U.S. Code of Federal Regulations
Regulations most recently checked for updates: Aug 13, 2024
§ 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.
(2) Perform calculations for calibrations and performance checks.
(3) Determine statistical values.
(b) You may use data from multiple systems to calculate test results for a single emission test, consistent with good engineering judgment. You may also make multiple measurements from a single batch sample, such as multiple weighings of a PM filter or multiple readings from a bag sample. Although you may use an average of multiple measurements from a single test, you may not use test results from multiple emission tests to report emissions.
(1) We allow weighted means where appropriate.
(2) You may discard statistical outliers, but you must report all results.
(3) For emission measurements related to durability testing, we may allow you to exclude certain test points other than statistical outliers relative to compliance with emission standards, consistent with good engineering judgment and normal measurement variability; however, you must include these results when calculating the deterioration factor. This would allow you to use durability data from an engine that has an intermediate test result above the standard that cannot be discarded as a statistical outlier, as long as good engineering judgment indicates that the test result does not represent the engine's actual emission level. Note that good engineering judgment would preclude you from excluding endpoints. Also, if normal measurement variability causes emission results below zero, include the negative result in calculating the deterioration factor to avoid an upward bias. These provisions related to durability testing are intended to address very stringent standards where measurement variability is large relative to the emission standard.
(c) You may use any of the following calculations instead of the calculations specified in this subpart G:
(1) Mass-based emission calculations prescribed by the International Organization for Standardization (ISO), according to ISO 8178, except the following:
(i) ISO 8178-4 Section 9.1.6, NO
(ii) [Reserved]
(2) Other calculations that you show are equivalent to within ±0.1% of the brake-specific emission results determined using the calculations specified in this subpart G.
§ 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 “
(b) Arithmetic mean. Calculate an arithmetic mean, y
(c) Standard deviation. Calculate the standard deviation for a non-biased (e.g., N-1) sample, σ, as follows:
(d) Root mean square. Calculate a root mean square, rms
(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
(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:
(2) For a paired t-test, calculate the t statistic and its number of degrees of freedom, v, as follows, noting that the ε
(3) Use Table 1 of this section to compare t to the t
Table 1 of § 1065.602—Critical
Confidence | ||
---|---|---|
90% | 95% | |
1 | 6.314 | 12.706 |
2 | 2.920 | 4.303 |
3 | 2.353 | 3.182 |
4 | 2.132 | 2.776 |
5 | 2.015 | 2.571 |
6 | 1.943 | 2.447 |
7 | 1.895 | 2.365 |
8 | 1.860 | 2.306 |
9 | 1.833 | 2.262 |
10 | 1.812 | 2.228 |
11 | 1.796 | 2.201 |
12 | 1.782 | 2.179 |
13 | 1.771 | 2.160 |
14 | 1.761 | 2.145 |
15 | 1.753 | 2.131 |
16 | 1.746 | 2.120 |
18 | 1.734 | 2.101 |
20 | 1.725 | 2.086 |
22 | 1.717 | 2.074 |
24 | 1.711 | 2.064 |
26 | 1.706 | 2.056 |
28 | 1.701 | 2.048 |
30 | 1.697 | 2.042 |
35 | 1.690 | 2.030 |
40 | 1.684 | 2.021 |
50 | 1.676 | 2.009 |
70 | 1.667 | 1.994 |
100 | 1.660 | 1.984 |
1000+ | 1.645 | 1.960 |
(g) F-test. Calculate the F statistic as follows:
(1) For a 90% confidence F-test, use the following table to compare F to the F
(2) For a 95% confidence F-test, use the following table to compare F to the F
(h) Slope. Calculate a least-squares regression slope, a
(1) If the intercept floats, i.e., is not forced through zero:
(2) If the intercept is forced through zero, such as for verifying proportional sampling:
(i) Intercept. For a floating intercept, calculate a least-squares regression intercept, a
(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:
(2) If the intercept is forced through zero, such as for verifying proportional sampling:
(k) Coefficient of determination. Calculate a coefficient of determination, r
(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
(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
(ii) Based on your engine design, estimate maximum power, P
(iii) Use your estimated values as described in the following example calculation:
(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
(ii) Multiply your CVS total molar flow rate by the time interval of the duty cycle, Δt
(iii) Use your estimated values as described in the following example calculation:
(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:
(ii) Determine the median as the average of the data point i and the data point i + 1 as follows:
Example:
(2) For odd numbers of data points, determine the rank of the data point whose value is the median and the corresponding median value as follows:
Example:
§ 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
(1) Determine a measured value for ƒ
(i) Determine maximum power, P
(ii) Determine the lowest and highest engine speeds corresponding to 98% of P
(iii) Determine the engine speed corresponding to maximum power, f
(iv) Transform the map into a normalized power-versus-speed map by dividing power terms by P
(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
(vii) The following example illustrates a calculation of f
P
(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
(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
(1) For constant speed engines mapped using the methods in § 1065.510(d)(5)(i) or (ii), determine a measured value for T
(i) Determine maximum power, P
(ii) Determine the lowest and highest engine speeds corresponding to 98% of P
(iii) Determine the engine speed corresponding to maximum power, f
(iv) Transform the map into a normalized power-versus-speed map by dividing power terms by P
(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
(vii) The measured T
(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
(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:
(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
(3) Intermediate speed. Based on the map, determine maximum torque, T
(i) f
(ii) 60% of maximum test speed if f
(iii) 75% of maximum test speed if f
(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
(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.
§ 1065.630 - Local acceleration of gravity.
(a) The acceleration of Earth's gravity, a
(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
§ 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
(b) PDP calibration calculations. Perform the following steps to calibrate a PDP flow meter:
(1) Calculate PDP volume pumped per revolution, V
(2) Calculate a PDP slip correction factor, K
(3) Perform a least-squares regression of V
(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:
Table 1 of § 1065.640—Example of PDP Calibration Data
(revolution/s) | (m ^{3}/s) | (m ^{3}/revolution) |
---|---|---|
12.6 | 0.841 | 0.056 |
16.5 | 0.831 | −0.013 |
20.9 | 0.809 | 0.028 |
23.4 | 0.788 | −0.061 |
(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
(1) Calculate molar flow rate, n
C
C
A
p
Z = compressibility factor.
M
R = molar gas constant.
T
(2) Using the data collected in § 1065.340, calculate C
(3) Determine C
(i) For CFV flow meters only, determine C
Table 2 of § 1065.640-
1.385 | 1.399 | |
---|---|---|
0.000 | 0.6822 | 0.6846 |
0.400 | 0.6857 | 0.6881 |
0.500 | 0.6910 | 0.6934 |
0.550 | 0.6953 | 0.6977 |
0.600 | 0.7011 | 0.7036 |
0.625 | 0.7047 | 0.7072 |
0.650 | 0.7089 | 0.7114 |
0.675 | 0.7137 | 0.7163 |
0.700 | 0.7193 | 0.7219 |
0.720 | 0.7245 | 0.7271 |
0.740 | 0.7303 | 0.7329 |
0.760 | 0.7368 | 0.7395 |
0.770 | 0.7404 | 0.7431 |
0.780 | 0.7442 | 0.7470 |
0.790 | 0.7483 | 0.7511 |
0.800 | 0.7527 | 0.7555 |
0.810 | 0.7573 | 0.7602 |
0.820 | 0.7624 | 0.7652 |
0.830 | 0.7677 | 0.7707 |
0.840 | 0.7735 | 0.7765 |
0.850 | 0.7798 | 0.7828 |
(ii) For any CFV or SSV flow meter, you may use the following equation to calculate C
(4) Calculate r as follows:
(i) For SSV systems only, calculate r
(ii) For CFV systems only, calculate r
(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
(iii) For diluted exhaust and dilution air, you may assume
(iv) For diluted exhaust and dilution air, you may assume the molar mass of the mixture, M
(v) For diluted exhaust and dilution air, you may assume a constant molar mass of the mixture, M
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:
Table 3 of § 1065.640—Examples of Dilution Air and Calibration Air
Dewpoints at Which You May Assume a Constant
If calibration | assume the following constant | for the following ranges of |
---|---|---|
dry | 28.96559 | dry to 18 |
0 | 28.89263 | dry to 21 |
5 | 28.86148 | dry to 22 |
10 | 28.81911 | dry to 24 |
15 | 28.76224 | dry to 26 |
20 | 28.68685 | -8 to 28 |
25 | 28.58806 | 12 to 31 |
30 | 28.46005 | 23 to 34 |
^{a} Range valid for all calibration and emission testing over the atmospheric pressure range (80.000 to 103.325) kPa.
(6) The following example illustrates the use of the governing equations to calculate C
(d) SSV calibration. Perform the following steps to calibrate an SSV flow meter:
(1) Calculate the Reynolds number, Re
Where, using the Sutherland three-coefficient viscosity model as captured in Table 4 of this section:
Table 4 of § 1065.640—Sutherland Three-Coefficient Viscosity Model Parameters
Gas ^{a} | µ | Temperature range within ±2% error ^{b} | Pressure limit ^{b} | ||
---|---|---|---|---|---|
(kg/(m·s)) | (K) | (K) | (K) | (kPa) | |
Air | 1.716·10 | 273 | 111 | 170 to 1900 | ≤1800 |
CO | 1.370·10 | 273 | 222 | 190 to 1700 | ≤3600 |
H | 1.12·10 | 350 | 1064 | 360 to 1500 | ≤10000 |
O | 1.919·10 | 273 | 139 | 190 to 2000 | ≤2500 |
N | 1.663·10 | 273 | 107 | 100 to 1500 | ≤1600 |
^{a} Use tabulated parameters only for the pure gases, as listed. Do not combine parameters in calculations to calculate viscosities of gas mixtures.
^{b} The model results are valid only for ambient conditions in the specified ranges.
(2) Create an equation for C
(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
(4) If the equation meets the criterion of SEE ≤ 0.5% · C
(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
(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
(1) Use the data collected at each calibration set point to calculate an individual C
(2) Calculate the mean and standard deviation of all the C
(3) If the standard deviation of all the C
(4) If the standard deviation of all the C
(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
(7) If the standard deviation of the remaining C
(8) If the standard deviation of the remaining C
§ 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
(2) Calculate V
(b) SSV molar flow rate. Calculate SSV molar flow rate, n
Using Eq. 1065.640-7:
Using Eq. 1065.640-6:
Using Eq. 1065.640-5:
(c) CFV molar flow rate. If you use multiple venturis and you calibrate each venturi independently to determine a separate discharge coefficient, C
(1) To calculate n
(2) To calculate the molar flow rate through one venturi or a combination of venturis, you may use its respective mean, K
§ 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
(b) Intake air. Calculate the mass of carbon in the intake air, m
(1) Calculate m
(2) Calculate m
(3) Calculate m
(4) Calculate m
(5) Determined m
(6) If you measure diluted exhaust, determine m
(c) Exhaust emissions. Calculate the mass of carbon in exhaust emissions, m
(d) Carbon balance error quantities. Calculate carbon balance error quantities as follows:
(1) Calculate carbon mass absolute error, ε
(2) Calculate carbon mass rate absolute error, ε
t = 1202.2 s = 0.3339 hr
(3) Calculate carbon mass relative error, ε
(4) Calculate composite carbon mass relative error, ε
(i) Calculate ε
(ii) The following example illustrates calculation of ε
(iii) The following example illustrates calculation of ε
§ 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):
Example:
§ 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
(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
(c) Relative humidity. If you measure humidity as a relative humidity, RH, determine the amount of water in an ideal gas, x
(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
§ 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., “
(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:
$$(2) For discrete-mode steady-state testing, you may calculate the brake-specific emissions over a test interval using the ratio of emission mass rate to power, as described in paragraph (e) of this section, using the following equation:
$$(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:
$$(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, t
(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
(iii) Correct all THC and CH
(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 CH
(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
(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:
Using Eq. 1065.650-5,
(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
(A) Calculate m for measuring gaseous emission constituents with sampling that results in a molar concentration, x
Using Eq. 1065.650-5:
(B) Calculate m for sampling PM or any other analysis of a batch sample that yields a mass per mole of exhaust, M
(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
(A) Calculate m for measuring gaseous emission constituents with sampling that results in a molar concentration, x
(B) Calculate m for sampling PM or any other analysis of a batch sample that yields a mass per mole of exhaust, M
(C) The following example illustrates a calculation of m
(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:
(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:
Using Eq. 1065.650-5:
(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
(1) To calculate, m
(2) To calculate an engine's mean steady-state total power, P
(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:
(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
(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
(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:
Using Eq. 1065.650-5,
(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
(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:
(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:
(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:
(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.
§ 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
(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
(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
(1) Convert your measured concentrations such as, x
(2) Enter the equations in paragraph (c)(4) of this section into a computer program to iteratively solve for x
(3) Use the following symbols and subscripts in the equations for performing the chemical balance calculations in this paragraph (c):
Table 1 of § 1065.655—Symbols and Subscripts for Chemical Balance Equations
Amount of dilution gas or excess air per mole of exhaust | |
---|---|
amount of dilution gas or excess air per mole of exhaust. | |
amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust | |
amount of H | |
water-gas reaction equilibrium coefficient; you may use 3.5 or calculate your own value using good engineering judgment | |
amount of H | |
amount of dry stoichiometric products per dry mole of intake air | |
amount of dilution gas and/or excess air per mole of dry exhaust | |
amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust | |
amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust | |
amount of intake air O | |
amount of intake air CO | |
amount of intake air H | |
amount of intake air CO | |
amount of dilution gas CO2 per mole of dilution gas | |
amount of dilution gas CO | |
amount of dilution gas H | |
amount of dilution gas H | |
amount of measured emission in the sample at the respective gas analyzer | |
amount of emission per dry mole of dry sample | |
amount of H | |
amount of H | |
α | atomic hydrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |
β | atomic oxygen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |
γ | atomic sulfur-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |
δ | atomic nitrogen-to-carbon ratio of the fuel (or mixture of test fuels) and any injected fluids |
(4) Use the following equations to iteratively solve for x
(5) The following example is a solution for x
(d) Carbon mass fraction of fuel. Determine carbon mass fraction of fuel, w
(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
Example:
(5) Table 2 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, n
(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
(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
(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:
(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
(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
§ 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
(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
(1) Convert your measured concentrations such as x
(2) Enter the equations in paragraph (c)(5) of this section into a computer program to iteratively solve for x
(3) Use the following symbols and subscripts in the equations for performing the chemical balance calculations in this paragraph (c):
Table 1 to Paragraph (
Amount of measured emission in the sample at the respective gas analyzer. | |
---|---|
Amount of emission per dry mole of exhaust. | |
Amount of emission per dry mole of dry exhaust. | |
Amount of H | |
Amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust. | |
Amount of hydrogen from fuel and any injected fluids in the exhaust per mole of dry exhaust. | |
Amount of dilution gas or excess air per mole of exhaust. | |
amount of dilution gas and/or excess air per mole of dry exhaust. | |
Amount of hydrogen from fuel and any injected fluids in the exhaust per mole of dry exhaust. | |
Amount of intake air required to produce actual combustion products per mole of dry (raw or diluted) exhaust. | |
Amount of undiluted exhaust, without excess air, per mole of dry (raw or diluted) exhaust. | |
Amount of intake air CO | |
amount of intake air CO | |
Amount of H | |
Amount of intake air H | |
Amount of intake air O | |
Amount of dilution gas CO | |
Amount of dilution gas CO | |
Amount of dilution gas H | |
Amount of dilution gas H | |
Effective carbon content of the fuel and any injected fluids. | |
Effective hydrogen content of the fuel and any injected fluids. | |
Effective oxygen content of the fuel and any injected fluids. | |
Effective sulfur content of the fuel and any injected fluids. | |
Effective nitrogen content of the fuel and any injected fluids. | |
Carbon mass fraction of the fuel (or mixture of test fuels) and any injected fluids. | |
Hydrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. | |
Oxygen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. | |
Sulfur mass fraction of the fuel (or mixture of test fuels) and any injected fluids. | |
Nitrogen mass fraction of the fuel (or mixture of test fuels) and any injected fluids. |
(4) Use the equations specified in this section to iteratively solve for x
(i) For x
(ii) The calculation of x
(iii) The calculation of x
(iv) The calculation of x
(5) The chemical balance equations are as follows:
(6) Depending on your measurements, use the equations and guess the quantities specified in the following table:
Table 2 to Paragraph (
When measuring | Guess . . . | Calculate . . . |
---|---|---|
(i) | (A) | |
(B) | ||
(ii) | (A) | |
(B) [Reserved] |
(7) The following example is a solution for
(d) Mass fractions of fuel. (1) For fuels other than carbon-containing fuels determine the mass fractions of fuel W
Example for NH
(2) For carbon-containing fuels and diesel exhaust fluid determine the mass fractions of fuel, W
Example:
(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
Example for a mixture of diesel and NH
w
w
w
w
w
(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).
Table 3 to Paragraph
Fuel | Atomic carbon, oxygen, and nitrogen-to-hydrogen ratios C |
---|---|
Hydrogen | C |
Ammonia | C |
(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
Example:
(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:
Example:
(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
(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:
Example:
§ 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
(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
(c) For a concentration measurement where you did not remove water, you may set x
(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:
§ 1065.660 - THC, NMHC, NMNEHC, CH4, and C2H6 determination.
(a) THC determination and initial THC/CH
Example:
(2) For the NMHC determination described in paragraph (b) of this section, correct
(3) For the NMNEHC determination described in paragraph (c) of this section, correct
(4) For the CH
(5) You may calculate THC as the sum of NMHC and CH
(6) You may calculate THC as the sum of NMNEHC, C
(b) NMHC determination. Use one of the following to determine NMHC concentration,
(1) If you do not measure CH
(2) For an NMC, calculate
(i) Use the following equation for an NMC configured as described in § 1065.365(d):
Eq. 1065.660-2
Where:
Example:
(ii) Use the following equation for penetration fractions determined using an NMC configuration as outlined in § 1065.365(e):
Example:
(iii) Use the following equation for an NMC configured as described in § 1065.365(f):
Example:
(3) For a GC-FID or FTIR, calculate
Example:
RF
(4) For an FTIR, calculate
Example:
(c) NMNEHC determination. Use one of the following methods to determine NMNEHC concentration,
(1) Calculate
(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) For a GC-FID, NMC FID, or FTIR, calculate
Example:
(3) For an FTIR, calculate x
Example:
(d) CH
(1) For an NMC, calculate x
(i) Use the following equation for an NMC configured as described in § 1065.365(d):
Example:
(ii) Use the following equation for an NMC configured as described in § 1065.365(e):
Example:
(iii) Use the following equation for an NMC configured as described in § 1065.365(f):
Example:
(2) For a GC-FID or FTIR, x
(e) C
§ 1065.665 - THCE and NMHCE 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 C
(b) If we require you to determine nonmethane hydrocarbon equivalent (NMHCE), use the following equation:
(c) The following example shows how to determine NMHCE emissions based on ethanol (C
§ 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
(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
(e) The following is an example of using the flow-weighted mean fraction of dilution air in diluted exhaust, x
(f) The following is an example of using the fraction of dilution air in diluted exhaust, x
§ 1065.670 - NOX intake-air humidity and temperature corrections.
See the standard-setting part to determine if you may correct NO
(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:
$$(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:
$$(c) Develop your own correction, based on good engineering judgment.
§ 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
(2) Correct for drift using the following equation:
(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
(6) If you do not record any pre-test interval analyzer response to the zero gas concentration, x
(7) Usually the reference concentration of the zero gas, x
§ 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
(c) Estimate the maximum expected CO
(d) Calculate quench as follows:
§ 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:
(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:
(3) Note that emissions for a given pollutant may be lower during regeneration, in which case EF
(4) Calculate the average emission factor, EF
(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:
(6) Use good engineering judgment to determine i
(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
(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
(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
(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.
§ 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
(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) For PTFE membrane (film) media with an integral support ring of PTFE, use a sample media density of 2144 kg/m
(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
(e) Correction calculation. Correct the PM sample media for buoyancy using the following equations:
§ 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, CH
(v) Chemical balance method—carbon-based or hydrogen-based chemical balance method.
(vi) NO
(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.