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unit of fuel (i.e., fuel efficiency of an airplane in level cruise flight). Airplane fuel efficiency defined by 506 SAR is commonly used by airplane manufacturers when describing airplane fuel efficiency performance 507 to customers (e.g., airlines). 508 509 510
6.2 Specific Air Range 511 512 As discussed in paragraph 6.1, Specific Air Range (SAR) is a measure of airplane cruise performance 513 that provides the distance an airplane can travel on a unit of fuel. 514 515 In accordance with § 38.13(a), for each airplane subject to part 38, the SAR value is calculated by using 516 either direct flight test measurements or using a performance model that is (i) validated by actual SAR 517 flight test data; and (ii) approved by the FAA before any SAR calculations are submitted. 518 519 The value of 1/SAR varies with airplane gross mass and is measured at three certification test points 520 based on gross mass. Section 38.13(b) provides that for each airplane model, a 1/SAR value is 521 determined at each of the following reference airplane masses: 522 523
1. High Gross Mass: 92 percent MTOM. 524
2. Low Gross Mass: (0.45 * MTOM) + (0.63 * (MTOM^0.924)). 525
3. Mid Gross Mass: simple arithmetic average of high gross mass and low gross mass 526 527 where all reference masses are expressed in kilograms (kg). 528 529 The three reference airplane masses were chosen with the objective of making the evaluation of fuel 530 burn performance relevant to day-to-day aircraft operations, and to make sure that the entire envelope of 531 cruise operations is accounted for. These three 1/SAR values, calculated at each of three certification 532 test points in accordance with §38.13(b), are weighted equally to give a single metric value. Section 533
38.13(c) requires that the value for (1/SAR)avg be obtained from the three 1/SAR points calculated in § 534
38.13(b), and subsequently used to determine the fuel efficiency metric value described in §38.11. An 535 illustrative example of the three representative cruise points is shown in the Figure 6-2. 536 537 538 539 Fig. 6-2. 540 541 An illustration of the three representative cruise points. 542 543 544 545 546
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The SAR values for each of the three reference masses defined in § 38.13(b) are to be calculated either 547 directly from flight measurements taken at each valid test point adjusted to reference specifications, or 548 indirectly from a performance model that has been validated by the test points, as required by § 549
38.13(a). The final SAR value for each reference mass is the simple arithmetic average of all valid test 550 points at the gross mass, or derived from a validated performance model as stated in § A38.5.2.3.1. No 551 data acquired from a valid test point shall be omitted unless approved by the FAA, as stated in Appendix 552 A § 38.5.2.3.1. 553 554 Note: Extrapolations consistent with accepted airworthiness practices to masses other than those tested 555 may be allowable using a validated performance model (for example, to validate new, higher MTOMs or 556 to validate the low gross weight range if it is not obtained during flight tests). The performance model 557 must be based on data covering an adequate range of lift coefficient, Mach number, and thrust specific 558 fuel consumption. No extrapolations of lift coefficient, Mach number, and thrust specific fuel consumption 559 are allowed. Use of any performance model is subject to AEE approval. See Appendix A § A38.5.2.3.2. 560 561
6.3 SAR Data Analysis 562 563 SAR data used to demonstrate compliance must consider both the selection of flight test data gathered 564 during each test condition used for each individual SAR point, as well as the distribution of the resulting 565 corrected SAR points relative to the three reference masses and the reference specifications. 566 567
6.3.1 SAR Measurement System 568 569 As stated in § A38.5.1.6 of part 38 Appendix A, the SAR measurement system consists of the 570 instruments and devices, including any associated procedures, used to acquire the parameter values 571 that are necessary for determination of the SAR for each flight test condition. Section A38.5.1.8 572 prescribes an accuracy level (1.5%) that must be achieved by the measurement system for the 573 resulting SAR values to be used without penalty. If this accuracy level is not achieved, the resulting 574 SAR values will be penalized by the amount the measurement system error exceeds the 1.5% accuracy 575 level. 576 577 Section A38.5.1.7 defines the accuracy level of the measurement system to be the root sum of squares 578 (RSS) of the accuracies of the individual elements that make up the measurement system. The 579 individual elements of the measurement system are identified in § A38.5.1.6. The RSS of the 580 measurement system is determined from the equation, 𝑆𝑆𝑆𝑆𝑆𝑆 = √𝑆𝑆2 + 𝐵𝐵2 + 𝐶𝐶2 + ⋯ 𝑍𝑍2 where A, B, C, ··· 581 Z, are the accuracies of each of the individual elements of the measuring system. The individual 582 elements must meet the accuracy requirements when showing compliance with part 38. 583 584
6.3.2 Selection of Flight Test Data 585 586 There are a number of methods that may be used by different airplane manufacturers in selecting flight 587 test data for analysis, reflecting a variety of tools and practices used within the industry. Whichever 588 method is chosen, the flight test data chosen by an applicant within a selected time frame for an 589 individual SAR data point must meet the stability criteria detailed in § A38.4.2.2.2 or alternative stability 590 criteria approved by the FAA as described in § A38.4.2.2.3. Test data that do not meet these stability 591 criteria would normally be discarded if not needed. However, if such test data appear to be valid when 592 compared with data that meet the stability criteria, and the overall stability of the conditions is 593 reasonably bounded, these data can be used, subject to FAA approval. 594 595 One acceptable method is to employ an algorithm that automatically selects the data that meet all the 596 stability criteria and discards data that do not. This method could be used to select the longest possible 597 duration SAR point that meets the required stability criteria, or to select multiple SAR points of the 598 minimum requirement duration (one minute), provided that these points are separated by a minimum of 599 two minutes or by an exceedance of the stability criteria, as specified in § A38.4.2.2.2. 600 601 Using a defined algorithm to select data in an automated process allows repeatable and consistent 602
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application to other SAR points. This method may also yield a greater number of SAR points to be used 603 in defining the FEM value and should represent a good statistical distribution. However, because the 604 amount of test data included in each SAR point is maximized, the resulting SAR points could exhibit 605 more scatter than if additional selection criteria are used. 606 607 Another method for the selection of flight test data is to more closely examine the collected flight test 608 data and select the time frame to be used to define the SAR point by choosing the best or most stable 609 data available and ignoring less stable data that technically still meet the stability criteria. Examples of 610 this are presented in Figures 6-3 and 6-4. 611 612 Figure 6-3 shows that the plotted parameters stay within the tolerances allowed by the stability criteria 613 for the duration of the test condition. (The changing altitude after the end of the condition reflects pilot 614 input to leave steady flight and transition to the next test condition.) While all parameters are within the 615 required tolerances as specified in § A38.4.2.2.2, fluctuations in ambient temperature and Mach are 616 evident. Figure 6-4 shows the same data, but with a manually selected range of shorter duration where 617 the parameters are more stable. 618 619 620 Figure 6-3. 621 622 Flight test data time interval selection – Example 1 623 624 625 626 627 Mach Ground speed (km/hr) OAT ( C)° ALT (m) +.005 -.005 +3.7 -3.7 +1 -1 +23 -23 0 60 120 180 Time (s) T est point duration = 2:40
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628 Figure 6-4. 629 630 Flight test data time interval selection – Example 2 631 632 633 634 Selecting data that meet more demanding stability criteria, instead of using all data that meet the 635 stability criteria indicated in § A38.4.2.2.2, may allow the applicant to filter out observed instabilities 636 caused by air quality, changing environmental conditions, flight control inputs, and airplane system 637 dynamics. This could result in a SAR point that is more representative of actual airplane performance. 638 Whichever approach the applicant takes to select data to define SAR points, the methodology needs to 639 be applied as consistently as possible to minimize potential unseen bias in the resulting distribution of 640 SAR points. 641 642 Another important aspect to consider when selecting data is to ensure that the time interval chosen is 643 representative of the airplane’s performance and not indicative of a larger trend. For example, the first 644 plot in Figure 6-3 shows a trend line drawn through ground speed data over a 60-second time interval. 645 This ground speed data meets the stability criteria and taken alone, would indicate the need for an 646 energy correction, which is used to correct for excess or inadequate potential or kinetic energy (i.e., a 647 deviation from the reference condition of steady, unaccelerated flight; see 648 Acceleration/deceleration (energy) in A38.5.2.2.1.1). 649 650 However, if the ground speed data trace was continued over a longer time interval, it becomes apparent 651 that it exhibits cyclical behavior. Cyclical data need not necessarily be discarded, but the applicant 652 -.005 +3.7 -3.7 +1 -1 +23 -23 Mach Ground speed (km/hr) OAT ( C)° ALT (m) +.005 -.005 0 60 120 180 Time (s) T est point duration = 1:00
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should ensure that an appropriate time interval is selected such that the arithmetic average is 653 representative. In the example shown in Figure 6-5, below, an energy correction would be 654 inappropriate. 655 656 Figure 6-5. 657 658 Cyclical behavior example 659 660 661 662
6.3.3 Distribution of Resulting SAR Points 663 Once the individual SAR points have been selected and corrected to reference specifications, they 664 need to be examined to ensure they reflect an accurate representation of the airplane’s performance. 665 This is described in the following paragraphs. 666 667 For example, if direct flight test is being used to collect 6 SAR points targeting one reference mass, 668 those 6 points, when corrected to reference specifications, should result in a reasonable grouping. If 5 669 of the points form a reasonable grouping and one point is a clear outlier, the outlier may require closer 670 scrutiny to ensure it is actually representative. In such a situation, collection of additional data may be 671 warranted or, if appropriate, and subject to the approval of the FAA, the offending data point could be 672 discarded. 673 674 If the applicant conducts tests across a range of weights to build a regression line of SAR versus 675 weight, the collected SAR points should be reasonably distributed across the weight range. If a large 676 portion of the regression line is unsupported by data, or is anchored by a single SAR point, then the 677 Time (s) Ground speed (km/hr) Linear best fit 2 0 -2 0 60 120 180 240 Ground speed (km/hr) Linear best fit 2 0 -2 0 60 Time (s)
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SAR determined for one of the reference masses may be an outlier. This is an important aspect to 678 consider during the development of the certification plan and flight test program. As with the direct test 679 method, if a single SAR point appears to be an outlier compared to the rest of the data points, it needs 680 to be examined more closely and may potentially be discarded. 681 682 The applicant should investigate the collection of SAR points for potential sources of unintended bias. 683 An example would be where all of the data points collected were during periods when ground speed 684 was increasing. If all of the test points require a large energy correction in one direction, resulting in all 685 SAR points being significantly increased (or decreased), further scrutiny may be needed to ensure that 686 a bias is not introduced, depending on the test data and correction techniques being used. 687 688
6.3.4 Correction of SAR Data to Reference Specifications 689 690 To ensure that the SAR data has a consistent baseline for use in determining the FEM, the SAR data 691 must be corrected to a set of reference specifications as required in part 38 by § A38.2. One set of 692 methods for correcting the SAR data to reference specifications, but not the only acceptable set of 693 methods, is provided in Appendix 3 to this AC. 694 695
6.4 Equivalent Procedures 696 Use of equivalent procedures must be approved by AEE, in advance, and on a case-by-case basis in 697 accordance with § 38.21. Section 38.13(a) establishes the methods of compliance as being direct flight 698 test or by use of a validated performance model that is approved before any SAR calculations are 699 submitted. 700 701 Examples of equivalent procedures are the following: 702 703
6.4.1 Example 1: FAA Approval based on existing data 704 Applicants could develop a regression curve approach for SAR values across the gross weight (MTOM) 705 range based on existing data. This regression curve approach using existing data could be used in 706 situations such as: 707 708
a) The existing performance model used company test data that may have not been witnessed 709 by the FAA or documentation of the conformity of the airplane type design may not have 710 been provided to the FAA, but the data obtained are found acceptable by the FAA at the time 711 of certification, or 712
b) The accuracy of the instrumentation and the data reduction processes may not have been 713 documented sufficiently for certification, or the original documentation may not have been 714 retained, but the data available are found acceptable by the FAA at the time of certification. 715 716 717
6.4.2 Example 2: FAA Approval of a change based on back-to-back testing 718 The use of back-to-back test data may be requested by applicants as an equivalent procedure for 719 determining the FEM for a relatively small type design change (e.g., antenna installations or other 720 simple drag changes). Back-to-back testing for determining a FEM value change means that a test is 721 first completed without the change applied to the airplane, and then the test is repeated with the change 722 made to the airplane. The difference in the FEM values of the before and after tests is presumed to be 723 the result of the change on the airplane FEM value. This approach may not be appropriate for engine 724 changes where the specific fuel consumption (SFC) of the engine may change due to internal changes. 725 This compliance approach will likely be especially useful for supplemental type certificate (STC) 726 modifiers who do not have access to the original flight test data from the airplane manufacturer, such 727 as: 728 729
a) Back-to-back testing should be performed on the same airplane and engines with the 730 modification installed and not installed. 731
b) Instrumentation adequate to provide data meeting the accuracy requirements of the standard 732 should be installed in the test airplane. 733
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c) The data reduction and comparison processes must be approved by the FAA in accordance 734 with § 38.21. 735 736
6.4.3 Example 3: FAA Approval of a change based on analysis 737 738 The use of analytical processes may be requested by an applicant to evaluate a change to the FEM of 739 a previously approved airplane type design and establish compliance with § 38.17, and the analytical 740 processes must be approved by the FAA in accordance with § 38.21. Paragraphs 6.4.3.1 and 6.4.3.2, 741 below, provide a non-exclusive list of possible analytical methods, but do not preclude the use of other 742 equivalent procedures. 743 744
6.4.3.1 Changes affecting characteristics of airplane aerodynamics 745 746 Subject to approval by the FAA, methods available to evaluate the effect of aerodynamic changes on 747 airplane drag could include: 748 749
• Semi-empirical methods (SEM), 750
• Computational fluid dynamics (CFD), 751
• Computational fluid dynamics combined with computational structural mechanics (CFD-CSM), 752 and 753
• Wind tunnel testing. 754 755 The FAA’s approval for the use of the above analytical methods to evaluate a change to the FEM 756 value may depend on the type of airplane modification as listed below. 757 758 For design changes affecting parasitic drag and/or profile drag (e.g., friction drag and/or viscous 759 pressure drag), SEM, CFD, or wind tunnel testing could be used. In this case, it is assumed that 760 airplane aeroelastics are not affected. 761 762 For all other design changes, CFD could be used for items not affecting airplane aeroelastics, 763 CFD-CSM could be used for items affecting airplane aeroelastics, and wind tunnel testing could be 764 used in all cases. 765 766
6.4.3.2 Changes to specific fuel consumption (SFC) affected by a change to the propulsion 767 system: 768 769 Possible methods available to evaluate the effect of propulsion system design changes on specific fuel 770 consumption (SFC) are: 771 772
a. Thermo dynamical models (engine performance decks), 773
b. Computational fluid dynamics (CFD), 774
c. Component testing, 775
d. Full engine testing, and 776
e. A combination of a. through d. 777 778 779
6.4.4 Example 4: FAA Approval based on first principle models 780 781 Introduction 782 783 Section 38.13(a) requires that the specific air range must be determined by direct flight test 784 measurements or the use of a performance model that is:- 785 786 I. validated by actual SAR flight test data and 787 II. approved by the FAA before any specific air range calculations are submitted. 788 789
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A performance model is defined in 38.3 as “an analytical tool (or a method) validated using corrected 790 flight test data that can be used to determine the specific air range values for calculating the fuel 791 efficiency metric value.” 792 793 Guidance on the approval of SAR values based on specific types of performance models known as 794 “first principle models” is provided below. A first principle model is defined as a tool that enables the 795 derivation of a SAR value, in given flight conditions, from flight mechanics equations using airplane 796 aerodynamics and engine performance data. 797 798 First principle models should be validated by actual SAR flight test data that is acquired in a manner 799 consistent with § A38.1.2 and as described in paragraph 6.3 of this AC. Validity of the model need only 800 to be shown for the test points and conditions relevant to demonstrating compliance with § 38.17. 801 802 The method proposed in this paragraph, 6.4.4, represents one possible method to show compliance 803 with § 38.17. 804 805
6.4.4.1 Selection of relevant flight test points for the model validation 806 807 First principle SAR models developed by airplane manufacturers typically cover most of the flight 808 envelope to provide many different operational fuel planning requirements. The range of flight test data 809 from these models typically spans large Mach and weight/δ ranges. 810 811 The example shown in Figure 6-6, below, illustrates the wide distribution of the flight test data across 812 the model, and that none of the test points generally fall exactly at the three SAR conditions defined in 813 § 38.13(b). 814 815 Figure 6-6. 816 817 Test points range 818 SAR •∞ Mach number Data range considered for regression Three defined masses for CO compliance2 Flight test points Lines of weight/ δ Optimum
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819 Figure 6-6 shows that the three SAR conditions required by § 38.13(b) are relatively close to each 820 other in terms of Mach and weight/δ because they represent the same optimum aerodynamic 821 conditions for achieving the best (lowest) 1/SAR values. Although these three SAR conditions may not 822 have been specifically flight tested, they are generally well framed by other relevant flight test data in a 823 local Mach and weight/δ range. 824 825 In order to validate the performance model in conditions relevant to demonstrating compliance with § 826
38.17, flight test points around the optimum Mach number and optimum weight/δ would be selected 827 based on the following criteria: 828 829
a) Weight/δ between ±5 percent of the optimum weight/δ; and 830
b) Mach number between -0.02 and +0.015 of the optimum Mach number. 831 832 Note 1.— The ±5 percent value in a) is used to capture flight test points on weight/δ lines above and 833 below the optimum weight/δ included in the airplane manufacturer’s flight test practices. 834 835 Note 2.— The density of test points is generally lower at Mach numbers below the optimum Mach 836 number and higher at Mach numbers above the optimum Mach number. Additionally, the Mach effect 837 on SAR is generally less at Mach numbers below the optimum Mach number than above, and a sharp 838 SAR decrease may occur when approaching high Mach numbers. For this reason, the Mach range for 839 the test point selection is larger at Mach numbers below the optimum Mach number (-0.02) than above 840 (+0.015). 841 842 Note 3.— Testing target weight/δ values non-dimensionalizes the pressure altitude so that weight/δ 843 varies as CL.M². Therefore, weight/δ at a given Mach varies similarly to CL at that Mach number. 844 845
6.4.4.2 SAR model justification 846 847
6.4.4.2.1 Flight test SAR versus SAR model 848 849 In order to use first principle models to determine the SAR values for calculating the FEM, 850 manufacturers are expected to explain their modelling validation principles and show that their 851 modelling correctly matches flight test data acquired in a manner consistent with part 38 Appendix A, 852 as described in paragraph 6.3 of this AC. 853 854 As shown in Figures 6-7 and 6-8, below, one possible method is to present plots of percent ∆SAR 855
(i.e. Measured SAR minus Computed SAR) versus Mach and versus weight/δ (or CL). These should 856 be shown in the Mach and weight/δ (or CL) range of the cruise envelope. 857 858 An increased number of test points, when available, may be used to qualitatively show that the test 859 point selection, described in paragraph 6.4.4.1 above (red points selected for optimum SAR in 860 Figures 6-7 and 6-8 below, which are within the orange dashed circle in Figure 6-6), is not differently 861 scattered or biased than other test points in the cruise envelope (green points that are all the flight 862 test data in Figures 6-7 and 6-8 below, and these are outside the orange dashed circle in Figure 6-6). 863 Figures 6-7 and 6-8 are examples of a set of data that show no significant biases or differences in 864 scatter inside and outside the cruise envelope. 865 866 867 868 869 870 871 872 873
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Figure 6-7 874 875 ∆SAR versus Mach number 876 877 878 879 880 881 882 Figure 6-8. 883 884 ∆SAR versus CL 885 886 887 888
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889 890
6.4.4.2.2 SAR model presentation 891 892 The comparison of flight test points with a model does not validate how that model is built and how 893 the optimum conditions represent the FEM. Accordingly, the SAR model used to demonstrate 894 compliance with § 38.17 must be approved by FAA per § 38.13(a)(2). 895 896 One possible method to present the SAR model is to present plots of computed SAR versus Mach 897 and computed SAR versus CL for the three masses referenced in § 38.13(b). Figures 6-9 and 6-10 898 show that there are no abnormal discontinuities in the Mach and CL ranges selection around SAR 899 conditions used for the FEM determination. 900 901 902 903 904 Figure 6-9 905 906 Computed SAR (model) versus Mach at optimum altitude 907 908 909 910 911 912 913
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Figure 6-10 914 915 Computed SAR (model) versus CL at optimum Mach 916 917 918 919 920
6.4.4.3 SAR model validation – confidence interval determination 921 922 As explained in paragraph 6.4.4 above, the SAR model needs to be validated under the conditions 923 relevant to demonstrating compliance with § 38.17. To be used for validation, flight test points need to 924 be selected using the criteria described in paragraph 6.4.4.1 above. The number of flight test points 925 selected will represent n measurements (number of data points) of SAR (SAR1, SAR2, …, SARn) 926 obtained in approximately the same conditions of Mach and CL. 927 928 Step 1 — Estimate of the mean ∆SAR value and of the standard deviation 929 For each flight test point (i), the SAR difference ∆SAR(i) between the measured SAR and the computed 930 SAR can be determined as follows (in percent): 931 932 ∆SAR(i)(%) = [(Measured SAR(i) - Computed SAR(i)) / Computed SAR(i)] x 100 (%). 933 934 The estimate of the mean ∆SAR value in percent, ∆SARAVG(%), can then be determined for the n 935 measurements as follows: 936 937 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴(%) = 𝐹𝐹𝑒𝑒𝑒𝑒𝐸𝐸𝑒𝑒𝑣𝑣𝑒𝑒𝐹𝐹 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝐹𝐹𝑣𝑣𝐸𝐸 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆 (%) = 1𝑛𝑛 �∑ 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆(𝑖𝑖)𝑖𝑖=𝑛𝑛𝑖𝑖=1 �(%). 938 939 The estimate of the standard deviation of the mean is found as follows: 940 𝑒𝑒 = 𝐹𝐹𝑒𝑒𝑒𝑒𝐸𝐸𝑒𝑒𝑣𝑣𝑒𝑒𝐹𝐹 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝑒𝑒𝑣𝑣𝐸𝐸𝑠𝑠𝑣𝑣𝑒𝑒𝑠𝑠 𝑠𝑠𝐹𝐹𝑣𝑣𝐸𝐸𝑣𝑣𝑒𝑒𝐸𝐸𝑜𝑜𝐸𝐸 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝐹𝐹𝑣𝑣𝐸𝐸 = �∑ �𝐷𝐷𝐷𝐷𝐴𝐴𝐷𝐷(𝑖𝑖)− 𝐷𝐷𝐷𝐷𝐴𝐴𝐷𝐷𝐴𝐴𝐴𝐴𝐴𝐴�2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−1 (%). 941