AE 451 Aeronautical Engineering Design IEstimation of Critical Performance Parameters

Prof. Dr. Serkan Özgen

Dept. Aerospace Engineering

Fall 2015

Airfoil selection

• The airfoil effects the cruise speed, takeoff and landingdistances, stall speed, handling qualities and overallaerodynamic efficiency during all phases of flight.

• The airfoil may be separated into:

– Thickness distribution, influences profile drag,

– Zero-thickness camber line, influences lift and drag due to lift.

• Upper surface of an airfoil or wing produces roughly 2/3 of total lift.

• Zero-lift angle of attack is roughly equal to the percentcamber of the airfoil (in deg).

2

Design lift coefficient

• This is the lift coefficient at which the airfoil has thebest L/D.

• The airplane should be designed such that it fliesthe design mission at ornear the design lift coefficient to maximize theaerodynamic efficiency.

3

Airfoil geometry

4

Stall

• Some airfoils show a gradual reduction in lift during stall, while othersshow a violent loss of lift with a rapid change in pitching moment.

5

Stall

• Thick airfoils (round leading edge, t/c>14%) stall starting from thetrailing edge. At around α=10o, the boundary-layer begins toseparate starting at the tariling edge and moving forward as theangle of attack is further increased. The loss of lift is gradual, pitching moment does not change significantly.

• Moderately thick airfoils (6%<t/c<14%) stall from the leadingedge. Flow separates over the nose at a very low angle of attack, but immediately reattaches, so the effect is initially small. At somehigher α, the flow does not reattach and the airfoil stalls almostimmediately. Lift and pitching moment vary violently.

6

Stall

• Thin airfoils (t/c<6%) stall from the leading edge and the flowreattaches immediately. As α is increased, the bubble contnues tostretch towards the trailing edge as the angle of attack is increased. At α where the bubble stretches all the way to the trailing edge, cl,max is reached. Beyond that α, the flow is separated over theentire airfoil, so stall occurs. The loss of lift is smooth, but largechanges in pitching moment are observed.

• Twisting the wing such that the tip airfoils have a reduced angle of attck compared to the root (washout) can cause the wing to stall at the root first.

7

Stall

• Different airfoil sections may be used at the root and the tip, witha tip airfoil that stalls at a higher angle of attack. This produces goodflow over the ailerons for roll control (aileron authority) at an angleof attack where the root has stalled.

• Stall characteristics for thinner airfoils may be improved withleading edge devices like slots, slats, leading edge flaps.

• Wing stall is directly related to airfoil stall only for high aspectratio, unswept wings. For low aspect ratio, swept wings, 3-D effectsdominate stall characteristics and airfoil stall characteristics can be ignored.

• Horizontal tail or canard size is directly related to the magnitudeof the wing pitching moment to be balanced.

8

Thickness ratio

• Airfoil thickness ratio has a direct effect on drag, maximum lift, stall characteristics and structural weight.

• A wing with a fairly high AR, moderate sweep, large nose radiusprovides a higher stall angle and a higher CL,max.

• For a wing with low AR, swept wings, a sharper leading edgeprovides greater CL,max due to the formation of vortices behind theleading edge.

• Wing structural weight ~1/ 𝑡/𝑐

•halving the thickness ratio increases the empty weight of theairplane by 6%.

9

Thickness ratio

10

Thickness ratio

11

Thickness ratio

12

Thickness ratio• For initial selection of the thickness ratio, historical trends can be

used. Supercritical airfoils can be chosen 10% thicker.

13

Thickness ratio

• In subsonic airplanes, the root airfoil can be 20-60% thicker thanthe tip airfoil without effecting the drag due to fuselage effects. This thicker root should not extend beyond 30% of span.

• This results in a structural weight reduction as well as morevolume for fuel and landing gear.

• Each airfoil is designed for a certain Reynolds number. Use of an airfoil at greatly different Reynolds numbers produce sectioncharacteristics much different than expected. This is especially truefor laminar flow airfoils.

14

Wing geometry

• The reference or trapezoidalwing is the basic geometryto begin the layout.

• The leading edge sweep is important for supersonicflight. In order to reducedrag, it is important tosweep the wing leadingedge behind the Machcone.

15

Wing geometry

• The quarter chord sweep is related to the subsonic flightsince the lift produced by a wing is proportional to thecomponent of thefreestream velocity vectorperpendicular to the quarterchord line.

16

Wing geometry

• For a complete trapezoidalwing, the aerodynamiccenter is at the quarterchord point of the meanaerodynamic chord.

• In supersonic flow, theaerodynamic center movesapproximately back to 40% of the mean aerodynamicchord.

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Aspect ratio

• For finite aspect ratio wing, tip vortices lower the pressuredifference between the upper and lower surfaces. This reduces thelift near the wingtip.

• The tip vortices reduce the effective angle of attack of the wing, more so at the wingtips.

• A high aspect ratio wing has wingtips further apart compared to an equal area wing with low AR. Therefore, the amount of wingeffected by the wingtip is less for a high aspect ratio wing and thestrength of the wingtip vortex is reduced.

loss of lift and induced drag is less for high aspect ratio wing.

𝐿/𝐷)𝑚𝑎𝑥~ 𝐴𝑅

𝑊𝑤𝑖𝑛𝑔~ 𝐴𝑅

18

Lift to drag ratio

• L/D is a measure of overall aerodynamic efficiency.

– Subsonic speeds: L/D=L/D(wing span,wetted area)

– Supersonic speeds: L/D=L/D(wing span, wetted area, Mach)

• Drag components at subsonic speeds:

– Induced drag or drag due to lift is a function of the wing span

– Parasite drag or zero lift drag is a function of total surface areaexposed to air

L/D is a function of “wetted aspect ratio”=b2/Swet

19

Wetted aspect ratio

20

Aspect ratio

• Due to reduced effectiveangle of attack of thewingtips, a low AR wing willstall at a higher angle of attack compared to a highaspect ratio wing.

• This is why tails have low AR compared to wings.

• This ensures adequatecontrol even when the wingstalls.

21

Aspect ratio

22

Wing sweep

• Wing sweep is used primarily to reduce the adverse effects of transonic and supersonic flow.

• The leading edge sweep must be such that it is behind the Machcone.

• Theoretically, the shock wave formation on a swept wing is determined by the air velocity in a direction perpendicular to theleading edge of the wing.

• In the transonic flow regime, wing sweep is determined by therequirement for a high critical Mach number, Mcrit. This requiressubsonic airflow over the airfoil measured perpendicular to theleading edge, thus a swept wing.

23

Wing sweep

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Wing sweep• The exact wing sweep selection depends on the selected airfoil,

thickness ratio, taper ratio, etc.

25

Wing sweep

• Wing sweep improves lateral stability (roll). A swept wing has a natural dihedral effect 10o sweep ≈ 1o dihedral.

• It may be necessary to use zero or negative dihedral on a sweptwing in order to avoid a stiff airplane.

• The wing sweep and aspect ratio together have a strong effect on the pitch-up characteristics

• Pitch-up is a highly undesirable tendency of some aircraft near thestall angle to suddenly and uncontrollably increase the angle of attack.

26

Wing sweep

27

Taper ratio

• An elliptical wing willproduce the lowest induceddrag but is difficult and morecostly to produce.

• A tapered wing is almostequally efficient in terms of induced drag.

28

Taper ratio

•There are two competing considerations:

― Smaller the taper ratio, lighter the wing structure. If λ is less, more lift will be produced at the wingroot center of pressure moves towards the wing root and the moment armfrom the wingroot to the center of pressure decreases andthe bending moment at the root decreasing the need forheavier structure.

― Wings with low λ show undesirable stall characteristics. Separation at the root has two advantages: Turbulent flow trailing downstream from the root causes buffeting as

it flows over the tail, giving a strong stall warning to the pilot.

The wingtips have attached flow so the ailerons will be more efficient.

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Taper ratio

• Low sweep wing: typically have taper ratios around 0.4-0.5.

• High sweep wings: have taper ratios around 0.2-0.3.

• A swept wing will direct the air outward towards the wingtips.

• This loads up the wingtips creating more lift there compared to an equivalent unswept wing.

• In order to restore the elliptic lift distribution, it is necessary toreduce the taper ratio.

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Taper ratio

31

Twist

• Wing twist is used to prevent tip stall and to revise the lift distribution to approximate an elliptical one.

• Typically, wings are twisted between 0o-5o.

• Geometric twist is the actual change in airfoil angle of incidencemeasured with respect to the root airfoil.

• A wing with a tip airfoil at a negative angle compared to the rootairfoil has «washout». For such a wing, the root will stall before thetip, which improves aileron control at high α and tends to reducewing rock.

• If a wing has linear twist, the twist angle changes in proportion tothe distance from the wingroot.

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Twist

• Aerodynamic twist = 𝛼𝐿=0,𝑟𝑜𝑜𝑡 − 𝛼𝐿=0,𝑡𝑖𝑝

• Optimizing the lift distribution by twisting the wing will be validonly for one geometric angle of attack.

• The more twist required to produce an elliptic lift distribution at the design lift coefficient, the worse the wing will perform at otherlift coefficients.

• For this reason, high amounts of twist (>5o) should be avoided.

• Typically, 3o twist provides adequate stall characteristics.

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Thrust-to-weight ratio and wing loading

• Thrust-to-weight ratio (T/W) and wing loading (W/S) are the twomost important parameters effecting aircraft performance. Optimization of these parameters forms a major part of conceptual design.

• Wing loading and thrust-to-weight ratio are not independent of each other. Takeoff distance, maximum velocity, rate of climb andmaximum load factor are dependent on both T/W and W/S.

• A good approach would be to guess one parameter and calculatethe other to meet various performance characteristics.

• Most of the time T/W appears as the guessed parameter becausestatistical norms are more meaningful and scatter is less amongairplanes of a given class.

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Thrust-to-weight ratio

• For propeller-driven airplanes, P/W or W/P (power loading) is a more convenient definition.

𝑇

𝑊=𝜂𝑝

𝑉∞

𝑃

𝑊=550𝜂𝑝

𝑉∞

ℎ𝑝

𝑊

• For jet-powered airplanes, 𝑇 𝑊𝑜 = 𝑎𝑀𝑚𝑎𝑥𝐶 ,

• For propeller-powered airplanes, 𝑃 𝑊𝑜 = 𝑎 𝑉𝑚𝑎𝑥𝐶

35

Thrust- and power-to weight ratio

36

Thrust- and power-to weight ratio

37

Thrust-to-weight ratio

• T/W directly effects the performance of an airplane. An airplanewith a high T/W will:

― Accelerate more quickly,

― Climb more rapidly,

― Reach a higher maximum speed,

― Sustain a higher turn rate,

― Consume more fuel, which will increase the takeoff gross weight.

• T/W varies throughout the flight as fuel is consumed.

• Engine thrust varies with altitude and velocity.

• T/W usually refers to sea-level static thrust (𝑉∞ = 0), at designtakeoff gross weight 𝑊𝑜 and maximum thrust setting.

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Thrust matching

𝑇

𝑊 𝑐𝑟𝑢𝑖𝑠𝑒=

1

𝐿 𝐷 𝑚𝑎𝑥

• Weight of the airplane at the beginning of the cruise is the takeoffweight minus the fuel burned during takeoff and climb.

• Thrust during cruise is also different from the takeoff value.

• For jet aircraft, optimum cruise altitude: 30 000-40 000 ft (bestspecific fuel consumption),

• For jet aircraft, optimum thrust setting: 70-100% of the continuousnon-ab thrust.

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Thrust matching

• High by-pass ratio turbofans, optimum thrust=20-25% takeoff thrust.

• Low by-pass ratio turbofans, optimum thrust=40-70% takeoff thrust.

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Thrust matching

• Piston-powered airplanes, optimum power setting=75% takeoffpower.

• Turboprop powered airplanes, optimum power setting=60-80% takeoff power.

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Wing loading

• Wing loading effects:― Stall speed,

― Climb rate,

― Takeoff and landingdistances,

― Maneuvrability, etc.

• Wing loading and thrust-to-weight ratio must be optimized together .

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Wing loading – stall speed

𝑊 = 𝐿 =1

2𝜌∞𝑉𝑠𝑡𝑎𝑙𝑙

2 𝐶𝐿,𝑚𝑎𝑥𝑆 ⇒ 𝑊 𝑆 =1

2𝜌∞𝑉𝑠𝑡𝑎𝑙𝑙

2 𝐶𝐿,𝑚𝑎𝑥

• Maximum lift coefficient depends on:

― Wing geometry,

― Airfoil shape,

― Flap geometry and span,

― Leading edge slat or flap geometry,

― Reynolds number, texture and interference with other components of theairplane.

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Wing loading – stall speed

• During landing, flaps will be deployed to maximum,

• During takeoff, they will be partially deployed.

𝐶𝐿,𝑚𝑎𝑥,𝑡𝑜 ≈ 0.8𝐶𝐿,𝑚𝑎𝑥,𝑙𝑎𝑛𝑑𝑖𝑛𝑔

• For AR>5, 𝐶𝐿,𝑚𝑎𝑥 ≈ 0.9𝑐𝑙,𝑚𝑎𝑥

44

Wing loading – takeoff distance

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Wing loading – takeoff distance

• Ground roll: actual distance travelled before the wheels leave theground, 𝑉𝐿𝑂 = 1.1𝑉𝑠𝑡𝑎𝑙𝑙 .

• Obstacle clearing distance: distance required from brake releaseuntil the airplane has reached some specified altitude, hOB=50 ft(military and small civilian airplanes), hOB=35 ft for civiliantransport airplanes.

• Decision speed: the speed at which the distance to stop after an engine failure exactly equals the distance to continue the takeoffon the remaining engines.

• Balanced field length: is the distance required to takeoff and clearthe specified obstacle when one engine fails exactly at the decisionspeed.

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Wing loading – takeoff distance• Factors effecting takeoff distance:

― T/W and W/S,

― Aerodynamic drag,

― Rolling resistance.

• Takeoff parameter:

𝑇𝑂𝑃 =𝑊/𝑆

𝜎𝐶𝐿,𝑡𝑜 𝑇 𝑊, jet engines,

𝑇𝑂𝑃 =𝑊/𝑆

𝜎𝐶𝐿,𝑡𝑜 𝑏ℎ𝑝 𝑊, propeller engines.

• Density ratio, 𝜎 =𝜌

𝜌𝑆𝐿, 𝐶𝐿,𝑡𝑜 =

𝐶𝐿,𝑚𝑎𝑥

1.21𝑉𝐿𝑂 = 1.1𝑉𝑠𝑡𝑎𝑙𝑙

• Lift coefficient during takeoff may be limited by the maximum taildown angle.

47

Wing loading – takeoff distance

• Jet-powered airplanes:𝑊

𝑆= 𝑇𝑂𝑃 𝜎𝐶𝐿,𝑡𝑜 𝑇/𝑊

• Propeller-poweredairplanes:𝑊

𝑆= 𝑇𝑂𝑃 𝜎𝐶𝐿,𝑡𝑜 ℎ𝑝/𝑊

48

Wing loading – landing distance

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Wing loading – landing distance

• Landing ground roll: actual distance the aircraft travels from thetime the wheels touch the runway, to the time the aircraft comesto a complete stop.

• Landing field length: includes clearing a 50 ft obstacle while theaircraft is still at approach speed.

• For military aircraft, 𝑉𝑎𝑝𝑝 = 1.2𝑉𝑠𝑡𝑎𝑙𝑙,

• For civilian aircraft, 𝑉𝑎𝑝𝑝 = 1.3𝑉𝑠𝑡𝑎𝑙𝑙 .

𝑠𝑔 = 80𝑊

𝑆

1

𝜎𝐶𝐿,𝑚𝑎𝑥, 𝑠 = 𝑠𝑔 + 𝑠𝑎 .

sa =1000 ft (airliners, 3o glideslope)

=600 ft (general aviation, power-off approach)

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Wing loading – landing distance

• If the aircraft is equipped with a thrust reverser or reversible pitchpropellers, multiply the ground portion of the distance by 0.66.

• For commercial aircraft, multiply total landing distance by 1.67 toprovide the required safety margin.

• For propeller-powered airplanes, Wlanding=0.85Wo,

• For jet aircraft, Wlanding=0.85 Wo.

• Military requirements, Wlanding=We+Wc+Wp+0.5Wf .

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Wing loading – cruise

• For propeller aircraft, range is maximized when L/D=L/D)max orwhen induced drag = parasite drag.

𝑞∞𝑆𝐶𝐷𝑜 = 𝑞∞𝑆𝐾𝐶𝐿2 = 𝑞∞𝑆

𝐶𝐿2

𝜋𝐴𝑅𝑒

e: Oswald span efficiency factor is a function of taper ratio andaspect ratio.

𝑊 = 𝐿 =1

2𝜌∞𝑉∞

2𝐶𝐿𝑆 ⇒ 𝐶𝐿 =𝑊/𝑆

𝑞∞Substituting above yields:

𝑊 𝑆 = 𝑞∞ 𝜋𝐴𝑅𝑒𝐶𝐷𝑜

52

Wing loading – cruise

• For jet aircraft, range is maximized when L/D=0.866L/D)max orwhen parasite drag = 3*induced drag.

𝑞∞𝑆𝐶𝐷𝑜 = 3𝑞∞𝑆𝐾𝐶𝐿2 = 3𝑞∞𝑆

𝐶𝐿2

𝜋𝐴𝑅𝑒

e: Oswald span efficiency factor is a function of taper ratio andaspect ratio.

𝑊 = 𝐿 =1

2𝜌∞𝑉∞

2𝐶𝐿𝑆 ⇒ 𝐶𝐿 =𝑊/𝑆

𝑞∞Substituting above yields:

𝑊 𝑆 = 𝑞∞𝜋𝐴𝑅𝑒𝐶𝐷𝑜

3

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Wing loading – loiter

• For propeller aircraft, endurance is maximized whenL/D=0.866L/D)max or when induced drag = 3*parasite drag.

3𝑞∞𝑆𝐶𝐷𝑜 = 𝑞∞𝑆𝐾𝐶𝐿2 = 𝑞∞𝑆

𝐶𝐿2

𝜋𝐴𝑅𝑒

e: Oswald span efficiency factor is a function of taper ratio andaspect ratio.

𝑊 = 𝐿 =1

2𝜌∞𝑉∞

2𝐶𝐿𝑆 ⇒ 𝐶𝐿 =𝑊/𝑆

𝑞∞Substituting above yields:

𝑊 𝑆 = 𝑞∞ 3𝜋𝐴𝑅𝑒𝐶𝐷𝑜

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Wing loading – loiter

• For jet aircraft, endurance is maximized when L/D=L/D)max or wheninduced drag = parasite drag.

𝑞∞𝑆𝐶𝐷𝑜 = 𝑞∞𝑆𝐾𝐶𝐿2 = 𝑞∞𝑆

𝐶𝐿2

𝜋𝐴𝑅𝑒

e: Oswald span efficiency factor is a function of taper ratio andaspect ratio.

𝑊 = 𝐿 =1

2𝜌∞𝑉∞

2𝐶𝐿𝑆 ⇒ 𝐶𝐿 =𝑊/𝑆

𝑞∞Substituting above yields:

𝑊 𝑆 = 𝑞∞ 𝜋𝐴𝑅𝑒𝐶𝐷𝑜

55

Oswald span efficiency factor

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Wing loading - loiter

• For initial estimates:

• Piston-props: Vloiter=80-120 knots

• Jet airplanes: Vloiter=150-200 knots

• Turboprops: Vloiter=150-200 knots

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Estimation of CDo

𝐶𝐷𝑜 =𝑆𝑤𝑒𝑡𝑆

𝐶𝑓𝑒

• Cfe: equivalent skin frictioncoefficient is a function of the Reynolds number, Re.

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Wing loading – instantaneous turn

• An aircraft designed for air-to-air combat (dogfight) must be capable of high turn rate.

• An aircraft with a higher turn rate will be able to maneuver behindthe other. A turn rate superiority of 2o/s is significant.

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Wing loading – instantaneous turn

• There are two important turn rates:

― Sustained turn: turn rate at which the thrust of the aircraft is just sufficientto maintain velocity and altitude in the turn (T=D); thrust available is thelimit. For a level turn:

𝜓 =𝑔 𝑛2−1

𝑉∞, 𝑛 =

𝐿

𝑊=

1

2𝜌∞𝑉∞

2 𝑆

𝑊𝐶𝐿

― Instantaneous turn is limited by the maximum lift, stall or CL,max is the limit.

• The speed at which the maximum lift is equal to the allowablestructural load factor is the «corner speed» and provides themaximum turn rate for a given altitude.

• Modern fighters have a corner speed around 300-350 knots.

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Wing loading – instantaneous turn

𝑛 = 𝜓𝑉∞𝑔

2

+ 1

Solving for W/S:

𝑊 𝑆 =1

2𝜌∞𝑉∞

2𝐶𝐿,𝑚𝑎𝑥

𝑛

CL,max≈0.6-0.8 for a fighter with a simple trailing edge flap,

CL,max≈1.0-1.5 for a fighter with leading and trailing edge flaps.

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Wing loading – sustained turn

• An aircraft will probably not be able to maintain speed andaltitude while turning at the maxium instantaneous turn rate.

• Sustained turn rate is usually specified in terms of the maximumload factor at a given flight condition that the aircraft can sustain, e.g. 4-5g at M=0.9 at 30000 ft.

𝑇 = 𝐷, 𝐿 = 𝑛𝑊 ⇒ 𝑛 =𝑇

𝑊

𝐿

𝐷

• Load factor in a sustained turn increases when T/W and L/D increases.

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Wing loading – sustained turn

• Equating thrust available and drag yields:

𝑊 𝑆 =𝑇/𝑊 ∓ 𝑇/𝑊 2 − 4𝑛2𝐶𝐷𝑜𝐾

2𝑛2𝐾/𝑞∞𝑇

𝑊≥ 2𝑛 𝐾𝐶𝐷𝑜

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Wing loading – climb and glide

𝑅

𝐶=𝑒𝑥𝑐𝑒𝑠𝑠 𝑝𝑜𝑤𝑒𝑟

𝑤𝑒𝑖𝑔ℎ𝑡=

𝑇 − 𝐷

𝑊⇒𝑅/𝐶

𝑉∞= 𝐺 =

𝑇 − 𝐷

𝑊⇒

𝐷

𝑊=

𝑇

𝑊− 𝐺

𝐷

𝑊=𝑞∞𝑆𝐶𝐷𝑜 + 𝑞∞𝑆𝐶𝐿

2

𝑊

• Equating the two yields:

𝑊

𝑆=

𝑇 𝑊 − 𝐺 ∓ 𝑇 𝑊 − 𝐺 2 − 4𝐾𝐶𝐷𝑂2𝐾/𝑞∞

𝑇

𝑊− 𝐺 ≥ 4𝐾𝐶𝐷𝑜 ⇒

𝑇

𝑊≥ 𝐺 + 4𝐾𝐶𝐷𝑜; T/W must be greater than the

climb gradient.

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Wing loading – climb and glide

• Takeoff flap setting, ∆𝐶𝐷𝑜 ≈ 0.02, ∆𝑒 ≈ −5%

• Landing flap setting, ∆𝐶𝐷𝑜 ≈ 0.07, ∆𝑒 ≈ −10%

• Landing gear down, ∆𝐶𝐷𝑜 ≈ 0.02

• The above equation can also be used to obtain the wingloading corresponding to a glide angle, T/W=0 with a negative G.

65

Wing loading – maximum ceiling

• The same equation can be used to find the absolute ceiling (G=0), service ceiling (R/C=100 ft/min) or combat ceiling(R/C=500 ft/min).

66

Wing loading

• Remember:

― For the wing loadings estimated above, choose the lowest oneto ensure that the wing is large enough for all flightconditions. Convert all the wing loadings calculated to takeoffconditions.

― A low wing loading (large wing) will always increase aircraftweight and cost.

― When W/S is selected, T/W should be rechecked to ensurethat all requirements are still met.

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