Example:

n _int = 3.780 mol/s

x_int/exhdry = 0.69021 mol/mol

x_raw/exhdry = 1.10764 mol/mol

x_H20exhdry = 107.64 mmol/mol = 0.10764 mol/mol

(3) Fluid mass flow rate calculation. This calculation may be used only for steady-state laboratory testing. See §1065.915(d)(5)(iv) for application to field testing. Calculate based on using the following equation:

Eq. 1065.656-40

Where:

n _exh = raw exhaust molar flow rate from which you measured emissions.

j = an indexing variable that represents one fuel or injected fluid, starting with j = 1.

N = total number of fuels and injected fluids over the duty cycle.

m _j = the mass flow rate of the fuel or any injected fluid j.

w_Cj = carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluid j.

w_Hj = hydrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluid j.

Example:

x_H20exhdry1 = 312.013 mmol/mol = 0.10764 mol/mol

M_C = 12.0107 g/mol

M_H = 1.00794 g/mol

x_Ccombdry1 = 6.45541 mmol/mol = 0.00645541 mol/mol

x_Hcombdry1 = 641.384 mmol/mol = 0.641384 mol/mol

m ₁ = 0.167974 g/s

m ₂ = 7.39103 g/s

w_C1 = 0.820628 g/g

w_C2 = 0 g/g

w_H1 = 0.123961 g/g

w_H2 = 0.177553 g/g

N = 2

(g) Calculated raw exhaust molar flow rate from measured intake air molar flow rate, dilute exhaust molar flow rate, and dilute chemical balance. You may calculate the raw exhaust molar flow rate, n _exh , based on the measured intake air molar flow rate, n _int , the measured dilute exhaust molar flow rate, n _dexh , and the values calculated using the chemical balance in paragraph (c) of this section. Note that the chemical balance must be based on dilute exhaust gas concentrations. For continuous-flow calculations, solve for the chemical balance in paragraph (c) of this section at the same frequency that you update and record n _int and n _dexh . This calculated n _dexh may be used for the PM dilution ratio verification in §1065.546; the calculation of dilution air molar flow rate in the background correction in §1065.667; and the calculation of mass of emissions in §1065.650(c) for species that are measured in the raw exhaust.

(1) Crankcase flow rate. If engines are not subject to crankcase controls under the standard-setting part, calculate raw exhaust flow as described in paragraph (f)(1) of this section.

(2) Dilute exhaust and intake air molar flow rate calculation. Calculate as follows:

n _exh = ( x_raw/exhdry − x_int/exhdry) · (1 − x_H20exh) · n _dexh + n _int

Eq. 1065.656-41

Example:

n _int = 7.930 mol/s

x_raw/exhdry = 0.1544 mol/mol

x_int/exhdry = 0.1451 mol/mol

x_H20exhdry = 32.46 mmol/mol = 0.03246 mol/mol

n _dexh = 49.02 mol/s

n _exh = (0.1544 − 0.1451) · (1 − 0.03246) · 49.02 + 7.930 = 0.4411 + 7.930 = 8.371 mol/s

[73 FR 37335, June 30, 2008, as amended at 76 FR 57462, Sept. 15, 2011; 79 FR 23804, Apr. 28, 2014; 86 FR 34566, Jun. 29, 2021; 89 FR 29810, Apr. 22, 2024]

§1065.659 Removed water correction.

(a) If you remove water upstream of a concentration measurement, x, correct for the removed water. Perform this correction based on the amount of water at the concentration measurement, x_{H2O[emission]meas}, and at the flow meter, x_H2Oexh, whose flow is used to determine the mass emission rate or total mass over a test interval. For continuous analyzers downstream of a sample dryer for transient and ramped-modal cycles, you must apply this correction on a continuous basis over the test interval, even if you use one of the options in §1065.145(e)(2) that results in a constant value for x_{H2O[emission]meas} because x_H2Oexh varies over the test interval. For batch analyzers, determine the flow-weighted average based on the continuous x_H2Oexh values determined as described in paragraph (c) of this section. For batch analyzers, you may determine the flow-weighted average x_H2Oexh based on a single value of x_H2Oexh determined as described in paragraphs (c)(2) and (3) of this section, using flow-weighted average or batch concentration inputs.

(b) Determine the amount of water remaining downstream of a sample dryer and at the concentration measurement using one of the methods described in §1065.145(e)(2). If you use a sample dryer upstream of an analyzer and if the calculated amount of water remaining downstream of the sample dryer and at the concentration measurement, x_{H2O[emission]meas}, is higher than the amount of water at the flow meter, x_H2Oexh, set x_{H2O[emission]meas} equal to x_H2Oexh. If you use a sample dryer upstream of storage media, you must be able to demonstrate that the sample dryer is removing water continuously (i.e., x_H2Oexh is higher than x_{H2O[emission]meas} throughout the test interval).

(c) For a concentration measurement where you did not remove water, you may set x_{H2O[emission]meas} equal to x_H2Oexh. You may determine the amount of water at the flow meter, x_H2Oexh, using any of the following methods:

(1) Measure the dewpoint and absolute pressure and calculate the amount of water as described in §1065.645.

(2) If the measurement comes from raw exhaust, you may determine the amount of water based on intake-air humidity, plus a chemical balance of fuel, DEF, intake air, and exhaust as described in §1065.655.

(3) If the measurement comes from diluted exhaust, you may determine the amount of water based on intake-air humidity, dilution air humidity, and a chemical balance of fuel, DEF, intake air, and exhaust as described in §1065.655.

(d) Perform a removed water correction to the concentration measurement using the following equation:

[73 FR 37335, June 30, 2008, as amended at 76 FR 57462, Sept. 15, 2011; 79 FR 23804, Apr. 28, 2014; 86 FR 34566, Jun. 29, 2021]

§1065.660 THC, NMHC, NMNEHC, CH4, and C2H6 determination.

(a) THC determination and initial THC/CH₄contamination corrections. (1) If we require you to determine THC emissions, calculate _{THC[THC-FID]cor} using the initial THC contamination concentration _{THC[THC-FID]init} from §1065.520 as follows:

_{THC[THC-FID]cor} = _{THC[THC-FID]uncor} − _{THC[THC-FID]init}

Eq. 1065.660-1

Example:

_THCuncor = 150.3 µmol/mol

_THCinit = 1.1 µmol/mol

_THCcor = 150.3—1.1

_THCcor = 149.2 µmol/mol

(2) For the NMHC determination described in paragraph (b) of this section, correct _THC[THC-FID] for initial THC contamination using Eq. 1065.660-1. You may correct _THC[NMC-FID] for initial contamination of the CH ₄ sample train using Eq. 1065.660-1, substituting in CH ₄ concentrations for THC.

(3) For the NMNEHC determination described in paragraph (c) of this section, correct _THC[THC-FID] for initial THC contamination using Eq. 1065.660-1. You may correct _THC[NMC-FID] for initial contamination of the CH ₄ sample train using Eq. 1065.660-1, substituting in CH ₄ concentrations for THC.

(4) For the CH ₄ determination described in paragraph (d) of this section, you may correct _THC[NMC-FID] for initial THC contamination of the CH ₄ sample train using Eq. 1065.660-1, substituting in CH ₄ concentrations for THC.

(5) You may calculate THC as the sum of NMHC and CH ₄ if you determine CH ₄ with an FTIR as described in paragraph (d)(2) of this section and NMHC with an FTIR using the additive method from paragraph (b)(4) of this section.

(6) You may calculate THC as the sum of NMNEHC, C ₂ H ₆ , and CH ₄ if you determine CH ₄ with an FTIR as described in paragraph (d)(2) of this section, C ₂ H ₆ with an FTIR as described in paragraph (e) of this section, and NMNEHC with an FTIR using the additive method from paragraph (c)(3) of this section.

(b) NMHC determination. Use one of the following to determine NMHC concentration, _NMHC :

(1) If you do not measure CH ₄ , you may omit the calculation of NMHC concentrations and calculate the mass of NMHC as described in §1065.650(c)(5).

(2) For an NMC, calculate _NMHC using the NMC's penetration fractions, response factors, and/or combined penetration fractions and response factors as described in §1065.365, the THC FID's CH ₄ response factor, RF_{CH4[THC-FID],} from §1065.360, the initial THC contamination and dry-to-wet corrected THC concentration, _{THC[THC-FID]cor,} as determined in paragraph (a) of this section, and the dry-to-wet corrected CH ₄ concentration, _{THC[NMC-FID]cor,} optionally corrected for initial THC contamination as determined in paragraph (a) of this section.

(i) Use the following equation for an NMC configured as described in §1065.365(d):

Eq. 1065.660-2

Where:

_NMHC = concentration of NMHC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the NMC FID during sampling through the NMC.

RF_CH4[THC-FID] = response factor of THC FID to CH _4, according to §1065.360(d).

RFPF_{C2H6[NMC-FID]} = NMC combined C ₂ H ₆ response factor and penetration fraction, according to §1065.365(d).

RFPF_CH4[NMC-FID] = NMC combined CH ₄ response factor and penetration fraction, according to §1065.365(d).

Example:

_{THC[THC-FID]cor} = 150.3 µmol/mol

_{THC[NMC-FID]cor} = 20.5 µmol/mol

RFPF_{C2H6[NMC-FID]} = 0.019

RFPF_CH4[NMC-FID] = 1.000

RF_CH4[THC-FID] = 1.05

(ii) Use the following equation for penetration fractions determined using an NMC configuration as outlined in §1065.365(e):

Eq. 1065.660-3

Where:

_NMHC = concentration of NMHC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

PF_CH4[NMC-FID] = NMC CH ₄ penetration fraction, according to §1065.365(e).

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the THC FID during sampling through the NMC.

PF_{C2H6[NMC-FID]} = NMC C ₂ H ₆ penetration fraction, according to §1065.365(e).

Example:

_{THC[THC-FID]cor} = 150.3 µmol/mol

PF_CH4[NMC-FID] = 0.990

_{THC[NMC-FID]cor} = 20.5 µmol/mol

PF_{C2H6[NMC-FID]} = 0.020

(iii) Use the following equation for an NMC configured as described in §1065.365(f):

Eq. 1065.660-4

Where:

_NMHC = concentration of NMHC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

PF_CH4[NMC-FID] = NMC CH ₄ penetration fraction, according to §1065.365(f).

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the THC FID during sampling through the NMC.

RFPF_{C2H6[NMC-FID]} = NMC combined C ₂ H ₆ response factor and penetration fraction, according to §1065.365(f).

RF_CH4[THC-FID] = response factor of THC FID to CH _4, according to §1065.360(d).

Example:

_{THC[THC-FID]cor} = 150.3 µmol/mol

PF_CH4[NMC-FID] = 0.990

_{THC[NMC-FID]cor} = 20.5 µmol/mol

RFPF_{C2H6[NMC-FID]} = 0.019

RF_CH4[THC-FID] = 0.980

(3) For a GC-FID or FTIR, calculate _NMHC using the THC analyzer's CH ₄ response factor, RF_{CH4[THC-FID],} from §1065.360, and the initial THC contamination and dry-to-wet corrected THC concentration, _{THC[THC-FID]cor,} as determined in paragraph (a) of this section as follows:

χ _NMHC = χ _{THC[THC-FID]cor} − RF_CH4[THC-FID] · χ _CH4

Eq. 1065.660-5

Where:

_NMHC = concentration of NMHC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID.

RF_CH4[THC-FID] = response factor of THC-FID to CH _4.

_CH4 = concentration of CH _4, dry-to-wet corrected, as measured by the GC-FID or FTIR.

Example:

_{THC[THC-FID]cor} = 145.6 µmol/mol

RF_CH4[THC-FID] = 0.970

_CH4 = 18.9 µmol/mol

_NMHC = 145.6—0.970 · 18.9

_NMHC = 127.3 µmol/mol

(4) For an FTIR, calculate _NMHC by summing the hydrocarbon species listed in §1065.266(c) as follows:

Eq. 1065.660-6

Where:

_NMHC = concentration of NMHC.

_HCi = the C ₁ -equivalent concentration of hydrocarbon species i as measured by the FTIR, not corrected for initial contamination.

_HCi-init = the C ₁ -equivalent concentration of the initial system contamination (optional) of hydrocarbon species i, dry-to-wet corrected, as measured by the FTIR.

Example:

_C2H6 = 4.9 µmol/mol

_C2H4 = 0.9 µmol/mol

_C2H2 = 0.8 µmol/mol

_C3H8 = 0.4 µmol/mol

_C3H6 = 0.5 µmol/mol

_C4H10 = 0.3 µmol/mol

_CH2O = 0.8 µmol/mol

_C2H4O = 0.3 µmol/mol

_CH2O2 = 0.1 µmol/mol

_CH4O = 0.1 µmol/mol

_NMHC = 4.9 + 0.9 + 0.8 + 0.4 + 0.5 + 0.3 + 0.8 + 0.3 + 0.1 + 0.1

_NMHC = 9.1 µmol/mol

(c) NMNEHC determination. Use one of the following methods to determine NMNEHC concentration, _NMNEHC :

(1) Calculate _NMNEHC based on the test fuel's ethane content as follows:

(i) If the content of your test fuel contains less than 0.010 mol/mol of ethane, you may omit the calculation of NMNEHC concentration and calculate the mass of NMNEHC as described in §1065.650(c)(6)(i).

(ii) If the content of your fuel test contains at least 0.010 mol/mol of C ₂ H ₆ , you may omit the calculation of NMNEHC concentration and calculate the mass of NMNEHC as described in §1065.650(c)(6)(ii).

(2) For a GC-FID, NMC FID, or FTIR, calculate _NMNEHC using the THC analyzer's CH ₄ response factor, RF_{CH4[THC-FID],} and C ₂ H ₆ response factor, RF_{C2H6[THC-FID],} from §1065.360, the initial contamination and dry-to-wet corrected THC concentration, _{THC[THC-FID]cor,} as determined in paragraph (a) of this section, the dry-to-wet corrected CH ₄ concentration, _CH4, as determined in paragraph (d) of this section, and the dry-to-wet corrected C ₂ H ₆ concentration, _C2H6, as determined in paragraph (e) of this section as follows:

_NMNEHC = _{THC[THC-FID}cor} − RF _CH4{THC-FID} . _CH4 − RF _{C2H6{THC-FID]} . _C2H6

Eq. 1065.660-7

Where:

_NMNEHC = concentration of NMNEHC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID.

RF_CH4[THC-FID] = response factor of THC-FID to CH _4.

_CH4 = concentration of CH _4, dry-to-wet corrected, as measured by the GC-FID, NMC FID, or FTIR.

RF_{C2H6[THC-FID]} = response factor of THC-FID to C ₂ H _6.

_C2H6 = the C ₁ -equivalent concentration of C ₂ H _6, dry-to-wet corrected, as measured by the GC-FID or FTIR.

Example:

_{THC[THC-FID]cor} = 145.6 µmol/mol

RF_CH4[THC-FID] = 0.970

_CH4 = 18.9 µmol/mol

RF_{C2H6[THC-FID]} = 1.02

_C2H6 = 10.6 µmol/mol

_NMNEHC = 145.6 − 0.970 · 18.9 − 1.02 · 10.6

_NMNEHC = 116.5 µmol/mol

(3) For an FTIR, calculate x_NMNEHC by summing the hydrocarbon species listed in §1065.266(c) as follows:

Eq. 1065.660-8

Where:

_NMNEHC = concentration of NMNEHC.

_HC = the C ₁ -equivalent concentration of hydrocarbon species i as measured by the FTIR, not corrected for initial contamination.

_HC-init = the C ₁ -equivalent concentration of the initial system contamination (optional) of hydrocarbon species i, dry-to-wet corrected, as measured by the FTIR.

Example:

_C2H4 = 0.9 µmol/mol

_C2H2 = 0.8 µmol/mol

_C3H8 = 0.4 µmol/mol

_C3H6 = 0.5 µmol/mol

_C4H10 = 0.3 µmol/mol

_CH2O = 0.8 µmol/mol

_C2H4O = 0.3 µmol/mol

_CH2O2 = 0.1 µmol/mol

_CH4O = 0.1 µmol/mol

_NMNEHC = 0.9 + 0.8 + 0.4 + 0.5 + 0.3 + 0.8 + 0.3 + 0.1 + 0.1

x_NMNEHC = 4.2 µmol/mol

(d) CH₄ determination. Use one of the following methods to determine methane (CH ₄) concentration, _CH4 :

(1) For an NMC, calculate x_CH4 using the NMC's penetration fractions, response factors, and/or combined penetration fractions and response factors as described in §1065.365, the THC FID's CH ₄ response factor, RF_{CH4[THC-FID],} from §1065.360, the initial THC contamination and dry-to-wet corrected THC concentration, _{THC[THC-FID]cor,} as determined in paragraph (a) of this section, and the dry-to-wet corrected CH ₄ concentration, _{THC[NMC-FID]cor,} optionally corrected for initial THC contamination as determined in paragraph (a) of this section.

(i) Use the following equation for an NMC configured as described in §1065.365(d):

Eq. 1065.660-9

Where:

_CH4 = concentration of CH ₄ .

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the NMC FID during sampling through the NMC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

RFPF_{C2H6[NMC-FID]} = NMC combined C ₂ H ₆ response factor and penetration fraction, according to §1065.365(d).

RF_CH4[THC-FID] = response factor of THC FID to CH _4, according to §1065.360(d).

RFPF_CH4[NMC-FID] = NMC combined CH ₄ response factor and penetration fraction, according to §1065.365(d).

Example:

_{THC[NMC-FID]cor} = 10.4 µmol/mol

_{THC[THC-FID]cor} = 150.3 µmol/mol

RFPF_{C2H6[NMC-FID]} = 0.019

RFPF_CH4[NMC-FID] = 1.000

RF_CH4[THC-FID] = 1.05

(ii) Use the following equation for an NMC configured as described in §1065.365(e):

Eq. 1065.660-10

Where:

x_CH4 = concentration of CH _4.

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the NMC FID during sampling through the NMC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

PF_{C2H6[NMC-FID]} = NMC C ₂ H ₆ penetration fraction, according to §1065.365(e).

RF_CH4[THC-FID] = response factor of THC FID to CH _4, according to §1065.360(d).

PF_CH4[NMC-FID] = NMC CH ₄ penetration fraction, according to §1065.365(e).

Example:

_{THC[NMC-FID]cor} = 10.4 µmol/mol

_{THC[THC-FID]cor} = 150.3 µmol/mol

PF_{C2H6[NMC-FID]} = 0.020

RF_CH4[THC-FID] = 1.05

PF_CH4[NMC-FID] = 0.990

(iii) Use the following equation for an NMC configured as described in §1065.365(f):

Eq. 1065.660-11

Where:

_CH4 = concentration of CH _4.

_{THC[NMC-FID]cor} = concentration of THC, initial THC contamination (optional) and dry-to-wet corrected, as measured by the NMC FID during sampling through the NMC.

_{THC[THC-FID]cor} = concentration of THC, initial THC contamination and dry-to-wet corrected, as measured by the THC FID during sampling while bypassing the NMC.

RFPF_{C2H6[NMC-FID]} = the combined C ₂ H ₆ response factor and penetration fraction of the NMC, according to §1065.365(f).

PF_CH4[NMC-FID] = NMC CH ₄ penetration fraction, according to §1065.365(f).

RF_CH4[THC-FID] = response factor of THC FID to CH _4, according to §1065.360(d).

Example:

_{THC[NMC-FID]cor} = 10.4 µmol/mol

_{THC[THC-FID]cor} = 150.3 µmol/mol

RFPF_{C2H6[NMC-FID]} = 0.019

PF_CH4[NMC-FID] = 0.990

RF_CH4[THC-FID] = 1.05

(2) For a GC-FID or FTIR, x_CH4 is the actual dry-to-wet corrected CH ₄ concentration as measured by the analyzer.

(e) C₂ H ₆ determination. For a GC-FID or FTIR, _C2H6 is the C ₁ -equivalent, dry-to-wet corrected C ₂ H ₆ concentration as measured by the analyzer.

[76 FR 57462, Sept. 15, 2011, as amended at 81 FR 74184, Oct. 25, 2016; 86 FR 34566, Jun. 29, 2021; 88 FR 4686, Jan. 24, 2023; 89 FR 29819, Apr. 22, 2024]

§1065.665 THC, NMHC, NMNEHC, CH ₄ , and C ₂ H ₆ determination.

(a) If you measured an oxygenated hydrocarbon's mass concentration, first calculate its molar concentration in the exhaust sample stream from which the sample was taken (raw or diluted exhaust), and convert this into a C₁-equivalent molar concentration. Add these C₁-equivalent molar concentrations to the molar concentration of non-oxygenated total hydrocarbon (NOTHC). The result is the molar concentration of total hydrocarbon equivalent (THCE). Calculate THCE concentration using the following equations, noting that Eq. 1065.665-3 is required only if you need to convert your oxygenated hydrocarbon (OHC) concentration from mass to moles:

Where:

χ_THCE = the sum of the C₁-equivalent concentrations of non-oxygenated hydrocarbon, alcohols, and aldehydes.

χ_NOTHC = the sum of the C₁-equivalent concentrations of NOTHC.

χOHCi = the C₁-equivalent concentration of oxygenated species i in diluted exhaust, not corrected for initial contamination.

χ_OHCi-init = the C₁-equivalent concentration of the initial system contamination (optional) of oxygenated species i, dry-to-wet corrected.

χ_{THC[THC-FID]cor} = the C₁-equivalent response to NOTHC and all OHC in diluted exhaust, HC contamination and dry-to-wet corrected, as measured by the THC-FID.

RF_{OHCi[THC-FID]} = the response factor of the FID to species i relative to propane on a C₁-equivalent basis.

M_dexh = the molar mass of diluted exhaust as determine in §1065.340.

m_dexhOHCi = the mass of oxygenated species i in dilute exhaust.

M_OHCi = the C₁-equivalent molecular weight of oxygenated species i.

m_dexh = the mass of diluted exhaust.

n_dexhOHCi = the number of moles of oxygenated species i in total diluted exhaust flow.

n_dexh = the total diluted exhaust flow.

(b) If we require you to determine nonmethane hydrocarbon equivalent (NMHCE), use the following equation:

Where:

x_NMHCE = the sum of the C₁-equivalent concentrations of nonoxygenated nonmethane hydrocarbon (NONMHC), alcohols, and aldehydes.

RF_CH4[THC-FID] = the response factor of THC-FID to CH₄.

x_CH4 = concentration of CH_4, HC contamination (optional) and dry-to-wet corrected, as measured by the gas chromatograph FID.

(c) The following example shows how to determine NMHCE emissions based on ethanol (C₂H₅OH), methanol (CH₃OH), acetaldehyde (C₂H₄O), and formaldehyde (CH₂O) as C₁-equivalent molar concentrations:

x_{THC[THC-FID]cor} = 145.6 µmol/mol

x_CH4 = 18.9 µmol/mol

x_C2H5OH = 100.8 µmol/mol

x_CH3OH = 1.1 µmol/mol

x_C2H4O = 19.1 µmol/mol

x_CH2O = 1.3 µmol/mol

RF_CH4[THC-FID] = 1.07

RF_{C2H5OH[THC-FID]} = 0.76

RF_{CH3OH[THC-FID]} = 0.74

RF_{H2H4O[THC-FID]} = 0.50

RF_{CH2O[THC-FID]} = 0.0

x_NMHCE = x_{THC[THC-FID]cor} − (x_C2H5OH · RF_{C2H5OH[THC-FID]} + x_CH3OH · RF_{CH3OH[THC-FID]} + x_C2H4O · RF_{C2H4O[THC-FID]} + x_CH2O · RF_{CH2O[THC-FID]}) + x_C2H5OH + x_CH3OH + x_C2H4O + x_CH2O − (RF_CH4[THC-FID] · x_CH4)

x_NMHCE = 145.6 − (100.8 · 0.76 + 1.1 · 0.74 + 19.1 · 0.50 + 1.3 · 0) + 100.8 + 1.1 + 19.1 + 1.3 − (1.07 · 18.9)

x_NMHCE = 160.71 µmol/mol

[79 FR 23805, Apr. 28, 2014, as amended at 81 FR 74187, Oct. 25, 2016; 86 FR 34567, Jun. 29, 2021]

§1065.667 Dilution air background emission correction.

(a) To determine the mass of background emissions to subtract from a diluted exhaust sample, first determine the total flow of dilution air, n_dil, over the test interval. This may be a measured quantity or a calculated quantity. Multiply the total flow of dilution air by the mean mole fraction (i.e., concentration) of a background emission. This may be a time-weighted mean or a flow-weighted mean (e.g., a proportionally sampled background). Finally, multiply by the molar mass, M, of the associated gaseous emission constituent. The product of n_dil and the mean molar concentration of a background emission and its molar mass, M, is the total background emission mass, m. In the case of PM, where the mean PM concentration is already in units of mass per mole of exhaust, multiply it by the total amount of dilution air flow, and the result is the total background mass of PM, m_PM. Subtract total background mass from total mass to correct for background emissions.

(b) You may determine the total flow of dilution air by a direct flow measurement.

(c) You may determine the total flow of dilution air by subtracting the calculated raw exhaust molar flow as described in §1065.655(g) from the measured dilute exhaust flow. This may be done by totaling continuous calculations or by using batch results.

(d) You may determine the total flow of dilution air from the measured dilute exhaust flow and a chemical balance of the fuel, DEF, intake air, and dilute exhaust as described in §1065.655. For this paragraph (d), the molar flow of dilution air is calculated by multiplying the dilute exhaust flow by the mole fraction of dilution gas to dilute exhaust, χ_dil/ex, from the dilute chemical balance. This may be done by totaling continuous calculations or by using batch results. For example, to use batch results, the total flow of dilution air is calculated by multiplying the total flow of diluted exhaust, n_dexh, by the flow-weighted mean mole fraction of dilution air in diluted exhaust, χ _dil/exh. Calculate χ _dil/exh using flow-weighted mean concentrations of emissions in the chemical balance, as described in §1065.655. The chemical balance in §1065.655 assumes that your engine operates stoichiometrically, even if it is a lean-burn engine, such as a compression-ignition engine. Note that for lean-burn engines this assumption could result in an error in emission calculations. This error could occur because the chemical balance in §1065.655 treats excess air passing through a lean-burn engine as if it was dilution air. If an emission concentration expected at the standard is about 100 times its dilution air background concentration, this error is negligible. However, if an emission concentration expected at the standard is similar to its background concentration, this error could be significant. If this error might affect your ability to show that your engines comply with applicable standards in this chapter, we recommend that you either determine the total flow of dilution air using one of the more accurate methods in paragraph (b) or (c) of this section, or remove background emissions from dilution air by HEPA filtration, chemical adsorption, or catalytic scrubbing. You might also consider using a partial-flow dilution technique such as a bag mini-diluter, which uses purified air as the dilution air.

(e) The following is an example of using the flow-weighted mean fraction of dilution air in diluted exhaust, x ͞_dil/exh, and the total mass of background emissions calculated using the total flow of diluted exhaust, n_dexh, as described in §1065.650(c):

Example:

M_NOx = 46.0055 g/mol

x ͞_bkgnd = 0.05 µmol/mol = 0.05⋅10⁻⁶ mol/mol

n_dexh = 23280.5 mol

x ͞_dil/exh = 0.843 mol/mol

m_bkgndNOxdexh = 46.0055⋅0.05⋅10⁻⁶⋅23280.5

m_bkgndNOxdexh = 0.0536 g

m_bkgndNOx = 0.843 ⋅ 0.0536

m_bkgndNOx = 0.0452 g

(f) The following is an example of using the fraction of dilution air in diluted exhaust, x_dil/exh, and the mass rate of background emissions calculated using the flow rate of diluted exhaust, n ̇_dexh, as described in §1065.650(c):

Example:

M_NOx = 46.0055 g/mol

x_bkgnd = 0.05 µmol/mol = 0.05⋅10⁻⁶ mol/mol

n ̇_dexh = 23280.5 mol/s

x_dil/exh = 0.843 mol/mol

m ̇_bkgndNOxdexh = 46.0055⋅0.05⋅10⁻⁶⋅23280.5

m ̇_bkgndNOxdexh = 0.0536 g/hr

m ̇_bkgndNOx = 0.843 ⋅ 0.0536

m ̇_bkgndNOx = 0.0452 g/hr

[76 FR 57465, Sept. 15, 2011, as amended at 81 FR 74188, Oct. 25, 2016; 86 FR 34567, Jun. 29, 2021; 88 FR 4686, Jan. 24, 2023]

§1065.670 NOX intake-air humidity and temperature corrections.

See the standard-setting part to determine if you may correct NO _X emissions for the effects of intake-air humidity or temperature. Use the NO _X intake-air humidity and temperature corrections specified in the standard-setting part instead of the NO _X intake-air humidity correction specified in this part 1065. If the standard-setting part does not prohibit correcting NO _X emissions for intake-air humidity according to this part 1065, correct NO _X concentrations for intake-air humidity as described in this section. See §1065.650(c)(1) for the proper sequence for applying the NO _X intake-air humidity and temperature corrections. You may use a time-weighted mean intake air humidity to calculate this correction if your intake air humidity remains within a tolerance of ±0.0025 mol/mol of the mean value over the test interval. For intake-air humidity correction, use one of the following approaches:

(a) For compression-ignition engines operating on carbon-containing fuels and lean-burn combustion engines operating on fuels other than carbon-containing fuels, correct for intake-air humidity using the following equation:<

Example:

x_NOxuncor = 700.5 µmol/mol

x_H2O = 0.022 mol/mol

x_NOxcor = 700.5 · (9.953 · 0.022 + 0.832)

x_NOxcor = 736.2 µmol/mol

(b) For spark-ignition engines operating on carbon-containing fuels and stoichiometric combustion engines operating on fuels other than carbon-containing fuels, correct for intake-air humidity using the following equation:

Example:

x_NOxuncor = 154.7 µmol/mol

x_H2O = 0.022 mol/mol

x_NOxcor = 154.7 · (18.840 · 0.022 + 0.68094)

x_NOxcor = 169.5 µmol/mol

(c) Develop your own correction, based on good engineering judgment.

[75 FR 23056, Apr. 30, 2010, as amended at 76 FR 57466, Sept. 15, 2011; 88 FR 4686, Jan. 24, 2023; 89 FR 29823, Apr. 22, 2024]

§1065.672 Drift correction.

(a) Scope and frequency. Perform the calculations in this section to determine if gas analyzer drift invalidates the results of a test interval. If drift does not invalidate the results of a test interval, correct that test interval's gas analyzer responses for drift according to this section. Use the drift-corrected gas analyzer responses in all subsequent emission calculations. Note that the acceptable threshold for gas analyzer drift over a test interval is specified in §1065.550 for both laboratory testing and field testing.

(b) Correction principles. The calculations in this section utilize a gas analyzer's responses to reference zero and span concentrations of analytical gases, as determined sometime before and after a test interval. The calculations correct the gas analyzer's responses that were recorded during a test interval. The correction is based on an analyzer's mean responses to reference zero and span gases, and it is based on the reference concentrations of the zero and span gases themselves. Validate and correct for drift as follows:

(c) Drift validation. After applying all the other corrections—except drift correction—to all the gas analyzer signals, calculate emissions according to §1065.650. Then correct all gas analyzer signals for drift according to this section. Recalculate emissions using all of the drift-corrected gas analyzer signals. Validate and report the emission results before and after drift correction according to §1065.550.

(d) Drift correction. Correct all gas analyzer signals as follows:

(1) Correct each recorded concentration, x_i, for continuous sampling or for batch sampling, x ͞.

(2) Correct for drift using the following equation:

Where:

x_{idriftcorrected} = concentration corrected for drift.

x_refzero = reference concentration of the zero gas, which is usually zero unless known to be otherwise.

x_refspan = reference concentration of the span gas.

x_prespan = pre-test interval gas analyzer response to the span gas concentration.

x_postspan = post-test interval gas analyzer response to the span gas concentration.

x_i or x ͞ = concentration recorded during test, before drift correction.

x_prezero = pre-test interval gas analyzer response to the zero gas concentration.

x_postzero = post-test interval gas analyzer response to the zero gas concentration.

Example:

x_refzero = 0 µmol/mol

x_refspan = 1800.0 µmol/mol

x_prespan = 1800.5 µmol/mol

x_postspan = 1695.8 µmol/mol

x_i or x ͞ = 435.5 µmol/mol

x_prezero = 0.6 µmol/mol

x_postzero = −5.2 µmol/mol

x_{idriftcorrected} = 450.2 µmol/mol

(3) For any pre-test interval concentrations, use the last concentration determined before the test interval. For some test intervals, the last pre-zero or pre-span might have occurred before one or more earlier test intervals.

(4) For any post-test interval concentrations, use the first concentration determined after the test interval. For some test intervals, the first post-zero or post-span might occur after one or more later test intervals.

(5) If you do not record any pre-test interval analyzer response to the span gas concentration, x_prespan, set x_prespan equal to the reference concentration of the span gas:

x_prespan = x_refspan.

(6) If you do not record any pre-test interval analyzer response to the zero gas concentration, x_prezero, set x_prezero equal to the reference concentration of the zero gas:

x_prezero = x_refzero.

(7) Usually the reference concentration of the zero gas, x_refzero, is zero: x_refzero = 0 µmol/mol. However, in some cases you might know that x_refzero has a non-zero concentration. For example, if you zero a CO₂ analyzer using ambient air, you may use the default ambient air concentration of CO₂, which is 375 µmol/mol. In this case, x_refzero = 375 µmol/mol. Note that when you zero an analyzer using a non-zero x_refzero, you must set the analyzer to output the actual x_refzero concentration. For example, if x_refzero = 375 µmol/mol, set the analyzer to output a value of 375 µmol/mol when the zero gas is flowing to the analyzer.

[70 FR 40516, July 13, 2005, as amended at 74 FR 8427, Feb. 24, 2009; 75 FR 23056, Apr. 30, 2010; 88 FR 4686, Jan. 24, 2023]

§1065.675 CLD quench verification calculations.

Perform CLD quench-check calculations as follows:

(a) Perform a CLD analyzer quench verification test as described in §1065.370.

(b) Estimate the maximum expected mole fraction of water during emission testing, x_H2Oexp. Make this estimate where the humidified NO span gas was introduced in §1065.370(e)(6). When estimating the maximum expected mole fraction of water, consider the maximum expected water content in intake air, fuel combustion products, and dilution air (if applicable). If you introduced the humidified NO span gas into the sample system upstream of a sample dryer during the verification test, you need not estimate the maximum expected mole fraction of water and you must set x_H2Oexp equal to x_H2Omeas.

(c) Estimate the maximum expected CO₂ concentration during emission testing, x_CO2exp. Make this estimate at the sample system location where the blended NO and CO₂ span gases are introduced according to §1065.370(d)(10). When estimating the maximum expected CO₂ concentration, consider the maximum expected CO₂ content in fuel combustion products and dilution air.

(d) Calculate quench as follows:

Where:

quench = amount of CLD quench.

χ_NOdry = concentration of NO upstream of a humidity generator, according to §1065.370(e)(4).

χ_NOwet = measured concentration of NO downstream of a humidity generator, according to §1065.370(e)(9).

χ_H2Oexp = maximum expected mole fraction of water during emission testing, according to paragraph (b) of this section.

χ_H2Omeas = measured mole fraction of water during the quench verification, according to §1065.370(e)(7).

χ_NOmeas = measured concentration of NO when NO span gas is blended with CO₂ span gas, according to §1065.370(d)(10).

χ_NOact = actual concentration of NO when NO span gas is blended with CO₂ span gas, according to §1065.370(d)(11) and calculated according to Eq. 1065.675-2.

χ_CO2exp = maximum expected concentration of CO₂ during emission testing, according to paragraph (c) of this section.

χ_CO2act = actual concentration of CO₂ when NO span gas is blended with CO₂ span gas, according to §1065.370(d)(9).

Where:

χ_NOspan = the NO span gas concentration input to the gas divider, according to §1065.370(d)(5).

χ_CO2span = the CO₂ span gas concentration input to the gas divider, according to §1065.370(d)(4).

Example:

χ_NOdry = 1800.0 μmol/mol

χ_NOwet = 1739.6 μmol/mol

χ_H2Oexp = 0.030 mol/mol

χ_H2Omeas = 0.030 mol/mol

χ_NOmeas = 1515.2 μmol/mol

χ_NOspan = 3001.6 μmol/mol

χ_CO2exp = 3.2%

χ_CO2span = 6.1%

χ_CO2act = 2.98%

quench = (−0.0036655−0.014020171) · 100% = −1.7685671%

[73 FR 59340, Oct. 8, 2008, as amended at 76 FR 57466, Sept. 15, 2011; 81 FR 74188, Oct. 25, 2016; 86 FR 34568, Jun. 29, 2021; 88 FR 4686, Jan. 24, 2023]

§1065.680 Adjusting emission levels to account for infrequently regenerating aftertreatment devices.

This section describes how to calculate and apply emission adjustment factors for engines using aftertreatment technology with infrequent regeneration events that may occur during testing. These adjustment factors are typically calculated based on measurements conducted for the purposes of engine certification, and then used to adjust the results of testing related to demonstrating compliance with emission standards. For this section, “regeneration” means an intended event during which emission levels change while the system restores aftertreatment performance. For example, exhaust gas temperatures may increase temporarily to remove sulfur from an adsorber or SCR catalyst or to oxidize accumulated particulate matter in a trap. The duration of this event extends until the aftertreatment performance and emission levels have returned to normal baseline levels. Also, “infrequent” refers to regeneration events that are expected to occur on average less than once over a transient or ramped-modal duty cycle, or on average less than once per mode in a discrete-mode test.

(a) Apply adjustment factors based on whether there is active regeneration during a test segment. The test segment may be a test interval or a full duty cycle, as described in paragraph (b) of this section. For engines subject to standards over more than one duty cycle, you must develop adjustment factors under this section for each separate duty cycle. You must be able to identify active regeneration in a way that is readily apparent during all testing. All adjustment factors for regeneration are additive.

(1) If active regeneration does not occur during a test segment, apply an upward adjustment factor, UAF, that will be added to the measured emission rate for that test segment. Use the following equation to calculate UAF:

Where:

EF_A[cycle] = the average emission factor over the test segment as determined in paragraph (a)(4) of this section.

EF_L[cycle] = measured emissions over a complete test segment in which active regeneration does not occur.

Example:

EF_ARMC = 0.15 g/kW·hr

EF_LRMC = 0.11 g/kW·hr

UAF_RMC = 0.15 − 0.11 = 0.04 g/kW·hr

(2) If active regeneration occurs or starts to occur during a test segment, apply a downward adjustment factor, DAF, that will be subtracted from the measured emission rate for that test segment. Use the following equation to calculate DAF:

Where:

EF_H[cycle] = measured emissions over the test segment from a complete regeneration event, or the average emission rate over multiple complete test segments with regeneration if the complete regeneration event lasts longer than one test segment.

Example:

EF_ARMC = 0.15 g/kW·hr

EF_HRMC = 0.50 g/kW·hr

DAF_RMC = 0.50 − 0.15 = 0.35 g/kW·hr

(3) Note that emissions for a given pollutant may be lower during regeneration, in which case EF_L would be greater than EF_H, and both UAF and DAF would be negative.

(4) Calculate the average emission factor, EF_A, as follows:

Where:

F_[cycle] = the frequency of the regeneration event during the test segment, expressed in terms of the fraction of equivalent test segments during which active regeneration occurs, as described in paragraph (a)(5) of this section.

Example:

F_RMC = 0.10

EF_ARMC = 0.10 · 0.50 + (1.00 − 0.10) · 0.11 = 0.15 g/kW·hr

(5) The frequency of regeneration, F, generally characterizes how often a regeneration event occurs within a series of test segments. Determine F using the following equation, subject to the provisions of paragraph (a)(6) of this section:

Where:

i_r[cycle] = the number of successive test segments required to complete an active regeneration, rounded up to the next whole number.

i_f[cycle] = the number of test segments from the end of one complete regeneration event to the start of the next active regeneration, without rounding.

Example:

i_rRMC = 2

i_fRMC = 17.86

(6) Use good engineering judgment to determine i_r and i_f, as follows:

(i) For engines that are programmed to regenerate after a specific time interval, you may determine the duration of a regeneration event and the time between regeneration events based on the engine's design parameters. For other engines, determine these values based on measurements from in-use operation or from running repetitive duty cycles in a laboratory.

(ii) For engines subject to standards over multiple duty cycles, such as for transient and steady-state testing, apply this same calculation to determine a value of F for each duty cycle.

(iii) Consider an example for an engine that is designed to regenerate its PM filter 500 minutes after the end of the last regeneration event, with the regeneration event lasting 30 minutes. If the RMC takes 28 minutes, i_rRMC = 2 (30 ÷ 28 = 1.07, which rounds up to 2), and i_fRMC = 500 ÷ 28 = 17.86.

(b) Develop adjustment factors for different types of testing as follows:

(1) Discrete-mode testing. Develop separate adjustment factors for each test mode (test interval) of a discrete-mode test. When measuring EF_H, if a regeneration event has started but is not complete when you reach the end of the sampling time for a test interval, extend the sampling period for that test interval until the regeneration event is complete.

(2) Ramped-modal and transient testing. Develop a separate set of adjustment factors for an entire ramped-modal cycle or transient duty cycle. When measuring EF_H, if a regeneration event has started but is not complete when you reach the end of the duty cycle, start the next repeat test as soon as possible, allowing for the time needed to complete emission measurement and installation of new filters for PM measurement; in that case EF_H is the average emission level for the test segments that included regeneration.

(3) Accounting for cold-start measurements. For engines subject to cold-start testing requirements, incorporate cold-start operation into your analysis as follows:

(i) Determine the frequency of regeneration, F, in a way that incorporates the impact of cold-start operation in proportion to the cold-start weighting factor specified in the standard-setting part. You may use good engineering judgment to determine the effect of cold-start operation analytically.

(ii) Treat cold-start testing and hot-start testing together as a single test segment for adjusting measured emission results under this section. Apply the adjustment factor to the composite emission result.

(iii) You may apply the adjustment factor only to the hot-start test result if your aftertreatment technology does not regenerate during cold operation as represented by the cold-start transient duty cycle. If we ask for it, you must demonstrate this by engineering analysis or by test data.

(c) If an engine has multiple regeneration strategies, determine and apply adjustment factors under this section separately for each type of regeneration.

[81 FR 74189, Oct. 25, 2016; 88 FR 4686, Jan. 24, 2023]

§1065.690 Buoyancy correction for PM sample media.

(a) General. Correct PM sample media for their buoyancy in air if you weigh them on a balance. The buoyancy correction depends on the sample media density, the density of air, and the density of the calibration weight used to calibrate the balance. The buoyancy correction does not account for the buoyancy of the PM itself, because the mass of PM typically accounts for only (0.01 to 0.10)% of the total weight. A correction to this small fraction of mass would be at the most 0.010%.

(b) PM sample media density. Different PM sample media have different densities. Use the known density of your sample media, or use one of the densities for some common sampling media, as follows:

(1) For PTFE-coated borosilicate glass, use a sample media density of 2300 kg/m ³.

(2) For PTFE membrane (film) media with an integral support ring of polymethylpentene that accounts for 95% of the media mass, use a sample media density of 920 kg/m ³.

(3) For PTFE membrane (film) media with an integral support ring of PTFE, use a sample media density of 2144 kg/m ³.

(c) Air density. Because a PM balance environment must be tightly controlled to an ambient temperature of (22 ±1)°C and humidity has an insignificant effect on buoyancy correction, air density is primarily a function of atmospheric pressure. Therefore you may use nominal constant values for temperature and humidity when determining the air density of the balance environment in Eq. 1065.690-2.

(d) Calibration weight density. Use the stated density of the material of your metal calibration weight. The example calculation in this section uses a density of 8000 kg/m ³, but you should know the density of your weight from the calibration weight supplier or the balance manufacturer if it is an internal weight.

(e) Correction calculation. Correct the PM sample media for buoyancy using the following equations:

Where:

m_cor = PM mass corrected for buoyancy.

m_uncor = PM mass uncorrected for buoyancy.

r_air = density of air in balance environment.

r_weight = density of calibration weight used to span balance.

r_media = density of PM sample media, such as a filter.

Where:

p_abs = absolute pressure in balance environment.

M_mix = molar mass of air in balance environment.

R = molar gas constant.

T_amb = absolute ambient temperature of balance environment.

[70 FR 40516, July 13, 2005, as amended at 73 FR 37339, June 30, 2008; 75 FR 23056, Apr. 30, 2010; 79 FR 23805, Apr. 28, 2014; 81 FR 74191, Oct. 25, 2016]

§1065.695 Data requirements.

(a) To determine the information we require from engine tests, refer to the standard-setting part and request from your EPA Program Officer the format used to apply for certification or demonstrate compliance. We may require different information for different purposes, such as for certification applications, approval requests for alternate procedures, selective enforcement audits, laboratory audits, production-line test reports, and field-test reports.

(b) See the standard-setting part and §1065.25 regarding recordkeeping.

(c) We may ask you the following about your testing, and we may ask you for other information as allowed under the Act:

(1) What approved alternate procedures did you use? For example:

(i) Partial-flow dilution for proportional PM.

(ii) CARB test procedures.

(iii) ISO test procedures.

(2) What laboratory equipment did you use? For example, the make, model, and description of the following:

(i) Engine dynamometer and operator demand.

(ii) Probes, dilution, transfer lines, and sample preconditioning components.

(iii) Batch storage media (such as the bag material or PM filter material).

(3) What measurement instruments did you use? For example, the make, model, and description of the following:

(i) Speed and torque instruments.

(ii) Flow meters.

(iii) Gas analyzers.

(iv) PM balance.

(4) When did you conduct calibrations and performance checks and what were the results? For example, the dates and results of the following:

(i) Linearity verification.

(ii) Interference checks.

(iii) Response checks.

(iv) Leak checks.

(v) Flow meter checks.

(5) What engine did you test? For example, the following:

(i) Manufacturer.

(ii) Family name on engine label.

(iii) Model.

(iv) Model year.

(v) Identification number.

(6) How did you prepare and configure your engine for testing? Consider the following examples:

(i) Dates, hours, duty cycle and fuel used for service accumulation.

(ii) Dates and description of scheduled and unscheduled maintenance.

(iii) Allowable pressure range of intake restriction.

(iv) Allowable pressure range of exhaust restriction.

(v) Charge air cooler volume.

(vi) Charge air cooler outlet temperature, specified engine conditions and location of temperature measurement.

(vii) Fuel temperature and location of measurement.

(viii) Any aftertreatment system configuration and description.

(ix) Any crankcase ventilation configuration and description (e.g., open, closed, PCV, crankcase scavenged).

(x) Number and type of preconditioning cycles.

(7) How did you test your engine? For example:

(i) Constant speed or variable speed.

(ii) Mapping procedure (step or sweep).

(iii) Continuous or batch sampling for each emission.

(iv) Raw or dilute sampling; any dilution-air background sampling.

(v) Duty cycle and test intervals.

(vi) Cold-start, hot-start, warmed-up running.

(vii) Absolute pressure, temperature, and dewpoint of intake and dilution air.

(viii) Simulated engine loads, curb idle transmission torque value.

(ix) Warm-idle speed value.

(x) Simulated vehicle signals applied during testing.

(xi) Bypassed governor controls during testing.

(xii) Date, time, and location of test (e.g., dynamometer laboratory identification).

(xiii) Cooling medium for engine and charge air.

(xiv) Operating temperatures of coolant, head, and block.

(xv) Natural or forced cool-down and cool-down time.

(xvi) Canister loading.

(8) How did you validate your testing? For example, results from the following:

(i) Duty cycle regression statistics for each test interval.

(ii) Proportional sampling.

(iii) Drift.

(iv) Reference PM sample media in PM-stabilization environment.

(v) Carbon balance error verification, if performed.

(9) How did you calculate results? For example, results from the following:

(i) Drift correction.

(ii) Noise correction.

(iii) “Dry-to-wet” correction.

(iv) NMHC, CH₄, and contamination correction.

(v) Chemical balance method—carbon-based or hydrogen-based chemical balance method.

(vi) NO_X humidity correction.

(vii) Brake-specific emission formulation - total mass divided by total work, mass rate divided by power, or ratio of mass to work.

(viii) Rounding emission results.

(10) What were the results of your testing? For example:

(i) Maximum mapped power and speed at maximum power.

(ii) Maximum mapped torque and speed at maximum torque.

(iii) For constant-speed engines: no-load governed speed.

(iv) For constant-speed engines: test torque.

(v) For variable-speed engines: maximum test speed.

(vi) Speed versus torque map.

(vii) Speed versus power map.

(viii) Brake-specific emissions over the duty cycle and each test interval.

(ix) Brake-specific fuel consumption.

(11) What fuel did you use? For example:

(i) Fuel that met specifications of subpart H of this part.

(ii) Alternate fuel.

(iii) Oxygenated fuel.

(12) How did you field test your engine? For example:

(i) Data from paragraphs (c)(1), (3), (4), (5), and (9) of this section.

(ii) Probes, dilution, transfer lines, and sample preconditioning components.

(iii) Batch storage media (such as the bag material or PM filter material).

(iv) Continuous or batch sampling for each emission.

(v) Raw or dilute sampling; any dilution air background sampling.

(vi) Cold-start, hot-start, warmed-up running.

(vii) Intake and dilution air absolute pressure, temperature, dewpoint.

(viii) Curb idle transmission torque value.

(ix) Warm idle speed value, any enhanced-idle speed value.

(x) Date, time, and location of test (e.g., identify the testing laboratory).

(xi) Proportional sampling validation.

(xii) Drift validation.

(xiii) Operating temperatures of coolant, head, and block.

(xiv) Vehicle make, model, model year, identification number.

[70 FR 40516, July 13, 2005, as amended at 73 FR 37339, June 30, 2008; 79 FR 23807, Apr. 28, 2014; 86 FR 34568, Jun. 29, 2021; 88 FR 4687, Jan. 24, 2023; 89 FR 29823, Apr. 22, 2024]