Analysis of Air Transportation Systems Fundamentals of Aircraft ...

Introductory RemarksAir vehicles are significant different than their groundvehicle counterparts in three aspects:• Most aircraft require a prepared surface to operate fromwhich affects the overall capability of the vehicle to carryuseful payload• Aircraft operate in a dynamic atmospheric environmentwhere changes in temperature, density, and speed ofsound are drastic and cannot be neglected• Aircraft mass expenditures are significant and thus needto be accounted for in the air vehicle performanceanalysis. For example, a Boeing 747-400 can takeoff atnear 390 metric tons and yet land at its destination at 220Virginia Tech - Air Transportation Systems Laboratory 2

metric tons thus making the fuel expenditure asignificant factor in how the vehicle performs along theflight path• The analysis of NAS performance is related to theperformance of the vehicles operating in it (i.e., airportrunway and airspace sector capacity depends on aircraftcharacteristics)• The analysis of airline operations requires a carefulexamination of the aircraft performance that matches aspecific route segment (i.e., DOC, travel time, seatingcapacity, etc.)Virginia Tech - Air Transportation Systems Laboratory 3

Aircraft Performance Basics(International Standard Atmosphere)Virginia Tech - Air Transportation Systems Laboratory 4

Assumptions of the International StandardAtmosphere• Linear variation in temperature with altitude up to 11,000meters (Troposphere)• Constant temperature betwen 11,000 and 82,300 ft (25.1kilometers) in the so-called stratosphere region• Linearly increasing temperature from 82,300 ft. andabove• Most of the analysis we do in this class requiresknowledge of temeperature variations up to 15,600meters (51,000 ft.) thus only the first two layers of theatmosphere are of interest to usVirginia Tech - Air Transportation Systems Laboratory 5

Basic Relationships to Uderstand theAtmosphereEquation of state:p = !RT(1)where:pis the air pressure (N/m 2 ),constant (287 N-m/ o K),Tis the absolute air temperature ( o K)!Ris the universal gasis the air density (kg/m 3 ), andVirginia Tech - Air Transportation Systems Laboratory 6

Basic Relationships (Hydrostatic Equation)the hydrostatic equation that relates air pressure, densityand height above sea level of a fluid is,dp=where: is rate of change in air pressure, is thegravity constant (9.81 m/s 2 ), is the air density (kg/m 3 ),h–!gdhdpand is the altitude of the fluid element above sea levelconditions (m)Note: For derivations of these equations consult any fluiddynamics textbook or aerodynamics text!g(2)Virginia Tech - Air Transportation Systems Laboratory 7

Atmosphere with Constant TemperatureUsing equations (1) and (2),dp-----p=–gdh------------RT(3)This equation can be integrated to obtain a basicrelationship between atmospheric pressures at variouslayers in the atmosphere as a function of altitudep"dp-----p=h"h 0–gdh------------RT(4)p 0where the subindex0denotes a reference condition.Virginia Tech - Air Transportation Systems Laboratory 8

Atmosphere with Constant Temperaturep--- = ep 0g– ------# % RT$& ( h – h0 )(5)and!---- = e! 0g– ------# % RT$& ( h – h0 )(6)if the temperature is constant - isothermal layer (only truein the stratosphere).In this analysis we have assumed a constant value for thegravity constant. This is a good approximation in thetropopause and stratosphere.Virginia Tech - Air Transportation Systems Laboratory 9

Atmosphere with Linear Temperature VariationAccording to the International Standard Atmosphere(ISA), the variation of temperature is linear up to 11,000meters. Then,dTT = T o + '( h – h o ) = T o + ----- ( h – h o )dhwhere:'=dT-----dhis the temperature lapse rate withaltitude (i.e., rate of change in temperature with altitude)(7)andT 0is the reference temperature (typically sea level)Virginia Tech - Air Transportation Systems Laboratory 10

Atmosphere with Linear Temperature VariationSincedh=dT-----'using the equation (4) we find anexpression to relate the change in pressure with altitude ina non-isothermal layer of the atmosphere,p"p 0dp-----p=h"h 0–g------ dT -----R' T(8)p---p 0=T----# % $&T 0g– ------# % R' $&(9)Virginia Tech - Air Transportation Systems Laboratory 11

Atmosphere with Linear Temperature VariationUsing the equation of state for two refence points (sealevel denoted by subidex zero and at altitude denoted bya function of altitude:p---p 0=----!----T# % $&! 0T o(10)----!! 0=----T# % $&T 0g– ------# % R' $& – 1(11)Virginia Tech - Air Transportation Systems Laboratory 12

Reference Values of Interest at ISA ConditionsConstantValueT 0'! op oaRreference temperature 273.2 o Ktemperature lapse rate -0.0065 o K per meterair density 1.225 kg/m 3air pressure 101,325 N/m 2speed of sound340.3 m/suniversal gas constant 287 N-m/ o KVirginia Tech - Air Transportation Systems Laboratory 13

International Standard AtmosphereCharacteristics of the International Standard Atmosphere.GeopotentialAltitude (m.)Temperature ( o K)TDensity (kg/m 3 )!0 288.2 1.225 340.31000 281.7 1.112 336.42000 275.2 1.007 332.53000 268.7 0.909 328.64000 262.2 0.819 324.65000 255.7 0.736 320.56000 249.2 0.660 316.47000 242.7 0.589 312.38000 236.2 0.525 308.1Speed of Sound(m/s)aVirginia Tech - Air Transportation Systems Laboratory 14

Characteristics of the International Standard Atmosphere.GeopotentialAltitude (m.)Temperature ( o K)TDensity (kg/m 3 )!9000 229.7 0.466 303.810000 223.2 0.413 299.511000 216.7 0.364 295.112000 216.7 0.311 295.113000 216.7 0.266 295.114000 216.7 0.227 295.115000 216.7 0.194 295.116000 216.7 0.169 295.1Speed of Sound(m/s)aVirginia Tech - Air Transportation Systems Laboratory 15

Important Aircraft Speed Terms to KnowIndicated Airspeed (IAS) - is the speed registered in thecockpit instrumentTrue Airspeed (TAS) - is the actual speed of the vehiclewith respect of the mass of air surrounding the aircraft(accounts for compressibility effects)Calibrated Airspeed (CAS) - similar to IAS but correctedfor instrument position errors (airflow problems outsidethe vehicle).Ground speed (GS) - TAS corrected for windStalling Speed (V stall) - minimum speed for safe flightVirginia Tech - Air Transportation Systems Laboratory 16

Mach Number - ratio of the aircraft speed to thespeed of sound, a (note a varies with altitude)Mach number can be easily computed using the followingequation,a=(RT(12)where:Ris the universal gas constant (287 N-m/ o K),(( = 1.4is the air temperature ( o K) andheat at constant volume ( for air)is the ratio of specificTVirginia Tech - Air Transportation Systems Laboratory 17

Air Compressibility EffectsA mathematical expression to estimate true airspeed (interms of true Mach number) from CAS follows:M true 5 ! 0---- 1 0.2 V CAS------------! # % 661.5$& 2 3.5=+– 1# % $& + 10.286– 1(13)where: M true is the true mach number, V CAS is the calibratedairspeed in knots (CAS = IAS) in our analysis, ! 0 is theatmospheric density at sea level, ! is the density at thealtitude the aircraft is flying, and the constants 0.2 and661.5 account for the specific heat of the air and the speedof sound at sea level (in knots), respectively.Virginia Tech - Air Transportation Systems Laboratory 18

Defining true mach number ( M true ) as the ratio of thetrue aircraft speed ( V TAS ) and the speed of sound ( a) at theflight level in question we have,V TAS=aM true(14)Virginia Tech - Air Transportation Systems Laboratory 19

Example ComputationBoeing 737-300 (a medium size jet transport) flies at 250knots (IAS) at an altitude of 5.0 km. in a standardatmosphere. What is TAS?A quick glance at the ISA Table reveals that air density at5.0 km. is about 0.736 kg/m 3 thus resulting in a true machnumber of 0.4824 (use Equation 10).Since the speed of sound at that altitude is 320.5 m/s (seeTable) then the true airspeed of the aircraft is 154.62 m/sor 300.56 knots.Virginia Tech - Air Transportation Systems Laboratory 20

Sample Computation (continuation)Note that in this case there is a difference of 50.56 knotsbetween IAS and TAS.As the aircraft climbs the value of TAS increases even ifIAS remains constant. True Airspeed (TAS) is needed toestimate Ground Speed (GS).GS is ultimately responsible for the travel time betweenairports and thus it is important to learn how to estimateTAS for any feasible flight condition.Later analysis will introduce more details on how toestimate travel times between Origin-Destination airportsVirginia Tech - Air Transportation Systems Laboratory 21

Sample Matlab Code Used (ISAM.m)Virginia Tech - Air Transportation Systems Laboratory 22

Plot of True Mach Number vs. AltitudeVirginia Tech - Air Transportation Systems Laboratory 23

Plot of CAS vs. TAS (Subsonic Aircraft)Virginia Tech - Air Transportation Systems Laboratory 24

Aircraft Performance Estimation(Runway Length)Virginia Tech - Air Transportation Systems Laboratory 25

Aircraft Runway Length PerformanceEstimationCritical issue in airport engineering and planning (errorsin runway length are costly to the operator and perhapsunsafe)LTED)mgF fFigure 1.Forces Acting in the Aircraft During Takeoff.Virginia Tech - Air Transportation Systems Laboratory 26

NomenclatureT - thrust force (also called tractive effort) provided by thevehicle powerplantL- lifting force provided by the wing-body of the vehicleD - drag force to the vehicle body, nacelle(s), landinggears, etc.,F f- friction force due to rolling resistanceThe functional form of these forces has been derived fromdimensional analysis (review your math course notes) andfrom extensive knowledge of fluid mechanics (windtunnels and water tank experiments)Virginia Tech - Air Transportation Systems Laboratory 27

Functional Forms of the ForcesThe functional form of these forces is as follows:L=1--!V 2 SC L2(15)D=1--!V 2 SC D2(16)T = f( V , !)F f = ( mg cos)– L)f roll(17)(18)V is the vehicle speed (TAS), ! is the air density (kg/m 3 ), Sis the aircraft gross wing area, C L is the lift coefficient(nondimensional), C D is the drag coefficient(nondimensional), f roll is the rolling friction coefficient(nondimensional), is the engine thrust iin Newtons andTVirginia Tech - Air Transportation Systems Laboratory 28

) is the angle comprised between the runway planeand the horizontalVirginia Tech - Air Transportation Systems Laboratory 29

Notes on Various Parameters1) C L and C D are specific to each airframe-flapconfiguration2) f roll is usually a function of runway surface conditionsand aircraft speedT (N)Sea Levelf rollBias-Ply TireHigh ElevationRadial TireV (m/s)V (m/sec)V (m/s)V (m/sec)Figure 2. Typical Variations of T and with Aircraft Speed.f rollVirginia Tech - Air Transportation Systems Laboratory 30

Estimating Runway AccelerationUsing Newton's second law and summing forces in thehorizontal direction of motion ( x),ma x = T( V , !)– D– ( mg cos) – L)f roll – mg sin)(19)linear variations of T (tractive effort or thrust) and f roll canbe assumed to be linear with respect to airspeed for therange of speed values encountered in practice. For smallangles this equation can be expressed as,ma x = T( V , !) – D – ( mg – L)f roll(20)ma x = T( V , !)11– --! V 2 sc D – mg – --! V 2 SC L2 # % 2 $& froll(21)1a x = --- ( T(V , ! )m+1--! V 2 S( C L f roll – C D ) – mgf roll2(22)Virginia Tech - Air Transportation Systems Laboratory 31

Remarks About the Aircraft AccelerationEquation• The acceleration capability of the aircraft decreases asspeed is gained during the takeoff roll due to a reductionin the thrust produced by the engines• If Eq. 22 is integrated twice between an initial speed, V 0and the lift-off speed, V lo the distance traversed during thetakeoff roll can be found• Usually this requires a computer simulation since manyparameters such as T and f roll vary with speed (timevarying) making the coefficient of the differentialequation of motion time dependent.Virginia Tech - Air Transportation Systems Laboratory 32

Aerodynamic Coefficients• The flap setting affects C D and C L and hence affectsacceleration and runway length required for a takeoff.Typical variations of C D with flap angle are shown belowC DConstant Angle of AttackC LConstant Angle of Attack5 10 15 20 255 10 15 20 25Flap Angle (degrees)Flap Angle (degrees)Figure 3.Typical Variations of C D and C L with Aircraft Wing Flap Angle.Virginia Tech - Air Transportation Systems Laboratory 33

Flap Angle• Angle formed between the flap chord and the wing chord• Flaps are used to increase lift (but they increase drag too)during takeoff and landing maneuvers• Flaps reduce the stalling speed of the aircraftWing cross section(cruise condition)Wing cross section(landing and takeoff)Flap angleVirginia Tech - Air Transportation Systems Laboratory 34

Remarks About Aerodynamic Coefficients• An increase in flap angle increases both C L and C D .However, these increments are not linear andconsequently are more difficult to interpret• Increasing the flap angle * f increases and thusreduces the lift-off speed required for takeoff due to anincrease in the lifting force generated.( ) C LC D• Increments in flap angle increases the value of morerapidly which tends to reduce more drastically theacceleration of the aircraft on the runway thus increasingthe runway length necessary to reach the lift off speedVirginia Tech - Air Transportation Systems Laboratory 35

Remarks• The mass of the aircraft affects its acceleration(according to Newton’s second law).+ Larger takeoff masses produce corresponding increments in therunway length requirement.• The density of the air,!decreases with altitude+ Lower thrust generation capability at high airfield elevations+ The runway length increases as the field elevation increases+ The density also affects the second and third terms in Equation2.10 (less drag at higher altitude)Virginia Tech - Air Transportation Systems Laboratory 36

Aircraft Operational Practices (Takeoff)• At small flap settings (i.e., 5 or 10 degrees) the takeoffrunway length is increased due to small gains in C L (littleincrease in the lifting force). Useful for high-hot takeoffconditions.• At medium flap angle settings (15-25 degrees) the gainsin lift usually override those of the drag force. These arethe flap settings typically used for takeoff except underextremely abnormal airport environments such as highelevation, hot temperature airport conditions and highaircraft weights or a combination of both. Note that themaximum allowable takeoff weight (MTOW)increases as the takeoff flap setting is reduced.Virginia Tech - Air Transportation Systems Laboratory 37

• At large flap angles (> 25 degrees) C D is excessiveand the airplane requires unreasonable large takeoffrunway lengths. These flap settings are only used forlanding since pilots want to land at the lowest speedpossible thus reducing runway length.Virginia Tech - Air Transportation Systems Laboratory 38

Application of Equations of Motion to TakeoffRunway Length Requirements• Equation 22 describes the motion of an air vehicle as itaccelerates on a runway from an initial speed V o to a finalliftoff speed V lof• This equation can be integrated twice with respect totime to obtain the distance traveled from a starting pointto the point of liftoff• With a little more effort we could also predict thedistance required to clear a 35 ft. obstacle as required byFederal Aviation Regulations Part 25 or 23 that setsairworthiness criteria for aircraft in the U.S.• Airport engineers use tabular or graphical data derivedfrom this integration procedureVirginia Tech - Air Transportation Systems Laboratory 39

A Word on Stalling and Lift-off SpeedsThe stalling speed can be estimated from the basic liftequationL=1--!V 2 SC L2Under steady flight conditionsL+mgso,V=2mg------------!SC LdefinethenC Lmaxas the maximum attainable lift coefficient,V stall=2mg-----------------!SC LmaxVirginia Tech - Air Transportation Systems Laboratory 40

FAR Regulation PrinciplesRegulations (FAR 25) specify that:• Aircraft should lift off at 10% above the stalling speed( V lof )• Aircraft climb initially at 20% above the stalling speed( V 2 )• Aircraft speed during a regular approach be 30% abovethe stalling speed ( V app )• During takeoff aircraft should clear an imaginary 11 m(35 ft.) obstacle• During landing aircraft should cross the runwaythreshold 15 m (50 ft.) above ground)Virginia Tech - Air Transportation Systems Laboratory 41

These considerations are necessary to estimatetakeoff and landing distances (and thus size runwaylength)Virginia Tech - Air Transportation Systems Laboratory 42

Variation of Approach Speed with Aircraft MassAircraft Mass x 10 4Virginia Tech - Air Transportation Systems Laboratory 43

Integration of Acceleration EquationFirst obtain the aircraft speed at time t,1 1V t = --- ( T ( V, ! ) + --!V 2 S( C Lf roll – C D ) – mg f roll ) dtm 2V lof"V o(23)Now get the distance traveled,S tD"lofoS t = V t dt(24)Virginia Tech - Air Transportation Systems Laboratory 44

Sample Results (Boeing 727-200 Data)The following results apply to a medium-size transportaircraft32.5Sea Level1250 m22500 m1.510 10 20 30 40 50Roll Time (s)Figure 4.Sensitivity of Aircraft Acceleration vs. Field Elevation.Virginia Tech - Air Transportation Systems Laboratory 45

Aircraft Speed During Takeoff RollNote how speed increases at a nonlinear pace120100Sea Level1250 m80602500 m402000 5 10 15 20 25 30 35 40Roll Time (s)Figure 5.Sensitivity of Aircraft Speed vs. Field Elevation.Virginia Tech - Air Transportation Systems Laboratory 46

Distance Traveled During the Takeoff Roll35003000250020001250 mSea Level150010002500 m50000 10 20 30 40 50Roll Time (s)Figure 6.Lift-Off Distance vs. Field Elevation.Virginia Tech - Air Transportation Systems Laboratory 47

Takeoff Roll Distance vs. Aircraft Mass35003000250020002500 m. Field ElevationDTW = 60,000 kgDTW = 66,000 kg15001000500DTW = 72,000 kg00 5 10 15 20 25 30 35 40 45Roll Time (s)Figure 7.Lift-Off Distance vs. Aircraft Weight.Virginia Tech - Air Transportation Systems Laboratory 48

Regulatory Method to EstimateRunway Length at AirportsVirginia Tech - Air Transportation Systems Laboratory 49

General Procedure for Runway Length Estimation(Runway Length Components)Runways can have three basic components:• Full strength pavement (FS)• Clearways (CL)• Stopways (SW)Full strength pavement should support the full weight of the aircraftClearway is a prepared area are beyond FS clear of obstacles (maxslope is 1.5%) allowing the aircraft to climb safely to clear animaginary 11 m (35’ obstacle)Stopway is a paved surface that allows and aircraft overrun to takeplace without harming the vehicle structurally (cannot be used fortakeoff)Virginia Tech - Air Transportation Systems Laboratory 50

Runway ComponentsEach runway end will have to be considered individually for runwaylength analysisStopway (SW)Clearway (CL)Full Strenght Pavement (FS)Virginia Tech - Air Transportation Systems Laboratory 51

FAR Certification ProceduresFAR 25 (for turbojet and turbofan powered aircraft) consider threecases in the estimation of runway length performance• Normal takeoff (all engines working fine)• Engine-out takeoff condition- Continued takeoff- Aborted takeoff• LandingAll these cases consider stochastic variations in piloting technique(usually very large for landings and smaller for takeoffs)Regulations for piston aircraft do not include the normal takeoff case(an engine-out condition is more critical in piston-powered aircraft)Virginia Tech - Air Transportation Systems Laboratory 52

NomenclatureFL = field length (total amount of runway needed)FS = full strength pavement distanceCL = clearway distanceSW = stopway distanceLOD = lift off distanceTOR = takeoff runTOD = takeoff distanceLD = landing distanceSD = stopping distanceD35 = distance to clear an 11 m (35 ft.) obstacleVirginia Tech - Air Transportation Systems Laboratory 53

Landing Distance CaseThe landing distance should be 67% longer than the demonstrateddistance to stop an aircraftLarge landing roll variations exist among pilotsExample touchdown point variations (µ=400 m, ,=125 m for Boeing727-200 landing in Atlanta)LD = 1.667 * SDFS land = LDSD15 m (50 ft)LDVirginia Tech - Air Transportation Systems Laboratory 54

Normal Takeoff CaseThe Takeoff Distance (TOD) should be 115% longer than thedemonstrated Distance to Clear an 11m (35 ft.) obstacle (D35)CL nClearwayTOD n = 1.15 * D35 nLOD nD35 n11 m (35 ft)1.15 LOD nTOD n - 1.15 LOD nRelationshipsCL n = 1/2 (TOD-1.15 LOD)TOR n = TOD n - CL nFS n = TOR nFL n = FS n + CL nVirginia Tech - Air Transportation Systems Laboratory 55

Engine-Out Takeoff CaseDictated by two scenarios:Continued takeoff subcase• Actual distance to clear an imaginary 11 m (35 ft.) obstacle D35(with an engine-out)Aborted or rejected takeoff subcase• Distance to accelerate and stop (DAS)Note: no correction is applied due to the rare nature of engine-outconditions in practice for turbofan/turbojet powered aircraftVirginia Tech - Air Transportation Systems Laboratory 56

Engine-Out AnalysisV 1 = decision speedStopwayClearway11 m (35 ft)D35 eoD35 eo - LOD eoAborted TakeoffFS eo-a = DAS - SWFL eo-a = FS eo-a + SWLOD eoDASContinued TakeoffTOD eo = D35 eoCL eo = 1/2 (D35 eo -LOD eo )TOR eo = D35 eo - CL eoFS eo-c = TOR eoFL eo-c = FS eo-c + CL eoVirginia Tech - Air Transportation Systems Laboratory 57

Runway Length Procedures (AC 150/5325-4)Two different views of the problem:• For aircraft with MTOW up to 27,200 kg (60,000 lb.) use theaircraft grouping procedure- If MTOW is less than 5,670 kg use Figures 2-1 and 2-2 in FAA AC150/5325-4- If MTOW is > 5,670 kg but less than 27,200 kg use Figures 2-3 and 2-4 provided in Chapter 2 of the AC 150/5325-4• For aircraft whose MTOW is more than 27,200 kg (60,000 lb.) usethe critical aircraft concept- The critical aircraft is that one with the longest runway performancecharacteristics- This aircraft needs to be operated 250 times in the year from thatairportReview some examplesVirginia Tech - Air Transportation Systems Laboratory 58

Advisory Circular 150/5325-4Virginia Tech - Air Transportation Systems Laboratory 59

Contents of Advisory Circular 150/5325-4Be familiar with all items contained in FAA AC 150/5325-4• Chapter 1 - Introduction (background)• Chapter 2 - Runway length design based on aircraft groupings• Chapter 3 - Runway length design for specific aircraft- Aircraft performance curves- Aircraft performance tables• Chapter 4 - Design rationale- Airport temperature and elevation- Wind and runway surface- Difference in runway centerline elevations• NOTE: The runway length procedure using declared the distanceconcept is outlined in FAA AC 150/5300-13Virginia Tech - Air Transportation Systems Laboratory 60

Advisory Circular 150/5325-4The following examples illustrates the use of Figures 2-1 through 2-4in AC 150/5325-4• These procedures apply to a collection of aircraft (a group ofaircraft)• The process requires correction of runway length due to runwayslope and wet pavement conditions- Wet pavement correction is critical for landing aircraft- Runway gradient (or slope) is critical for departing aircraft- Apply the largest correction possibleVirginia Tech - Air Transportation Systems Laboratory 61

Groupings Method AC 150/5325-4 (Figure 2-1)Virginia Tech - Air Transportation Systems Laboratory 62

Example # 1 AC 150/5325-4Suppose we want to size a runway for a small general aviation airportall serving single engine aircraft (MTOW < 5,670 kg)The airport is to be located on plateau 915 m. above sea levelThe proposed airport site has a mean daily temperature of the hottestmonth of 24 o C (75 o F)Solution:Consulting Figure 2-1 in AC 150/5325-4 we obtain:RL = 4,600 ft. (or 1,403 m.)Virginia Tech - Air Transportation Systems Laboratory 63

Sample Calculations (FAA AC 150-5325-4 Individual Aircraft)Virginia Tech - Air Transportation Systems Laboratory 64

Runway Length Requirements Using AC/150-5325-4Outline of runway length requirement procedures from FAAAdvisory AC 150/5325-4.The method considers takeoff and landing phases as independentevents. This method already factors for a takeoff engine failure andwet runways in the solution. Three intermediate computations are:NOTE: the new advisory circular has eliminated a large numberof aircraft tables. The procedure advocated by the new advisorycircular is to use design charts provided by each aircraftmanufacturer for aircraft above 60,000 lb. (MTOW)I) Landing AnalysisEstimate the maximum allowable landing weight (MALW) at thegiven airport conditions.Compare this MALW with that of the desired weight (DTW).Virginia Tech - Air Transportation Systems Laboratory 65

a) If MALW > DTW use DTW in your computationsb) If MALW < DTW use MALW for in your computations.FAA method - Estimate the runway length required and use theshortest Landing Runway Length of all possible flap configurationsallowed.NOTE: This method is dangerous because if an engine failure occursafter takeoff and the pilot would want to come back and land theaircraft it would have to dump large amounts of fuel. Using the lowestflap setting provides a safer design and thus can be used instead.II) Takeoff Analysisa) Estimate the desired takeoff weight (DTW) for payload/range dataprovided.DTW = OEW + FW + PYLwhere:Virginia Tech - Air Transportation Systems Laboratory 66

OEW = Operating empty weightPYL = PayloadFW = Fuel weight (be sure to include reserve fuel)b) Estimate the maximum allowable takeoff weight for each flapsetting (allowable)NOTE: Discard those flap settings that do not allow a takeoff atDTW.c) For each flap setting/aircraft operation combination find referencefactors and required takeoff distances.NOTE: This procedure is executed in two steps.d) Select the shortest runway length from step (c) as this will be thepilot’s choice from an operational point of view since pilots wouldlike to depart using the shortest takeoff roll possible.e) Adjust the takeoff runway length as needed for effective gradient.Virginia Tech - Air Transportation Systems Laboratory 67

III) Landing and Takeoff Runway Length ReconciliationOnce the previous computations have been done select the longestrunway length of this method.Virginia Tech - Air Transportation Systems Laboratory 68

Sample Computation (Old Tabular Method)• Boeing 727-200 with Pratt and Whitney JTD8-15 engines• 20 o mean daily maximum temperature of the hottest month• 1000 m. field elevation• 1,200 statute mile stage length• 150 passengers• Maximum difference in elevation of runway centerlines is 30 ft.Virginia Tech - Air Transportation Systems Laboratory 69

I) Landing Analysisa) Estimate the Desired Takeoff Weight (DTW) as a preliminary stepDTW = OEW + FW + PAYOEW = 54,325 kg. (from table AC 150/5325-4)FW = (6.2 kg/km) (1200) (1.609) = 11,970.96 kg.PAY = (150 Pax/kg) (100 kg) = 15,000 kg.DTW = 54,325 + 15,000 + 11,970.96 + 0DTW = 81,296 kg. OK, below MTOW (maximum allowablestructural weight)For several flap settings (- f )the following numbers were obtained.Note that using a flap setting of 40 degrees will exceed the MALWfor this flap setting and thus 40 degrees is not recommended for alanding in case of an engine failure and return to the airfield. In thisVirginia Tech - Air Transportation Systems Laboratory 70

case the small flap setting is used because the aircraft is notcapable of landing at the departing airport even after all the fuel hasbeen expended.- f(Deg.)MALW(kg)ELWa (kg.)40 64,600 69,325*Runway(m)Check30 72,500 69,325 1,777.50 NOa.ELW stands for emergency landing weight(assuming all fuel is dumped after takeoff toreturn for a landing.Virginia Tech - Air Transportation Systems Laboratory 71

Simple interpolation for a flap angle of 30 degrees yields arunway length needed of 1,777 meters thus is rounded off to thenearest largest integer, say 1,800 m.Weight(kg.)72,000(72,500)74,000Elevation = 1000mts.1,765( ? )1,815R 0f = 30f= 1777.50 mR L0S30== 1,800 mVirginia Tech - Air Transportation Systems Laboratory 72

- f2520155II) Takeoff Analysisa) Recall the desired takeoff weight DTW = 82,396 kg.b) Verify all flap settings that will allow the aircraft to execute a safetakeoff.The following table illustrates all possible flap angle takeoffconfigurations for the Boeing 727-200.(Deg.) MTOW (kg) Check76,50081,80086,90089,400Note that the aircraft can use 3 flap settings at this elevation/payloadcombination. Therefore, 3 options for runway length requirementsneed to be investigated.NO aOKOKOKa.DTW is greater than the maximum allowable takeoff weight so do not consider.Virginia Tech - Air Transportation Systems Laboratory 73

c) Compute the takeoff runway length requirements for allpermissible flap angle configurations.- f (Deg.) “R” Factor RL TO (mts.) “Round Off” (m)2015570.6074.3084.502,6962,8623,3032,7002,9003,300- fd) The values of runway length were obtained using double linearinterpolation from each table (see AC 150/5325-4 for a samplecomputation). The optimum flap angle for these conditions is =20 0 and the one that should be used by pilots and airport engineers tosize the runway. the resulting runway length is 2,800 m.e) Correct for runway gradient. For a 30 ft. change in elevation isequivalent to 9.146 m. For a 2,700 m. runway this implies a 0.339%effective gradient Increase 10% for every 1% in effective gradientR LTO = ( 2,700) ( 1.0339) = 2,787.40rounding off we get 2,800 m of runway needed for takeoff.Virginia Tech - Air Transportation Systems Laboratory 74

III) Landing and Takeoff Runway LengthReconciliationSince the runway needed for takeoff is larger than that required toland select the takeoff runway length as this is the critical dimension.RL = 2,800 metersNOTE: This procedure accounts for wet runways so no furthercorrection is needed.Virginia Tech - Air Transportation Systems Laboratory 75

Runway Length Analysis usingAircraft Manufacturer Data forAirport DesignVirginia Tech - Air Transportation Systems Laboratory 76

Boeing 777-200 High Gross WeightEstimate the runway length to operate a Boeing 777-200 High GrossWeight (HGW) from Washington Dulles to Sao Paulo Guarulhosairport in Brasil (a stage length of 4,200 nm) at Mach .84.After consultation with the airline you learned that their B777s have agross weight of 592,000 lb. (HGW option) and have a standard threeclassseating arrangement.The airline has B 777-200 HGW withGeneral Electric engines. Assume hot day conditions.Virginia Tech - Air Transportation Systems Laboratory 77

IAD-BGR TripIAD4,200 nmBGRVirginia Tech - Air Transportation Systems Laboratory 78

Discussion of Computations1) Estimation of Desired Takeoff Weight (DTW)where:DTW = PYL + OEW + FWPYLis the payload carried (passengers and cargo)OEWis the operating empty weightFWis the fuel weight to be carried (usually includes reserve fuel)Note: PYL and OEW can be easily computedVirginia Tech - Air Transportation Systems Laboratory 79

Boeing 777-200 (GE Engines)Virginia Tech - Air Transportation Systems Laboratory 80

Computation of Payload and OEWJust look at the tables for the specific aircraft:OEW = 592,000 lb. = 138,100 kg.PYL = (305 passengers)(200 lb. /passengers) = 61,000 lb. = 27,727kg.OEW + PYL = 165,827 kg. = 364,820 lb.The fuel weight requires knowledge of fuel consumption rates duringthe flight. These can be extracted from the Payload-Range diagramnext.Virginia Tech - Air Transportation Systems Laboratory 81

Computation of Fuel WeightThis analysis requires information on fuel consumption for thisaircraft flying at a specific cruising condition. Use the payload rangediagram of the aircraft to estimate the average fuel consumption inthe trip.The Payload-Range Diagram is a composite plot that shows theoperational trade-off to carry fuel and payload.• As the payload carried increases the amount of fuel to conduct aflight might be decreased thus reducing the actual range (distance)of the mission• P-R diagrams consider operational weight limits such as MZFW,MTOW and MSPLVirginia Tech - Air Transportation Systems Laboratory 82

Range-Payload Diagram for Boeing 777-200(I)(II)(III)Virginia Tech - Air Transportation Systems Laboratory 83

Explanation of Payload-Range DiagramBoundariesFrom this diagram three corner points representing combinations ofrange and payload are labeled with roman numerals (I-III). Anexplanation of these points follows.Operating point (I) represents an operational point where theaircraft carries its maximum payload at departs the origin airport atmaximum takeoff gross weight (note the brake release gross weightboundary) of 297.6 metric tons.The corresponding range for condition (I) is a little less than 5,900nautical miles. Note that under this conditions the aircraft can carryits maximum useful payload limit of 56,900 kg (subtract 195,000 kg.from 138,100 kg. which is the OEW for this aircraft).Virginia Tech - Air Transportation Systems Laboratory 84

Payload-Range Diagrams ExplanationsOperating Point (II) illustrates a range-payload compromise whenthe fuel tanks of the aircraft are full (note the fuel capacity limitboundary).Under this condition the aircraft travels 8,600 nm but can only carry20,900 kg of payload (includes cargo and passengers), and a fuelcomplement of fuel (171,100 liters or 137,460 kg.).The total brake release gross weight is still 297.6 metric tons forcondition (II).Virginia Tech - Air Transportation Systems Laboratory 85

Payload-Range Diagrams ExplanationsOperating Point (III) represents the ferry range condition where theaircraft departs with maximum fuel on board and zero payload. Thiscondition is typically used when the aircraft is delivered to itscustomer (i.e., the airline) or when a non-critical malfunctionprecludes the carrying of passengers.This operating point would allow this aircraft to cover 9,600 nauticalmiles with 137,460 kg.of fuel on board and zero payload for a brakerelease gross weight of 275,560 kg. (137,460 + 138,100 kg.) or belowMTOW.Virginia Tech - Air Transportation Systems Laboratory 86

Limitations of P-R Diagram InformationA note of caution about payload range diagrams is that they onlyapply to a given set of flight conditions.For example, the previous Payload-Range diagram is only applicableto zero wind conditions, 0.84 Mach, standard day conditions (e.g.,standard atmosphere) and Air Transport Association (ATA) domesticfuel reserves (this implies enough fuel to fly 1.25 hours at economyspeed at the destination point).If any of these conditions changes so does the payload-rangediagram. Later on we examine the sensitivity of Range to variousother conditions.Virginia Tech - Air Transportation Systems Laboratory 87

Sample Payload Range DiagramsPayload RangeDiagrams (B747)Virginia Tech - Air Transportation Systems Laboratory 88

Payload Range Diagrams (B767)Virginia Tech - Air Transportation Systems Laboratory 89

Payload Range Diagrams (B777)Virginia Tech - Air Transportation Systems Laboratory 90

Payload Range Diagrams (B757)Virginia Tech - Air Transportation Systems Laboratory 91

Payload Range Diagrams (A320)Virginia Tech - Air Transportation Systems Laboratory 92

Payload Range Dagrams (A330)Virginia Tech - Air Transportation Systems Laboratory 93

Payload Range Dagrams (A380)Virginia Tech - Air Transportation Systems Laboratory 94

Back to Our Problem!Our critical aircraft flying (B777-200 HGW option) would fly 4,200nm with full passengers.• From the P-R diagram read off the DTW as ~230,000 kg.• OEW + PYL = 165,827 kg.• The amount of fuel carried for the trip would be:FW = DTW - OEW - PYLFW = 64,173 kg.Since the P-R diagram tells us the DTW we could even skip the fuelcomputation and use DTW in our runway length analysis directly(see following pages).Virginia Tech - Air Transportation Systems Laboratory 95

Presentation of Runway Length InformationFor the aircraft in question we have two sets of curves available tocompute runway length:• Takeoff• LandingThese curves apply to specific airfield conditions so you shouldalways use good judgement in the analysis. Typically two sets ofcurves are presented by Boeing:• Standard day conditions• Standard day + .T conditionswhere .T represents some increment from standard day conditions(typically 15 o ).Virginia Tech - Air Transportation Systems Laboratory 96

Boeing 777-200 HGW Takeoff PerformanceVirginia Tech - Air Transportation Systems Laboratory 97

Boeing 777-200 HGW Takeoff PerformanceVirginia Tech - Air Transportation Systems Laboratory 98

Takeoff Runway Length AnalysisFrom the performance chart we conclude:• RL takeoff = 1,950 m.• Optimum flap setting = 20 degrees for takeoff (see flap settinglines in the diagram)• DTW is way below the maximum capability for this aircraft.Virginia Tech - Air Transportation Systems Laboratory 99

Landing AnalysisThis analysis is similar to that performed under FAA AC 150/5325-4.Consider an emergency situation and compute the landing weight atthe departing airport.DTW = 230,000 kg.The maximum allowable landing weight for the aircraft is:MALW = 208,700 kg.Since DTW > MALW use MALW in the rest of the calculations.RL land = 1,850 m.Virginia Tech - Air Transportation Systems Laboratory 100

Boeing 777-200 HGW Landing PerformanceVirginia Tech - Air Transportation Systems Laboratory 101

Reconcile Takeoff and Landing CasesSelect worst case scenario and use that as runway length requirement.RL takeoff = 1,950 m.RL land = 1,850 m.Takeoff dominates so use the RL takeoff as the design number.Virginia Tech - Air Transportation Systems Laboratory 102

Observe Some Trends from Takeoff Curves• If DTW increases the RL values increase non-linearly (explainusing the fundamental aircraft acceleration equation)• As field elevation increases (pressure altitude) the RL valuesincrease as well (temperature effect on air density)• As DTW and field elevation increase the optimum flap setting fortakeoff decreases- This is consistent with our knowledge of C d and C L . Hot and highairfield elevations require very low flap settings during takeoff toreduce the drag of the aircraft.• High airfield elevations (and large to moderate DTWs) could hit atire speed limit boundary. Aircraft tires are certified to this limitand thus an airline would never dare to depart beyond this physicalboundary.Virginia Tech - Air Transportation Systems Laboratory 103

Other Considerations in Runway Length Analysis• So far the runway length analysis assumed that we haveplenty of land to build the runway.• There are many practical situations when this is not true.• Under land limited conditions use the Declared DistanceConcept for runway length estimation described inAppendix 14 of FAA AC 150/5300-13.• The application of declared distance is done on a caseby-casebasis and should be part of the Airport LayoutPlan (ALP)Virginia Tech - Air Transportation Systems Laboratory 104

Basic ConceptAccording to the FAA “by treating the airplane's runway performancedistances independently, provides an alternative airport designmethodology by declaring distances to satisfy the airplane's takeoffrun, takeoff distance, accelerate-stop distance, and landingrequirements”.Declared distances are:• Takeoff Run Available (TORA)• Takeoff Distance Available (TODA)• Accelerate to Stop Distance Available (ASDA)• Landing Distance Available (LDA).Virginia Tech - Air Transportation Systems Laboratory 105

Some Runway Design TermsThe following are some definitions of terms employed in the declareddistance concept analysis.Runway Safety Area (RSA) -Runway Protection Zone (RPZ)Runway Object Free Area (ROFA)These critical runway areas are defined in Chapters 2 and 3 of theFAA AC 150/5300-13Virginia Tech - Air Transportation Systems Laboratory 106

Runway Protection Zone (RPZ)Trapezoidal shape area at the end of every runway and centered withthe runway centerlineTwo components make up the PRZ:• Controlled activity area• A portion of the Runway Object Free Area (ROFA)According to the FAA AC 5300-13 the function of the RPZ is to“enhance the protection of people and property on the ground.”• The airport controls the RPZ• RPZ are clear of incompatible objects• Ideally the control is exercised by buying the land of the RPZVirginia Tech - Air Transportation Systems Laboratory 107

Sketch of RPZVirginia Tech - Air Transportation Systems Laboratory 108

RPZ Dimensions (Table 2.4 in AC 5300-13)Virginia Tech - Air Transportation Systems Laboratory 109

Runway Object Free Area (ROFA or OFA)The runway object free area (OFA) is centered on the runwaycenterline and extends beyond the runway thresholds.Clearing standards:• no ground objects protruding above the runway safety area edgeelevation• Navigation equipment can be located inside OFA• Maneuvering aircraft OK• No parked aircraft or agricultural operations are allowed insideOFACheck out Tables 3.1 through 3.3 for OFA dimensional standards.Virginia Tech - Air Transportation Systems Laboratory 110

OFA Dimensions (Approach Cat. A/B and 3/4 mile)Virginia Tech - Air Transportation Systems Laboratory 111

OFA Dimensions (Approach Cat. C and D)Virginia Tech - Air Transportation Systems Laboratory 112

Runway Safety Area (RSA)Another area surrounding the runway that should be clear of objects,except for objects that need to be located in the runway or taxiwaysafety area because of their function (i.e., navigation equipment)• Objects higher than 3 inches (7.6 cm) should be mounted onfrangible structures• Manholes should be constructed at grade (or 7.6 cm. in height atmost)• No underground fuel storage facilities are allowed inside RSA (ortaxiway safety areas)Check out Tables 3.1 through 3.3 for RSA dimensional standards.Virginia Tech - Air Transportation Systems Laboratory 113

Example Runway Design for Boeing 777-200Assume a precision approach is needed for IFR conditionsRPZ =>• W 1 = 1,000 ft.• W 2 = 1,750 ft.• L = 2,500 ft.OFA• 800 ft. width and 1,000 ft. beyond runway endRSA• 500 ft. width and 1,000 ft. beyond runway endVirginia Tech - Air Transportation Systems Laboratory 114

Example Runway Design for Boeing 777-200OFARPZRunwayRSAVirginia Tech - Air Transportation Systems Laboratory 115

Climb PerformanceMany airport and airspace simulation models employsimplified algorithms to estimate aircraft climbperformance in the terminal area.TL(DmgVirginia Tech - Air Transportation Systems Laboratory 116

Basic Climb Performance AnalysisThe basic equations of motion along the climbing flightpath and normal to the flight path of an air vehicle are:dVm dt=T– D – mg sin((25)d(m V L – mg cos(dt(26)=Vwhere: m is the vehicle mass, is the airspeed, T and D are thetractive and drag forces, respectively; ( is the flight path angle. L isthe lift force and mg cos(is the gravitational component normal to theflight path.Virginia Tech - Air Transportation Systems Laboratory 117

Climb Performance Model SimplificationsFor small ( (flight path angle):sin(=T – D------------ –mg1dV--g dtwhere: the first term in the RHS accounts for possible changes inthe potential state of the vehicle (i.e., climb ability) and thesecond terms is the acceleration capability of the aircraft whileclimbing. Further algebraic manipulation yields,V sin(dh V[ T – D]= = --------------------- –dt mgVdV--g dtwhere: dh dt is the rate of climb and V is the true airspeed. Note thatif one neglects the second term (acceleration factor) assuming smallchanges in V as the vehicle climbs one can easily estimate the rate ofthe climb of the vehicle for a prescribed climb schedule.(27)Virginia Tech - Air Transportation Systems Laboratory 118

Incorporation of a Parabolic Drag Polar ModelLet lift and drag be expressed in the simple parabolicform,L=1--!SC L V 22(28)D=1--!SC D V 22where: C L and C D are the lift and drag coefficients (nondimensional),V is the airspeed, S is the wing area (reference area) and ! is thedensity of the air surrounding the vehicle.(29)Virginia Tech - Air Transportation Systems Laboratory 119

Final Derivation of Climb Rate ExpressionThe functional form of the lift and drag coefficients (simplest form is,C L,C D) in its2CC D = C D0 + C Di = C LD0 + -------------/ARe(30)C L=2mg-----------!SV 2(31)where: C D0 is the zero lift drag coefficient, and the second drag termaccounts for drag due to lift generation (i.e., induced drag).Then therate of climb function becomes,dhdt=1CV T (!,V)--!V 2 S C D0 ( M)L2 ( M,V)– 2 4 + --------------------- 352 0 /ARe 1--------------------------------------------------------------------------------------------------------mg(32)Virginia Tech - Air Transportation Systems Laboratory 120

Mathematical Approximation for AircraftThrust and DragThrust and drag are two fundamental variables extracted fromwind-tunnel and flight tests.Drag CoefficientC D (total drag coefficient)C D0C DiThrust (KiloNewtons)200100Low SpeedBoundaryh = 0 m.h = 3000 m.High Speed Boundaryh = 6000 m.h = 9000 m.h = 12000 m.0.4 0.5 0.6 0.7 0.8Mach Number (M true )0.90.4 0.5 0.6 0.7 0.8 0.9Mach Number (M true )Virginia Tech - Air Transportation Systems Laboratory 121

Modeling Aircraft Thrust• Thrust is a function of aircraft speed and altitude• Basic thermodynamics dictates that thrust is the netresult of the speed differential between inlet and outlet ofthe engineAir Flowp oTurbinep eCompressorCombustionChamberV oT = f(V f - V o ) and f(p o -p e )V fVirginia Tech - Air Transportation Systems Laboratory 122

Basic Propulsion Forces Modeling Ideas• Thrust is a function of altitude (or density)+ A general thrust lapse function can be obtained using real enginedata (empirical data)• Thrust is a function of aircraft speed+ A more complex function can be obtained using real engine data(empirical data)+ The thrust losses during takeoff troll are significant as illustratedin the figures below• Thrust functions are provided by the enginemanufacturer in terms of tables (thrust vs altitude andmach number and thrust specific fuel consumption vsaltitude and mach number)Virginia Tech - Air Transportation Systems Laboratory 123

Sample Thrust Variations (PW JT9D Engine)Observe the large variations of thrust with respect toaircraft altitudeMaximum Continuous ThrustVirginia Tech - Air Transportation Systems Laboratory 124

Modeling Thrust Using a Thrust Lapse GradientA simple way to model thrust as a function of altitude ispresented below:!T h Th0 ----# % $& m=! 0(33)where:T h is the thrust at altitude, T 0is the sea level static thrust,! h ! 0and are the density values at altitude and at sealevel, respectivelymis an empirical coefficient derived from real dataVirginia Tech - Air Transportation Systems Laboratory 125

Takeoff Thrust Variations with SpeedRolls-Royce RB211-535E4EngineThrust ratio = T v / T staticSource: Mair and Birdsall (1992)Virginia Tech - Air Transportation Systems Laboratory 126

Variations of Climb TSFC (PW JT9D Engine)Virginia Tech - Air Transportation Systems Laboratory 127

Variations of Cruise TSFC (PW JT9D Engine)Virginia Tech - Air Transportation Systems Laboratory 128

Sample Climb Trajectory ResultsNumerical integration of equation (30) for a given flight speedschedule (speed time history) yields the following climb profiles.30000Four engine, turbofan-powered aircraftBoeing 747-200B Aircraft DataTakeoff Weight = 750,000 lbsClimb Profile25000ISAISA+20Altitude (ft.)200001500010000Speed Schedule250 KIAS < 10 kft300 KIAS > 10 kft500000255075100125150175200225250Distance Traveled (n.m.)Virginia Tech - Air Transportation Systems Laboratory 129

Typical Rate of Climb EnvelopeIterative analysis of the rate of climb equation yields thefollowing results across the complete flight envelope.Rate of Climb (m/min.)1000600200Optimum Rate of Climb Pointsh = 0 m.h = 3,000 m.h = 6,000 m.h = 9,000 m.h = 12,000 m.0.3 0.4 0.5 0.6 0.7 0.8 0.9True Mach NumberVirginia Tech - Air Transportation Systems Laboratory 130