jet transport equations

Jet Transport

Performance Equations

Revised May 2009

© by Ralf M. Dittmer

Jet Transport Performance Equations

Table of Contents 1. CONVERSION FACTORS ......................................................................................................4 2. NOMENCLATURE ..................................................................................................................5 3. AERODYNAMICS...................................................................................................................6

3.1 Basics ................................................................................................................................6 3.2 Flow Relations near the Speed of Sound ...........................................................................6 3.3 Standard Atmosphere ........................................................................................................7 3.4 Airfoil Properties.................................................................................................................9 3.5 Force and Moment Coefficients .........................................................................................9 3.6 Generalized Lift and Drag ..................................................................................................9 3.7 Drag Analyses..................................................................................................................10 3.8 Airspeeds.........................................................................................................................10 3.9 Airspeed Conversions......................................................................................................10 3.10 Thrust Required .............................................................................................................12

4. JET ENGINE .........................................................................................................................14 4.1 Thrust Specific Fuel Consumption....................................................................................14 4.2 Net Thrust Equation .........................................................................................................14 4.3 Gross Thrust Equation .....................................................................................................14 4.4 Gross Thrust Function......................................................................................................14 4.5 Parameter Correction.......................................................................................................15

5. PERFORMANCE ..................................................................................................................16 5.1 Flight Capabilities.............................................................................................................16 5.2 Takeoff.............................................................................................................................17 5.3 Takeoff with Slush or Standing Water ..............................................................................20 5.4 Climb ...............................................................................................................................21 5.5 Enroute Climb ..................................................................................................................26 5.6 Cruise ..............................................................................................................................27 5.7 Economy Operation .........................................................................................................28 5.8 Descent ...........................................................................................................................29 5.9 Landing............................................................................................................................29

6. STABILITY AND CONTROL.................................................................................................31 6.1 Weight and Balance Control.............................................................................................31 6.2 Moments..........................................................................................................................32 6.3 Static Longitudinal Stability ..............................................................................................32

APPENDIX................................................................................................................................33 Table of A Values for Reynolds Number Correction ...............................................................33 Table of Primary Geometry Parameters for Boeing Airplanes ................................................34


1. CONVERSION FACTORS Multiply By To obtain Mass Kilogram 2.2046 Pounds Pound 0.04536 Kilograms Length Feet 0.3048 Meters Feet 12 Inches Yard 3 Feet Meter 3.281 Feet Nautical Mile 6076 Feet Area Square Feet 0.0929 Square Meters Square Meter 10.76 Square Feet Volume US Gallon 3.785 Liters Liter 0.2642 US Gallons Speed Knot 1.689 Feet/sec Knot 101.34 Feet/sec Acceleration m/sec² 3.28084 ft/sec² Power Horse Power (HP) 550 ft-lbs/sec Pressure Lbs/in² 144 Lbs/ft² Temperature

4040C59F 4040F

95C

459.67FR 273.15CK


2. NOMENCLATURE a = acceleration, ft/sec² A = cross-sectional area, ft² A = Reynolds Number drag constant a = lift curve slope, per degree a = speed of sound, ft/sec or knots a = standard day temperature lapse rate AR = aspect ratio Aj = jet nozzle area, ft² b = wing span, ft c = chord of wing, ft CAS = Calibrated Airspeed, knots CD = drag coefficient CDI = induced drag coefficient CDM = compressible drag coefficient CDp = parasite drag coefficient Cg = gross thrust coefficient CL = lift coefficient CM = moment coefficient CN = yawing moment coefficient Cp = pressure coefficient cr = root chord, ft ct = tip chord, ft D = drag, lbs e = Oswalds’ efficency factor EAS = Equivalent Airspeed, knots FG = gross thrust, lbs FN = net thrust, lbs le = engine arm, ft lt = tail arm, ft M = Mach Number MAC = Mean Aerodynamic Chord, ft n = load factor p = pressure, lbs/ft² q = dynamic pressure, lbs/ft² R = radius of turn, ft R/C = rate of climb, ft/min R/D = rate of descent, ft/min Re = Reynolds Number S = distance, ft S = wing area, ft² T = absolute temperature, K or °R T = thrust, lbs t = time, sec TAS = True Airspeed, knots V = velocity, ft/sec or knots VG = ground Speed, knots Vj = nozzle exhaust velocity, ft/sec

W = weight, lbs WA = airflow, lbs/sec WF = fuel flow, lbs/hr or lbs/sec = angel of attack, degree = bank angel, degree = gradient = ratio of specific heat = spindown factor


3. AERODYNAMICS

3.1 Basics Continuity Equation constAVρ [3.1.1] Bernoulli Equation Incompressible:

222

211 ρV

21pρV

21p [3.1.2]

Compressible:

2

Vρp

12V

ρp

1

22

2

2

2

221

1

1

1

1

[3.1.3]

Dynamic (Impact) Pressure

2ρV21q with V in knots:

295.375σVq

2TAS [3.1.4]

3.2 Flow Relations near the Speed of Sound Mach Number

aVM [3.2.1]

Total Temperature Ratio 2

t 0.2M1θθ [3.2.2] Total Pressure Ratio

3.52t 0.2M1δδ [3.2.3]

Total Density Ratio

2.52t 0.2M1ρρ [3.2.4]


3.3 Standard Atmosphere Temperature Below 36089 feet: pSTD 0.0019812h288.15T [3.3.1]

p6

0

STD h106.8755861T

Tθ [3.3.2]

Above 36089 feet: TSTD = 216.65 K = 0.7519 Pressure Ratio Below 36089 feet:

5.25588p

6

0

STD h106.8755861p

pδ [3.3.3]

Above 36089 feet:

2080636089h

0.2234eδ [3.3.4] Density Ratio

θδ

ρρσ

0

STD [3.3.5]

Tapeline Altitude

geo

geotape hr

rhh

[3.3.6]

r = 20855531 ft (average radius of the earth) Speed of Sound θ661.4786a [3.3.7a]

RT29.04a [3.3.7b]


STANDARD ATMOSPHERE TABLE

hp OAT a/a0 atmospheric pressure feet °F °C = T/T0 in.Hg lb/ft² mb = p/p0 = /0

0 59.0 15.0 1.0000 1.0000 29.921 2116.2 1013.2 1.0000 1.0000

1000 55.5 13.0 0.9932 0.9966 28.868 2041.7 977.5 0.9648 0.9714 2000 51.9 11.1 0.9863 0.9931 27.830 1968.3 942.4 0.9301 0.9430 3000 48.3 9.1 0.9794 0.9896 26.821 1897.0 908.2 0.8964 0.9153 4000 44.8 7.1 0.9726 0.9862 25.855 1828.6 875.5 0.8641 0.8884 5000 41.2 5.1 0.9657 0.9827 24.906 1761.5 843.4 0.8324 0.8620

6000 37.6 3.1 0.9588 0.9792 23.985 1696.3 812.2 0.8016 0.8360 7000 34.1 1.1 0.9519 0.9757 23.093 1633.3 782.0 0.7718 0.8108 8000 30.5 -0.8 0.9451 0.9722 22.237 1572.8 753.0 0.7432 0.7864 9000 26.9 -2.8 0.9382 0.9686 21.397 1513.3 724.5 0.7151 0.7622

10000 23.4 -4.8 0.9313 0.9650 20.583 1455.7 697.0 0.6879 0.7386

11000 19.8 -6.8 0.9244 0.9615 19.796 1400.1 670.3 0.6616 0.7157 12000 16.2 -8.8 0.9176 0.9579 19.042 1346.7 644.8 0.6364 0.6935 13000 12.7 -10.7 0.9107 0.9543 18.300 1294.3 619.7 0.6116 0.6716 14000 9.1 -12.7 0.9038 0.9507 17.585 1243.7 595.5 0.5877 0.6503 15000 5.5 -14.7 0.8969 0.9470 16.890 1194.6 572.0 0.5645 0.6294

16000 2.0 -16.7 0.8900 0.9434 16.217 1147.0 549.2 0.5420 0.6090 17000 -1.6 -18.7 0.8832 0.9398 15.577 1101.7 527.5 0.5206 0.5894 18000 -5.2 -20.6 0.8763 0.9361 14.949 1057.3 506.2 0.4996 0.5701 19000 -8.7 -22.6 0.8694 0.9324 14.338 1014.1 485.5 0.4792 0.5512 20000 -12.3 -24.6 0.8625 0.9287 13.752 972.6 465.7 0.4596 0.5329

21000 -15.9 -26.6 0.8557 0.9250 13.189 932.8 446.6 0.4408 0.5151 22000 -19.4 -28.6 0.8488 0.9213 12.642 894.1 428.1 0.4225 0.4978 23000 -23.0 -30.6 0.8419 0.9176 12.109 856.4 410.0 0.4047 0.4807 24000 -26.6 -32.5 0.8350 0.9138 11.597 820.2 392.7 0.3876 0.4642 25000 -30.1 -34.5 0.8282 0.9101 11.110 785.7 376.2 0.3713 0.4483

26000 -33.7 -36.5 0.8213 0.9063 10.631 751.9 360.0 0.3553 0.4326 27000 -37.3 -38.5 0.8144 0.9024 10.170 719.3 344.4 0.3399 0.4174 28000 -40.8 -40.5 0.8075 0.8986 9.727 688.0 329.4 0.3251 0.4026 29000 -44.4 -42.4 0.8007 0.8948 9.302 657.9 315.0 0.3109 0.3883 30000 -48.0 -44.4 0.7938 0.8910 8.890 628.7 301.0 0.2971 0.3743

31000 -51.5 -46.4 0.7869 0.8871 8.492 600.6 287.5 0.2838 0.3607 32000 -55.1 -48.4 0.7800 0.8832 8.106 573.3 274.5 0.2709 0.3473 33000 -58.7 -50.4 0.7732 0.8793 7.741 547.5 262.1 0.2587 0.3346 34000 -62.2 -52.3 0.7663 0.8754 7.385 522.3 250.1 0.2468 0.3221 35000 -65.8 -54.3 0.7594 0.8714 7.043 498.2 238.5 0.2354 0.3100

36000 -69.4 -56.3 0.7525 0.8675 6.714 474.9 227.4 0.2244 0.2982 36089 -69.7 -56.5 0.7519 0.8671 6.684 472.7 226.3 0.2234 0.2971 37000 -69.7 -56.5 0.7519 0.8671 6.397 452.4 216.6 0.2138 0.2843 38000 -69.7 -56.5 0.7519 0.8671 6.098 431.3 206.5 0.2038 0.2710 39000 -69.7 -56.5 0.7519 0.8671 5.811 411.0 196.8 0.1942 0.2583 40000 -69.7 -56.5 0.7519 0.8671 5.538 391.7 187.5 0.1851 0.2462

41000 -69.7 -56.5 0.7519 0.8671 5.278 373.3 178.7 0.1764 0.2346 42000 -69.7 -56.5 0.7519 0.8671 5.030 355.7 170.3 0.1681 0.2236 43000 -69.7 -56.5 0.7519 0.8671 4.793 339.0 162.3 0.1602 0.2131 44000 -69.7 -56.5 0.7519 0.8671 4.569 323.1 154.7 0.1527 0.2031 45000 -69.7 -56.5 0.7519 0.8671 4.354 307.9 147.4 0.1455 0.1935

T0 = 288.15 K = 15°C = 59°F = 518.67°R p0 = 29.92 inHg = 1013.25 mbar = 14.7 psi 0 = 0.002377 slug/ft³ a0 = 1116.45 ft/sec = 661.4786 knots


3.4 Airfoil Properties Taper Ratio

r

t

ccλ [3.4.1]

Aspect Ratio

SbAR

2

[3.4.2]

Mean Aerodynamic Chord (MAC)

Sdbc

MAC2 [3.4.3]

3.5 Force and Moment Coefficients Lift Force

δS1481.351M

LiftSσVLift295.369C 22

TASL [3.5.1]

Drag Force

δS1481.351M

DragSσVDrag295.369C 22

TASD [3.5.2]

Moment

δSc1481.351M

MomentScσV

Moment295.369C 22TAS

M [3.5.3]

3.6 Generalized Lift and Drag Lift

SM1481.351CδL 2

L [3.6.1]

Drag

SM1481.351CδD 2

D [3.6.2]


3.7 Drag Analyses Total Drag Coefficient

DM

2L

DPDSD0D CπARe

CCCCC [3.7.1]

Induced Drag Coefficient

πARe

CC2L

Di [3.7.2]

Reynolds Number Effect on Drag DREDNOMD ΔCCC [3.7.3a]

nominal2

actual2

4-DRE

θ0.38312θδθ

0.38312θδ

logA10ΔC [3.7.3b]

3.8 Airspeeds Calibrated Airspeed (CAS) PIASCAS ΔVVV [3.8.1] Equivalent Airspeed ( EAS ) CCASEAS ΔVVV [3.8.2] True Airspeed ( TAS )

σ

VV EASTAS [3.8.3]

Mach Number

a

VM TAS [3.8.4]

3.9 Airspeed Conversions CAS to EAS (Requires Knowing )

111

661.4786CAS.21

δ1δ1479.1EAS

3.51

3.52

[3.9.1]


EAS to CAS (Requires Knowing )

1111479.1EAS

δ11δ1479.1CAS

3.51

3.52

[3.9.2]

CAS to TAS (Requires Knowing and )

111

661.4786CAS.21

δ1θ1479.1TAS

3.51

3.52

[3.9.3]

TAS to CAS (Requires Knowing and )

1111479.1TAS

θ11δ1479.1CAS

3.51

3.52

[3.9.4]

EAS to TAS (Requires Knowing , or and )

δθEAS

σEASTAS [3.9.5]

TAS to EAS (Requires Knowing , or and )

θδTASσTASEAS [3.9.6]


3.10 Thrust Required

Liftcoefficient

2L 1481.351SMδW

C [3.10.1]

Thrust Required

SM1481.351CδT 2

D [3.10.2]


COMPRESSIBILITY CORRECTION VC


4. JET ENGINE

4.1 Thrust Specific Fuel Consumption

N

F

FWTSFC [4.1.1]

4.2 Net Thrust Equation Turbojet

aA

GambjjjF

ajA

N Vg

WFppAVg

WVVg

WF [4.2.1]

Turbofan (Common Exhaust)

ambjjjF

ajAp

ajAf

N ppAVg

WVVg

WVV

gWF [4.2.2]

Turbofan

ambjjjF

ajAp

afAf

N ppAVg

WVVg

WVV

gWF [4.2.3]

4.3 Gross Thrust Equation Turbojet

coldj

hotjgjambG A

ACAψpF [4.3.1]

4.4 Gross Thrust Function Unchocked Nozzle

1pp

12ψ

1

amb

tNγγ

γγ

[4.4.1]

Chocked Nozzle

11

2pp2ψ

11

amb

tN

γ

γ [4.4.2]

By-Pass engine with common exhaust

111pp

12

pppp

ψ

1

sMN

tMN

sMN

tMN

amb

tMN

γγ

γγ

with: 1.8

.8ppp t7Ft7tMN

[4.4.3]


4.5 Parameter Correction Thrust

δFCF N

N [4.5.1]

Speed

Xt

11 θ

NCN [4.5.2]

Fuel Flow

Xtt

FF θδ

WCW [4.5.3]

Airflow

δθWCW

XA

A [4.5.4]

Gas Temperature

XθEGTCEGT [4.5.5]


5. PERFORMANCE

5.1 Flight Capabilities Load Factor

cosφ

1WLn [5.1.1]

Stall Speed FAR-Stall

S

295.375V

WC2eMin

LsFAR

[5.1.2]

1g-Stall

S

295.375V

nWC2eMaxL

gLs1

[5.1.3]

CG Correction

AftFwd

tLsRefCGLsFwdCG cgcg

lMAC1CC [5.1.4]

Buffet Altitude

LBuffet

2SC1481.351MnWδ [5.1.5]

Radius of Turn

tanφg

2.852721VR2TAS [5.1.6]


5.2 Takeoff Acceleration and Minimum Rotation Speed

φWSqµCCµWTWga LD [5.2.1a]

GMMLM

-TGM

R

µZXXXXCCcgSρ

TZµZ2XW2Vmin

[5.2.1b]

Segment A (All engine acceleration distance to V1)

1

W

V

V

WGA dV

aVVS [5.2.2]

Segment A1 (One engine inoperative acceleration distance from VEF to V1)

1

EF

V

V

WGA1 dV

aVVS [5.2.3]

with

φW

295.375σVSµCCµWηT

Wga

21

LD [5.2.4]

Engine Failure Speed (VEF)

φW

295.375σV

WSµCCµ

WTη

1.6878ΔtgVV

21

LDV

1EF1

[5.2.5]


Segment B (One engine inoperative acceleration distance from V1 to VLOF) GB2GB1GB SSS [5.2.6] with:

R

1

V

V

WGB1 dV

aVVS where: φWSqµCCµWηT

Wga LD

ΔtV2VV1.6878S W

LOFRGB2

where:

2LOF2R toVVtoVV ttΔt

Segment C (One engine inoperative flare distance to V2 at 35 feet)

2LOFtoVVW

2LOFC tV

2VV1.6878S

[5.2.7]


Segment D (Distance traveled from V1 to the establishment of the full braking configuration)

B

1

V

V

WGD dV

aVVS [5.2.8]

φW

295.375σVSµCCWµηT

Wga

21

LDavg

Brake Application Speed (VB)

φW

295.375σV

WSµCCµ

WTη

1.6878ΔtgVV

21

LDavgV

1B1

[5.2.9]

Average Friction Coefficient (µavg)

BR

FMSP

FTBASPBavg µµ

2ttt

µµ

[5.2.10a]

for 707 and 737

BR

FMSP

FTSPBABavg µµ

2ttt

µµ

[5.2.10b]

where: µB Braking coefficient µR Rolling coefficient of friction tBA Flight test time between engine failure recognition and brake application, [sec] tSP Flight test time between engine failure recognition and spoiler application, [sec] tSP FM Flight Manual time between engine failure recognition and spoiler action, [sec] Segment E (Stopping distance from VB to VW)

W

B

V

V

WGE dV

aVVS [5.2.11]

Balanced Field Length GEGDCGB SSSS [5.2.12] Distance and time to VR (simplified method)

Rat0.707V

2WR

G 2aVV2.849S

[5.2.13]


Rat0.6V

WRG 2a

VV1.6878t [5.2.14]

Wind Correction

71

2

1

2

1

HeightHeight

WindWind

[5.2.15]

Airplane Height2 Height1 Wind1/Wind2

707 50 feet 10 feet .795 727 50 feet 10 feet .795 737 50 feet 8 feet .770

737-300 32.8 feet 8 feet .8174 747 50 feet 16 feet .850 757 32.8 feet 12.5 feet .8713 767 32.8 feet 13.5 feet .881

5.3 Takeoff with Slush or Standing Water Slush Force

TireslushD2GS ACσV

21F [5.3.1]

= Slush density, 1.65 slugs/ft³ Equal to specific gravity of 0.85 VG = Ground Speed – Feet per second CDslush = Slush drag coefficient for airplane’s specific gear arrangement ATire = Reference area for slush force calculation Hydroplaning Speed

Gravityspecific

PressureTire8.63VHP [5.3.2a]

Tire Pressure must be in psi newer airplane’s: PressureTire8.63VHP [5.3.2b] Slush Force Including Hydroplaning

HPTireslushD2GS fACσV

21F

[5.3.3]

with fHP above VHP:


1.5V

2.5V

HP

GHPHP

HP

G

0.6VV1.6Vf

5.4 Climb

Rate of Climb

dhdV

gV1

VW

DT

101.27R/C

[5.4.1]

Climb Gradient

dhdV

gV1

CC

WT

L

D

[5.4.2]

Geometric Gradient

G

geometric VR/C

γ with: WTASG VcosVV γ [5.4.3]

Climb Trade

ga

ResidualTotal γγ [5.4.4]


Turning

dhdV

gV1

WΔDDT φbankZero

φ

γ [5.4.5a]

dhdV

gV1

CCC

Δ bankZeroL

bankZeroDDφ

φ

γ [5.4.5b]

FAR Minimum Climb Gradient Requirements

Segment 1 2 3 Final Number of

engines Minimum Gross Gradient [%] 2 positive 2.4 1.2 3 0.3 2.7 1.5 4 0.5 3.0 1.7

Net Gradient Reduction 2 Engines: 0.8% 3 Engines: 0.9% 4 Engines: 1.0% FAR Takeoff Path


Acceleration Factor dhdV

gV1

Temperature Constant Below Above Speed Tropopause Tropopause M 20.133184M1 0 Standard VC 0.190263φ0.7M1 2 φ0.7M1 2 VE 20.566816M1 20.7M1 M 20.133184M1 0

Non Standard VC

TT0.190263φ0.7M1 std2 φ0.7M1 2

VE

TT0.19026310.7M1 std2 20.7M1

2.522

3.52

0.2M10.7M10.2M1φ

One Engine Inoperative Climb Yawing Moment Coefficient

blΔC

δSb1481.351MlF

C eWMD2

eOPERATINGNN [5.4.6]

Engine Inoperative Drag ControlDWMDDOutEngD ΔCΔCCC [5.4.7]


ACCELERATION FACTOR


5.5 Enroute Climb Time At ISA

average

12

R/ChhΔt

[5.5.1a]

At Non ISA

average

stdp1p2

R/CTThh

Δt

[5.5.1b]

Distance

60

ΔtVΔnam average [5.5.2]

Fuel

60

ΔtWΔW averageF

F [5.5.3]


5.6 Cruise Still Air Distance

WTAS

TAS

VVVnmnam

[5.6.1]

Fuel Mileage

F

TAS

WV

lbsnam

[5.6.2]

Range

2

1

XWWln

DLM

θTSFC

θ661.4786R [5.6.3]

Integrated Range Range

ΔWlbs

namΔRaverage

[5.6.4a]

ΣΔRR [5.6.4b] Time

averageVΔRΔt [5.6.5a]

ΣΔtt [5.6.5b] Non Standard Temperature Effects when maintaining a constant Mach Number Speed

std

std TTTASTAS [5.6.6a]

Fuel Flow, where Fuel Flow is a function of

X

stdStdFF T

TWW

[5.6.6b]

Specific Range, where Fuel Flow is a function of

X0.5

stdstd TT

lbsnam

lbsnam

[5.6.6c]


5.7 Economy Operation Cost Index

cents/lb

$/hr100C

CCostFuelCostTimeCI

F

T [5.7.1]

Total Trip Cost FCTCC FT [5.7.2] Economy Cruise Speed Cost Index

dMlbs

namd

lbsnam

Mθ661.4786CI 2

2

[5.7.3]

Economy Cruise Cost Function

G

F

VW100CIECCF

[5.7.4]


5.8 Descent

Rate of Descent

dhdV

gV1

VW

TD

101.27R/D

[5.8.1]

Descent Time, Fuel and Distance Refer to Enroute Climb Geometric Gradient

G

geometric VR/D

γ with: WTASG VcosVV γ [5.8.2]

5.9 Landing


Approach Speed FARSg1SREFAPP 1.30Vor1.23VVV [5.9.1] Distance from 50 feet to Touchdown

airWTDAPP

A ΔtV2

VV1.6878S

[5.9.2a]

L0

L

D

L

DA C1ngσρ

WT

CC

SW

WT

CC

50S

[5.9.2b]

Distance from Touchdown Speed to full braking

TRANWBTD

TRAN ΔtV2

VV1.6878S

[5.9.3]

Distance from full Braking Speed to full stop

W

B

V

V

WB dV

aVVS [5.9.4]

with: φWSqµCCWµTWga LDB

Landing Distance BTRANAL SSSS [5.9.5] FAR Landing Field Length LFARL 1.667SS [5.9.6] Wet FAR Landing Field Length FARLWetFARL 1.15SS [5.9.7]


6. STABILITY AND CONTROL

6.1 Weight and Balance Control

100

MACLEMACarmCG%MAC

[6.1.1]

Index Units according AHM560

K

CRef.StaarmWI

[6.1.2]

100MAC

LEMACRef.StaW

CKI

%MAC

[6.1.3]

W = Weight actual arm = Station horizontal distance in inches or meters from datum

to the location of the weight. Ref. Sta = Reference station/axis. Selected station around which all index values are calculated. K = Constant used as a plus value to avoide negative index figures. C = Constant used as a denominator to convert moment

values into index values. I = Index value corresponding to respective weight. MAC = Length of Mean Aerodynamic Chord in inches or meters. LEMAC = Horizontal distance in inches or meters from datum to location of the Leading Edge of the MAC.


6.2 Moments Pitching Moment Yawing Moment Rolling Moment

qScCM m [6.2.1] qSbCN N [6.2.2] qSbCl l [6.2.3]

6.3 Static Longitudinal Stability

Pitching Moment Coefficient

VηCCCcSqZT

cXCC tLtmfusm.25c

TLmCG [6.3.1]

with:

qqη t

t and Sc

XSV tt

Slope

VηdCdC

dCdC

dCdC

cX

dCdC

tL

Lt

L

mwb

L

mE

L

mCG [6.3.2]

with:

mfusm.25cmwb CCC qScTZC T

mE

αddε1Vη

aa

dCdC

dCdC.25

cX

dCdC

tw

t

L

mwb

L

mECG

L

mCG


APPENDIX

Table of A Values for Reynolds Number Correction single-aisle models A twin-aisle models A 737-300 -59.57 747-200 -39.826 737-400 -63.99 747-300 -39.826 737-500 -59.58 747-400 -43.60 737-600 -59.98 767-200 -42.222 737-700 -59.623 767-300 -43.65 737-800 -63.99 767-400 -45.23 737-900 -64.80 757-200 -49.434 777-200 -45.29 757-300 -56.24 777-300 -46.89


Table of Primary Geometry Parameters for Boeing Airplanes Many of the equations require airplane geometry parameters such as the reference wing area Sref, reference wingspan bref and the engine moment arm. Those are contained in the following table. Additionally, parameters MAC and LEMAC are used in weight and balance calculations and the wing angle of incidence is used in body attitude calculations. Model Sref bref MAC LEMAC eng mom arm wing (ft²) (ft) (in) (in) (ft) incid -------------------------------------------------------------------------------------------------------------------------- 707-100, -100B 2433 130.83 241.88 786.2 27.17 (inbd) 2°

46.08 (outbd) 707-200 2433 130.83 241.88 786.2 27.17 (inbd) 2°

46.08 (outbd) 707-300/B/Badv, C 2892 142.42 272.29 762.97 33.0 (inbd) 2°

52.0 (outbd) 707-400 2892 142.42 272.29 762.97 33.0 (inbd) 2°

52.0 (outbd) ------------------------------------------------------------------------------------------------------------------------- 720/B 2433 130.83 241.88 786.2 27.17 (inbd) 2°

46.08 (outbd) ------------------------------------------------------------------------------------------------------------------------- 727-100, -200 1560 106 180.0 860.2 10.0 (pod) 2° ------------------------------------------------------------------------------------------------------------------------- 737-100 thru -500 980 93.0 134.46 625.6 16.14 1° 737-600 thru -900 1340 112.58 153.8 627.1 16.14 ------------------------------------------------------------------------------------------------------------------------- 747-100 thru -300 5500 195.67 327.78 1258.0 39.17 (inbd) 2°

69.5 (outbd) 747-400 5500 195.67 327.78 1258.0 39.17 (inbd) 2°

69.5 (outbd) 747SP 5500 195.67 327.78 1258.0 39.17 (inbd) 2°

69.5 (outbd) ------------------------------------------------------------------------------------------------------------------------- 757 (all) 1951 124.5 199.7 991.9 21.67 ------------------------------------------------------------------------------------------------------------------------- 767 (all) 3050 155.0 237.5 913.2 25.69 ------------------------------------------------------------------------------------------------------------------------- 777 (all) 4605 196.9 278.5 1174.5 32.67 -------------------------------------------------------------------------------------------------------------------------

jet transport equations

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