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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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