# AC 38-1: AIRPLANE FUEL EFFICIENCY CERTIFICATION - Type: Advisory circular (guidance, not mandatory unless a rule or AD requires it) - Status: Current - Approved: December 13, 2023 - Family: AC 38-1 - Pages: 74 - FAA DRS: https://drs.faa.gov/browse/excelExternalWindow/DRSDOCID178966874520240815212315.0001 - Page: https://openairdocs.org/ac/38-1 ## Versions - AC 38-1 (Current), approved Dec 13, 2023 ## Text ### Page 1 U.S. Department of Transportation Federal Aviation Administration Subject: AIRPLANE FUEL EFFICIENCY **CERTIFICATION** Date: 12/13/2023 Initiated By: AEE-300 AC No: 38-1 1 This advisory circular (AC) contains information and provides guidance on the implementation of the fuel 2 efficiency certification requirements for airplanes that are required by Title 14 of the Code of Federal 3 Regulations (14 CFR) part 38. 4 5 6 7 Ralph Iovinelli 8 9 10 11 12 FAA Office of Environment and Energy 13 AEE-300 Emissions Division 14 15 ### Page 2 12/05/2023 AC 38-1: 14 CFR Part 38 Airplane Fuel Certification 16 17 Table of Contents 18 1. Purpose ................................................................................................................................................... 1 19 1.1 Contents ................................................................................................................................................ 1 20 1.2 Advisory Nature ..................................................................................................................................... 1 21 1.3 Audience ............................................................................................................................................... 1 22 1.4 Intent...................................................................................................................................................... 1 23 1.5 Approval of Equivalent Procedures ....................................................................................................... 2 24 1.6 FAA Certification Process ..................................................................................................................... 2 25 1.7 Related Documents ............................................................................................................................... 2 26 1.8 Definitions and Abbreviations/Acronyms/Symbols ................................................................................ 2 27 2. References ............................................................................................................................................... 2 28 3. [Reserved] ............................................................................................................................................... 3 29 4. Development of Airplane Fuel Efficiency Regulations ...................................................................... 3 30 4.1 Establishment of Airplane Fuel Efficiency Regulations ......................................................................... 3 31 4.2 Relationship Between the EPA and the FAA ........................................................................................ 3 32 4.3 Relationship Between 14 CFR Part 38 and 40 CFR Part 1030 ............................................................ 3 33 4.4 Differences Between ICAO Annex 16 Volume III and 14 CFR Part 38 ................................................ 4 34 5. Part 38 Subpart A – General .................................................................................................................. 4 35 5.1 Section 38.1 Applicability ...................................................................................................................... 4 36 5.1.1 Modified Airplanes ........................................................................................... 6 37 5.1.2 Non-Applicability of the Fuel Efficiency Metric ................................................. 6 38 5.2 Certification of Lower Takeoff Mass Variant ......................................................................................... 7 39 5.3 Exemptions ............................................................................................................................................ 7 40 5.4 Incorporation by Reference ................................................................................................................... 7 41 5.5 Fuel Efficiency Compliance Demonstration Plans ................................................................................ 8 42 5.6 Fuel Efficiency Compliance Demonstration for Airplanes with Intermixed Engines ............................. 8 43 ### Page 3 6. Expanded Discussion of 14 CFR part 38 Subpart B Requirements .................................................. 9 44 6.1 Fuel Efficiency Metric ............................................................................................................................ 9 45 6.2 Specific Air Range ............................................................................................................................... 10 46 6.3 SAR Data Analysis .............................................................................................................................. 11 47 6.3.1 SAR Measurement System ........................................................................... 11 48 6.3.2 Selection of Flight Test Data ......................................................................... 11 49 6.3.3 Distribution of Resulting SAR Points ............................................................. 14 50 6.3.4 Correction of SAR Data to Reference Specifications ..................................... 15 51 6.4 Equivalent Procedures ........................................................................................................................ 15 52 6.4.1 Example 1: FAA Approval based on existing data ......................................... 15 53 6.4.2 Example 2: FAA Approval of a change based on back-to-back testing ......... 15 54 6.4.3 Example 3: FAA Approval of a change based on analysis ............................ 16 55 6.4.4 Example 4: FAA Approval based on first principle models ............................ 16 56 6.5 Validity of Results – Confidence Interval ............................................................................................. 24 57 6.6 Reference Geometric Factor ............................................................................................................... 24 58 6.6.1 RGF General Guidelines ............................................................................... 24 59 6.6.2 Orthogonal Projection and Width Boundary .................................................. 24 60 6.6.3 Forward and Aft Boundaries ....................................................................... 25 61 6.6.4 Floor Plane ................................................................................................. 25 62 6.6.6 Floor Plane ................................................................................................. 26 63 6.6.7 RGF Sensitivity ........................................................................................... 26 64 6.7 Fuel Efficiency Limits ........................................................................................................................... 26 65 6.8 Change Criteria ................................................................................................................................... 27 66 7. Additional Guidance ............................................................................................................................. 28 67 Appendix 1: Definitions ............................................................................................................................ 29 68 Appendix 2: Abbreviations/Acronyms/Symbols .................................................................................... 30 69 Appendix 3: Correcting SAR Data to Reference Specifications .......................................................... 32 70 Appendix 4: Confidence Interval Evaluation .......................................................................................... 52 71 Appendix 5: References ........................................................................................................................... 71 72 73 ### Page 4 12/13/2023 1 1. Purpose 74 75 This AC provides guidance on the implementation of fuel efficiency certification requirements for 76 airplanes. These guidelines provide an acceptable means of demonstrating compliance with the 77 regulations of Title 14 of the Code of Federal Regulations (14 CFR) part 38. The methods and procedures 78 described herein have been proposed as recommended certification practice for showing compliance with 79 the fuel efficiency requirements. 80 81 See Appendix 1 for definitions and Appendix 2 for acronyms, abbreviations, and symbols used throughout 82 this AC. 83 84 1.1 Contents 85 86 This Advisory Circular (AC) contains information describing the standards and requirements for new 87 aircraft fuel efficiency regulations in 14 CFR part 38. The information contained in this document sets 88 forth acceptable means, but not the sole means, by which compliance may be shown with the 89 requirements of 14 CFR part 38 (part 38). 90 91 In this AC, the word “paragraph” is used to refer to a part of the AC. The word “section” (or the symbol 92 “§”) is used to refer to a part of a regulation or statute. 93 94 Pursuant to §§ 231 and 232 of the Clean Air Act Amendments of 1970 (42 USC §§ 7571-7572), FAA’s 95 part 38 fuel efficiency regulations implement the standards adopted by U.S. Environmental Protection 96 Agency (EPA) in 40 CFR part 1030 (see paragraphs 4.1 - 4.3 of this AC) by enforcing the EPA 97 regulations at the time of certification. Any deviations from the procedures required under 14 CFR part 98 38 or 40 CFR part 1030 must be coordinated and approved by the Administrators of both the EPA and 99 FAA (see paragraphs 4.2 and 4.3 of this AC). Users of this AC, and those subject to the regulations of 100 part 38, are responsible for cognizance of any later amendments to 40 CFR part 1030 that may not be 101 reflected immediately in 14 CFR Part 38 or this AC. In such instances, applicants may contact the AEE-102 300 Emissions Division Manager with the FAA Office of Environment and Energy at 103 ralph.iovinelli@faa.gov for further guidance. 104 105 1.2 Advisory Nature 106 107 The contents of this AC do not have the force and effect of law and are not meant to bind the public in 108 any way. This AC is intended only to provide information to the public regarding compliance with existing 109 requirements under the law or agency policies. The use of mandatory language, such as “must” and 110 “require” in this AC describe a mandatory requirement established by statute or regulation that exists 111 independent of the material in this AC. The term “should” is used in this AC to indicate a 112 recommendation described in this document and not a requirement. This AC describes one or more 113 acceptable means, but not the only means, of complying with part 38 fuel efficiency certification 114 standards. If an applicant chooses to use the guidance presented here as an acceptable means of 115 compliance, it must be followed in all respects to be considered a valid means of compliance. 116 117 1.3 Audience 118 119 The intended audience for this AC includes airplane performance engineers, engine specialists, and 120 propulsion engineers from the FAA’s Aircraft Certification Service (AIR) and Aircraft Certification 121 Branches; aircraft and aircraft engine industry specialists; aircraft certification applicants; other 122 certification authorities, airlines, airport operators, engineering and scientific communities; and other 123 persons that are interested in the certification of airplanes to the fuel efficiency standards of part 38. 124 125 1.4 Intent 126 127 The intent of this AC is to provide guidance for complying with the fuel efficiency requirements of part 38. 128 129 ### Page 5 12/13/2023 2 1.5 Approval of Equivalent Procedures 130 131 As provided in § 38.21, applicants may submit equivalent testing, measurement, and data reduction 132 procedures to comply with part 38 airplane fuel efficiency regulations that apply to their airplane. Any 133 such alternatives must be approved, in advance of part 38 compliance document submittals, by the 134 FAA’s Office of Environment and Energy (AEE), at FAA Headquarters in Washington DC. Further 135 information on equivalent procedures is provided in paragraph 6.4 of this AC. If you have further 136 questions, please contact the AEE-300 Emissions Division Manager with the Office of Environment and 137 Energy at ralph.iovinelli@faa.gov. 138 139 1.6 FAA Certification Process 140 141 As of publication of AC38-1, the fuel efficiency certification requirements of part 38 are newly adopted in 142 2023, and it is expected that the FAA and U.S. manufactures will gain experience with their application 143 through ongoing findings of compliance with part 38. The FAA-AIR line of business will work directly 144 with the applicant in this process, and FAA’s environmental office, AEE-300, is to remain fully involved 145 with the FAA-AIR line of business in all fuel efficiency compliance efforts to provide guidance as 146 experience is gained. Questions about part 38 from applicants should be submitted to the FAA-AIR line 147 of business, that will then confer with the FAA-AEE environmental office for their resolution. 148 149 1.7 Related Documents 150 151 Part 38 contains the fuel efficiency certification requirements for certain airplanes. These regulations 152 reference or are related to the following: 153 154 • Clean Air Act (CAA) §§ 231-232 (Aircraft Emissions Standards) Title 42 USC §§ 7571-7572. 155 • 40 CFR part 1030, Control of Greenhouse Gas Emissions from Engines Installed on Airplanes 156 157 Part 38 requirements are also referenced in the following regulations in 14 CFR: 158 159 • Part 21, Certification Procedures for Products and Articles including §§ 21.5, 21.17, 21.21, 21.29, 160 21.31, 21.93, 21.101, 21.115, 21.183, and 21.187, 161 • Part 121, Operating Requirements: Domestic, Flag, and Supplemental Operations including § 162 21.141, and 163 • Part 125, Certification and Operations: Airplanes Having a Seating Capacity of 20 or More 164 Passengers or a Maximum Payload Capacity of 6,000 Pounds or More; and Rules Governing 165 Persons on Board such Aircraft including § 125.75. 166 167 168 1.8 Definitions and Abbreviations/Acronyms/Symbols 169 170 Definitions are provided in Appendix 1 and abbreviations, acronyms, and symbols in this AC are 171 provided in Appendix 2. 172 173 174 2. References 175 176 This AC references the following: 177 178 • Clean Air Act Amendments of 1970 (CAA), 42 U.S.C. § 7571 et seq. 179 • Control of Greenhouse Gas Emissions from Engines Installed on Airplanes; Emission Standards 180 and Test Procedures, 40 CFR part 1030. 181 • International Civil Aviation Organization (ICAO) International Standards and Recommended 182 Practices, Annex 16 — Volume III — Aeroplane CO2 Emissions, May 2019 183 • International Civil Aviation Organization (ICAO) Environmental Technical Manual (Doc 9501), 184 ### Page 6 12/13/2023 3 Volume III — Procedures for the CO2 Emissions Certification of Aeroplanes, May 2019 185 186 Additional references are provided in Appendix 5. 187 188 3. [Reserved] 189 190 4. Development of Airplane Fuel Efficiency Regulations 191 192 The United States is one of 193 signatory states to International Civil Aviation Organization's (ICAO) 193 Convention on International Civil Aviation (the Chicago Convention). Article 12 of the Chicago Convention 194 requires signatory states to keep their own regulations uniform, to the greatest extent possible, with those 195 established under the Chicago Convention. In March of 2017, the ICAO Council adopted a new CO2 196 Emissions Certification Standard with an effective date of July 2017. The ICAO considered three 197 categories of technology associated with the fuel efficiency of an airplane design (propulsion, 198 aerodynamics, and structures) in its adoption of a CO2 emissions certification standard for airplanes. 199 200 4.1 Establishment of Airplane Fuel Efficiency Regulations 201 202 49 USC § 40105(b)(1)(A) states that the Secretary of Transportation and FAA Administrator shall act 203 consistently with obligations of the United States Government under international agreements. For 204 development of aviation emissions standards, the FAA leads the U.S. delegation at ICAO meetings with 205 assistance from the EPA. 206 207 4.2 Relationship Between the EPA and the FAA 208 209 The Clean Air Act authorizes the EPA to set standards for aircraft engine emissions in the United States 210 (42 USC § 7571), while the FAA is authorized to enforce those standards. Section 7571 states the 211 following: 212 213 (2)(A) The Administrator shall, from time to time, issue proposed emission standards applicable to the 214 emission of any air pollutant from any class or classes of aircraft engines which in his 215 judgment causes, or contributes to, air pollution which may reasonably be anticipated to 216 endanger public health or welfare. 217 (B)(i) The Administrator shall consult with the Administrator of the Federal Aviation Administration 218 on aircraft engine emission standards. 219 (ii) The Administrator shall not change the aircraft engine emission standards if such change 220 would significantly increase noise and adversely affect safety. 221 222 The standards promulgated by the EPA in 40 CFR part 1030 apply to certain classes of engines used by 223 certain civil subsonic jet and propeller-driven airplanes (40 CFR part 1030.1). In developing airplane 224 emissions regulations, the CAA requires that the EPA consult with the FAA Administrator and ensure 225 that changes to emission standards do not significantly increase noise and adversely affect safety. 226 227 4.3 Relationship Between 14 CFR Part 38 and 40 CFR Part 1030 228 229 The fuel efficiency standards in 14 CFR part 38 implement those adopted by the EPA in 40 CFR part 230 1030. Accordingly, if the EPA takes any action to change any regulation or standard in 40 CFR part 1030 231 that is also promulgated in 14 CFR part 38, the Administrator of the FAA will grant a general 232 administrative waiver of those outdated requirements in 14 CFR part 38 until 14 CFR part 38 can be 233 amended to reflect the changes in 40 CFR Part 1030. (14 CFR § 38.9) The FAA will enforce the 40 CFR 234 part 1030 requirements, for which a waiver has been granted, as part of the 14 CFR part 38 fuel 235 efficiency certification. Under these circumstances, the certification documentation will reflect that it 236 complies with both 40 CFR part 1030 and 14 CFR part 38. 237 238 239 ### Page 7 12/13/2023 4 4.4 Differences Between ICAO Annex 16 Volume III and 14 CFR Part 38 240 241 Under the Chicago Convention, the FAA is obligated to notify ICAO of any U.S. regulatory differences 242 between the ICAO standards and those adopted in the United States. The EPA refers to its regulations 243 as greenhouse gas emissions in part 1030; FAA refers to its regulations as airplane fuel efficiency; and 244 the ICAO standard is titled “Certification Standard for Aeroplane CO2 Emissions Based on the 245 Consumption of Fuel.” The FAA, EPA, and ICAO each use different terminology to reference the same 246 standards and there are no substantive differences with the meaning of these terms. The FAA has not 247 identified any substantive differences between U.S. regulations and Annex 16 Volume III. 248 249 5. Part 38 Subpart A – General 250 251 5.1 Section 38.1 Applicability 252 253 Section 38.1(a) requires fuel efficiency certification for certain subsonic jets, propeller-driven airplanes, 254 and modified airplanes. Fuel efficiency certification applicability is based on the date for which an 255 application for a type certificate is submitted. In general, the standards apply to airplanes with new type 256 designs (submitted on or after January 11, 2021); airplanes that were type certificated before January 257 11, 2021, but continue production with certain modifications on or after January 1, 2023; and all 258 airplanes that are in production on and after January 1, 2028. The exact terms of applicability should be 259 determined using the language of § 38.1, not from this brief description. 260 261 For subsonic jet and propeller-driven airplanes for which an application for a type certificate is submitted 262 on or after January 11, 2021, part 38 applies as specified in Table 5.1. See § 38.1(a)(1)-(3). 263 264 Table 5.1. 265 266 Fuel Efficiency Certification Applicability for New Airplane Designs 267 268 For an airplane that is a: With a passenger seating capacity of: With a maximum takeoff mass (MTOM) in kg of: For which an application for original type certification is submitted: Subsonic Jet 20 or more > 5,700 On or after January 11, 2021 Subsonic Jet 19 or fewer > 60,000 On or after January 11, 2021 Subsonic Jet 19 or fewer > 5,700 and < 60,000 On or after January 1, 2023 Propeller-driven --- > 8,618 On or after January 11, 2021 269 Table 5.2 shows part 38 applicability to newly produced modified versions of airplanes (i.e. airplanes 270 receiving their first certificate of airworthiness that are newly built with the modified type design) whose 271 type design was not required to have fuel efficiency certification under part 38, and for which an 272 application by the type certificate holder for a type design change is submitted on or after January 1, 273 2023. See § 38.1(a)(4)-(5) 274 275 Table 5.2. 276 277 Fuel Efficiency Certification Applicability for Modified Version of an Airplane Whose Type 278 Design was not certificated under part 38 279 280 For an airplane that is a: With a maximum takeoff mass (MTOM) in kg of: For which an application by a type certificate holder for a type design change is submitted: Subsonic Jet > 5,700 On or after January 1, 2023 ### Page 8 12/13/2023 5 Propeller-driven > 8,618 On or after January 1, 2023 281 Table 5.3 shows part 38 applicability to the production of individual airplanes for which the airplane type 282 design was not originally required to meet 14 CFR part 38. See §§ 38.1(a)(6)-(7). 283 284 Table 5.3. 285 286 Fuel Efficiency Certification Applicability for Airplanes issued Airworthiness Certificates 287 on or after January 1, 2028 288 289 For an airplane that is a: With a maximum takeoff mass (MTOM) in kg of: For which the first certificate of airworthiness is issued: Subsonic Jet > 5,700 On or after January 1, 2028 Propeller-driven > 8,618 On or after January 1, 2028 290 Note: 14 CFR 38 and 40 CFR 1030 requirements apply based on aircraft thresholds such as MTOM 291 “greater than 8,618 kg,” while airworthiness applicability thresholds such as those of parts 21 and 23 292 might otherwise be expressed as 8,618 kg (19,000 lb). The FAA acknowledges that conversion from 293 8,618 kg to lbs is approximately 0.5 lbs less than the 19,000 lbs threshold of other FAA regulations. 294 However, when applying the conversion in reverse, going from 19,000 lbs to kg, the result is 295 approximately 0.25 kg greater than 8,618 kg. This less than 1 lb or 1 kg difference is extremely small 296 and it is unlikely that an airplane would fall within this conversion difference. Importantly, differences less 297 than 1 lb or 1 kg would not be reflected in either a type certificate data sheet (TCDS) or an airplane flight 298 manual. Additionally, the use of kilograms as the applicability threshold is consistent with the EPA 299 standard. 300 301 Table 5.4, below, provides examples of the applicability of part 38. 302 303 304 Table 5.4. 305 306 Examples of Part 38 Applicability 307 308 Individual Airplane Status Applicability Today Effective Dates for Applicability of part 38 Applicability when modified Fuel Efficiency Metric (FEM) Limit In service, and type is no longer being produced EX: 757 None None None None Airplanes still being produced EX: 787-9 None 1/1/2023 for newly built modified airplanes § 38.1(a)(4) - (5); or 1/1/2028 for all newly built airplanes § 38.1(a)(6) - (7) Must comply with the in-production limit if: (1) produced after 1/1/2023 (§ 38.1(a)(4) – (5)); and (2) includes a modification that changes the FEM value (§ 38.19(c)). In-production limit § 38.17(b)(5) - (8) New (Original) Type: large jet § 38.1(a)(1) and (3) 1/11/2021 All airplanes; New certification New type limit § 38.17(b)(1) - ### Page 9 12/13/2023 6 airplanes and propeller-driven airplanes required if triggered by change criteria (§ 38.19(a)) (4) New (Original) Type: small airplanes § 38.1(a)(2) 1/1/2023 All airplanes; New certification required if triggered by change criteria (§ 38.19(a)) New type limit § 38.17(b)(1) 309 310 311 312 5.1.1 Modified Airplanes 313 314 Section 38.1(b) states that part 38 fuel efficiency requirements apply to an airplane for which an 315 application in type design is submitted that incorporates a modification that meets the change criteria in 316 § 38.19. A new airplane produced with modifications meeting the change criteria may not exceed the 317 applicable fuel efficiency limit of part 38. The applicability criteria for modified airplanes is described in 318 § 38.19 and guidance is provided in paragraph 6.8 of this AC. A modified airplane is subject to the 319 same fuel efficiency metric value limit in § 38.17 as the airplane was prior to modification. 320 321 Applicants may choose to apply for a new fuel efficiency metric certification value even when not 322 required by part 38. 323 324 5.1.2 Non-Applicability of the Fuel Efficiency Metric 325 326 Part 38 fuel efficiency certification requirements do not apply to: 327 328 (1) Subsonic jet airplanes having a MTOM at or below 5,700 kg. 329 330 (2) Propeller-driven airplanes having a MTOM at or below 8,618 kg. 331 332 (3) Amphibious airplanes. 333 334 (4) Airplanes initially designed, or modified and used, for specialized operations. These airplane 335 designs may include characteristics or configurations necessary to conduct specialized operations 336 that the FAA and the United States Environmental Protection Agency (EPA) have determined may 337 cause a significant increase in the fuel efficiency metric value. 338 339 The FAA shares some examples of specialized operations from the ICAO Environmental 340 Technical Manual, Volume 3, (ETM) that include: 341 342 • Airplanes with mission requirements for carrying cargo that is not possible by using less 343 specialized airplanes (e.g., ramped back cargo door);1 344 • Airplanes with mission requirements for conducting very short or vertical takeoffs and 345 landings; or 346 • Airplanes with mission requirements for conducting scientific, research or humanitarian 347 missions exclusive of commercial service. 348 349 (5) Airplanes designed with a reference geometric factor of zero. 350 351 (6) Airplanes designed for, or modified and used for, firefighting (i.e. dispensing firefighting materials). 352 1 Example includes hinged fuselage sections such as Airbus’ Beluga [A300-600]. ### Page 10 12/13/2023 7 (7) Airplanes powered by reciprocating engines. 354 355 Generally, airplanes in categories (3), (4), (5) and (6) are designed or modified in such a way that their 356 designs are significantly different from the typical passenger or cargo-carrying airplanes. See 357 § 38.1(c). 358 359 5.2 Certification of Lower Takeoff Mass Variant 360 361 The calculation of specific air range (SAR) is based on reference masses that are a function of the 362 MTOM, which is defined in §38.3 as the maximum certified takeoff mass, expressed in kilograms, for an 363 airplane type design. The MTOM is intended to mean the maximum takeoff mass an airplane type 364 design is certificated to that is stated in the TCDS. The TCDS may contain several maximum takeoff 365 masses for different variants of the same airplane type design, and the MTOM is the highest of these 366 maximum takeoff masses. In other words, for a specific airplane type design, applicants may develop 367 multiple take-off mass (TOM) variants for operational purposes. The highest TOM variant of an 368 airframe/engine combination for which certification of that variant under part 38 will be sought must 369 demonstrate compliance with part 38.17. All lesser TOMs are considered to have the same fuel 370 efficiency certification value as at MTOM. 371 372 However, applicants may also apply for certification of fuel efficiency metric values for TOM variants 373 lower than MTOM. For such a case, the calculated reference airplane mass required by §38.13(b) and 374 the maximum permitted fuel efficiency certification limits shown in §38.17 would be based on the TOM 375 variant requested to be certified. The FEM value determined for such a lower TOM variant can be also 376 used for any TOM variants that are even lower than for that specific airplane type design. 377 378 If an applicant chooses to certify a lower TOM variant, the applicant should be aware that the FEM at the 379 highest weight variant (MTOM) of an airplane has the lowest margin to the regulatory limit level. 380 Certification at MTOM is required regardless of the certification of any lower TOM variants. The 1/SAR 381 value used in the FEM determination is calculated as an average of 1/SAR values that are established at 382 three reference masses (high, medium, and low). 383 384 In establishing the reference specifications for specific air range (SAR) determination, the highest SAR 385 value usually will be sought at the maximum range cruise condition at the reference specifications. A 386 greater non-linearity in the 1/SAR versus mass relationship could be introduced by a constraint unrelated 387 to the aerodynamic and propulsive efficiency of the airplane (e.g., an altitude pressurization limitation). In 388 this instance, particular care should be taken to ensure that the principle of the highest weight variant 389 having the lowest margin to the regulatory limit level continues to hold. 390 391 5.3 Exemptions 392 393 Pursuant to 49 U.S.C. § 44701(f), the Administrator may grant an exemption from a regulatory 394 requirement if the Administrator finds the exemption is in the public interest. An application for an 395 exemption from any requirements of part 38 must be submitted to the Administrator in accordance with 396 part 11. For all § 38.5 exemption requests, denials, or grants, AEE will be the responsible FAA office and 397 will consult with EPA’s Designated Program Officer and other FAA offices as needed before taking any 398 action. Petitioners for part 38 exemptions are encouraged to contact AEE prior to filing exemption 399 requests. 400 401 5.4 Incorporation by Reference 402 403 Section 38.7 incorporates, by reference, ICAO Doc 7488/3, Manual of the ICAO Standard Atmosphere 404 (extended to 80 kilometres (262 500 feet)), 1993. ICAO Doc 7488/3 provides the standard values of 405 atmospheric parameters, the values of constants and coefficients, and the underlying equations used in 406 the calculation of the atmospheric parameters. The manual is intended for use in calculations in the 407 design of airplanes, in presenting test results of airplanes and their components under identical 408 ### Page 11 12/13/2023 8 conditions, and in facilitating standardization in the development and calibration of instruments. ICAO 409 Doc 7488/3 is referenced in the Appendix to part 38, paragraphs A38.2.1.3.1, A38.5.2.2.1.9, and 410 A38.5.2.2.1.10. In these paragraphs, the applicant must use ICAO Doc 7488/3 to establish certain 411 reference specifications when determining SAR. Interested persons can purchase ICAO Doc 7488/3 412 from the ICAO Store at 999 Robert-Bourassa Boulevard Montréal (Quebec) Canada H3C 5H7, 413 (www.store.icao.int). 414 415 5.5 Fuel Efficiency Compliance Demonstration Plans 416 417 Prior to undertaking a demonstration of fuel efficiency, the applicant must submit procedures, weights, 418 configurations, and other information or data that are used to establish a fuel efficiency level to the FAA. 419 This submission must contain a complete description of the methodology and procedures by which an 420 applicant proposes to demonstrate compliance with part 38. This submission must be approved by an 421 FAA certification office in accordance with §38.21. 422 423 Use of any equivalent procedures or technical procedures not otherwise specified in part 38 must be 424 approved by AEE and documented in the submission as stated in §38.21. The submission should 425 include the following information: 426 427 a. A description of the applicable sections of part 38 for the airplane 428 b. Airplane description, including type, model number, and if applicable, the specific design 429 being certificated. The applicant should demonstrate and document the conformity of the test 430 airplane, particularly with regard to those parts which might affect the test airplane’s fuel 431 efficiency metric (FEM). 432 c. FEM certification methodology which should include the means of compliance and proposed 433 equivalent procedures. 434 d. Test plan that would include: 435 436 i. Test description. Test methods to comply with the test stability conditions in Appendix 437 A § A38.4.2.2.2 of part 38; 438 ii. Test points. The planned number of test points and the planned test conditions in 439 terms of weight or mass, center of gravity position, altitude, and speed; 440 iii. Airplane mass. The procedures for determining the mass of the airplane is in 441 Appendix A § A38.4.2.3 of part 38; and 442 iv. Test fuel properties. The procedures for determining the test fuel properties is in 443 Appendix A § A38.4.2.1.3 through A38.4.2.1.5 of part 38. 444 445 e. Deliverables: List the documents that should show compliance with Appendix A § 38.6 of part 446 38. 447 448 5.6 Fuel Efficiency Compliance Demonstration for Airplanes with Intermixed Engines 449 450 Typically, an applicant demonstrates compliance with part 38 for an airplane type design in which all 451 engines are of the same design. If there are engines of different design on an airplane, the design is 452 commonly referred to as having an “engine intermix” configuration, An applicant may choose to 453 demonstrate compliance of an airplane type design that includes an engine intermix. 454 In such a case, the applicant may, subject to the approval of the FAA, demonstrate compliance in one of 455 three ways: 456 457 a. In accordance with the test procedures defined in part 38, the test airplane must be 458 representative of the intermix arrangement for which certification is requested; or 459 b. In cases where the FEM value has been established for airplanes on which each of the 460 intermix engine models has been exclusively installed, compliance can be demonstrated on 461 the basis of either: 462 i. The average of the fuel efficiency evaluation metrics for identical airplanes on which each 463 of the intermix engine models has been exclusively installed; or 464 ### Page 12 12/13/2023 9 ii. The highest fuel efficiency evaluation metric for identical airplanes on which each of the 465 intermix engine models has been exclusively installed. 466 467 468 6. Expanded Discussion of 14 CFR part 38 Subpart B Requirements 469 470 6.1 Fuel Efficiency Metric 471 472 The fuel efficiency metric (FEM) in § 38.11 is a transport capability neutral measure of airplane fuel 473 efficiency. The FEM system is intended to promote advances in technologies that contribute to 474 improvements in fuel efficiency (structural, propulsive, and aerodynamic efficiencies) as well as 475 differentiate among generations of such technologies. In addition, the fuel efficiency metric system was 476 designed to accommodate a wide range of technologies and designs that manufacturers may employ to 477 improve the fuel efficiency of an airplane in a manner that is transport capability neutral. The FEM 478 system is based on three elements associated with airplane technology and design: 479 480 1. Cruise point fuel burn performance; 481 2. Airplane size; and 482 3. Airplane mass. 483 484 Section 38.11 requires that, for each airplane subject to part 38, a fuel efficiency metric value is 485 calculated using the following equation (rounded to three decimal places): 486 487 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐹𝐹𝐸𝐸𝐸𝐸𝐸𝐸 m𝐹𝐹𝑒𝑒𝑒𝑒𝐸𝐸𝐸𝐸 𝑣𝑣𝑣𝑣𝐹𝐹𝐹𝐹𝐹𝐹 = � 1𝑆𝑆𝑆𝑆𝑆𝑆�𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆𝑅𝑅𝐹𝐹0.24 488 489 The specific air range (SAR) is determined in accordance with § 38.13. The reference geometric factor 490 (RGF) is determined in accordance with § 38.15. SAR is expressed in units of km traveled per kg of fuel 491 burned, while RGF is dimensionless. The FEM value uses the inverse of SAR, (1/SAR)avg , so FEM is 492 expressed in units of kg of fuel burned per km of flight. The fuel efficiency metric is determined using an 493 average of three SAR test points that are normalized by RGF, which is a geometric factor representing 494 the physical size of an airplane. A lower FEM value represents greater fuel efficiency. An overview of the 495 fuel efficiency metric system elements is shown in Figure 6-1, below. 496 497 Fig. 6-1. 498 499 Overview of the fuel efficiency metric system elements 500 501 502 Unlike the specific fuel consumption (SFC) of an engine, which provides the engine’s fuel consumption 503 per unit of thrust (i.e., fuel efficiency of thrust production by an individual engine), SAR is a measure of 504 fuel efficiency at the airplane level. Specifically, SAR provides the distance an airplane can travel per 505 ### Page 13 12/13/2023 10 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 ### Page 14 12/13/2023 11 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 ### Page 15 12/13/2023 12 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 ### Page 16 12/13/2023 13 628 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 ### Page 17 12/13/2023 14 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) ### Page 18 12/13/2023 15 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 ### Page 19 12/13/2023 16 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 ### Page 20 12/13/2023 17 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 ### Page 21 12/13/2023 18 819 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 ### Page 22 12/13/2023 19 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 ### Page 23 12/13/2023 20 889 890 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 ### Page 24 12/13/2023 21 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 ### Page 25 12/13/2023 22 942 Step 2 — Confidence interval determination 943 944 The low number of test points in a small range of Mach and CL results in a statistical population that 945 follows the Student law, and allows the 90 percent confidence interval to be defined in accordance with 946 the methodology for Direct Flight Testing, as described in appendix 4 of this AC. The objective is to 947 determine an average ∆SAR value (%) and its associated 90 percent confidence interval. The 948 minimum acceptable sample size is twelve points (see § A38.5.3.4.). 949 950 Following this step and using the Student t-distribution, the 90 percent confidence interval (CI90) for the 951 estimate of the mean ∆SARAVG can be determined as: 952 953 𝐶𝐶𝐶𝐶90 (%) = �𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 ± 𝑒𝑒(.95,𝑛𝑛−1) s √𝑛𝑛� (%) 954 955 where t(.95, n-1) = Student t-distribution (for 90 percent confidence) for the degrees of freedom (i.e., n-1, 956 where n is number of data points). (See Table A4-1 in Appendix 4 of this AC). 957 958 Step 3 — Validity of results 959 960 Section A38.5.3.2 contains the following requirements: 961 962 “A38.5.3.2 If the 90 per cent confidence interval of the SAR value at any of the three reference 963 airplane masses – 964 965 A38.5.3.2.1 Is less than or equal to ±1.5 per cent, the SAR value may be used. 966 967 A38.5.3.2.2 Exceeds ±1.5 per cent, a penalty equal to the amount that the 90 per cent confidence 968 interval exceeds ±1.5 per cent must be applied to the SAR value, as approved by the FAA.” 969 970 Applying those requirements to a use of a first principle model for showing compliance: 971 972 a) If the 90 percent confidence interval remains within the ±1.5 percent limits, then the ∆SARAVG 973 (%) value can be retained as the reference deviation for model correction. 974 b) If the 90 percent confidence interval exceeds the ±1.5 percent limits, then a penalty equal to 975 the amount that the 90 percent confidence interval exceeds ±1.5 percent should be applied to 976 the ∆SARAVG(%) value, subject to the approval of AEE. For example, if the 90 percent 977 confidence interval is 5 percent, then the corrected ∆SARAVG(%) is 3.5 percent (5 percent -1.5 978 percent). The corrected ∆SARAVG(%) value then becomes the reference deviation for the 979 model correction. 980 981 Step 4 — SAR Model correction 982 983 When used to determine the FEM, the SAR values computed with a first principle model at each of the 984 three reference airplane masses must be corrected by a percentage amount that is equal to the 985 reference deviation determined in Step 3. 986 987 988 6.4.4.4. Example of the determination of 90 percent confidence intervals 989 990 The set of 12 flight test points are presumed to meet the selection criteria of paragraph 6.4.4.1 above. 991 The difference between the measured SAR and the computed SAR has been established as follows: 992 993 994 995 996 ### Page 26 12/13/2023 23 Table 6-1 997 998 Test point selection 999 1000 Selected test point number ∆SAR (%) 1 0.08 2 -0.6 3 -0.42 4 0.19 5 -0.43 6 0.23 7 -0.28 8 0.45 9 0.10 10 -0.28 11 -0.80 12 -0.64 1001 1002 a) The number of data points (n) = 12. 1003 b) The degrees of freedom (n-1) = 11. 1004 c) The Student t-distribution for 90 percent confidence and 11 degrees of freedom (𝑒𝑒(.95 ,11) ) = 1.797. 1005 (See examples in Table A4-1 in Appendix 4 to this AC.). 1006 1007 1008 Step 1 — Estimate of the mean ∆SAR (%) and of the standard deviation(s) 1009 1010 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴(%) = 112 �∑ 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆(𝑖𝑖)𝑖𝑖=12𝑖𝑖=1 � = -0.200 % 1011 1012 𝑒𝑒 = �∑ �𝐷𝐷𝐷𝐷𝐴𝐴𝐷𝐷(𝑖𝑖)− 𝐷𝐷𝐷𝐷𝐴𝐴𝐷𝐷𝐴𝐴𝐴𝐴𝐴𝐴�2𝑖𝑖=12𝑖𝑖=1 𝑛𝑛−1 = 0.39950 % 1013 1014 Step 2 — 90 percent confidence interval (CI90) 1015 1016 𝐶𝐶𝐶𝐶90 = 𝐷𝐷𝑆𝑆𝑆𝑆𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴 ± 𝑒𝑒(.95,11) s √12 = −0.200 ± 0.207 % 1017 1018 Step 3 — Check of confidence interval limits 1019 1020 The confidence interval extends to ±0.207 percent around the mean ∆SAR value (-0.200 percent), 1021 which is within the confidence interval limit of ±1.5 percent. As a result, a ∆SAR value of -0.200 1022 percent can be retained for model correction. 1023 1024 Step 4 — SAR Model correction 1025 1026 The SAR value calculated for each reference mass of the FEM can be determined by computation 1027 with the first principle model and would be corrected by the -0.200 percent value determined in Step 3 1028 ### Page 27 12/13/2023 24 as follows: 1029 1030 SARcorrected = SARcomputed x 0.998 1031 1032 6.5 Validity of Results – Confidence Interval 1033 1034 Section A38.5.3.1 requires the 90 percent confidence interval to be calculated for each of the SAR 1035 values at the three reference masses. Appendix 4 of this AC provides guidance regarding confidence 1036 interval evaluation, including examples. 1037 1038 6.6 Reference Geometric Factor 1039 1040 6.6.1 RGF General Guidelines 1041 1042 The reference geometric factor (RGF) is a non-dimensional parameter used to adjust the value of 1043 (1/SAR)AVG. RGF is based on a measure of fuselage size normalized with respect to 1 m2, and is derived 1044 as prescribed in §38.15. 1045 1046 The basic concept of RGF, and the exponent of 0.24 for RGF in the fuel efficiency metric, is to give 1047 appropriate credit for the size of the cabin. The RGF represents the area that is available for the 1048 transport of passengers or cargo on the main deck, and on an upper deck. §§ 38.15 and A38.3 provide 1049 a description of RGF and list some areas that are to be included in the RGF calculation, including 1050 figures cross-sectional and longitudinal views of notional RGF boundary conditions. This list of included 1051 areas is not comprehensive; RGF also includes, for example, any space in the cabin used for 1052 wardrobes, or for cabinets containing equipment such as passenger entertainment systems or life 1053 rafts. 1054 1055 Most airplanes have a single deck, or floor, for passengers or cargo. Many single-deck airplanes also 1056 have an underfloor cargo bay, but that does not mean that they should be considered as two-deck 1057 airplanes. 1058 1059 6.6.2 Orthogonal Projection and Width Boundary 1060 1061 For a single-deck airplane, the RGF is determined by making an orthogonal projection of the outer mold 1062 line (OML) of the fuselage pressure shell, onto a plane that is parallel to the main deck floor. The term 1063 orthogonal means that the projection is made using theoretical lines of projection which are orthogonal, 1064 or perpendicular, to the main deck floor, and also orthogonal to the plane where the projection is made. 1065 In the case of an airplane in which the main deck is perfectly horizontal when it stands on the ground, 1066 the projection is similar to the ‘shadow area’ on the ground, or the top view area of the fuselage. The 1067 terms ‘shadow area’ and ‘top view’ can be misleading however, and orthogonal projection is the proper 1068 term for obtaining a true projection. The term ‘shadow area’ could imply projection lines emanating 1069 from a single point, effectively like the sun. It is possible to make a projection using lines which emanate 1070 from any single point, but that is not intended, and would not be a true projection for RGF. The term 1071 ‘top view’ can be misleading for an airplane in which the main deck is not perfectly horizontal when it 1072 stands on the ground. Typically the main deck of an airplane is at a constant height (or constant Z 1073 station) in terms of the X, Y, Z coordinate system for the airplane, and in that case the orthogonal 1074 projection is the same as a plan view drawing, viewing either up or down along the Z axis. However, 1075 there is no requirement for any deck to be at a constant Z station. 1076 1077 Typically the maximum width of the fuselage cross section is above the main deck for a single-deck 1078 airplane, and if the fuselage has a constant cross section for part of its length, then the maximum width 1079 will be at the same height above the main deck (i.e. at the same Z station) for part of the fuselage 1080 length. At the aft end of the fuselage however, there will no longer be a constant cross section, and it is 1081 common for the point of maximum width to rise up higher above the main deck towards the tail, with 1082 fuselage upsweep. Towards the nose, typically the point of maximum width descends closer to the main 1083 ### Page 28 12/13/2023 25 deck. For the orthogonal projection, the maximum external width of the OML is always ‘captured’ at 1084 whatever height above the deck that it occurs. 1085 1086 For an airplane that has a main deck and also an upper deck, the RGF for the main deck is determined 1087 using the fuselage OML as the width boundary, as for a single-deck airplane. The upper deck is 1088 considered separately, and the width boundary for the upper deck RGF is defined as the fuselage OML 1089 at or above the upper deck floor level. This means that to determine the upper deck RGF, all of the 1090 fuselage below the upper deck floor can be removed from consideration, and then an orthogonal 1091 projection should be made of the remaining part of the fuselage, the entire upper cabin, onto a plane 1092 that is parallel to the upper deck. This projection will capture the maximum width of the fuselage OML 1093 at any height at or above the upper deck floor. The upper deck may be parallel to the main lower deck, 1094 but there is no requirement for this to be the case. The total RGF is simply the sum of the RGF values 1095 for the two decks. 1096 1097 6.6.3 Forward and Aft Boundaries 1098 1099 The aft boundary to be used for calculating RGF is the aft surface of the aft pressure bulkhead skin. 1100 This bulkhead may be a flat or domed skin to take the pressure loads, and typically has supporting 1101 structure attached either to the forward or aft face of the bulkhead. This aft boundary definition is 1102 consistent with the concept of using the external surface of the pressure shell for the width boundary. 1103 1104 The forward boundary to be used for calculating RGF is the forward surface of the forward pressure 1105 bulkhead skin except for the cockpit crew zone. For all airplanes, a plane will need to be defined for the 1106 aft boundary of the cockpit crew zone. If there is a cockpit door, this aft boundary is the plane of the 1107 forward face of the cockpit door. If there is no cockpit door, a boundary plane will need to be defined 1108 that is aft of the cockpit crew seats. Some airplanes may have optional approved cockpit layouts, for 1109 example to provide for one or two ‘jump seats’ aft of the two standard pilot seats; in that case the RGF 1110 should be based on the smallest approved cockpit layout (see § A38.3). 1111 1112 Some airplanes are certified for single-pilot operations, as illustrated in Appendix A38.3 Figure A38-1113 2. This figure shows that a passenger may be in the right cockpit seat, and the right side of the cockpit 1114 can be included in the RGF, even if a cockpit door is standard equipment. In this case, the aft 1115 boundary of the cockpit crew zone applies to the left side of the fuselage only. 1116 1117 For an airplane with two decks, the cockpit may be accessed from the main deck, or the upper deck, 1118 but the two decks are considered separately. One deck may extend forward, above or below a cockpit 1119 crew zone, and in that case the aft boundary of the cockpit crew zone should only apply to the RGF of 1120 the deck that provides direct access to the cockpit, not to both decks. 1121 1122 6.6.4 Floor Plane 1123 1124 For the floor plane of the main deck, and any upper deck, it is assumed that most, or all, of the floor 1125 area is on the same flat plane. It is common to have some local anomalies, such as a step up in the 1126 floor of the cabin towards the tail, typically in a baggage area. If there is a relatively small, elevated 1127 floor it is usually flat and parallel to the main floor, but there is no requirement for it to be so. Some 1128 airplanes may have other local floor changes, possibly even changes in slope. Some smaller airplanes 1129 have a dropped aisle, with elevated seating areas on both sides of the aisle. There is no requirement 1130 for any deck floor to be parallel with the upper or lower skin of the fuselage, but this will usually be the 1131 case. For each deck, there should be no difficulty in identifying a nominal flat plane which should apply 1132 to it, which then allows for the identification of a true flat plane (with no local anomalies) parallel to the 1133 deck, for the purpose of the orthogonal projection. 1134 1135 6.6.5 RGF Sensitivity 1136 1137 Although RGF is an important component of the CO2 emissions evaluation metric value, the exponent 1138 of 0.24 means that the metric value is less sensitive to a change in RGF as compared to a change in 1139 ### Page 29 12/13/2023 26 the average 1/SAR value. As an example, if the average 1/SAR value is changed by a factor of 1.01, 1140 then the metric value will also change by a factor of 1.01 (a 1% increase). However, if the RGF 1141 changes by a factor of 0.99 (a 1% decrease) then the metric value will increase by only a factor of 1142 1.0024150 (an increase of 0.2415%). The change in metric value as a result of a change in RGF, can 1143 be expressed as the reciprocal of the factor applied to RGF, with an exponent of 0.24 applied. For this 1144 example: ( 1 / 0.99 ) = 1.010101 ; and ( 1.010101 )0.24 = 1.002415. 1145 1146 The RGF sensitivity may lead an applicant to declare positions for the forward boundary and aft 1147 boundary that are slightly conservative in order to avoid lengthy geometric explanations and 1148 justifications. Typically, a small amount of conservatism, by declaring a forward and/or aft boundary that 1149 is displaced by 1 or 2 cm will lead to a very small change in RGF, much less than 1%, and an extremely 1150 small penalty in the metric value of less than 0.1%. 1151 1152 An applicant may also consider the potential for future geometric changes, and the no-FEM-change 1153 criteria. It may be administratively easier to deal with a small geometric change in the future, if the RGF 1154 has been defined in a slightly conservative way. 1155 1156 6.6.6 Floor Plane 1157 1158 For the floor plane of the main deck, and any upper deck, it is assumed that most, or all, of the floor area 1159 is on the same flat plane. It is common to have some local anomalies, such as a step up in the floor of 1160 the cabin towards the tail, typically in a baggage area. If there is a relatively small, elevated floor it is 1161 usually flat and parallel to the main floor, but there is no requirement for it to be so. Some airplanes may 1162 have other local floor changes, possibly even changes in slope. Some smaller airplanes have a dropped 1163 aisle, with elevated seating areas on both sides of the aisle. There is no requirement for any deck floor to 1164 be parallel with the upper or lower skin of the fuselage, but this will usually be the case. For each deck, 1165 there should be no difficulty in identifying a nominal flat plane which should apply to it, which then allows 1166 for the identification of a true flat plane (with no local anomalies) parallel to the deck, for the purpose of 1167 the orthogonal projection. 1168 1169 6.6.7 RGF Sensitivity 1170 1171 Although RGF is an important component of the CO2 emissions evaluation metric value, the exponent 1172 of 0.24 means that the metric value is less sensitive to a change in RGF as compared to a change in 1173 the average 1/SAR value. As an example, if the average 1/SAR value is changed by a factor of 1.01, 1174 then the metric value will also change by a factor of 1.01 (a 1% increase). However, if the RGF 1175 changes by a factor of 0.99 (a 1% decrease) then the metric value will increase by only a factor of 1176 1.0024150 (an increase of 0.2415%). The change in metric value as a result of a change in RGF, can 1177 be expressed as the reciprocal of the factor applied to RGF, with an exponent of 0.24 applied. For this 1178 example: ( 1 / 0.99 ) = 1.010101 ; and ( 1.010101 )0.24 = 1.002415. 1179 1180 The RGF sensitivity may lead an applicant to declare positions for the forward boundary and aft 1181 boundary that are slightly conservative in order to avoid lengthy geometric explanations and 1182 justifications. Typically, a small amount of conservatism, by declaring a forward and/or aft boundary that 1183 is displaced by 1 or 2 cm will lead to a very small change in RGF, much less than 1%, and an extremely 1184 small penalty in the metric value of less than 0.1%. 1185 1186 An applicant may also consider the potential for future geometric changes, and the no-FEM-change 1187 criteria. It may be administratively easier to deal with a small geometric change in the future, if the RGF 1188 has been defined in a slightly conservative way. 1189 1190 6.7 Fuel Efficiency Limits 1191 1192 Section 38.17 provides the maximum permitted fuel efficiency metric values for airplanes defined under 1193 § 38.1(a), as determined pursuant to § 38.11. In accordance with § 38.17(b), the fuel efficiency metric 1194 value may not exceed the values detailed in the table with fuel efficiency limits in § 38.17. Notably, the 1195 ### Page 30 12/13/2023 27 values determined in accordance with the equations in the table with fuel efficiency limits in § 38.17 1196 should be rounded to three decimal places. The maximum permitted fuel efficiency metric values are 1197 based on the type of airplane as defined in § 38.1 (applicability section) and the airplane’s MTOM. A 1198 more detailed discussion on the applicability of § 38.1 can be found in paragraph 5.1 of this AC. 1199 1200 6.8 Change Criteria 1201 1202 A modification requiring compliance with part 38 is determined by the change criteria in § 38.19. The 1203 requirements differ depending on whether an airplane has previously demonstrated compliance with part 1204 38 before a modification is made, or whether an airplane was type certificated before January 1, 2023, 1205 and was not required to demonstrate compliance with part 38. 1206 1207 The change criteria in § 38.19(a) specifies when a compliance demonstration to this new rule is required 1208 if a modification to an airplane, that has been shown to comply with § 38.17, will increase the MTOM of 1209 the airplane as written in § 38.19(a)(1) or increases the FEM value above the thresholds provided in § 1210 38.19(a)(2)(i) through (iii). Figure 6.11, below, illustrates the FEM change threshold limits of § 38.19 for 1211 any MTOM. 1212 1213 Fig. 6.11 1214 1215 FEM change threshold limits with variation in MTOM 1216 1217 1218 1219 Under § 38.19(b), where an airplane has been shown to comply with § 38.17, for a modification that 1220 does not increase either the MTOM or the FEM value, the airplane may retain the same FEM value as 1221 prior to modification. 1222 1223 Section 38.19(c) provides that an airplane, which meets the applicability provisions of § 38.1(a)(4) or (5) 1224 on or after January 1, 2023 and before January 1, 2028, must demonstrate compliance if the 1225 modification exceeds 1.5%. Alternatively, an airplane modification that is shown to have less than a 1226 1.5% increase in FEM does not have to demonstrate compliance. For an airplane whose type design 1227 was not previously certified to part 38, an applicant can estimate the change in the FEM value of the 1228 ### Page 31 12/13/2023 28 modified version of such an airplane by using one of the methods described in this AC38, if approved by 1229 the FAA. For example, for a change to the exterior of the airplane, the change in drag can be estimated 1230 using methods described in paragraph 6.4.3 of this AC, and this estimated change in drag can be 1231 directly related to changes in FEM value. 1232 1233 1234 7. Additional Guidance 1235 1236 If an applicant needs additional guidance, contact the AEE-300 Emissions Division Manager with the FAA 1237 Office of Environment and Energy at ralph.iovinelli@faa.gov. 1238 1239 ### Page 32 12/13/2023 29 Appendix 1: Definitions 1240 1241 1242 The following terms are defined in § 38.3, which is reproduced here for convenience: 1243 Amphibious Airplane means an airplane that is capable of takeoff and landing on both land and water. 1244 Such an airplane uses its hull or floats attached to the landing gear for takeoff and landing on water, and 1245 either extendable or fixed landing gear for takeoff and landing on land. 1246 1247 ICAO Annex 16, Volume III means Volume III of Annex 16 to the Convention on International Civil 1248 Aviation (incorporated by reference in § 38.7). 1249 1250 Maximum takeoff mass (MTOM) is the maximum certified takeoff mass, expressed in kilograms, for an 1251 airplane type design. 1252 1253 Performance model is an analytical tool (or a method) validated using corrected flight test data that can 1254 be used to determine the specific air range values for calculating the fuel efficiency metric value. 1255 Reference geometric factor (RGF) is a non-dimensional number derived from a two-dimensional 1256 projection of the fuselage. 1257 1258 Specific air range (SAR) is the distance an airplane travels per unit of fuel consumed. Specific air range is 1259 expressed in kilometers per kilogram of fuel. 1260 1261 Subsonic means an airplane that has not been certificated under 14 CFR to exceed Mach 1 in normal 1262 operation. 1263 1264 Type certificated maximum passenger seating capacity means the maximum number of passenger seats 1265 that may be installed on an airplane as listed on its type certificate data sheet, regardless of the actual 1266 number of seats installed on an individual airplane. 1267 ### Page 33 12/13/2023 30 Appendix 2: Abbreviations/Acronyms/Symbols 1268 1269 1270 1271 The abbreviations/acronyms/symbols used in this AC have the following meanings whether expressed in 1272 upper or lower case: 1273 1274 a Earth’s radius at the equator 1275 A Airplane reference wing area 1276 b Earth’s radius at the poles 1277 B Value representing the variation of drag with Reynolds number 1278 AEE FAA’s Office of Environment and Energy 1279 AVG Average 1280 CD Drag coefficient 1281 CFD Computational fluid dynamics 1282 CG Center of gravity 1283 CI Confidence interval 1284 CI90 90% Confidence interval 1285 CL Lift coefficient 1286 CO2 Carbon dioxide 1287 EPA United States Environmental Protection Agency 1288 FAA Federal Aviation Administration, United States Department of Transportation 1289 FEM Fuel Efficiency Metric 1290 g Gravitational acceleration 1291 g0 Standard acceleration due to gravity at sea level and a geodetic latitude of 45.5 degrees 1292 gref Gravitational acceleration, based on g0, for an airplane travelling true north in still air at the 1293 reference altitude and a geodetic latitude of 45.5 degrees 1294 gCoriolis Component of gravitational acceleration that is due to Coriolis effect 1295 gcent Component of gravitational acceleration that is due to centrifugal effect 1296 gtest Gravitational acceleration at the test values of latitude, geometric altitude, true track, and ground 1297 speed 1298 gφ,alt Component of the gravitational acceleration at the test altitude and latitude at zero ground speed 1299 h Altitude 1300 ICAO International Civil Aviation Organization 1301 Kg Kilogram(s) 1302 LHV Lower heating value 1303 m Meters 1304 M Mach number 1305 MTOM Maximum Takeoff Mass 1306 n Number of data points 1307 N Newtons 1308 OML Outer Mold Line 1309 Pa Pascals 1310 PS Static pressure 1311 re Earth’s radius 1312 RE Reynolds number 1313 RGF Reference Geometric Factor 1314 s Time in seconds or estimate of the standard deviation of the mean 1315 SAR Specific Air Range 1316 SEM Semi-empirical methods 1317 SFC Specific fuel consumption 1318 STC Supplementary type certificate 1319 T Temperature 1320 t(.95, n-1 Student t-distribution for 90 percent confidence for n degrees of freedom 1321 TAS True airspeed 1322 TC Type certificate 1323 ### Page 34 12/13/2023 31 TCDS Type certificate data sheet 1324 TOM Takeoff mass 1325 TSFC Thrust Specific Fuel Consumption 1326 V Speed 1327 Vg Ground speed 1328 δ Ratio of atmospheric pressure at a given altitude to the atmospheric pressure at sea level 1329 ∆ Change in value of a parameter 1330 % Percent 1331 µ Mean value 1332 ρ Density of air 1333 σ Track angle 1334 φ Latitude 1335 ∑ Summation of a series of values 1336 ζ Degrees of freedom of confidence interval 1337 ωE Earth’s rotation rate 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 ### Page 35 12/13/2023 32 Appendix 3: Correcting SAR Data to Reference Specifications 1354 1355 1356 A3-1. Corrections to Reference Specifications 1357 1358 This appendix covers corrections that must be made to the tested values of airplane weight, drag, and 1359 fuel flow. These corrections address any differences between the conditions at which the airplane was 1360 tested and the reference specifications. 1361 1362 For steady-state cruise flight, it is a reasonable approximation to assume lift equals weight and thrust 1363 equals drag. Since drag is a function of lift, fuel flow is a function of thrust, SAR is a function of fuel flow, 1364 and the FEM is a function of SAR, any deviation from the reference specifications that affect weight, drag, 1365 or fuel flow will affect SAR and the FEM. Each of these corrections will result in either increasing or 1366 decreasing the test SAR and the resulting FEM. 1367 1368 As stated in Appendix A § A38.5.2.2, each correction method is subject to the approval by the FAA, 1369 including any time an applicant considers a particular correction to be unnecessary (with acceptable 1370 justification). Any correction that would result in an increase in SAR (i.e., a lower FEM value) may be 1371 considered optional by the applicant. The effect of not making such a correction would be to increase the 1372 FEM value. 1373 1374 Table A3-1 lists all the corrections and the conditions under which a given correction might be optional: 1375 1376 Table A3-1. 1377 1378 Corrections to reference specifications 1379 1380 Correction Paragraph of this appendix Type of correction Conditions under which correction may be optional Remarks Latitude effect on g A3-1.2 Apparent gravity Test latitude greater than 45.5 degrees Gravitational acceleration is greatest at the poles and lowest at the equator. Testing at latitudes greater than 45.5 degrees will decrease SAR and increase the FEM as the airplane will be heavier. Altitude effect on g A3-1.2 Apparent gravity Test altitude lower than reference altitude Increasing the height above the Earth’s surface reduces the gravitational acceleration. Therefore, testing at an altitude lower than the reference altitude will decrease SAR and increase the FEM due to the effect of altitude on gravitational acceleration. Centrifugal effect on g A3-1.2 Apparent Headwind (negative The reduction in velocity ### Page 36 12/13/2023 33 Correction Paragraph of this appendix Type of correction Conditions under which correction may be optional Remarks gravity wind) (relative to the earth) provided by a headwind increases gravitational acceleration due to the centrifugal effect. This increases the airplane weight, which decreases SAR and increases the FEM. Coriolis effect on g A3-1.2 Apparent gravity Test true track angles from 180 to 360 degrees Flying in a westerly direction, the opposite direction as the Earth’s rotation, will increase gravitational acceleration due to the Coriolis effect. This increases the airplane weight which decreases SAR and increases the FEM. Acceleration/decelerat ion (energy) A3-1.3 Drag (dVG/dT) greater than 0 (positive acceleration in terms of ground speed) An accelerated flight condition (excess energy) results in a higher drag force, decreasing SAR and increasing the FEM. Reynolds number A3-1.4 Drag Test outside air temperature higher than standard air temperature Higher temperatures result in higher drag forces due to Reynold number effects. At temperatures higher than the reference temperature, SAR will be decreased and the FEM will increase. CG position A3-1.5 Drag Test CG position forward of the reference CG position A test CG position forward of the reference CG position results in higher drag, decreasing SAR and increasing the FEM. Aeroelastics A3-1.6 Drag - Wing aeroelastics may not be a concern depending on the size/weight/payload of the airplane and on wing stiffness. Fuel lower heating value (LHV) A3-1.7 Fuel flow Test fuel LHV less than 43.217 MJ/kg Testing with fuel that has an LHV lower than the reference value requires more fuel to ### Page 37 12/13/2023 34 Correction Paragraph of this appendix Type of correction Conditions under which correction may be optional Remarks be burned to achieve the same engine thrust level, hence decreasing SAR and increasing the FEM. Altitude effect on fuel flow A3-1.8 Fuel flow May always be considered optional Testing at any altitude other than the optimum altitude will result in decreasing SAR and increasing the FEM due to higher fuel burn at offoptimum altitude. Temperature effect on fuel flow A3-1.9 Fuel flow Test outside air temperature higher than standard day temperature Testing at a temperature higher than the reference temperature will result in decreasing SAR and increasing the FEM due to higher fuel burn at higher temperatures. Engine deterioration level A3-1.10 Fuel flow - In general, this correction should not be made. See paragraph A3-1.10 of this AC. Electrical and mechanical power extraction and bleed flow A3-1.11 Fuel flow Test electrical and mechanical power extraction and bleed flow higher than the reference electrical and mechanical power extraction and bleed flow Testing with higher than reference power extraction and bleed flow will require more fuel to be burned, hence decreasing SAR and increasing the FEM. Modifications and non-standard equipment that will not be included on the production airplane A3-1.12 Drag and/or fuel flow Any modification or non-standard equipment that reduces SAR Not accounting for modifications or non-standard equipment that decreases SAR and increases the FEM. 1381 1382 The selection of a reference airspeed is used to determine the target airspeed for acquiring SAR test data 1383 for determination of the FEM. For applicants using either SAR data clustered around each of the three 1384 reference masses (see § A38.5.3.3) or SAR data obtained over a range of masses (see § A38.5.3.4), no 1385 correction is made for any differences between the target reference airspeed and the test airspeed. Since 1386 the reference airspeed is generally expected to be the optimum airspeed (see § A38.2), any difference 1387 ### Page 38 12/13/2023 35 between the test airspeed and the reference airspeed will decrease SAR and increase the FEM. For 1388 applicants using a first principle model to show compliance (see paragraph 6.4.4 of this AC), the 1389 reference airspeed is used to identify the portion of the performance model to be validated. The reference 1390 airspeed is also used as the airspeed (or Mach number) at which the SAR value for each reference mass 1391 is to be computed from the performance model. 1392 1393 The overall process for determining SAR at the reference specifications for each test data point consists 1394 of the following steps: 1395 1396 Step 1) Determine the airplane weight from the airplane mass for both the test condition and the 1397 reference specifications for gravitational acceleration, as described in paragraph A3-1.1 below. Determine 1398 the drag correction due to the difference in lift between the test weight and the weight at the reference 1399 specifications for gravitational acceleration using the airplane’s drag model and the relationship that lift 1400 equals weight for non-accelerated, level flight, as described in paragraph A3-1.2.1. 1401 1402 Note.— As described in paragraph A3-1.2.2, this step is not necessary when using method 2 for the 1403 gravitational acceleration correction. 1404 1405 Step 2) Determine all other applicable drag corrections as described in paragraphs A3-1.3, A3-1.4, A3-1406 1.5, and A3-1.6, and sum them together with the drag correction from paragraph A3-1.2.1. 1407 1408 Step 3) Determine the airplane drag for the test condition. An approximation can be made that for these 1409 unaccelerated, level flight test conditions, the airplane drag for the test condition is equal to the engine 1410 thrust for the test condition. The engine thrust should be determined from: 1411 1412 • a calibrated engine or an engine performance model; and 1413 • the average value of the parameters needed to determine thrust from the engine performance 1414 model measured during the test condition. 1415 1416 Step 4) Add the sum of drag corrections from Step 2 to the airplane drag for the test condition from Step 3 1417 to obtain the airplane drag corrected to the reference specifications. 1418 1419 Step 5) Determine the change in engine fuel flow for the corrections that were made for drag. The change 1420 in engine fuel flow due to the drag corrections can be determined as follows: 1421 1422 ∆Fuel FlowDrag = Fuel FlowRef Drag – Fuel FlowTest Drag 1423 1424 where: 1425 1426 Fuel FlowRef Drag is the fuel flow from an engine performance model at the airplane drag corrected for the 1427 reference specifications (assuming thrust equals drag) at the average speed, altitude and temperature for 1428 the test condition; and 1429 1430 Fuel FlowTest Drag is the fuel flow from an engine performance model at the airplane drag for the test 1431 condition (assuming thrust equals drag) at the average speed, altitude and temperature for the test 1432 condition. 1433 1434 Step 6) Correct the measured test engine fuel flow to reference specifications as follows: 1435 1436 Fuel Flowref = Fuel Flowtest + ∆Fuel FlowDrag + ∆Fuel FlowLHV + ∆Fuel Flowalt + ∆Fuel Flowtemp + 1437 ∆Fuel FlowCorr bleed 1438 1439 where: 1440 1441 Fuel Flowtest is the average engine fuel flow measured during the test condition, corrected to the reference 1442 engine deterioration level (if applicable) in kg/h; 1443 ### Page 39 12/13/2023 36 1444 ∆Fuel FlowDrag is the fuel flow correction for drag from Step 5 in kg/h; 1445 1446 ∆Fuel FlowLHV is the fuel flow correction for fuel lower heating value calculated from paragraph A3-1.7 in 1447 kg/h; 1448 1449 ∆Fuel Flowalt is the fuel flow correction for altitude calculated from paragraph A3-1.8 in kg/h; 1450 1451 ∆Fuel Flowtemp is the fuel flow correction for temperature calculated from paragraph A3-1.9 in kg/h; and 1452 1453 ∆Fuel FlowCorr bleed is the fuel flow correction for electrical and mechanical power extraction and bleed flow 1454 calculated from paragraph A3-1.10 in kg/h. 1455 1456 Step 7) The SAR value corrected to reference specifications is given by the following relationship: 1457 1458 𝑆𝑆𝑆𝑆𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟 = � 𝑇𝑇𝑆𝑆𝑆𝑆𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝑜𝑜𝐹𝐹𝑟𝑟𝑟𝑟𝑟𝑟� 1459 1460 where: 1461 1462 SARref is the SAR for the reference specifications in km/kg; 1463 1464 TAS is the average airplane true airspeed for the test specifications in km/h; and 1465 1466 Fuel Flowref is the engine fuel flow for the reference specifications from Step 6 in kg/h. 1467 1468 A3-1.1 Test Weight. Since the weight of the airplane during each test condition cannot be directly 1469 measured, it is determined using the following process, in accordance with §§ A38.4.2.1.2 and A38.4.2.3: 1470 1471 Begin with weighing the airplane on the ground, where the local gravitational acceleration can be readily 1472 determined using the process described in paragraph A3-1.2.1. The pre-flight airplane mass is 1473 determined from the following relationship: 1474 1475 𝑀𝑀𝑣𝑣𝑒𝑒𝑒𝑒𝑤𝑤𝑟𝑟𝑖𝑖𝑎𝑎ℎ𝑖𝑖𝑛𝑛𝑎𝑎 = 𝑊𝑊𝐹𝐹𝐸𝐸𝑊𝑊ℎ𝑒𝑒𝑤𝑤𝑟𝑟𝑖𝑖𝑎𝑎ℎ𝑖𝑖𝑛𝑛𝑎𝑎𝑊𝑊𝑤𝑤𝑟𝑟𝑖𝑖𝑎𝑎ℎ𝑖𝑖𝑛𝑛𝑎𝑎 1476 1477 where: 1478 1479 Weightweighing is the airplane weight from the scale weighing in N; and 1480 1481 gweighing is the gravitational acceleration at rest at the weighing site latitude and elevation in 1482 meters/second2. See paragraph A-3.1.2.1 for determining gweighing using the weighing site latitude and 1483 elevation for the test latitude, φ, and test geometric altitude, h, respectively. 1484 1485 Any change in mass after the weighing, and prior to the test flight, should be accounted for to establish 1486 the mass of the airplane at the start of the test flight. The mass for each test condition can be determined 1487 by subtracting the integrated fuel flow (mass of fuel burned) from the mass of the airplane at the start of 1488 the test flight. The test weight, in N, for each test condition is determined from the following equation: 1489 1490 𝑊𝑊𝐹𝐹𝐸𝐸𝑊𝑊ℎ𝑒𝑒𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 = (𝑀𝑀𝑣𝑣𝑒𝑒𝑒𝑒𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡)(𝑊𝑊𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡) 1491 1492 where: 1493 1494 Masstest is the average mass of the airplane during the test condition in kg; and 1495 1496 ### Page 40 12/13/2023 37 gtest is the gravitational acceleration at the test latitude, test geometric altitude, test true track, and test 1497 ground speed in m/s2. See paragraph A-3.1.2.1 for determining gtest. 1498 1499 A3-1.2 Apparent gravity. Acceleration, caused by the local effects of gravity and inertia, affects the test 1500 weight of the airplane. The apparent gravity at the test conditions varies with latitude, altitude, ground 1501 speed, and direction of motion, relative to the Earth’s axis. The reference gravitational acceleration is the 1502 gravitational acceleration, based on g0, for the airplane travelling in the direction of true north in still air at 1503 the reference altitude, a geodetic latitude of 45.5 degrees. 1504 1505 If the test conditions differ from the conditions for the reference gravitational acceleration, the airplane 1506 weight at the reference gravitational acceleration will be different than the airplane weight at the test 1507 conditions. This will result in a SAR and FEM that are not representative of the SAR and FEM at the 1508 reference gravitational acceleration. If the test conditions are at a gravitational acceleration that is less 1509 than the reference gravitational acceleration, then a correction will be necessary, as described below. 1510 1511 There are two methods provided below for determining the acceleration correction. Method 1 is a general 1512 method for determining the effect of gravitational acceleration on the airplane test weight, which is then 1513 used along with the airplane’s drag model to determine the effect on airplane drag. This drag correction 1514 for gravitational acceleration is then combined with the other drag corrections to determine the effect on 1515 airplane fuel flow and the value of SAR. 1516 1517 Method 2 is a simplified approach that does not require use of an airplane drag model. This method is 1518 acceptable for FEM certification when SAR is determined by direct flight test measurement of SAR test 1519 points in accordance with § A38.1.2.1. Method 2 is based on the same equations for determining g as 1520 Method 1, and provides the same results for SAR data at (or near) optimum flight conditions. For SAR 1521 data that is not at (or near) reference specifications, Method 2 may result in small errors in the SAR 1522 correction for gravitational acceleration correction, but the overall SAR and FEM values will be 1523 conservative because these errors will be much smaller than the SAR decrease (thus FEM increase) 1524 resulting from testing outside optimum flight conditions. 1525 1526 A3-1.2.1 Method 1 for the gravitational acceleration correction 1527 1528 The overall process for determining the drag correction due to the effect of gravitational acceleration on 1529 airplane weight consists of the following steps: 1530 1531 Step 1) Determine the airplane test weight, as described in paragraph A3-1.1. 1532 1533 Step 2) Determine the airplane weight for the reference gravitational acceleration conditions from 1534 the airplane test mass and the reference gravitational acceleration: 1535 1536 𝑊𝑊𝐹𝐹𝐸𝐸𝑊𝑊ℎ𝑒𝑒𝑟𝑟𝑟𝑟𝑟𝑟 𝑎𝑎 = (𝑀𝑀𝑣𝑣𝑒𝑒𝑒𝑒𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡)�𝑊𝑊𝑟𝑟𝑟𝑟𝑟𝑟� 1537 where: 1538 1539 Weightref g is the airplane weight at the reference gravitational acceleration conditions in N; 1540 1541 Masstest is the average mass of the airplane during the test condition in kg; 1542 1543 1544 gref is the gravitational acceleration for the airplane travelling in the direction of true north in still air at the 1545 reference altitude and a geodetic latitude of 45.5 degrees, and based on g0, in m/s2; and 1546 1547 g0 is the standard acceleration due to gravity at sea level and a geodetic latitude of 45.5 degrees, 9.80665 1548 m/s2. 1549 1550 Step 3) Determine the drag correction for the difference between Weighttest and Weightref g, as described 1551 later in this paragraph. 1552 ### Page 41 12/13/2023 38 1553 The value of gravitational acceleration, g, consists of the following components: 1554 1555 a) Distance from the center of Earth’s mass. This is a function of the geometric altitude and the 1556 latitude of the airplane relative to a mathematical representation of the shape of the Earth. 1557 1558 b) Centrifugal effect. An airplane in flight will experience a force acting outwards in the radial 1559 direction that is proportional to the square of the ground speed of the airplane and inversely 1560 proportional to the distance of the airplane from the center of mass of the Earth. 1561 1562 c) Coriolis effect. An airplane in flight will experience a force that is proportional to its ground speed, 1563 the rotation rate of the Earth, the direction of travel, and the latitude of operation. For example, an 1564 airplane flying east, in the same direction that the Earth rotates, will experience a lower 1565 gravitational acceleration, while an airplane flying west will experience a higher gravitational 1566 acceleration. The effect will be greatest at the equator. 1567 1568 The following equations are based on the World Geodetic System 84 Ellipsoidal Gravity definition. Other 1569 formulations and simplifications may provide essentially equivalent results. 1570 1571 The gravitational acceleration experienced for each test data point (gtest) is determined as follows: 1572 1573 gtest = gφ,alt + gcent + gCoriolis 1574 1575 where: 1576 1577 gφ,alt is the component of the gravitational acceleration at zero ground speed, at the test altitude and 1578 latitude in m/s2; 1579 1580 gcent is the component of the gravitational acceleration due to centrifugal effect in m/s2; and 1581 1582 gCoriolis is the component of the gravitational acceleration due to Coriolis effect in m/s2. 1583 1584 The gravitational acceleration for the test geometric altitude and latitude component at zero ground 1585 speed, gφ,alt, is determined as follows: 1586 1587 First, determine the component of gravitational acceleration at the test latitude at sea level and zero 1588 ground speed from the following equation: 1589 1590 𝑊𝑊𝜑𝜑 = �9.7803267714 1 + 0.00193185138639 𝑒𝑒𝐸𝐸𝐸𝐸2𝜑𝜑�1 − 0.00669437999013 𝑒𝑒𝐸𝐸𝐸𝐸2𝜑𝜑� 1591 1592 where φ is the test latitude in degrees. 1593 1594 1595 1596 The component of gravitational acceleration at zero ground speed for the test geometric altitude and 1597 latitude is then determined from the following equation: 1598 1599 𝑊𝑊𝜑𝜑,𝑎𝑎𝑙𝑙𝑡𝑡 = 𝑊𝑊𝜑𝜑 � 𝑒𝑒𝑟𝑟𝑒𝑒𝑟𝑟 + ℎ�2 1600 1601 1602 where: 1603 1604 𝑊𝑊𝜑𝜑 is the component of gravitational acceleration at the test latitude at sea level and zero ground speed; 1605 ### Page 42 12/13/2023 39 1606 h is the test geometric altitude in m; and 1607 1608 re is the radius of the Earth at the test latitude, which is determined from the following equation: 1609 1610 𝑒𝑒𝑟𝑟 = �(𝑣𝑣2𝐸𝐸𝑜𝑜𝑒𝑒 𝜑𝜑)2 + (𝑏𝑏2𝑒𝑒𝐸𝐸𝐸𝐸 𝜑𝜑)2(𝑣𝑣 𝐸𝐸𝑜𝑜𝑒𝑒 𝜑𝜑)2 + (𝑏𝑏 𝑒𝑒𝐸𝐸𝐸𝐸 𝜑𝜑)2 1611 1612 where: 1613 1614 a is the Earth’s radius at the equator = 6,378,137 m; 1615 1616 b is the Earth’s radius at the pole = 6,356,752 m; and 1617 1618 φ is the test latitude in degrees. 1619 1620 As an alternative to using the equation for gφ,alt provided above, gφ,alt can be approximated by linear 1621 interpolation using Table A3-2: 1622 1623 1624 1625 ### Page 43 12/13/2023 40 Table A3-2. 1626 1627 gφ,alt 1628 1629 gφ,alt (m/s2) Geometric Height (ft) Latitude (either North or South) (d ) 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 0 9.78033 9.77565 9.77099 9.76632 9.76166 9.75700 9.75234 9.74769 9.74304 9.73840 9.73376 10 9.78188 9.77721 9.77254 9.76787 9.76321 9.75855 9.75389 9.74924 9.74459 9.73994 9.73530 20 9.78637 9.78169 9.77702 9.77235 9.76768 9.76302 9.75836 9.75370 9.74905 9.74440 9.73975 30 9.79325 9.78857 9.76302 9.77921 9.77454 9.76987 9.76521 9.76054 9.75588 9.75123 9.74658 40 9.80170 9.79701 9.79232 9.78764 9.78296 9.77829 9.77362 9.76895 9.76428 9.75962 9.75496 45.5 9.80665 9.80196 9.79727 9.79258 9.78790 9.78322 9.77855 9.77387 9.76920 9.76454 9.75988 50 9.81070 9.80601 9.80132 9.79663 9.79194 9.78726 9.78258 9.77790 9.77323 9.76856 9.76390 60 9.81918 9.81448 9.80978 9.80508 9.80039 9.79570 9.79101 9.78633 9.78165 9.77698 9.77230 70 9.82610 9.82139 9.81668 9.81198 9.80728 9.80259 9.79790 9.79321 9.78853 9.78385 9.77917 80 9.83062 9.82590 9.82120 9.81649 9.81179 9.80709 9.80240 9.79771 9.79302 9.78833 9.78365 90 9.83219 9.82747 9.82276 9.81806 9.81336 9.80866 9.80396 9.79927 9.79458 9.78989 9.78521 1630 The component of the gravitational acceleration due to centrifugal effect, gcent, is determined from the 1631 following equation: 1632 1633 𝑊𝑊𝑐𝑐𝑟𝑟𝑛𝑛𝑡𝑡 = − 𝑉𝑉𝑎𝑎2𝑒𝑒𝑟𝑟 + ℎ 1634 1635 where: 1636 1637 Vg is the ground speed in m/s; 1638 1639 re is the radius of the Earth in m at the test latitude, which is determined from the same equation as 1640 provided above for how to determine gφ,alt: 1641 1642 𝑒𝑒𝑟𝑟 = � (𝑎𝑎2𝑐𝑐𝑐𝑐𝑡𝑡 𝜑𝜑)2+ (𝑏𝑏2𝑡𝑡𝑖𝑖𝑛𝑛 𝜑𝜑)2 (𝑎𝑎 𝑐𝑐𝑐𝑐𝑡𝑡 𝜑𝜑)2+ (𝑏𝑏 𝑡𝑡𝑖𝑖𝑛𝑛 𝜑𝜑)2 ; and 1643 1644 h is the test geometric altitude in m. 1645 1646 As an alternative to using the equation for gcent, gcent can be approximated by linear interpolation using 1647 Table A3-3: 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 Table A3-3. 1658 ### Page 44 12/13/2023 41 1659 gcent 1660 1661 gcent Ground Speed (kts) 0 100 200 300 400 500 600 700 800 gcent 0.00000 -0.00041 -0.00166 -0.00373 -0.00663 -0.01036 -0.01492 -0.02030 -0.02652 1662 The component of the gravitational acceleration due to Coriolis effect, gCoriolis, can be calculated using the 1663 following equation: 1664 1665 𝑊𝑊𝐶𝐶𝑐𝑐𝑟𝑟𝑖𝑖𝑐𝑐𝑙𝑙𝑖𝑖𝑡𝑡 = −2 𝜔𝜔𝐸𝐸 𝑉𝑉𝑎𝑎 𝐸𝐸𝑜𝑜𝑒𝑒 𝜑𝜑 sin 𝜎𝜎 1666 1667 1668 where: 1669 1670 ωE is the Earth’s rotation rate = 7.29212 x 10-5 radians/s; 1671 1672 Vg is the airplane’s ground speed in m/s; 1673 1674 𝜑𝜑 is the test latitude in degrees; and 1675 1676 σ is the track angle of the airplane as measured from true north in degrees. 1677 1678 As an alternative to using the equation , gCoriolis can be approximated by linear interpolation using Table 1679 A3-4: 1680 1681 Table A3-4 1682 1683 gCoriolis 1684 1685 gCoriolis for ground speeds from 200 to 400 knots GS (kts) 200 300 400 Latitude (either N or S) (degrees) 0 30 60 90 0 30 60 90 0 30 60 90 True Track Angle (degrees) 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 30 -0.00750 -0.00650 -0.00650 0.00000 -0.01125 -0.00975 -0.00563 0.00000 -0.01501 -0.01300 -0.00750 0.00000 60 -0.01300 -0.01125 -0.01125 0.00000 -0.01949 -0.01688 -0.00975 0.00000 -0.02599 -0.02251 -0.01300 0.00000 90 -0.01501 -0.01300 -0.01300 0.00000 -0.02251 -0.01949 -0.01125 0.00000 -0.03001 -0.02599 -0.01501 0.00000 120 -0.01300 -0.01125 -0.01125 0.00000 -0.01949 -0.01688 -0.00975 0.00000 -0.02599 -0.02251 -0.01300 0.00000 150 -0.00750 -0.00650 -0.00650 0.00000 -0.01125 -0.00975 -0.00563 0.00000 -0.01501 -0.01300 -0.00750 0.00000 180 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 210 0.00750 0.00650 0.00650 0.00000 0.01125 0.00975 0.00563 0.00000 0.01501 0.01300 0.00750 0.00000 240 0.01300 0.01125 0.01125 0.00000 0.01949 0.01688 0.00975 0.00000 0.02599 0.02251 0.01300 0.00000 270 0.01501 0.01300 0.01300 0.00000 0.02251 0.01949 0.01125 0.00000 0.03001 0.02599 0.01501 0.00000 300 0.01300 0.01125 0.01125 0.00000 0.01949 0.01688 0.00975 0.00000 0.02599 0.02251 0.01300 0.00000 330 0.00750 0.00650 0.00650 0.00000 0.01125 0.00975 0.00563 0.00000 0.01501 0.01300 0.00750 0.00000 Table A3-4 (continued) 1686 1687 ### Page 45 12/13/2023 42 gCoriolis for ground speeds from 500 to 700 knots GS (kts) 500 600 700 Latitude (either N or S) (degrees) 0 30 60 90 0 30 60 90 0 30 60 90 True Track Angle (degrees) 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 30 -0.01876 -0.01624 -0.00938 0.00000 -0.02251 -0.01949 -0.01125 0.00000 -0.02626 -0.02274 -0.01313 0.00000 60 -0.03249 -0.02814 -0.01624 0.00000 -0.03899 -0.03376 -0.01949 0.00000 -0.04548 -0.03939 -0.02274 0.00000 90 -0.03751 -0.03249 -0.01876 0.00000 -0.04502 -0.03899 -0.02251 0.00000 -0.05252 -0.04548 -0.02626 0.00000 120 -0.03249 -0.02814 -0.01624 0.00000 -0.03899 -0.03376 -0.01949 0.00000 -0.04548 -0.03939 -0.02274 0.00000 150 -0.01876 -0.01624 -0.00938 0.00000 -0.02251 -0.01949 -0.01125 0.00000 -0.02626 -0.02274 -0.01313 0.00000 180 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 210 0.01876 0.01624 0.00938 0.00000 0.02251 0.01949 0.01125 0.00000 0.02626 0.02274 0.01313 0.00000 240 0.03249 0.02814 0.01624 0.00000 0.03899 0.03376 0.01949 0.00000 0.04548 0.03939 0.02274 0.00000 270 0.03751 0.03249 0.01876 0.00000 0.04502 0.03899 0.02251 0.00000 0.05252 0.04548 0.02626 0.00000 300 0.03249 0.02814 0.01624 0.00000 0.03899 0.03376 0.01949 0.00000 0.04548 0.03939 0.02274 0.00000 330 0.01876 0.01624 0.00938 0.00000 0.02251 0.01949 0.01125 0.00000 0.02626 0.02274 0.01313 0.00000 1688 1689 The reference gravitational acceleration, gref, is the gravitational acceleration for the airplane travelling in 1690 the direction of true north in still air at the reference altitude and a geodetic latitude of 45.5 degrees. 1691 Because the reference gravitational acceleration condition is for the airplane travelling in the direction of 1692 true north, the reference gravitational acceleration does not include any Coriolis effect. Because the 1693 reference specification is for the airplane travelling in still air, the effect of the centrifugal effect on the 1694 reference gravitational acceleration is determined using the airplane’s true airspeed (which is the same as 1695 the zero wind ground speed). The reference gravitational acceleration can be determined for each test 1696 point as follows: 1697 1698 Determine the component of gravitational acceleration for the reference altitude and latitude at zero 1699 ground speed using the process defined above, using the reference altitude and 45.5 degrees latitude as 1700 the altitude and latitude, respectively, instead of the test values. 1701 1702 Determine the component of the reference gravitational acceleration due to centrifugal effect using the 1703 process above, using the airplane’s true airspeed as the ground speed. 1704 1705 The reference gravitational acceleration, gref, is the sum of the component of gravitational acceleration for 1706 the reference altitude and latitude at zero ground speed, and the component of the reference gravitational 1707 acceleration due to centrifugal effect. 1708 1709 The drag correction for gravitational acceleration (due to the difference between the airplane test weight, 1710 (Weighttest) and the airplane weight at the reference gravitational acceleration conditions (Weightref g)) is 1711 determined from the airplane drag model. The airplane’s drag model provides the drag coefficient (CD) as 1712 a function of the lift coefficient (CL) and Mach number. The lift coefficient for Weighttest and Weightref g can 1713 be determined from the following equation: 1714 1715 𝐶𝐶𝐿𝐿 = � 𝑊𝑊𝐹𝐹𝐸𝐸𝑊𝑊ℎ𝑒𝑒 𝛿𝛿⁄70927.5 𝑀𝑀2𝑆𝑆� 1716 ### Page 46 12/13/2023 43 1717 where: 1718 1719 CL is the lift coefficient; 1720 1721 Weight is the weight of the airplane in N (either Weighttest or Weightref g, depending on which lift coefficient 1722 is being calculated); 1723 1724 δ is the ratio of the ambient air pressure at the test altitude to the ambient air pressure at sea level; 1725 1726 M is the airplane’s average Mach number during the test condition; and 1727 1728 A is the airplane’s reference wing area in m2. 1729 1730 The drag correction for gravitational acceleration can be determined from the drag equation: 1731 1732 ∆𝐷𝐷𝑒𝑒𝑣𝑣𝑊𝑊𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎 = 12 𝜌𝜌𝑉𝑉2 �𝐶𝐶𝐷𝐷𝑟𝑟𝑟𝑟𝑟𝑟 𝑔𝑔 − 𝐶𝐶𝐷𝐷𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 � 𝑆𝑆 1733 1734 where: 1735 1736 ΔDraggrav is the drag correction in N for gravitational acceleration; 1737 1738 ρ is the density of air at the test altitude and test temperature in kg/m3; 1739 1740 V is the airplane’s average true airspeed during the test condition in m/s; 1741 1742 A is the airplane’s reference wing area in m2; 1743 1744 CDref g is the drag coefficient from the airplane’s drag model at the CL for Weightref g; and 1745 1746 CD test is the drag coefficient from the airplane’s drag model at the test CL for Weighttest. 1747 1748 A3-1.2.2 Method 2 for the gravitational acceleration correction 1749 1750 The process for determining gravitational acceleration correction to SAR consists of the following steps: 1751 1752 Step 1) Determine the airplane test mass, as described in paragraph A3-1.1. 1753 1754 Step 2) Determine gtest/gref for the test latitude by linear interpolation from Table A3-5: 1755 1756 1757 ### Page 47 12/13/2023 44 Table A3-5. 1758 1759 gtest/gref for latitude (latitude correction) 1760 1761 gtest/gref for latitude (latitude correction) Test Latitude (either north or south) (degrees) 0 10 20 30 40 50 60 70 80 90 (gtest/gref)lat 0.9973 0.9975 0.9979 0.9986 0.9995 1.0004 1.0013 1.0020 1.0024 1.0026 1762 Step 3) Determine gtest/gref to correct for test altitude by linear interpolation from Table A3-6: 1763 1764 Table A3-6. gtest/gref for altitude (altitude correction) 1765 1766 gtest/gref for altitude (altitude correction) Reference Altitude - Test Geometric Altitude (ft) -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 (gtest/gref)alt 0.9995 0.9996 0.9997 0.9998 0.9999 1.0000 1.0001 1.0002 1.0003 1.0004 1.0005 1767 Step 4) Determine gtest/gref for headwind/tailwind (centrifugal correction) by linear interpolation from Table 1768 A3-7: 1769 1770 1771 Table A3-7. 1772 1773 gtest/gref for headwind/tailwind (centrifugal correction) 1774 1775 gtest/gref for headwind/tailwind (centrifugal correction) TAS (kts) 200 300 400 500 600 Tailwind (kts) 300 0.9991 0.9989 0.9986 0.9983 0.9981 200 0.9995 0.9993 0.9991 0.9990 0.9988 100 0.9998 0.9997 0.9996 0.9995 0.9994 0 1.0000 1.0000 1.0000 1.0000 1.0000 Headwind (kts) -100 1.0001 1.0002 1.0003 1.0004 1.0005 -200 1.0002 1.0003 1.0005 1.0007 1.0009 -300 1.0001 1.0004 1.0006 1.0009 1.0011 1776 1777 Step 5) Determine gtest/gref for track angle (Coriolis correction) by linear interpolation from Table A3-8: 1778 1779 1780 1781 1782 1783 ### Page 48 12/13/2023 45 Table A3-8. 1784 1785 gtest/gref for track angle (Coriolis correction) 1786 1787 gtest/gref for track angle (Coriolis correction) for ground speeds from 200 to 400 knots GS (kts) 200 300 400 Latitude (either north or south) (degrees) 0 30 60 90 0 30 60 90 0 30 60 90 True Track Angle (degrees) 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 30 0.9992 0.9993 0.9996 1.0000 0.9988 0.9990 0.9994 1.0000 0.9985 0.9987 0.9992 1.0000 60 0.9987 0.9988 0.9993 1.0000 0.9980 0.9983 0.9990 1.0000 0.9973 0.9977 0.9987 1.0000 90 0.9985 0.9987 0.9992 1.0000 0.9977 0.9980 0.9988 1.0000 0.9969 0.9973 0.9985 1.0000 120 0.9987 0.9988 0.9993 1.0000 0.9980 0.9983 0.9990 1.0000 0.9973 0.9977 0.9987 1.0000 150 0.9992 0.9993 0.9996 1.0000 0.9988 0.9990 0.9994 1.0000 0.9985 0.9987 0.9992 1.0000 180 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 210 1.0008 1.0007 1.0004 1.0000 1.0012 1.0010 1.0006 1.0000 1.0015 1.0013 1.0008 1.0000 240 1.0013 1.0012 1.0007 1.0000 1.0020 1.0017 1.0010 1.0000 1.0027 1.0023 1.0013 1.0000 270 1.0015 1.0013 1.0008 1.0000 1.0023 1.0020 1.0012 1.0000 1.0031 1.0027 1.0015 1.0000 300 1.0013 1.0012 1.0007 1.0000 1.0020 1.0017 1.0010 1.0000 1.0027 1.0023 1.0013 1.0000 330 1.0008 1.0007 1.0004 1.0000 1.0012 1.0010 1.0006 1.0000 1.0015 1.0013 1.0008 1.0000 1788 1789 1790 ### Page 49 12/13/2023 46 Table A3-8 (continued) 1791 1792 gtest/gref for track angle (Coriolis correction) for ground speeds from 500 to 700 knots GS (kts) 500 600 700 Latitude (either North or South) (degrees ) 0 30 60 90 0 30 60 90 0 30 60 90 True Track Angle (degrees) 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 30 0.9981 0.9983 0.9990 1.0000 0.9977 0.9980 0.9988 1.0000 0.9973 0.9977 0.9987 1.0000 60 0.9967 0.9971 0.9983 1.0000 0.9960 0.9965 0.9980 1.0000 0.9953 0.9960 0.9977 1.0000 90 0.9961 0.9967 0.9981 1.0000 0.9954 0.9960 0.9977 1.0000 0.9946 0.9953 0.9973 1.0000 120 0.9967 0.9971 0.9983 1.0000 0.9960 0.9965 0.9980 1.0000 0.9953 0.9960 0.9977 1.0000 150 0.9981 0.9983 0.9990 1.0000 0.9977 0.9980 0.9988 1.0000 0.9973 0.9977 0.9987 1.0000 180 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 210 1.0019 1.0017 1.0010 1.0000 1.0023 1.0020 1.0012 1.0000 1.0027 1.0023 1.0013 1.0000 240 1.0033 1.0029 1.0017 1.0000 1.0040 1.0035 1.0020 1.0000 1.0047 1.0040 1.0023 1.0000 270 1.0039 1.0033 1.0019 1.0000 1.0046 1.0040 1.0023 1.0000 1.0054 1.0047 1.0027 1.0000 300 1.0033 1.0029 1.0017 1.0000 1.0040 1.0035 1.0020 1.0000 1.0047 1.0040 1.0023 1.0000 330 1.0019 1.0017 1.0010 1.0000 1.0023 1.0020 1.0012 1.0000 1.0027 1.0023 1.0013 1.0000 1793 1794 Step 6) Determine Massgrav, as defined below. Couple this mass with the tested SAR values, corrected for 1795 reference specifications from Step 7 above, in a regression model to determine the SAR values at each of 1796 the three reference masses of the FEM, and to determine the 90 percent confidence intervals. 1797 1798 Massgrav = Masstest x (gtest/gref)lat x (gtest/gref)alt x (gtest/gref)cent x (gtest/gref)Coriolis 1799 1800 where: 1801 1802 Massgrav is the mass at which the reference SAR value should be associated in a regression model to 1803 provide a SAR versus mass corrected for gravitational acceleration; 1804 1805 Masstest is the test mass, as defined in paragraph A3-1.1, in kg; 1806 1807 (gtest/gref)lat is gtest/gref for the test latitude, from Table A3-5; 1808 1809 (gtest/gref)alt is gtest/gref for altitude, from Table A3-6; 1810 1811 (gtest/gref)cent is gtest/gref for headwind/tailwind (centrifugal correction) from Table A3-7; and 1812 1813 (gtest/gref)Coriolis is gtest/gref for track angle (Coriolis correction) from Table A3-8. 1814 1815 A3-1.3 Acceleration/deceleration (energy). Drag determination is based on an assumption of steady, 1816 unaccelerated flight. Acceleration or deceleration relative to the ground occurring during a test condition 1817 affects the assessed drag level. The reference specification is steady, unaccelerated flight. 1818 ### Page 50 12/13/2023 47 1819 The correction for the change in drag force resulting from acceleration during the test condition can be 1820 determined from the following equation: 1821 ∆𝐷𝐷𝑎𝑎𝑐𝑐𝑐𝑐𝑟𝑟𝑙𝑙 = −𝑀𝑀𝑣𝑣𝑒𝑒𝑒𝑒𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 �𝑠𝑠𝑉𝑉𝑎𝑎𝑠𝑠𝑇𝑇 � 1822 where: 1823 1824 ΔDaccel is the drag correction in N due to acceleration occurring during the test condition; 1825 1826 Masstest is the average mass of the airplane during the test condition, as defined in paragraph A3-1.1 in 1827 kg; and 1828 1829 (dVg/dT) is the change in ground speed over time during the test condition in m/s2. 1830 1831 A3-1.4 Reynolds number. The RE needs to be calculated to determine its contribution to airplane drag. 1832 For a given test condition, the RE is a function of the density and viscosity of air at the test altitude and 1833 temperature. The reference RE is derived from the density and viscosity of air from the ICAO standard 1834 atmosphere at the reference altitude. 1835 1836 The value of the drag coefficient correction for RE during the test can be expressed as: 1837 1838 ∆𝐶𝐶𝐷𝐷 𝐷𝐷𝐸𝐸 = −𝐵𝐵 𝐹𝐹𝑜𝑜𝑊𝑊 � 1 𝑀𝑀 �𝑆𝑆𝐸𝐸𝑒𝑒 �𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 1 𝑀𝑀 �𝑆𝑆𝐸𝐸𝑒𝑒 �𝐷𝐷𝑟𝑟𝑟𝑟 � 1839 1840 where: 1841 1842 ∆CD RE is the change in drag coefficient when correcting from test RE to the reference RE; 1843 1844 B is a value representing the variation of drag with RE for the specific airplane (see guidance below); 1845 1846 M is Mach number; and 1847 1848 RE/m is RE per meter. 1849 1850 One method to obtain B is to use a drag model to obtain the incremental drag variation in response to 1851 changing Mach and altitude from a reference cruise condition. The value for B is the value of a single 1852 representative slope of a plot of the drag variation, ∆Drag versus Log10� 1 𝑀𝑀 � 𝐷𝐷𝐸𝐸 𝑚𝑚 � 𝑥𝑥10−6�. 1853 1854 The term � 1 𝑀𝑀�𝑅𝑅𝑅𝑅𝑚𝑚 �𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 1 𝑀𝑀�𝑅𝑅𝑅𝑅𝑚𝑚 �𝑅𝑅𝑟𝑟𝑟𝑟�is the term 1 𝑀𝑀 � 𝐷𝐷𝐸𝐸 𝑚𝑚 � determined at the temperature and altitude for the test condition, 1855 divided by the same term determined at the standard day temperature and the reference altitude for the 1856 test mass/δ using the following equation: 1857 1858 1 𝑀𝑀 𝑆𝑆𝐸𝐸 𝑒𝑒 = 4.7899 𝑥𝑥 105 𝑃𝑃𝐷𝐷 �𝑇𝑇𝐷𝐷 + 110.4𝑇𝑇𝐷𝐷2 � 1859 1860 where: 1861 1862 RE/m is RE per m; 1863 1864 PS is static pressure in Pa; and 1865 1866 ### Page 51 12/13/2023 48 TS is static temperature in K. 1867 1868 The effect on airplane drag can then be determined from ∆CD RE and the airplane drag equation as 1869 follows: 1870 1871 ∆𝐷𝐷𝐷𝐷𝐸𝐸 = 12 𝜌𝜌 𝑉𝑉2∆𝐶𝐶𝐷𝐷 𝐷𝐷𝐸𝐸 𝑆𝑆 1872 1873 where: 1874 1875 ∆DRE is the airplane drag correction in N due to the test RE being different than the reference RE; 1876 1877 ρ is the density of air at the test altitude and test temperature in kg/m3; 1878 1879 V is the airplane’s average true airspeed during the test condition in m/s; 1880 1881 A is the airplane’s reference wing area in m2; and 1882 1883 ∆CD RE is the change in drag coefficient due to being off the reference RE.. 1884 1885 A3-1.5 CG position. The position of the airplane center of gravity (CG) affects the drag due to longitudinal 1886 trim. 1887 1888 The drag correction for CG position during the test is the difference between the drag at the reference CG 1889 position and the drag at the test CG position. This drag correction can be determined by adjusting the 1890 longitudinal trim drag, determined from the airplane’s drag model at the reference CG, to adjust for the 1891 test CG position. For example, testing at a CG position aft of the reference CG used in the drag model 1892 would yield a positive drag correction (that is, a decrease to the test SAR). 1893 1894 A method to determine the change in longitudinal trim drag for CG position from the reference is to first 1895 determine the amount of longitudinal trim drag (CD Trim Ref CG) that exists at the reference CG position as a 1896 function of Mach and CL. This can be done using wind tunnel testing and analytical methods. The change 1897 of the longitudinal trim drag with CG, which is specific to an airplane type design, can be estimated with 1898 wind tunnel and analytical methods, and verified by flight test data. This relationship can then be used to 1899 determine the longitudinal trim drag (CD Trim Test CG) at the test CG position. 1900 1901 Once the trim drag coefficients are determined from the airplane drag model, the airplane drag correction 1902 for the CG position can be determined from the drag equation: 1903 1904 ∆𝐷𝐷𝑇𝑇𝑟𝑟𝑖𝑖𝑚𝑚 𝐶𝐶𝐴𝐴 = 12 𝜌𝜌 𝑉𝑉2�𝐶𝐶𝐷𝐷 𝑇𝑇𝑟𝑟𝑖𝑖𝑚𝑚 𝐷𝐷𝑟𝑟𝑟𝑟 𝐶𝐶𝐴𝐴 − 𝐶𝐶𝐷𝐷 𝑇𝑇𝑟𝑟𝑖𝑖𝑚𝑚 𝑇𝑇𝑟𝑟𝑡𝑡𝑡𝑡 𝐶𝐶𝐴𝐴�𝑆𝑆 1905 1906 where: 1907 1908 ∆DTrim CG is the airplane drag correction in N due to the test CG being different than the reference CG; 1909 1910 ρ is the density of air at the test altitude and test temperature in kg/m3; 1911 1912 V is the airplane’s average true airspeed during the test condition in m/s; 1913 1914 A is the airplane’s reference wing area in m2; and 1915 1916 CD Trim Ref CG and CD TrimTest CG are the trim drag coefficients from the airplane’s drag model at the reference 1917 CG and test CG positions, respectively. 1918 1919 A3-1.6 Aeroelastics. Wing aeroelastics may cause a variation in drag as a function of airplane wing mass 1920 distribution. Airplane wing mass distribution will be affected by the fuel load distribution in the wings and 1921 ### Page 52 12/13/2023 49 the presence of any external fuel stores. 1922 1923 There are no simple analytical means to correct for different wing structural loading conditions. If 1924 necessary, corrections to the reference specification should be developed by flight test or a suitable 1925 analysis process, subject to the approval of the FAA. 1926 1927 The reference specification for the wing structural loading is to be selected by the applicant based on the 1928 amount of fuel and/or removable external stores to be carried by the wing, based on the airplane’s 1929 payload capability and the manufacturer’s standard fuel management practices. The reference to the 1930 airplane’s payload capability is for establishing the zero fuel mass of the airplane, while the reference to 1931 the manufacturer’s standard fuel management practices is for establishing the distribution of that fuel and 1932 how that distribution changes as fuel is burned. 1933 1934 The reference specification for the wing structural loading reference specification should be based on an 1935 operationally representative empty weight and payload which defines the zero fuel mass of the airplane. 1936 The total amount of fuel loaded for each of the three reference masses would be the reference mass 1937 minus the zero fuel mass. Standard fuel management practices will determine the amount of fuel present 1938 in each fuel tank. An example of standard fuel management practice is to load the main (wing) fuel tanks 1939 before loading the center (body) fuel tanks and to first empty fuel from the center tanks before using the 1940 fuel in the main tanks. This helps keep the CG aft and reduces trim drag. 1941 1942 Commercial freighters may be designed from scratch, but more often are derivatives of or converted from 1943 passenger model airplanes. In determining aeroelastic effects, it is reasonable to assume that the 1944 reference loading for a freighter is the same as the passenger model it was derived from. If there is no 1945 similar passenger model, the reference zero-fuel-mass of a freighter can be based on its payload design 1946 density. The payload design density is defined by the full use of the volumetric capacity of the freighter 1947 and the highest mass it is designed to carry, expressed in kg/m3. For example, a typical payload design 1948 density for large commercial freighters is 160 kg/m3. 1949 1950 Using a reference payload significantly lower than the passenger interior limits or structural limited 1951 payload could potentially provide a more beneficial aeroelastic effect. An applicant would need to justify 1952 the reference payload assumptions in the context of the capability of the airplane and what could be 1953 considered typical for the type design. 1954 1955 A3-1.7 Fuel lower heating value. The fuel lower heating value defines the energy content of the fuel. The 1956 lower heating value directly affects the fuel flow at a given test condition. 1957 1958 The fuel flow measured during the flight test is corrected to the fuel flow for the reference lower heating 1959 value as follows: 1960 1961 ∆𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝑜𝑜𝐹𝐹𝐶𝐶𝑐𝑐𝑟𝑟𝑟𝑟 𝐿𝐿𝐿𝐿𝐴𝐴 = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝑜𝑜𝐹𝐹𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 𝐿𝐿𝐿𝐿𝐴𝐴 �𝐿𝐿𝐿𝐿𝑉𝑉𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡𝐿𝐿𝐿𝐿𝑉𝑉𝐷𝐷𝑟𝑟𝑟𝑟 � − 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝐹𝐹𝐹𝐹𝑜𝑜𝐹𝐹𝑡𝑡𝑟𝑟𝑡𝑡𝑡𝑡 𝐿𝐿𝐿𝐿𝐴𝐴 1962 1963 where: 1964 1965 ∆Fuel FlowCorr LHV is the fuel flow correction in kilograms/hour due to the fuel lower heating value being 1966 different than the reference fuel lower heating value; 1967 1968 Fuel Flowtest LHV is the measured fuel flow in kilograms/hour during the test (at the test fuel lower heating 1969 value); 1970 1971 LHVtest is the fuel lower heating value of the fuel used for the test in MJ/kg; and 1972 1973 LHVRef is the reference fuel lower heating value = 43.217 MJ/kg. 1974 1975 ### Page 53 12/13/2023 50 A3-1.8 Altitude. The altitude at which the airplane is flown affects the fuel flow. As noted in Table A3-1, 1976 since testing at any altitude other than the reference optimum altitude increases the FEM, this correction 1977 is considered optional. For applicants choosing to make this correction, the selection of the reference 1978 altitude depends on the method used for determining SAR for the three reference airplane masses 1979 specified in § 38.13 (b). For SAR data clustered around each of the three reference masses (see § 1980 A38.5.3.3), a reference altitude is selected by the applicant for each of the specified reference masses. If 1981 SAR data is obtained over a range of masses (see § A38.5.3.4), the applicant should select a reference 1982 altitude for each test point (since none of the test points are directly associated with any of the reference 1983 masses). For applicants using a first principle model (see paragraph 6.4.4 of this AC), the applicant 1984 should select a reference altitude for each target Weight/δ value (see Figure 6-6 of this AC). 1985 1986 The engine model should be used to determine the fuel flow at the test altitude (Fuel Flowtest alt) and the 1987 fuel flow at the reference altitude (Fuel Flowref alt). The fuel flow correction for altitude is determined as 1988 follows: 1989 1990 ∆Fuel Flowalt = Fuel Flowref alt – Fuel Flowtest alt. 1991 1992 A3.9 Temperature. The ambient temperature affects the fuel flow. The reference temperature is the 1993 standard day temperature from the ICAO standard atmosphere at the reference altitude. 1994 1995 The engine model should be used to determine the difference between the fuel flow at the test 1996 temperature (Fuel Flowtest temp) and the fuel flow at the reference temperature (Fuel Flowref temp). The fuel 1997 flow correction for temperature is determined as follows: 1998 1999 ∆Fuel Flowtemp = Fuel Flowref temp – Fuel Flowtest temp. 2000 2001 A3-1.10 Engine deterioration level. When first used, engines undergo a rapid, initial deterioration in fuel 2002 efficiency. Thereafter, the rate of deterioration significantly decreases. Engines with less than the 2003 reference deterioration level may be used, subject to the approval of the FAA, as stated in 14 CFR part 2004 38, Appendix A, § 5.2.2.1.7.1. In such a case, the fuel flow is to be corrected to the reference engine 2005 deterioration level using an approved method. Engines with more deterioration than the reference engine 2006 deterioration level may be used. In this case, a correction to the reference specification shall not be 2007 permitted in accordance with 14 CFR part 38, Appendix A, 5.2.2.1.7.2. 2008 2009 As stated above, a correction should generally not be made for engine deterioration level. If an applicant 2010 proposes to use an engine or engines with less than the reference deterioration level for testing, it may be 2011 possible to establish a conservative correction level to apply to the test fuel flow to represent engines at 2012 the reference deterioration level. Such a correction should be substantiated by engine fuel flow 2013 deterioration data from the same engine type or family and approved by the FAA. 2014 2015 A3-1.11 Electrical and mechanical power extraction and bleed flow. Electrical and mechanical power 2016 extraction and bleed flow both affect the fuel flow. 2017 2018 The engine model should be used to determine the difference between the fuel flow at the test power 2019 extraction (Fuel Flowtest bleed) and bleed flow and the fuel flow at the reference power extraction and bleed 2020 flow (Fuel Flowref bleed). The fuel flow correction for electrical and mechanical power extraction and bleed 2021 flow is determined as follows: 2022 2023 ∆Fuel FlowCorr bleed = Fuel Flowref bleed – Fuel Flowtest bleed. 2024 2025 A3-1.12 Modifications and non-standard equipment that will not be included on the production airplane. 2026 The test airplane may contain modifications and non-standard equipment, such as flight test 2027 instrumentation, that will not be included on the production airplane. Examples of such flight test 2028 instrumentation includes trailing cones, precision total air temperature probes, air data booms, telemetry 2029 antennas, and engine pressure rakes. Where these modifications or non-standard equipment increase 2030 drag or fuel flow, this effect may be corrected out of the tested drag and fuel flow levels used to determine 2031 ### Page 54 12/13/2023 51 the SAR used for calculating the FEM. 2032 2033 ### Page 55 12/13/2023 52 2034 Appendix 4: Confidence Interval Evaluation 2035 2036 2037 A4-1 Direct flight testing 2038 2039 If n measurements of SAR (𝐸𝐸1, 𝐸𝐸2, …., 𝐸𝐸n) are obtained under approximately the same conditions, and it 2040 can be assumed that they constitute a random sample from a normal population with true population 2041 mean, µ, and true standard deviation, σ, then the following statistics can be derived: 2042 2043 𝐸𝐸 = 𝐹𝐹𝑒𝑒𝑒𝑒𝐸𝐸𝑒𝑒𝑣𝑣𝑒𝑒𝐹𝐹 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝐹𝐹𝑣𝑣𝐸𝐸 = 1𝐸𝐸 �� 𝐸𝐸(𝑖𝑖) 𝑖𝑖=𝑛𝑛 𝑖𝑖=1 � 2044 𝑒𝑒 = 𝐹𝐹𝑒𝑒𝑒𝑒𝐸𝐸𝑒𝑒𝑣𝑣𝑒𝑒𝐹𝐹 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝑒𝑒𝑣𝑣𝐸𝐸𝑠𝑠𝑣𝑣𝑒𝑒𝑠𝑠 𝑠𝑠𝐹𝐹𝑣𝑣𝐸𝐸𝑣𝑣𝑒𝑒𝐸𝐸𝑜𝑜𝐸𝐸 𝑜𝑜𝐸𝐸 𝑒𝑒ℎ𝐹𝐹 𝑒𝑒𝐹𝐹𝑣𝑣𝐸𝐸 = �∑ (𝑦𝑦𝑖𝑖−𝑦𝑦�)2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−1 . 2045 2046 From these and the Student t-distribution, the confidence interval, CI, for the estimate of the mean, 𝐸𝐸, can 2047 be determined as: 2048 2049 CI = ȳ ± 𝑒𝑒�1−𝛼𝛼2,𝜁𝜁� 𝑒𝑒 √𝐸𝐸 2050 2051 where 𝑒𝑒�1−𝛼𝛼2,𝜁𝜁� denotes the �1 − 𝛼𝛼 2� percentile of the single-sided Student t-test with 𝜁𝜁 degrees freedom 2052 (for a clustered data set 𝜁𝜁 = 𝐸𝐸 − 1) and where α is defined such that 100(1 − 𝛼𝛼) percent is the desired 2053 confidence level for the confidence interval. In other words, it denotes the probability with which the 2054 interval will contain the unknown mean, µ. For fuel efficiency metric certification purposes, 90 percent 2055 confidence intervals are required and thus 𝑒𝑒.95,𝜁𝜁 is used. See Table A4-1 for a listing of values of 𝑒𝑒.95,𝜁𝜁 for 2056 different values of 𝜁𝜁. 2057 2058 2059 A4-2 Regression model 2060 2061 If n measurements of SAR (𝐸𝐸1, 𝐸𝐸2, …., 𝐸𝐸n) are obtained under significantly varying values of mass (𝑥𝑥1, 𝑥𝑥 2, 2062 …., 𝑥𝑥 n), respectively, then a polynomial can be fitted to the data by the method of least squares. For 2063 determining the mean SAR, µ , the following polynomial regression model is assumed to apply: 2064 2065 μ= B0 + B1𝑥𝑥 + B2𝑥𝑥2 +…..+ Bk𝑥𝑥k. 2066 2067 The estimate of the mean line through the data of the SAR is given by: 2068 2069 𝐸𝐸= b0 + b1𝑥𝑥 + b2𝑥𝑥2 +…..+ bk𝑥𝑥k. 2070 2071 Each regression coefficient (Bi) is estimated by bi from the sample data using the method of least squares 2072 in a process summarized as follows: 2073 2074 Each observation (xi,yi) satisfies the equations: 2075 2076 𝐸𝐸i= B0 + B1𝑥𝑥i + B2𝑥𝑥i2 +…..+ Bk𝑥𝑥ik + ɛi 2077 2078 = b0 + b1𝑥𝑥i + b2𝑥𝑥i2 +…..+ bk𝑥𝑥ik + ei 2079 2080 where ɛi and ei are, respectively, the random error and residual associated with the SAR. The random 2081 error is assumed to be a random sample from a normal population with mean zero and standard deviation 2082 σ . The residual (ei) is the difference between the measured value and the estimate of the value using the 2083 ### Page 56 12/13/2023 53 estimates of the regression coefficients and 𝑥𝑥i. Its root mean square value (s) is the sample estimate for 2084 σ. These equations are often referred to as the normal equations. 2085 2086 2087 Table A4-1. 2088 2089 Student t-distribution (for 90 percent confidence) for various degrees of freedom 2090 2091 Degrees of freedom (ζ) t.95, ζ 1 6.314 2 2.920 3 2.353 4 2.132 5 2.015 6 1.943 7 1.895 8 1.860 9 1.833 10 1.812 12 1.782 14 1.761 16 1.746 18 1.734 20 1.725 24 1.711 30 1.697 60 1.671 >60 1.645 2092 2093 The n data points of measurements (𝑥𝑥i,yi) are processed as follows: 2094 2095 Each elemental vector (𝑥𝑥i) and its transpose (𝑥𝑥’i) are formed such that: 2096 2097 𝑥𝑥i = (1 𝑥𝑥i 𝑥𝑥𝑖𝑖2 . . 𝑥𝑥𝑖𝑖𝑘𝑘), a row vector; and 2098 2099 𝑥𝑥𝑖𝑖′ = ⎝ ⎜ ⎛ 1 x𝑖𝑖 𝑥𝑥𝑖𝑖2. . 𝑥𝑥𝑖𝑖𝑘𝑘⎠ ⎟ ⎞, a column vector. 2100 2101 A matrix X is formed from all the elemental vectors xi for i = 1, ….., n. X’ is the transpose of X. A matrix A 2102 is defined such that A = X’X and a matrix A-1 is the inverse of A. In addition, y = (𝐸𝐸1 𝐸𝐸2 … 𝐸𝐸n) and b = (b0 b1 2103 ### Page 57 12/13/2023 54 … b2), with b determined as the solution of the normal equations: 2104 2105 y = Xb and X’y = X’Xb = Ab 2106 2107 to give 2108 2109 b = A-1X’y. 2110 2111 The 90 percent confidence interval CI90 for the mean value of the SAR estimated with the associated 2112 value of the mass x0 is then defined as: 2113 2114 CI90 = ȳ (x0) ± t.95,ζ s v(x0) 2115 2116 where 𝑣𝑣(𝑥𝑥0) = �𝑥𝑥0 𝑆𝑆−1 𝑥𝑥0′ . 2117 2118 Thus, CI90 = ȳ (𝑥𝑥0) ± 𝑒𝑒.95,𝜁𝜁 𝑒𝑒 �𝑥𝑥0 𝑆𝑆−1 𝑥𝑥0′ , 2119 2120 where: 2121 2122 𝑥𝑥0 = (1 𝑥𝑥0 𝑥𝑥02 ... 𝑥𝑥0𝑘𝑘); 2123 2124 x’ is the transpose of 𝑥𝑥0; 2125 2126 ȳ (𝑥𝑥0) is the estimate of the mean value of the SAR at the associated value of the mass xo; 2127 2128 t.95,ζ is obtained for ζ degrees of freedom. For the general case of a multiple regression analysis involving 2129 K independent variables (i.e. K + 1 coefficients), ζ is defined as ζ = n – K – 1 ; and 2130 2131 𝑒𝑒 = �∑ (𝑦𝑦𝑖𝑖− ȳ(𝑥𝑥𝑖𝑖 ))2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−𝐾𝐾−1 is the estimate of σ, the true standard deviation. 2132 2133 2134 A4-3 Worked examples of the determination of 90 percent confidence intervals 2135 2136 Direct flight testing 2137 2138 Example 1: In which the confidence interval is less than the confidence interval limit. 2139 2140 Consider the following set of 6 independent measurements of SAR obtained by flight test around one of 2141 the three reference masses of the CO2 emissions evaluation metric. After correction to reference 2142 specifications, the following clustered data set of SAR values is obtained: 2143 2144 2145 Table A4-2. 2146 2147 Measurements of SAR — Example 1 2148 2149 Measurement number Corrected SAR (km/kg) 1 0.38152 2 0.38656 3 0.37988 ### Page 58 12/13/2023 55 Measurement number Corrected SAR (km/kg) 4 0.38011 5 0.38567 6 0.37820 2150 2151 The number of data points (n) = 6 2152 2153 The degrees of freedom (n-1) = 5 2154 2155 The Student t-distribution for 90 percent confidence and 5 degrees of freedom (𝑒𝑒(.95 ,5) ) = 2.015. (See 2156 Table A4-1.) 2157 2158 Note.— 6 is the minimum number of test points required, as stated in § A38.5.3.3. 2159 Estimate of the mean SAR ( 𝑆𝑆𝑆𝑆𝑆𝑆 ) for the clustered data set: 2160 2161 𝑆𝑆𝑆𝑆𝑆𝑆 = 1 𝑛𝑛 �∑ 𝑆𝑆𝑆𝑆𝑆𝑆(𝑖𝑖)𝑖𝑖=𝑛𝑛𝑖𝑖=1 � = 0.38282 km/kg. 2162 2163 Estimate of the standard deviation(s): 2164 2165 𝑒𝑒 = �∑ �𝐷𝐷𝐴𝐴𝐷𝐷(𝑖𝑖)−𝐷𝐷𝐴𝐴𝐷𝐷�������2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−1 = 0.00344 km/kg . 2166 2167 2168 Confidence interval determination 2169 2170 The 90 percent confidence interval (CI90) is calculated as follows (see 3.3.2): 2171 2172 𝐶𝐶𝐶𝐶90 = 𝑆𝑆𝑆𝑆𝑆𝑆 ± 𝑒𝑒(.95,𝑛𝑛−1) s √𝑛𝑛 = 0.38282 ± 2.015 x 0.00344 √6 = 0.38282 ± 0.00283 km/kg. 2173 2174 2175 Check of confidence interval limits 2176 2177 The confidence interval extends to ±0.00283 km/kg around the mean SAR value of the clustered data set 2178 (0.38282 km/kg). This represents ±0.74 percent of the mean SAR value, which is below the confidence 2179 interval limit of 1.5 percent, as defined in § A38.5.3.2. 2180 2181 As a result, the SAR value of 0.38282 km/kg associated to one of the reference masses of the FEM can 2182 be used for the metric determination. 2183 2184 Example 2: In which the confidence interval exceeds the confidence interval limit. 2185 2186 Consider the following set of 6 independent measurements of SAR obtained by flight test around one of 2187 the three reference masses of the FEM. After correction to reference specifications, the following 2188 clustered data set of SAR values is obtained: 2189 2190 2191 2192 2193 2194 2195 ### Page 59 12/13/2023 56 Table A4-3. 2196 2197 Measurements of SAR — Example 2 2198 2199 Measurement number Corrected SAR (km/kg) 1 0.15208 2 0.15795 3 0.15114 4 0.15225 5 0.15697 6 0.15834 2200 The number of data points (n) = 6 2201 2202 The degrees of freedom (n-1) = 5 2203 The Student t-distribution for 90 percent confidence and 5 degrees of freedom (𝑒𝑒(.95 ,5) ) = 2.015. (See 2204 Table A4-1) 2205 2206 Estimate of the mean SAR ( 𝑆𝑆𝑆𝑆𝑆𝑆 ) for the clustered data set: 2207 2208 𝑆𝑆𝑆𝑆𝑆𝑆 = 1 𝑛𝑛 �∑ 𝑆𝑆𝑆𝑆𝑆𝑆(𝑖𝑖)𝑖𝑖=𝑛𝑛𝑖𝑖=1 � = 0.15479 km/kg. 2209 2210 Estimate of the standard deviation(s): 2211 2212 𝑒𝑒 = �∑ �𝐷𝐷𝐴𝐴𝐷𝐷(𝑖𝑖)−𝐷𝐷𝐴𝐴𝐷𝐷�������2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−1 = 0.0033 km/kg . 2213 2214 2215 Confidence interval determination 2216 2217 The 90 percent confidence interval (CI90) is calculated as follows (see 3.3.2): 2218 2219 𝐶𝐶𝐶𝐶90 = 𝑆𝑆𝑆𝑆𝑆𝑆 ± 𝑒𝑒(.95,𝑛𝑛−1) s √𝑛𝑛 = 0.15479 ± 2.015 x 0.0033 √6 = 0.15479 ± 0.00271 km/kg. 2220 2221 2222 Check of confidence interval limits 2223 2224 The confidence interval extends to ±0.00271 km/kg around the mean SAR value of the clustered data set 2225 (0.15479 km/kg). This represents ±1.75 percent of the mean SAR value, which is above the confidence 2226 interval limit of 1.5 percent, as defined in § A38.5.3.2. 2227 2228 In such case, a penalty equal to the amount that the 90 percent confidence interval exceeds ±1.5 percent 2229 is applied to the mean SAR value, i.e. (1.75-1.50) = 0.25 percent. The mean SAR value is therefore be 2230 penalized by an amount of 0.25 percent as follows: 2231 2232 𝑆𝑆𝑆𝑆𝑆𝑆 = (1 − 0.25 100) 𝑥𝑥 0.15479 = 0.15440 km/kg. 2233 2234 As a result, the SAR value of 0.15440 km/kg associated to one of the reference masses of the FEM can 2235 be used for the metric determination. 2236 ### Page 60 12/13/2023 57 2237 Regression model 2238 2239 Example 3: In which the confidence interval at each of the three reference masses of FEM is less than 2240 the confidence interval limit. 2241 2242 Consider the following set of 12 measurements of SAR obtained by flight test at optimum speed and 2243 optimum altitude as a function of the airplane gross mass. After SAR correction to reference 2244 specifications, the following data set is obtained: 2245 2246 Table A4-4. 2247 2248 Measurements of SAR — Example 3 2249 2250 Measurement number and reference mass Gross mass (mi) (kg) Corrected SAR (SARi) (km/kg) 1 17,800 0.928 Low mass (*) 17,825 2 17,970 0.905 3 18,400 0.908 4 18,850 0.884 5 19,500 0.850 6 19,950 0.845 Mid mass (*) 19,953 7 20,180 0.833 8 20,350 0.818 9 21,000 0.792 10 21,500 0.781 11 21,870 0.779 High mass (*) 22,080 12 22,150 0.771 2251 (*) Low, mid and high mass represent the reference masses of the FEM, as defined in §38.13(b). 2252 2253 The number of data points (n) = 12 2254 2255 Note.— 12 is the minimum number of test points requested, as stated in § A38.5.3.4. 2256 2257 A representation of the above measurement points is proposed in Figure A4-5. 2258 2259 ### Page 61 12/13/2023 58 2260 Figure A4-5. Measured SAR versus gross mass — Example 3 2261 2262 2263 Estimate of the mean SAR model by polynomial regression 2264 2265 In order to estimate the SAR model (SARav) as a function the airplane gross mass (m), a polynomial 2266 regression of second order is proposed so that: 2267 2268 SARav = B0 + B1 m + B2 m² 2269 2270 Each observation (mi, SARi), for I = 1, …, 12 satisfies the equation: 2271 2272 SAR(i) = b0 + b1 mi + b2 mi² + ei 2273 2274 where ei = residual error (difference between the measured SAR value and its estimate). 2275 2276 Under a matrix form this gives: 2277 2278 ⎝ ⎜ ⎛ 𝑆𝑆𝑆𝑆𝑆𝑆1 𝑆𝑆𝑆𝑆𝑆𝑆2 𝑆𝑆𝑆𝑆𝑆𝑆3 ⋮ 𝑆𝑆𝑆𝑆𝑆𝑆12⎠ ⎟ ⎞ = ⎝ ⎜ ⎛ 1 𝑒𝑒1 𝑒𝑒1² 1 𝑒𝑒2 𝑒𝑒2² 1 𝑒𝑒3 𝑒𝑒3² ⋮ ⋮ ⋮ 1 𝑒𝑒12 ⋯ 𝑒𝑒12²⎠ ⎟ ⎞ �𝑏𝑏0𝑏𝑏1 𝑏𝑏2 � + ⎝ ⎜ ⎛ 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 ⋮ 𝐹𝐹12⎠ ⎟ ⎞ 2279 2280 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 3 — Measured SAR versus gross mass SAR (km/kg) Measured data points High mass Mid mass Low mass ### Page 62 12/13/2023 59 SAR = M b + e 2281 2282 where: 2283 2284 SAR = ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 0.928 0.905 0.908 0.884 0.850 0.845 0.833 0.818 0.792 0.781 0.779 0.771⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ M = ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 17800 17800² 1 17970 17970² 1 18400 18400² 1 18850 18850² 1 19500 19500² 1 19950 19950² 1 20180 20180² 1 20350 20350² 1 21000 21000² 1 21500 21500² 1 21870 21870² 1 22150 22150²⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ b = � 𝑏𝑏0 𝑏𝑏1 𝑏𝑏2 � e = ⎝ ⎜ ⎛ 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 ⋮ 𝐹𝐹n⎠ ⎟ ⎞. 2285 2286 The least square principle consists in looking for the parameter values of vector B, minimizing the sum of 2287 the squares of residuals, i.e.: 2288 2289 Min ∑ 𝐹𝐹i²𝑖𝑖=12𝑖𝑖=1 = min ∑ (𝑆𝑆𝑆𝑆𝑆𝑆(i) − 𝑏𝑏0 − 𝑏𝑏1 𝑒𝑒i − 𝑏𝑏2 𝑒𝑒i2)𝑖𝑖=12𝑖𝑖=1 ². 2290 2291 It is equivalent to look for the solutions of 𝜕𝜕(∑ 𝑟𝑟i²) 𝜕𝜕𝑏𝑏j = 0 for j = (0, 1, 2). 2292 2293 The solution B = � 𝐵𝐵0 𝐵𝐵1 𝐵𝐵2 � is given by: 2294 2295 A-1 M’ SAR (see A4-2) 2296 2297 where: 2298 2299 M’ = transpose of M; and 2300 2301 A-1 = (M’ M)-1 = inverse of (M’ M). 2302 2303 Finally, B = � 2.402921963 −0.000120515 2.10695 𝑥𝑥10-09 �; and 2304 2305 SARav = 2.402921963 – 0.000120515 m + 2.10695.10-9 m². 2306 2307 Figure A4-6 provides a representation of the mean SAR model as a function of the airplane gross mass. 2308 2309 ### Page 63 12/13/2023 60 2310 Figure A4-6. SAR model (trend line) versus gross mass — Example 3 2311 2312 2313 The mean SAR values at each of the three reference gross masses of the FEM are as follows: 2314 2315 Table A4-7. 2316 2317 Mean SAR values — Example 3 2318 2319 Reference mass Mass value (kg) Mean SAR value (km/kg) Low mass 17,825 0.92418 Mid mass 19,953 0.83710 High mass 22,080 0.76914 2320 Estimate of the standard deviation(s): 2321 2322 𝑒𝑒 = �∑ (SARi−SARav(i))2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−𝐾𝐾−1 = 0.00765 km/kg 2323 2324 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 3 — SAR model (trend line) versus gross mass SAR (km/kg) Measured data points High mass Low mass Mid mass Trend line ### Page 64 12/13/2023 61 where: 2325 2326 the number of data points (n) = 12; 2327 2328 K = 2 for a second order polynomial regression (see A4-2); and 2329 2330 the degrees of freedom (n-K-1) = 9. 2331 2332 2333 Confidence interval determination 2334 2335 The 90 percent confidence interval (CI90) at an airplane gross mass m0 is calculated as follows (see A4-2336 2): 2337 2338 𝐶𝐶𝐶𝐶90 = SARav(m0) ± 𝑒𝑒(.95 ,𝑛𝑛−𝐾𝐾−1) 𝑒𝑒 �m0 A-1 m0' 2339 2340 where: 2341 2342 the Student t-distribution for 90 percent confidence and 9 degrees of freedom t(.95, 9) = 1.833. (See Table 2343 A4-1); 2344 2345 m0 = (1 m0 m0²) and m0’ = � 1 𝑒𝑒0 𝑒𝑒0² �; and 2346 2347 A-1 = (M’ M)-1 = inverse of (M’ M). 2348 2349 Figure A4-8 provides a representation of the 90 percent confidence interval as a function of airplane 2350 gross mass. 2351 2352 2353 ### Page 65 12/13/2023 62 2354 Figure A4-8. 90 percent confidence interval versus gross mass — Example 3 2355 2356 2357 The 90 percent confidence intervals at each of the three reference gross masses of the FEM are as 2358 follows: 2359 2360 Table A4-9. 2361 2362 Confidence intervals — Example 3 2363 2364 Reference mass Mass value (kg) 90% confidence interval (kg/km) Low mass 17 825 CI90 = 0.92418 ± 0.00915 Mid mass 19 953 CI90 = 0.83710 ± 0.00619 High mass 22 080 CI90 = 0.76914 ± 0.00925 2365 Check of confidence interval limits 2366 2367 For each of the three reference gross masses of the FEM, the confidence interval extends around the 2368 mean SAR value by a percentage, as shown in Table A4-10. 2369 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 3 — 90% confidence interval versus gross mass SAR (km/kg) Measured data points High mass 90% CI line - upper 90% CI line - lower Low mass Mid mass Trend line ### Page 66 12/13/2023 63 2370 Table A4-10. 2371 2372 Check of confidence intervals — Example 3 2373 2374 Reference mass Mass value (kg) 90% confidence interval (percentage of mean SAR) Low mass 17,825 (0.00915/0.92418) x 100 = 0.99% Mid mass 19,953 (0.00619/0.83710) x 100 = 0.74% High mass 22,080 (0.00925/0.76914) x 100 = 1.2% 2375 2376 The 90 percent confidence intervals at each of the three reference gross masses of the FEM are all below 2377 the confidence interval limit of 1.5 percent, as defined in § A38.5.3.2. 2378 2379 As a result, the following mean SAR values associated to each of the three reference masses of the FEM 2380 can be used for the metric determination: 2381 2382 Table A4-11. 2383 2384 Mean SAR values — Example 3 2385 2386 Reference mass Mass value (kg) Mean SAR value (km/kg) Low mass 17,825 0.92418 Mid mass 19,953 0.83710 High mass 22,080 0.76914 2387 2388 Example 4: In which the confidence interval of at least one of the three reference masses of the FEM 2389 exceeds the confidence interval limit. 2390 2391 Consider the following set of 12 measurements of SAR obtained by flight test at optimum speed and 2392 optimum altitude as a function of the airplane gross mass. After SAR correction to reference 2393 specifications, the following data set is obtained: 2394 2395 2396 ### Page 67 12/13/2023 64 Table A4-12. 2397 2398 Measurements of SAR — Example 4 2399 2400 Measurement number and reference mass Gross mass (mi) (kg) Corrected SAR (SARi) (km/kg) 1 17,800 0.932 Low mass (*) 17,825 2 18,200 0.925 3 18,620 0.913 4 18,890 0.889 5 19,350 0.868 6 19,610 0.848 Mid mass (*) 19,953 7 19,920 0.838 8 20,510 0.830 9 20,790 0.806 10 21,220 0.815 11 21,480 0.779 High mass (*) 22,080 12 22,100 0.788 2401 (*) Low, mid and high mass represent the reference masses of the CO2 emissions evaluation metric, as 2402 defined in §38.13(b). 2403 2404 The number of data points (n) = 12 (minimum required, as stated in § A38.5.3.4). 2405 2406 A representation of the above measurement points is proposed in Figure A4-13. 2407 2408 2409 ### Page 68 12/13/2023 65 2410 Figure A4-13. Measured SAR versus gross mass — Example 4 2411 2412 Estimate of the mean SAR model by polynomial regression 2413 2414 In order to estimate the SAR model (SARav) as a function the airplane gross mass (m), a polynomial 2415 regression of second order is proposed, so that: 2416 2417 SARav = B0 + B1 m + B2 m². 2418 2419 Each observation (mi, SARi), for i = 1, …, 12 satisfies the equation: 2420 2421 SAR(i) = b0 + b1 mi + b2 mi² + ei 2422 2423 with ei = residual error (difference between the measured SAR value and its estimate). 2424 2425 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 4 — Measured SAR versus gross mass SAR (km/kg) Measured data points High mass Mid mass Low mass ### Page 69 12/13/2023 66 Under a matrix form this gives: 2426 2427 ⎝ ⎜ ⎛ 𝑆𝑆𝑆𝑆𝑆𝑆1 𝑆𝑆𝑆𝑆𝑆𝑆2 𝑆𝑆𝑆𝑆𝑆𝑆3 ⋮ 𝑆𝑆𝑆𝑆𝑆𝑆12⎠ ⎟ ⎞ = ⎝ ⎜ ⎛ 1 𝑒𝑒1 𝑒𝑒1² 1 𝑒𝑒2 𝑒𝑒2² 1 𝑒𝑒3 𝑒𝑒3² ⋮ ⋮ ⋮ 1 𝑒𝑒12 ⋯ 𝑒𝑒12²⎠ ⎟ ⎞ �𝑏𝑏0𝑏𝑏1 𝑏𝑏2 � + ⎝ ⎜ ⎛ 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 ⋮ 𝐹𝐹12⎠ ⎟ ⎞ 2428 2429 SAR = M b + e 2430 2431 where: 2432 2433 SAR = ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 0.932 0.925 0.913 0.889 0.868 0.848 0.838 0.830 0.806 0.815 0.779 0.788⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ M = ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎛ 1 17800 17800² 1 18200 18200² 1 18620 18620² 1 18890 18890² 1 19350 19350² 1 19610 19610² 1 19920 19920² 1 20510 20510² 1 20790 20790² 1 21220 21220² 1 21480 21480² 1 22100 22100²⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞ b = � 𝑏𝑏0 𝑏𝑏1 𝑏𝑏2 � e = ⎝ ⎜ ⎛ 𝐹𝐹1 𝐹𝐹2 𝐹𝐹3 ⋮ 𝐹𝐹n⎠ ⎟ ⎞. 2434 2435 The least square principle consists in looking for the parameter values of vector B, minimizing the sum of 2436 the squares of residuals, i.e.: 2437 2438 Min ∑ 𝐹𝐹i²𝑖𝑖=12𝑖𝑖=1 = min ∑ (𝑆𝑆𝑆𝑆𝑆𝑆(i) − 𝑏𝑏0 − 𝑏𝑏1 𝑒𝑒i − 𝑏𝑏2 𝑒𝑒i2)𝑖𝑖=12𝑖𝑖=1 ². 2439 2440 It is equivalent to look for the solutions of 𝜕𝜕(∑ 𝑟𝑟i²) 𝜕𝜕𝑏𝑏j = 0 for j = (0, 1, 2). 2441 2442 The solution B = � 𝐵𝐵0 𝐵𝐵1 𝐵𝐵2 � is given by: 2443 A-1 M’ SAR (see A4-2) 2444 2445 where: 2446 2447 M’ = transpose of M; and 2448 2449 A-1 = (M’ M)-1 = inverse of (M’ M). 2450 2451 Finally, B = � 3.26727172 −0.000205692 4.21798 𝑥𝑥10-09 �; and 2452 2453 SARav = 3.26727172 – 0.000205692 m + 4.21798.10-9 m². 2454 2455 Figure A4-14 provides a representation of the mean SAR model as a function of the airplane gross mass. 2456 2457 2458 ### Page 70 12/13/2023 67 2459 Figure A4-14. SAR model (trend line) versus gross mass — Example 4 2460 2461 2462 The mean SAR values at each of the three reference gross masses of the FEM are as follows: 2463 2464 Table A4-15. 2465 2466 Mean SAR value — Example 4 2467 2468 Reference mass Mass value (kg) Mean SAR value (km/kg) Low mass 17,825 0.94100 Mid mass 19,953 0.84238 High mass 22,080 0.78198 2469 Estimate of the standard deviation(s): 2470 2471 𝑒𝑒 = �∑ (SARi−SARav(i))2𝑖𝑖=𝑛𝑛𝑖𝑖=1 𝑛𝑛−𝐾𝐾−1 = 0.01050 km/kg 2472 2473 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 4 — SAR model (trend line) versus gross mass SAR (km/kg) Measured data points High mass Low mass Mid mass Trend line ### Page 71 12/13/2023 68 where: 2474 2475 the number of data points (n) = 12; 2476 2477 K = 2 for a second order polynomial regression (see A4-2); and 2478 2479 the degrees of freedom (n-K-1) = 9. 2480 2481 2482 Confidence interval determination 2483 2484 The 90 percent confidence interval (CI90) at an airplane gross mass m0 is calculated as follows (see A4-2485 2): 2486 2487 𝐶𝐶𝐶𝐶90 = SARav(m0) ± 𝑒𝑒(.95 ,𝑛𝑛−𝐾𝐾−1) 𝑒𝑒 �m0 A-1 m0' 2488 2489 where: 2490 2491 the Student t-distribution for 90 percent confidence and 9 degrees of freedom t(.95, 9) = 1.833 (See Table 2492 A4-1); 2493 2494 m0 = (1 m0 m0²) and m0’ = � 1 𝑒𝑒0 𝑒𝑒0² �; and 2495 2496 A-1 = (M’ M)-1 = inverse of (M’ M). 2497 2498 Figure A4-16 provides a representation of the 90 percent confidence interval as a function of airplane 2499 gross mass. 2500 2501 ### Page 72 12/13/2023 69 2502 Figure A4-16. 90 percent confidence interval versus gross mass — Example 4 2503 2504 The 90 percent confidence intervals at each of the three reference gross masses of the CO2 emissions 2505 evaluation metric are as follows: 2506 2507 Table A4-17. 2508 2509 Confidence intervals — Example 4 2510 2511 Reference mass Mass value (kg) 90% confidence interval (kg/km) Low mass 17,825 CI90 = 0.94100 ± 0.01399 Mid mass 19,953 CI90 = 0.84238 ± 0.00823 High mass 22,080 CI90 = 0.78198 ± 0.01505 2512 Check of confidence interval limits 2513 2514 For each of the three reference gross masses of the FEM, the confidence interval extends around the 2515 mean SAR value by an amount provided in Table A4-18. 2516 2517 0.95 0.90 0.85 0.80 0.75 17 000 18 000 19 000 20 000 21 000 22 000 23 000 Gross mass - m (kg) Example 4 — 90% confidence interval versus gross mass SAR (km/kg) Measured data points High mass 90% CI line - upper 90% CI line - lower Low mass Mid mass Trend line ### Page 73 12/13/2023 70 2518 Table A4-18. 2519 2520 Check of confidence intervals — Example 4 2521 2522 Reference mass Mass value (kg) 90% confidence interval (percentage of mean SAR) Low mass 17,825 (0.01399/0.94100) x 100 = 1.52% Mid mass 19,953 (0.00823/0.84238) x 100 = 0.98% High mass 22,080 (0.01505/0.78198) x 100 = 1.93% 2523 The 90 percent confidence intervals at the low and high reference gross masses of the FEM are above 2524 the confidence interval limit of 1.5 percent, as defined in § A38.5.3.4. 2525 2526 In such case, a penalty equal to the amount that the 90 percent confidence interval exceeds ±1.5 percent 2527 is applied to the mean SAR values as follows: 2528 2529 2530 Table A4-19. 2531 2532 Corrected SAR values — Example 4 2533 2534 Reference mass Mass value (kg) Corrected SAR value (km/kg) Low mass 17,825 0.94100 x [1 - (1.52-1.5)/100] = 0.94081 High mass 22,080 0.78198 x [1 - (1.93-1.5)/100] = 0.77862 2535 2536 As a result, the following mean SAR values associated to each of the three reference masses of the FEM 2537 can be used for the metric determination. 2538 2539 Table A4-20. 2540 2541 Mean SAR values — Example 4 2542 2543 Reference mass Mass value (kg) Mean SAR value (km/kg) Low mass 17,825 0.94081 Mid mass 19,953 0.84238 High mass 22,080 0.77862 2544 2545 ### Page 74 12/13/2023 71 Appendix 5: References 2546 2547 2548 2549 1. International Standards and Recommended Practices, Annex 16 to the Convention 2550 on International Civil Aviation, Environmental Protection, Volume III – Aeroplane CO2 2551 Emissions, First Edition, July 2017, Applicable 1 January 2018, Including Amendment 2552 1 of January 1, 2021 2553 2554 2. International Standards and Recommended Practices, Annex 16 to the Convention 2555 on International Civil Aviation, Environmental Protection, Doc 9501 Environmental 2556 Technical Volume III, Procedures for the CO2 Emissions Certification of Aeroplanes, 2557 First Edition, 2018 2558 2559 3. ASTM International D1655-15 entitled “Standard Specification for Aviation Turbine 2560 Fuels”. This ASTM International publication may be obtained from the ASTM 2561 International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA, 2562 19428-2959 USA, www.astm.org. 2563 2564 4. UK MOD DEF-STAN 91-91, Issue 7, Amendment 3, entitled “Turbine Fuel, Kerosene 2565 Type, Jet A-1”. This United Kingdom Ministry of Defence Standard may be obtained 2566 from Defence Equipment and Support, UK Defence Standardization, Kentigern 2567 House, 65 Brown Street, Glasgow G2 8EX, UK. 2568 2569 5. ASTM International D4809-13 entitled “Standard Test Method for Heat of Combustion 2570 of Liquid Hydrocarbon Fuels by Bomb Calorimeter (Precision Method)”. This ASTM 2571 International publication may be obtained from the ASTM International, 100 Barr 2572 Harbor Drive, PO Box C700, West Conshohocken, PA, 19428-2959 USA, 2573 www.astm.org. 2574 2575 6. ASTM International D4052-11 entitled “Standard Test Method for Density and 2576 Relative Density and API Gravity of Liquids by Digital Density Meter”. This ASTM 2577 International publication may be obtained from the ASTM International, 100 Barr 2578 Harbor Drive, PO Box C700, West Conshohocken, PA, 19428-2959 USA, 2579 www.astm.org. 2580 2581 7. ASTM International D445-15 entitled “Standard Test Method for Kinematic Viscosity 2582 of Transparent and Opaque Liquids (and Calculation of Dynamic Viscosity)”. This 2583 ASTM International publication may be obtained from the ASTM International, 100 2584 Barr Harbor Drive, PO Box C700, West Conshohocken, PA, 19428-2959 USA, 2585 www.astm.org. 2586 2587 2588 2589 2590 2591 2592 --- From OpenAirDocs.org, an independent open copy of FAA data. Only the Federal Register edition on govinfo.gov is the official legal text of an AD.