Vertical tail Horizontal tail
This lesson covers selecting the airfoil, wing and tail geometries.
AIRCRAFT
ZEPLİN
HELİCOPTER
UAV
SPACE SHUTTLE
PARACHUTE
WIND TURBINE
ROCKET
RACE
ENGINE
SHIP
SUBMARINE
Navy Ship Propulsion Technologies: Options for Reducing Oil Use
Airfoil Selection SLO
The airfoil affects the
1.44W 2 gSL 2Sc L max TSL 1/ 2
2(W / S ) cruise speed Vstall takeoff and landing distances c SL L stall speed handling qualities (especially near the stall) overall “aerodynamic efficiency” during all phases of flight. max
Airfoil Geometry t
Angle of attack
Leading edge radius
The key geometric parameters. Total airfoil camber is defined as the maximum distance of the mean camber line from the chord line, expressed as percent of the chord. The “airfoil thickness ratio” (t/c) refers to the maximum thickness of the airfoil divided by its chord.
Airfoil Lift and Drag An airfoil generates lift by changing the velocity of the air passing over and under itself. The airfoil angle of attack causes the air over the top of the wing to travel faster than the air beneath the wing.
The integrated differences in pressure between top and bottom of the airfoil generate the net lifting force. Note that the upper surface of the wing contributes about two-thirds of the total lift.
Pressure Coefficient Cp
P P 1
2 V 2
Lift, Drag, and Moment Coefficients
Lift, drag, and moment on an airfoil: l lift/unit span d drag/unit span m moment/unit span
The forces and moment are functions of:
angle of attack V freesteam velocity
freestream density
Dimensional analysis can be applied to reduce the number of free parameters: Cl Cd
c airfoil chord length
freestream viscosity a freestream sonic speed
q freestream dynamic pressure
l 1
2 V c 2
d 1
Cm
where
2 V c 2
f , Re, M f , Re, M
m 1
2 2 V 2 c
Re
f , Re, M
V c
M
V a
Airfoil characteristics are strongly affected by the “Reynolds number” at which they are operating. The Reynolds number influences whether the flow will be laminar or turbulent and whether flow separation will occur. A typical aircraft wing operates at a Reynolds number of about ten milllion.
Flow separation from an airfoil at an angle of attack , due to a large adverse pressure gradient, results in lift decrease and drag increase.
Cl vs. Cd ‐ shows best locations where to fly Drag bucket: low drag region
Airfoil Families The early airfoils were developed mostly by trial and error. In the 1930s, the NACA developed a widely used family of mathematically defined airfoils called the “four digit” airfoils. While rarely used for wing design today, the uncambered four‐digit airfoils are still commonly used for tail surfaces of subsonic aircraft. The NACA five‐digit airfoils were developed to allow shifting the position of maximum camber forward for greater maximum lift. The six‐series airfoils were designed for increased laminar flow, and hence reduced drag. Six‐series airfoils such as the 64A series are still widely used as a starting point for high‐speed‐wing design. (example: F15) These two shapes are low‐drag sections designed to have laminar flow over 60 to 70 percent of chord on both the upper and the lower surface.
Airfoil Design In the past, the designer would select an airfoil from such a catalog by considering: airfoil drag during cruise stall and pitching-moment characteristics, the thickness available for structure, fuel the ease of manufacture. With today’s computational airfoil design capabilities, it is becoming common for the airfoil shapes for a wing to be custom-designed. Methods have been developed for designing an airfoil such that : • the pressure diferantial between the top and bottom of the airfoil quickly reaches a maximum value attainable without flow separation. • toward the rear of the airfoil, various pressure recovery schemes are employed to prevent separation near the trailing edge.
Airfoils with substantial pressure diferentials over a much percent of chord than a classical airfoil. This permits a reduced wing area for a required amount of lift.
Round leading edge - increases pressure quickly: • Gradual tapering to a sharp trailing edge – reduces likelihood of separation under adverse pressure grad. • Camber - this curvature determines how much lift is generated at zero angle of attack Most airfoils are designed using numerical codes based around potential flow theory with boundary layer corrections, but one can also use wind tunnel data or inverse design methods:
• Most airfoils are designed for a specific design point, such as: max lift, max thickness, transonic flight, laminar b.l., low Re, or low pitching moment
If the airplane is flying at just under the speed of sound, the faster air traveling over the upper surface will reach supersonic speeds causing a shock to exist on the upper surface. The speed at which supersonic flow first appears on the airfoil is called the “critical Mach number” Mcrit.
V
LITTLE CAMBER
HIGHLY CAMBERED
A supercritical airfoil is one designed to increase the critical Mach number.
Design Lift Coefficient The first consideration in initial airfoil selection is the “design lift coefficient.” This is the lift coefficient at which the airfoil has the best (L/D).
cLmd cDmd
tan max
cLmd cDmd
L D max
In subsonic flight a well-designed airfoil operating at its design lift coefficient has a drag coefficient that is little more than skin-friction drag. The aircraft should be designed so that it flies the design mission at or near the design lift coefficient to maximize the aerodynamic efficiency.
1 W W L qScL qScl cl q S Wing lift coefficient
q f (V , h) cl
Airfoil lift coefficient
(First approximation)
Wing loading
can be calculated for the velocity and altitude of the design mission.
During the mission fuel is burned:
W S
to flight with the design lift coefficient
q h “cruise climb flight” “maximum range”
In actual practice, a design lift coefficient usually will be based upon past experience, and for most types of aircraft typically will be around “0.5.” In fact, the initial selection of the airfoil is often simply based upon prior experience or copied from some successfull design.
Stall Stall characteristics play an important role in airfoil selection. Some airfoils exhibit a gradual reduction in lift during a stall, whereas others show a violent loss of lift, accompanied by a rapid change in pitching moment. This differerence reflects the existance of three entirely different types of airfoil stall.
“Fat airfoils” (t/c > %14) Stall from the trailing edge: • ; turbulent boundary layer • At 100 boundary layer begins to separate starting at the trailing edge, ; moving forward • The loss of lift is gradual, the pitching moment changes only a small amount. “Thinner airfoils” (%6 < t/c < %14) Stall from the leading edge: • The flow separates near the nose at a very small angle of attack, but immediately reattaches itself : little effect is felt. • ; the flow fails to reattach: entire stall • An abrupt change in lift and pitching moment. • “Very thin airfoils” (t/c < %6) • The flow separates from the nose at a small angle of attack and reattaches immediately. • ; “bubble” continues to stretch toward the trailing edge. The airfoil reaches its maximum lift where the bubble completely stretches. • The loss of lift is smooth, but large changes in pitching moment.
NACA 4412 versus NACA 4421 • •
• •
•
•
•
Both NACA 4412 and NACA 4421 have same shape of mean camber line Thin airfoil theory predict that linear lift slope and L=0 should be the same for both Leading edge stall shows rapid drop of lift curve near maximum lift Trailing edge stall shows gradual bending‐over of lift curve at maximum lift, “soft stall” High cl,max for airfoils with leading edge stall Flat plate stall exhibits poorest behavior, early stalling Thickness has major effect on cl,max
The wing twist angle is introduced to prevent stall from occurring at the wing tip before than the wing root. Usually wings are 'washout' twisted, resulting in a decreasing angle of attack starting from the root and towards the tip. Precisely, the twist angle is the angle between the zero‐lift line of the profile in the current section and the zero‐lift line of the root profile. As the twist angle increases along the span, the lower is the local angle of attack and the lower is the lift generated. By this we prevent the wing tip from generating as much lift as the wing root, which may cause the stall to occur at the worst place we'd like it to occur, the ailerons. By washout twist, we obtain to make stall occur at the wing root, without lost of ailerons control.
The designer may elect to use different airfoils at the root and tip:with a tip airfoil selected which stalls at a higher angle of attack than the root airfoil. This provides good flow over the ailerons for roll controll at an angle of attack where the root is stalled.
Boeing 737
Root
Mid‐Span Tip
Airfoil Thickness Ratio Airfoil thickness ratio has a direct effect on drag, maximum lift, stall characteristics, structural weight.
t / c cd M cr
Supercritical Airfoils •
Supercritical airfoils designed to delay and reduce transonic drag rise, due to both strong normal shock and shock-induced boundary layer separation
•
Relative to conventional, supercritical airfoil has reduced amount of camber, increased leading edge radius, small surface curvature on suction side, and a concavity in rear part of pressure side
SUPERCRITICAL AIRFOILS
Optimum Airfoil Thickness •
The thickness ratio affects the maximum lift and stall characteristics primarily by its effect on the nose shape. • A larger nose radius provides a higher stall angle and a greater maximum lift coefficient (with hight AR and moderate sweep) (vise verse for low AR). • NACA 63‐2XX, NACA 63‐212 ; example of optimum selection NACA 63‐212 cl,max
Thickness Effect on Structural Weight
1 Structural weight t/c
Halving the thickness ratio: wing weight (%41) Wing weight is typically about %15 of empty weight Halving the thickness ratio: empty weight (%6)
A supercritical airfoil would tend to be about %10 thicker than the historical trend.
Frequently the thickness is varied from root to tip: Due to fuselage effects, the root airfoil of a subsonic aircraft can be as mush as 20-60% thicker than the tip airfoil without greatly affecting the drag. This is very benefical, resulting in a structural weight reduction as well as more volume for fuel and landing gear. This thicker root airfoil should extend to no more than about 30% of the span.
Other Airfoil Considerations Another important aspect of airfoil selection is the intended Reynolds number. Each airfoil is designed for a certain Reynolds number. Use of an airfoil at a greately different Reynolds number (1/2 order) can produce section characteristics much different from those expected. This is important for the laminar-flow airfoils and is most crucial when an airfoil is operated at a lower-than-design Reynolds number. The laminar airfoils require extremely smooth skins. An aircraft designer should not spend too much time trying to pick exactly the “right airfoil” in early conceptual design. Later trade studies and analytical design tools will determine the desired airfoil characteristics and geometry. For early conceptual layout, the selected airfoil is important mostly determining the thickness available for structure, landing gear, and fuel. For swept-wing supersonic aircraft, the NACA 64A and 65A sections are good airfoils for initial design.
Wing Geometry Important considerations/constraints: – Performance (cruise, loiter, take‐off, landing) – Flying qualities (handling and stability) – Structural considerations (spar placement) – Internal volume (for fuel/payload) – Stealth characteristics (for military subsonic) – Airport limitations (wing‐span)
Wing Planform
The “reference” wing is the basic wing geometry used to begin the layout. • • • • • • • • •
S, reference wing area c, chord b, span A, aspect ratio (b2/S) t/c, thickness ratio , sweep , taper ratio (ctip / croot) Twist (aerodynamic and geometric) Dihedral
Graphical method for finding the mean aerodynamic chord.
Jenkinson
Planform area: It is the area of wing planform obtained by extending the exposed wing up to the fuselage centre line. Reference (or Equivalent) wing: It is a trapezoidal wing whose root chord is at the fuselage centre line and has the area same as the planform area.
The root airfoil is the airfoil of the trapezoidal reference wing at the centerline of the aircraft, not where the actual wing connects to the fuselage.
The reference wing area is fictitious: • wing area includes the part of the reference wing that sticks into the fuselage.
3‐D Effect
C L
AR C l 2 2 (C l / ) (C l / ) AR
Comparison of a NACA 65‐210 airfoil lift curve with that of a wing using the same airfoil (McCormick).
There are two key sweep angles: • the “leading edge sweep” is the angle of concern in supersonic flight: to reduce drag it is common to sweep the leading edge behind the Mach cone. • the “sweep of the quarter-chord line” is the sweep most related to subsonic flight. It is important to avoid confusing these two sweep angles. Airfoil pitching moment is generally provided about a point, where the pitching moment is essentially constant with changing angle of attack: • In subsonic flow, this is at the quarter-chord point on the mean aerodynamic chord. • In supersonic flow, the aerodynamic center moves back to about 40% of the mean aerodynamic chord. Also, the mean aerodynamic center will be important for stability. The required reference wing area S can be determined only after the takeoff gross weight is determined. The shape of the reference wing is determined by its aspect ratio, taper ratio, and sweep.
W/S, A, known parameters
S W /(W / S ) b AS c root 2 S /[ b (1 )] ctip c root tan LE tan c / 4 [(1 ) / A (1 )]
Aspect Ratio
b A c
for rectangular wings.
Aspect ratio affects the slope of the lift curve of wing (cLα), induced drag (cDi) , structural weight of the wing the wing span.
When a wing is generating lift, it has a reduced pressure on the upper surface and an increased pressure on the lower surface. Near the tip of the wing, the high‐pressure air will slip around to reach the top of the wing. This circulation of air around the tip creates a vortex and also pushes down on the top of the wing, spoiling lift and creating drag. A high aspect ratio planform shape has wingtips spaced further apart. Therefore, the formation of vortices will have less of an effect because less of the wing will be exposed to the vortices.
b2 A S
for delta wings.
Trailing Vortices Producing Downwash
Effect of aspect ratio on slope of the lift curve The slope of lift curve of an elliptic wing in a low subsonic flow is given as:
cL
A cl A 2
For other types of wing, the CLα would in general be slightly lower than that for elliptic wing. However equation shows that CLα decreases as aspect ratio decreases. Effect of aspect ratio on induced drag: The induced drag coefficient of a subsonic airplane is given by:
c Di
c L2 (1 ) A
where δ depends on wing geometry i.e. Aspect ratio, taper ratio and sweep. A wing with a high aspect ratio will generate more lift and less induced drag than a wing with a low aspect ratio.
Effect of aspect ratio on structural weight: 0.4 Wwing CSW0.649 A0.5 (t / c) root (1 ) 0.1 (cos( )) 1
Equation shows that the wing weight increases as square root of the aspect ratio. The reason for this is that the span increases as the aspect ratio increases (A = b2/S). An increase in the span would increase the bending moment at the wing root. This would require higher moment of inertia of the spar and hence higher weight. Effect of aspect ratio on span: For a chosen wing area, the aspect ratio determines the span of the wing. In turn the span determines the hanger space needed for the airplane. • For personal airplanes, a moderate aspect ratio of 6 to 7 is generally chosen. • Agricultural and other airplanes, which fly in proximity of ground, are subjected to air turbulence and have moderate aspect ratio of 6 to 7.
Aspect ratio also has a direct impact on stall angle (and overall lift coefficient of the wing): For a given Re, the wing with higher A (with long wingspan and small chord) reaches higher lift coefficient, but stalls at a lower angle of attack than the wing with low A. This is one reason why tails tend to be of lower aspect ratio. Conversely, a canard can be made to stall before the wing by making it a very high aspect ratio surface. This prevents the pilot from stalling the wing. However, for a given wing area, increasing the aspect ratio may result in a too small wing chord with a too low Reynolds number, which may significantly reduce the lift coefficient.
In this design stage, the aspect ratio will be determined by a trade study in which the aerodynamic advantages of a higher aspect ratio are balanced against the increased weight. For initial wing layout, the values and equations provided in the table can be used.
Propeller Aircraft Flying boat
Equivalent Aspect Ratio 8.0
Jet Aircraft
a
C
Jet transport
7.500
0
5.570
‐1.075
Twin turboprop
9.2
Military cargo/bomber
Agricultural aircraft
7.5
Jet fighter (other)
4.110
‐0.622
General aviation‐twin engine
7.8
Jet fighter (dogfighter)
5.416
‐0.622
General aviation‐single engine
7.6
Jet trainer
4.737
‐0.979
Homebuilt
6.0
A aM
c max
Mmax = Maximum flight Mach number
b2 For Sailplane: A S 0.69 A 4.464( L / D) best
Jet aircraft show a strong trend of aspect ratio decreasing with increasing Mach number. This is probably due to drag‐due‐lift becoming relatively less important at higher speeds. Designers of high‐speed aircraft thus use lower‐aspect‐ratio wings to save weight.
Wing Sweep • • •
Airfoil has same thickness but longer effective chord, Effective airfoil section is thinner, Making airfoil thinner increases critical Mach number.
The wing sweep affects slope of the lift curve (cLα), induced drag coefficient (cDi), critical Mach number (Mcr), wing weight tip stalling.
Effect of sweep on slope of lift curve:
1 M , 2
2
cL
cl 2 /
Λmax t = sweep of the line of maximum thickness, Clα is the slope of lift curve of the airfoil used on wing at chosen flight Mach number. In the absence of this information , η can be taken as 1.
2A 2 tan max t A 2 4 2 1 2 2
2
CLα decreases as sweep increases A = 8, M=0.8 CLα decrease by about 25% when sweep increases from 00 to 350.
Effect of sweep on induced drag Based on experimental data on swept wing, induced drag of a swept wing is inversely proportional to cosine of (Λ‐50).
1 cDi , 75 0 cos( 5 )
•
•
• •
At M ~ 0.6, severely reduced L/D Benefit of this design is at M > 1, to sweep wings inside Mach cone.
Wing sweep beneficial in that it increases drag‐divergences Mach number Increasing wing sweep reduces the lift coefficient
Effect of sweep on critical Mach number (Mcr) or drag divergence Mach number (MDD): The critical Mach number in connection with the airfoil was defined as the free stream Mach number at which the maximum Mach number on the airfoil is unity. This quantity can be obtained theoretically by calculating the pressure distribution on the airfoil, but cannot be determined experimentally. However when the critical Mach number is exceeded, the drag coefficient starts to increase. Making use of this behavior we define the term “Drag divergence Mach number (MDD)” as the Mach number at which the drag coefficient shows an increase of 0.002 over the subsonic drag value.
Some authors define MDD as the Mach number at which the slope of the Cd vs. M curve has a value of 0.1 i.e. (dCd / dM) = 0.1. For a swept wing the change in drag divergence Mach number due to sweep angle Λ, is given by the following equation:
1 ( M DD ) 1 1 ( M DD ) 0 90 Drag divergence Mach number of a Supercritical airfoil
(MDD)Λ=0 and (MDD)Λ are the drag divergence Mach numbers of the unswept and the swept wings. Λ is quarter‐chord sweep in degrees.
Remark: As regards the effect of sweep on critical Mach number is concerned a sweep back or sweep forward has the same effect. However from structural point of view a swept forward wing has lower flutter speed and is seldom use.
Effect of sweep on wing weight 0.4 Wwing CSW0.649 A0.5 (t / c) root (1 ) 0.1 (cos( )) 1
The weight of the wing is proportional to (1/cos Λ). Thus the weight of the wing increases as sweep increases. Remarks: i) The final choice of sweep will be done after trade‐off studies. Following can be given as guidelines. • Low subsonic airplanes have unswept wings. • For high speed airplanes, the angle of sweep can be chosen based on Figure:
Guidelines for selection of wing sweep
ii) Wing with cranked trailing edge: Instead of having a trapezoidal wing planform, the wings of high subsonic airplanes have an unswept trailing edge up to about 30% of semi‐span in the inboard region. These wings have the following favorable effects.
a) Higher thickness at the root and b) Span‐wise center of pressure is brought slightly inboard which reduces the bending moment at the root as compared to the trapezoidal wing. These two effects tend to reduce the weight of wing structure. The thicker inboard section also provides room for accommodating the backup structure for the landing gear.
Remarks: • sweep improves lateral stability • dihedral effect (roll due to sideslip) is proportional to sin(2LE) • variable sweep can be used as compromise • obvious penalty in weight and complexity
Why Sweep the Wing? Transonic (significant, 30°‐35°) Subsonic (usually small) • Delay drag rise Mach • Adjust wing aero center relative to cg • On flying wing, get moment arm length for control Wing sweep increases Supersonic (large, 45°‐70°) wing weight for fixed span • Wing concept changes, ‐ must distribute load longitudinally as well as laterally • reduce cross‐sectional area and area variation Why Variable Sweep? • Swept back: low supersonic drag, good “on‐the‐deck” ride quality • Unswept position: low landing speed, efficient loiter • Optimum sweep back available over transonic speed range • But: adds weight/complexity, currently unfashionable
F‐14 Tomcat
Why Sweep the Wing Forward? • For transonic maneuver, strong shock is close to trailing edge, highly swept TE (shock) reduces drag. ‐ forward swept wing allows highly swept TE ‐ equivalent structural AR less than aft swept wing • Synergistic with canard • Good high angle of attack (root stall, ailerons keep working) • But: ‐ must be balanced at least 30% unstable ‐ not stealthy ‐ poor supersonic volumetric wave drag
X‐29
Taper Ratio () The taper raio influences Induced drag Structural weight Ease of fabrication Effect of taper ratio on induced drag:
cL2 cD (1 ) A
It is known that an elliptic wing has the lowest induced drag (δ = 0.0). However this planform shape is difficult to fabricate. A rectangular wing is easy to fabricate but has about 7% higher CDi as compared to the elliptic wing (δ = 0.07). It is also heavier structurally. An unswept wing, with λ between 0.3 to 0.5, has a slightly positive value of δ. Further in a tapered wing, the span loading is concentrated in the inboard portions of the wing and the airfoil at the root is thicker than near the tip. These factors help in reducing the wing weight. Tip stalling is also not a problem when the taper ratio is between 0.3 and 0.5.
From these considerations, a taper ratio between 0.3 and 0.5 is common for low speed airplanes. For swept wings, a taper ratio of 0.2 is commonly used. This would necessitate measures for avoiding tip‐stalling. Guidelines for taper ratio of swept wings
• untapered wing is less efficient • sweep causes extra lift near wingtip • effect is reduced by additional taper
Raymer, D.P., Aircraft Design, 2006
Effect of taper on lift distribution
Twist It is given to prevent tip stalling. Tip stalling: Geometric twist It is a phenomenon in which the stalling on the wing begins in the region near the wing tips. This is because the distribution of local lift coefficient (Cl) is not uniform along the span and as the angle of attack of the wing increases, the stalling will begin at a location where the local lift coefficient exceeds the value of maximum lift coefficient (Clmax) there. To appreciate this phenomenon let us consider an un‐swept tapered wing. The lift distribution on such a wing has a maximum at the root and goes to zero at the tip. This distribution is also known as Γ distribution.
1 1 2 L V cl S V2 cl cy 2 2 Aerodynamic twist Cl is the local lift coefficient over an element (Δy) of span. Thus Γ distribution is proportional to the product cCl.
The local lift coefficient (Cl) is proportional to Γ/c and is not uniform along the span. The Γ distribution along the span can be approximately obtained by Schrenk’s method. According to this method, cCl distribution is roughly midway between chord distribution of the actual wing and that of an elliptic wing of the same area.
Schrenk’s Method
From these distributions, the variation of Cl along the span can be calculated. It can be shown that for a wing with taper ratio λ, the local maximum of Cl will occur at a span‐wise location where
y / b / 2 (1 ) Typical Distribution of Cl
It is known that the maximum lift coefficient (Cl max) of an airfoil depends on the airfoil shape, surface roughness and Reynolds number. For simplicity, we can assume that Cl max is approximately constant along the span.
Then from the distribution of Cl, we observe that as the angle of attack of the wing increases, the stalling will begin at the span‐wise location where local Cl equals local Cl max.
Subsequently, stalling will progress along the wing span and finally the wing will stall (i.e. CL of wing will reach a maximum and then decrease). The beginning of stall near the tip is undesirable as ailerons are located in tip region. Stalling there would reduce aileron effectiveness. For a wing of a taper ratio 0.3, the stall is likely to begin around y/(b/2) of 0.7.
Remarks: In the case of swept wings, there is a cross flow along the span and the tendency for the tip stall is enhanced. Tip stalling can be prevented if the sections in the tip region have angles of attack lower than those at the root. In this case, the wing acquires a twist. The difference between the angle of attack of the airfoil at the root and that near the tip is called twist and denoted by ε. Twist is negative when airfoil near the tip is at an angle of attack lower than that at the root. This is also called wash‐out. Sometimes airfoils with higher Cl max are used near the tip. Thus airfoils at the root and near the tip may have a different values of angle of zero lift (α0l). This leads to two different kinds of twists – geometric twist and aerodynamic twist. Geometric twist is the angle between the chords of the airfoils at the root and near the tip. Aerodynamic twist is the angle between the zero lift lines at the root and that near the tip. To completely eliminate the occurrence of tip stalling, may require complex variation of the angle of twist. However for ease of fabrication, linear twist is given in which the angle of twist varies linearly along the span. i) Actual value of twist can be obtained by calculating Cl distribution on untwisted wing and then varying the twist such that tip‐stalling is avoided. A value of 30 can be used as an initial estimate.
ii) Early swept wing airplanes had the following features to avoid tip stalling . (a) Vortex generators, (b) Fences on top surface.
Wing Incidence The mean aerodynamic chord is the reference line on the wing. Fuselage reference line (FRL) is the reference line for the entire airplane. The angle between fuselage reference line and the wing reference line is called wing incidence and denoted by iw.
The wing incidence is given for the following reason. For the economy in fuel consumption, the drag should be minimum during the cruise. The fuselage has a minimum drag when its angle of attack is zero. However, during cruise, the wing should produce sufficient lift to support the weight of the airplane. Keeping these factors in view, the wing is mounted on the fuselage in such a manner that it produces required amount of lift in cruise while the fuselage is at zero angle of attack.
During the preliminary design phase, iw can be obtained as follows. a) Obtain CL design corresponding to cruise or any other design condition i.e. W cL design where ρ and V correspond to the 1 V 2 S design flight conditions 2 b) Obtain CL α for the wing . c) Obtain zero lift angle (α0 L ) for wing. This depends on α0 l of the airfoil used on the wing and the wing twist. d) Calculate iw from the following equation:
cL design cL (iw 0L )
Remark: The final choice of iw may be arrived at from wind tunnel tests on the airplane model. For preliminary design purposes Airplane type Wing incedence angle Suggested wing incidence angle
General aviation / home built
20
Transport
10
Military
00
Dihedral () Dihedral angle is the angle that the wings form with respect to the horizon when viewed from the front.
Its value is decided after the lateral dynamic stability calculations have been carried out for the airplane. For preliminary design purposes. Suggested dihedral angle [ 0 ] Wing Location
Airplane type Low
Mid
High
Unswept (civil)
5 to 7
2 to 4
0 to 2
Subsonic swept
3 to 7
‐2 to 2
‐5 to ‐2
Supersonic swept
0 to 5
‐5 to 0
‐5 to 0
Dihedral helps to maintain aircraft “roll stability”: A positive dihedral, wingtips angled up, tends to bring an aircraft back to level when it is banked. The counter rolling moment is caused by a sideslip that results from the banking of the aircraft. The craft will tend to «slide» toward the lowered wing, which will increase that wing’s angle of attack, thereby increasing its lift. Since there is an unbalanced lift, the aircraft will tend to be righted. Dihedral must be carefully calculated, because an excess of dihedral comes with a penalty. Excessive dihedral can lead to an oscillatory disturbance in motion known as a Dutch roll. Dutch roll is a repeated side to side oscillation that is a result of both yawing and rolling. Such a phenomenon can be disastrous for a craft, but can be countered by increasing vertical tail area. This, in turn, will result in an increase in both the weight and drag of the aircraft. Therefore, tail size and dihedral must be considered together to achieve the optimal design for stability, weight, and drag concerns.
Wing Vertical Location There are three choices for the location of the wing on the fuselage namely high‐wing, mid‐wing, low‐ wing.
Low Wing configuration Advantages: i. Landing gear can be located in the wing thereby avoiding pods on the fuselage and hence lower drag. However to provide adequate ground clearance, the fuselage has to be at a higher level as compared to the high wing configuration. ii. Wing structure can be through the fuselage. Disadvantages: i. Low ground clearance. ii. A low‐wing configuration has unstable contribution to the directional stability. Hence a larger vertical tail area is needed.
Mid Wing configuration Advantages: i. Lower drag. ii. Advantages of ground clearance as in the high wing configuration. iii. No blockage of visibility. Hence used on some military airplanes. Disadvantages: i. Wing root structure passing through the fuselage is not possible, which leads to higher weight. However in HFB Hansa airplane, a swept forward mid‐wing is located behind the passenger cabin and has carry through structure.
Low wing
Mid wing
High wing
Parasol wing
High Wing configuration: Advantages: i) Allows placing fuselage closer to ground, thus allowing loading and unloading without special ground handling equipment. (good for cargo handling) ii) Jet engines & propeller have sufficient ground clearance without excessive landing gear length leading to lower landing gear weight. iii) For low speed airplanes, weight saving can be effected by strut braced wing. iv) For short take off and landing (STOL) airplanes with high wing configuration have following specific advantages. (a) Large wing flaps can be used (b) Engines are away from the ground and hence ingestion of debris rising from unprepared runways is avoided (c) Prevents floating of wing due to ground effect which may occur for low wing configuration. Disadvantages: i) Fuselage generally houses the landing gear in special pods leading to higher weight and drag. ii) Pilot’s visibility may be blocked in a turn.
Wing Tips Wing tip shape affects the aircraft wetted area, but only to a small extent. the tip vortices. A smoothly‐rounded tip easily permits the air to flow around the tip. A tip with sharp edge makes it more difficult, thus reducing the induced drag. Most of the new low‐drag wing tips use some form of sharp edge. The sweep of the wing tipalso affects the drag. The tip vortex tends to be located at the trailing edge: an aft‐swept wig tip, with a greater trailing edge span, tends to have lower drag. Wingtip vortices behind a conventional wingtip and blended winglet
• A sharp edge (looking from front) prevents leakage around tips • lower induced drag • Hoerner tip has lower surface cutting upward • F-15 has forward swept tips on all surfaces • keeps trailing edge out of tip vortex
• Winglets • wetted area increase vs reduced drag • structural weight added at tip
Biplane Wings Each wing contributes one-half of the required lift • induced drag reduced by factor of 2! • but parasite drag (c D0) will go up • wing interference reduces benefit wing #1 wing #2
assume wings share lift equally induced drag reduced by 1/2!
Biplanes are still worth considering if: • span is limited but wing area is needed for low speed flight • high roll rates are needed (aerobatics) Mean aerodynamic chord for the airplane is defined by the weighted average of the aerodynamic chords for each wing • weights set by area of each wing
Tail Geometry and Arrangement Tail Functions “Tails are little wings.” Much of the previous discussion concerning wings can also be applied to tail surface. The major difference between a wing and a tail is that, while the wing is designed to routinely carry a substantial amount of lift, a tail is designed to operate normally at only a fraction of its lift potential. Any time in flight that a tail comes close to its maximum lift potential, and hence its stall angle, something is very wrong. Tails provide for trim, stability, and control. Trim refers to the generation of a lift force that, by acting through some other moment arm about the center of gravity, balances some other moement produced by the aircraft. For the horizontal tail, trim primarily refers to the balancing of the moment created by the wing. An aft horizontal tail typically has a negative incidence angle of about 20 ‐ 30 to balance the wing pitching moment. For vertical tail, most aircraft are left‐right symmetric, and so unbalanced aerodynamic yawing moments requiring trim are not created during normal flight. The major function of the tail is control of the aircraft.
Propeller aircraft experience a yawing moment called “p‐effect,” which has several thrust‐ related causes. When the disk of the propeller is at an angle, such as during climb, the blade going downward has a higher angle of attack and is also at a slightly higher forward velocity. This condition produces higher thrust on the downward‐moving side and hence a yawing moment away from that side. Also, the propeller tends to “drag” the air into a rotational corkscrew motion. The vertical tail is pushed on sideways by the rotating propwash causing a yawing moment, which adds to the p‐effect. To counter p‐effect many single‐engine propeller airplanes have the vertical tail offset several degress. The vertical tails of multi‐engine aircraft must be capable of providing sufficient trim in the event of an engine failure. This produces yawing both from lack of thrust on one side and the extra drag of the stopped or windmilling engine. Some multi‐engine aircraft have counter‐rotating propellers to minimize the engine‐out yawing. The tails are also a key element of stability, acting much like the fins on an arrow to restore the aircraft from an upset in pitch or yaw. The vertical stabilizer acts like the tail of a weathercock. The action of the horizontal stabilizer is much more complex, and involves a delicate balance of the pitching moment due to the location of the wing center of lift relative to the center of gravity, the inherent pitching moment of the wing, the pitching moment generated by the horizontal stabilizer, and the way these moments change with angle of attack.
Tail Arrangement
For most aircraft designs, the conventional tail will use to provide adequate stability and control at the lightest weight. A T‐tail is inherently heavier than a conventional tail because the vertical tail must be strengthened to support the horizontal tail, but the T‐tail provides compensating advantages in many cases:
Due to end‐plate effect, the T‐tail allows a smaller vertical tail. The T‐tail lifts the horizontal tail clear of the wing wake and propwash, which makes it more efficient and hence allows reducing its size..
This also reduces buffet on the horizontal tail, which reduces fatigue for both the structure and the pilot.
A deep stall is a dangerous type of stall that affects certain aircraft designs, notably those with a T‐tail configuration. In these designs, the turbulent wake of a stalled main wing "blankets" the horizontal stabilizer, rendering the elevators ineffective and preventing the aircraft from recovering from the stall. The boundaries of the acceptable locations for horizontal tail to avoid this problem is given in the figure. Low tails are best for stall recovery. A tail approximately in line with the wing is acceptable for a subsonic aircraft, but may cause problems at supersonic speeds due to the wake of the wing.
In jet transport aircraft, the T‐tail allows the use of engines mounted in pods on the aft fuselage. This increases the wing lift and decreases the wing drag.
Aft tail positioning
cruciform
The cruciform tail, a compromise between the conventional and T‐tail arrangements, lifts the horizontal tail to avoid proximity to a jet exhaust, or to expose the lower part of the rudder to undisturbed air during high‐angle of attack conditions and spins. It has less of a weight penalty according to T‐tail. However, it will not provide a tail‐area reduction due to endplate effect. The H‐tail is used primarily to position the vertical tails in undisturbed air during high angle‐of‐attack conditions or to position the rudders in the propwash on a multiengine aircraft to enhance engine‐out control. H‐tail is heavier than the conventional tail, but its endplate effect allows a smaller horizontal tail.
triple‐tail
The H‐tail serves to hide the hot engine nozzle from heat‐seeking missiles when viewed from an angle off the rear of the aircraft. H‐tails and and the related Triple‐tails have also been used to lower the tail height to allow an aircraft to fit into existing hangars. Twin tails on the fuselage can position the rudders away from the aircraft centerline, which may become blanketed by the wing or forward fuselage at high angles of attack. Also, twin tails have been used simply to reduce the height required with single tail. Twin tails are usually heavier than an equal‐ area centerline‐mounted single tail, but are often more effective. Twin tails are seen on most large modern fighters.
The V‐tail is intended to reduce wetted area .The horizontal and vertical tail forces are the result of horizontal and vetical projections of the force exerted upon the “V” surfaces. The tail dihedral angle would be found as the arctangent of the ratio of required vertical and horizontal areas. The resulting wetted area would be clearly be less. V‐tails offer reduced interference drag but at some penalty in control‐actuation complexity, as the rudder and elevator control inputs must be blended in a “mixer” to provide the proper movement of the V‐tail “ruddervators”. When the right rudder pedal of a V‐tail aircraft is pressed, the right ruddervator deflects downward, and the left ruddervator deflects upward. The combined forces push the tail to the left, so the nose goes to the right as desired. However, the ruddervators also produce a rolling moment toward the left‐in opposition to the desired direction of turn an action called “adverse roll‐ yaw coupling” The inverted V‐tail avoids this problem: Produces a desirable “proverse‐roll‐ yaw coupling.” This tail arrangement can cause difficulties in providing adequate ground clearance. The Y‐tail is similar to the V‐tail, except that the dihedral angle is reduced and a third surface is mounted vertically beneath the V. This third surface contains the rudder, whereas the V surfaces provide only pitch control. This tail arrangement avoids the complexity of the ruddervator while reducing interference drag when compared to a conventional tail.
Boom‐mounted tails have been used to allow pusher propeller or allow location of a heavy jet engine near the center of gravity. Tailbooms are typically heavier than a conventional fuselage construction, but can desirable in some applications. Boom‐mounted tails can have a mid‐mounted horizontal tail or a high horizontal. Also, the inverted V‐tail arrangement can be used with tail booms.
The ring‐tail concept attempts to provide all tail contributions via an airfoil‐ sectioned ring attached to the aft fuselage, usually doubling as a propeller shroud. While conceptually appealing, the ring‐tail has proven inadequate in application.
Tail Arrangement for Spin Recovery The vertical tail plays a key role in spin recovery. An aircraft in a spin is essentially falling vertically and rotating about a vertical axis, with the inside wing fully stalled. The aircraft is also typically at a large sideslip angle. To recover from the spin requires that the wing will be unstalled, so the angle of attack must be reduced. However, first the rotation must be stooped and the sideslip angle reduced, or the aircraft will immediately enter another spin. This requires adequate rudder control even at the high angles of attack seen in the spin. The effect of tail arrangement upon rudder control at high angles of attack: At high angle of attack the horizontal tail is stalled, producing a turbulent wake extending upward at approximately 450.
Unblankated portion
The rudder lies entirely The effect of moving within the wake of the the horizontal tail horizontal tail. forward with respect to the vertical tail.
Moving the horizontal The T‐tail arrangement completely uncovers tail upward. the rudder, but can result in pitchup and loss of elevator control.
Moving of the horizontal tail aft with respect to the vertical tail. The use of dorsal fin improves tail effectiveness at high angles of sideslip by creating a vortex that attaches to the vertical tail. This tends to prevent the high angles of sideslip seen in spins, and augments rudder control in the spin. The ventral tail also tends to prevent high sideslip, and has the extra advantage of being where it cannot be blankated by the wing wake. Ventral tails are also used to avoid lateral instability in high‐speed flight.
Tail Geometry The surface areas required for all types of tails are directly proportional to the aircraft’s wing area, so the tail areas can not be selected until the initial estimate of aircraft takeoff gross weight has been made. The initial estimation of tail area is made using the “tail volume coefficient” method. Other geometric parameters for the tails can be selected: Tail aspect ratio and taper ratio show little variation over a wide range of aircraft types. Tail aspect ratio and taper ratio. (Raymer) Horizontal tail A
Vertical tail A
Fighter
3 – 4
Sail plane
6 – 10 0.3 – 0.5 1.5 – 2.0 0.4 – 0.6
Others
3 – 5
T‐tail
‐
0.2 – 0.4 0.6 – 1.4 0.2 – 0.4 0.3 – 0.6 1.3 – 2.0 0.3 – 0.6 ‐
0.7 – 1.2 0.6 – 1.0
T‐tail aircraft have lower vertical‐ tail aspect ratios to reduce the weight impact of the horizontal tail’s location on top of the vertical tail. Some general‐aviation aircraft use untapered horizontal tails (=1.0) to reduce manufacturing costs.
Leading‐edge sweep of the horizontal tail is usually set to about 50 more than the wing sweep. This tends to make the tail stall after the wing, and also provides the tail with a higher Mcr than the wing, which avoids loss of elevator effectiveness due to shock formation.
For low‐speed aircraft, the horizontal tail sweep is frequently set to provide a straight hinge line for the elevator, which usually has the left and right sides connected to reduce flutter tendencies. Vertical‐tail sweep varies between 350 and 550. For a low‐speed aircraft, there is little reason for vertical‐tail sweep beyond about 200 other than asthetics. For a high‐speed aircraft, vertical‐tail sweep is used primarily to ensure that the tail’s Mcr is higher than the wing’s. The exact planform of the tail surfaces is actually not very critical in the early stages of the design process. The tail geometries are revised during later analytical and wind‐tunnel studies. For conceptual design, it is usually acceptable simply to draw tail surfaces tht “look right,” based upon prior experience and similar designs. Tail thickness ratio is usually similar to the wing thickness ratio, as determined by the historical guidelines provided in the wing‐geometry section. For a high‐speed aircraft, the horizontal tail is frequently about 10% thinner than the wing to ensure that the tail has a higher Mcr.
Airbus 380
Airbus 300
Krüger flaps Spoilers Air‐brakes
Three slotted inner flaps High Speed Aileron Flap track fairing Spoilers Three slotted outer flaps Low Speed Aileron Slats Wingtip
Three slotted inner flaps Flap track fairing Spoilers Air‐brakes High Speed Aileron Three slotted outer flaps Spoilers
Low Speed Aileron
Krüger flaps
Slats
Wingtip
Plain flap: the rear portion of airfoil rotates downwards on a simple hinge mounted at the front of the flap.[2] Used in this form as early as 1917 (during World War I) on the widely produced Breguet 14 and possibly earlier on experimental types.[3] Due to the greater efficiency of other flap types, the plain flap is normally only used where simplicity is required. A modern variation on the plain flap exploits the ability of composites to be designed to be rigid in one direction, while flexible in another. When such a material forms the skin of the wing, its camber can be altered by the geometry of the internal supporting structure, allowing such a surface to be used either as a flap or as an aileron. While most currently use a complex system of motors and actuators, the simplest such installation uses ribs that resemble bent carrots ‐ when the bend is nearly horizontal, there is no deflection, but when the carrot is rotated so the bend is downward, the camber of the airfoil is changed in the same manner as on a plain flap.[citation needed]
Split flap: the rear portion of the lower surface of the airfoil hinges downwards from the leading edge of the flap, while the upper surface stays immobile.[4] Like the plain flap, this can cause large changes in longitudinal trim, pitching the nose either down or up, and tends to produce more drag than lift. At full deflection, a split flaps acts much like a spoiler, producing lots of drag and little or no lift. It was invented by Orville Wright and James M. H. Jacobs in 1920 but only became common in the 1930s and was then quickly superseded. The Douglas DC‐3 & C‐47 used a split flap. Slotted flap: a gap between the flap and the wing forces high pressure air from below the wing over the flap helping the airflow remain attached to the flap, increasing lift compared to a split flap.[5] Additionally, lift across the entire chord of the primary airfoil is greatly increased as the velocity of air leaving its trailing edge is raised, from the typical non‐flap 80% of freestream, to that of the higher‐speed, lower‐pressure air flowing around the leading edge of the slotted flap.[6] Any flap that allows air to pass between the wing and the flap is considered a slotted flap. The slotted flap was a result of research at Handley‐Page, a variant of the slot and dates from the 1920s but wasn't widely used until much later. Some flaps use multiple slots to further boost the effect. Fowler flap: split flap that slides backward flat, before hinging downward, thereby increasing first chord, then camber.[7] The flap may form part of the uppersurface of the wing, like a plain flap, or it may not, like a split flap but it must slide rearward before lowering. It may provide some slot effect but this is not a defining feature of the type.[8] Invented by Harlan D. Fowler in 1924, and tested by Fred Weick at NACA in 1932. They were first used on the Martin 146 prototype in 1935, and in production on the 1937 Lockheed Electra,[9] and is still in widespread use on modern aircraft, often with multiple slots. As mentioned under the plain flaps, variable geometry wings are making a comeback, and a General Dynamics F‐111 Aardvark was modified with such a system that acted as fowler flaps by NASA for trials on the AFTI/F‐111 Mission Adaptive Wing.
Junkers Flap: a slotted plain flap where the flap is fixed below the trailing edge of the wing, rotating about its forward edge.[10] When not in use, it has more drag than other types but is more effective at creating additional lift than a plain or split flap, while retaining their mechanical simplicity. Invented by O. Mader at Junkers in the late 1920s, it was widely used on the Junkers Ju 52, though it can be found on many modern ultralights. Gouge flap: a type of split flap that slides backward along curved tracks that force the trailing edge downward, increasing chord and camber without affecting trim or requiring any additional mechanisms.[11] It was invented by Arthur Gouge for Short Brothers in 1936 and used on the Short Empire and Sunderland flying boats which used the very thick Shorts A.D.5 airfoil. Short Brothers may have been the only company to use this type. Fairey‐Youngman flap: drops down (becoming a Junkers Flap) before sliding aft and then rotating up or down. Fairey was one of the few exponents of this design, which was used on the Fairey Firefly and Fairey Barracuda. When in the extended position, it could be angled up (to a negative angle of incidence) so that the aircraft could be dived vertically without needing excessive trim changes. Zap Flap or commonly but incorrectly Zapp Flap: Invented by Edward F. Zaparka while he was with Berliner/Joyce and tested on a General Aircraft Corporation Aristocrat in 1932 and on other types periodically thereafter, but it saw little use on production aircraft other than on the Northrop P‐61 Black Widow. The leading edge of the flap is mounted on a track, while a point at mid chord on the flap is connected via an arm to a pivot just above the track. When the flap's leading edge moves aft along the track, the triangle formed by the track, the shaft and the surface of the flap (fixed at the pivot) gets narrower and deeper, forcing the flap down.[12] Krueger flap: hinged flap which folds out from under the wing's leading edge while not forming a part of the leading edge of the wing when retracted. This increases the camber and thickness of the wing, which in turn increases lift and drag.[13][14] This is not the same as a leading edge droop flap, as that is formed from the entire leading edge.[15] Invented by Werner Krüger in 1943 and evaluated in Goettingen,[16] Krueger flaps are found on many modern swept wing airliners. Gurney flap: A small fixed perpendicular tab of between 1 and 2% of the wing chord, mounted on the high pressure side of the trailing edge of an airfoil. It was named for racing car driver Dan Gurney who rediscovered it in 1971, but has since used on some helicopters such as the Sikorsky S‐76B to correct control problems without having to resort to a major redesign. It boosts the efficiency of even basic theoretical airfoils (made up of a triangle and a circle overlapped)
Leading edge droop: entire leading edge of the wing rotating downward,[17] effectively increasing camber but slightly reducing chord. Most commonly found on fighters with very thin wings unsuited to other leading edge high lift devices. Blown flaps: also known as Boundary Layer Control Systems, are systems that blow engine air over the upper surface of any of the previously mentioned types of flap to improve lift characteristics. Two types exist ‐ the original type blew air out of channels or holes in the surface of the flap, while newer systems simply blow engine exhaust over the top of the flap. These require ample reserves of power and are maintenance intensive thus limiting their use but they provide lots of lift at low airspeeds. Although invented by the British, the first production aircraft with blown flaps was the Lockheed F‐104 Starfighter. The later type was trialled on the Boeing YC‐14 in 1976. Controls that look like flaps but are not: Handley Page leading edge slats/slots may be confused for flaps but are mounted on the top of the wings' leading edge and while they may be either fixed or retractable, when deployed they provide a slot or gap under the slat to force air against the top of the wing which is absent on a Krueger flap. They offer excellent lift and enhance controllability at low speeds. Other types of flaps may be equipped with one or more slots to increase their effectiveness, a typical setup on many modern airliners. These are known as slotted flaps as described above. Frederick Handley Page experimented with fore and aft slot designs in the 20s and 30s. Spoilers may also be confused for flaps but are intended solely to create drag and not lift. A spoiler is much larger than a Gurney flap, and can be retracted. Ailerons are similar to flaps (and work the same way) but are intended to provide lateral control, rather than to change the lifting characteristics of both wings together, and so operate differentially ‐ when an aileron on one wing increases the lift, the opposite aileron does not, and will often work to decrease lift. Some aircraft use flaperons, which combine both the functionality of flaps and ailerons in a single control, working together to increase lift, but to slightly different degrees so the aircraft will roll toward the side generating the least lift. Flaperons were used by the Fairey Aviation Company as early as 1916 but didn't become common until after World War II.
