aerodinamika : wing

1.     Wing design

Before a wing is designed, its mission has to be determined. What type of aircraft will this wing be attached to? Will it need to operate at high altitudes with thin atmospheres? Will it have to carry heavy loads? Will it need space to mount the engines? How much fuel will we want to store inside? How fast or agile will the aircraft need to be? The list of potential specifications is long and highly complex.

During the wing design process, eighteen parameters must be determined. They are as follows:

1.      Wing reference (or planform) area (SW or S_ref or S)

2.      Number of the wings

3.      Vertical position relative to the fuselage (high, mid, or low wing)

4.      Horizontal position relative to the fuselage

5.      Cross section (or airfoil)

6.      Aspect ratio (AR)

7.      Taper ratio (λ)

8.      Tip chord (Ct)

9.      Root chord (Cr)

10.  Mean Aerodynamic Chord (MAC or C)

11.  Span (b)

12.  Twist angle (or washout) (αt)

13.  Sweep angle (Ʌ)

14.  Dihedral angle 

15.  Incidence (iw) (or setting angle, αset)

16.  High lifting devices such as flap

17.  Aileron

18.  Other wing accessories

            One of the necessary tools in the wing design process is an aerodynamic technique to calculate wing lift, wing drag, and wing pitching moment. With the progress of the science of aerodynamics, there are variety of techniques and tools to accomplish this time consuming job. A variety of tools and software based on aerodynamics and numerical methods have been developed in the past decades. The application of such software packages–which is expensive and time-consuming – at this early stage of wing design seems un-necessary. Instead, a simple approach, namely Lifting Line Theory is introduced. Using this theory, one can determine those three wing productions (L, D, and M) with an acceptable accuracy.

·      Number of Wings

One of the decisions a designer must make is to select the number of wings. The options are:

1.      Monoplane (i.e. one wing)

2.      Two wings (i.e. biplane)

3.      Three wings

·      Wing Vertical Location

One of the wing parameters that could be determined at the early stages of wing design process is the wing vertical location relative to the fuselage centerline. This wing parameter will directly influence the design of other aircraft components including aircraft tail design, landing gear design, and center of gravity. In principle, there are four options for the vertical location of the wing. They are:

·      Dihedral Angle

When you look at the front view of an aircraft, the angle between the chord-line plane of a wing with the “xy” plane is referred to as the wing dihedral . The chord line plane of the wing is an imaginary plane that is generated by connecting all chord lines across span. If the wing tip is higher than the xy plane, the angle is called positive dihedral or simply dihedral, but when the wing tip is lower than the xy plane, the angle is called negative dihedral or anhedral.

·      High Lift Device

One of the design goals in wing design is to maximize the capability of the wing in the generation of the lift. This design objective is technically shown as maximum lift coefficient (CLmax).

The application of the high lift device tends to change the airfoil section’s and wing’s camber (in fact the camber will be positively increased). This in turn will change the pressure distribution along the wing chord.

At the airfoil level, a high lift device deflection tends to cause the following six changes in the airfoil features:

1.      Lift coefficient (Cl) is increased,

2.      Maximum lift coefficient (Clmax) is increased,

3.      Zero-lift angle of attack  in changed, 

4.      Stall angle is changed,

5.      Pitching moment coefficient is changed.

6.      Drag coefficient is increased.

7.      Lift curve slope is increased.

·      Type of Wing

1.      Rectangular Wing

The rectangular wing, sometimes referred to as the “Hershey Bar” wing in reference to the candy bar it resembles, is a good general purpose wing. It can carry a reasonable load and fly at a reasonable speed, but does nothing superbly well. It is ideal for personal aircraft as it is easy to control in the air as well as inexpensive to build and maintain.

2.      Elliptical Wing

            The elliptical wing is similar to the rectangular wing and was common on tail-wheel aircraft produced in the 1930s and 40s. It excels however in use on gliders, where its long wingspan can capture the wind currents easily, providing lift without the need for a lot of forward momentum, or airspeed.

3.      Swept Wing

            The swept wing is the “go to” wing for jet powered aircraft. It needs more forward speed to produce lift than the rectangular wing, but produces much less drag in the process, meaning that the aircraft can fly faster. It also works well at the higher altitudes, which is where most jet aircraft fly.

4.      Delta Wing

            The delta wing advances the swept wing concept, pulling the wings even further back and creating even less drag. The downside to this however is that the aircraft has to fly extremely fast for this wing to be effective. This is why it’s only found on supersonic aircraft (aircraft that fly faster than the speed of sound) such as fighter jets and the Space Shuttle orbiter.

2.     Swept vs unswept (sweep)

Swept wing cut down on drag caused by turbulence at the wingtips. But the real advantage of swept wing s comes in supersonic flight. The configuration cuts down on wave drag by redistributing the shockwaves along the plane’s aerodynamic profile. They are ideal for these high-speed conditions,less drag, yaw stability, roll stability, less induced drag, delay of stall Unfortunately, they do not allow for heavy payloads at lower speeds. Swept wings are also inefficient and burn too much fuel to stay aloft, which reduces the range of the aircraft,

Unswept wings are efficient at low speeds, providing a great amount of lift compared to the amount of induced drag exerted on the plane. Unswept wings are very bad at dealing with wave drag.

3.     Root chord dan tip chord

Tip Chord (Ct) is the chord at the tip of an airfoil, measured parallel to the plane of symmetry, and at points where straight leading or trailing edges meet the curvature at the tip. In variable-sweep wings, the tip chord is measured when the sweep is minimum.

Root Chord (Cr) is the chord of an airfoil measured from its leading edge to the trailing edge at its root.

In addition, since the tip chord is smaller than root chord, the tip Reynolds number will be lower, as well as a lower tip induced downwash angle. Both effects will lower the angle of attack at which stall occurs. This will result in the tip may stall before the root. This is undesirable from the viewpoint of lateral stability and lateral control.

4.     AR (Aspect Ratio)

In aerodynamics, the aspect ratio of a wing is essentially the ratio of its length to its breadth (chord). A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings.

Aspect ratio (AR)10 is defined as the ratio between the wing span; b (see figure 5.31) and the wing Mean Aerodynamic Chord (MAC)

For most wings the length of the chord is not a constant but varies along the wing, so the aspect ratio AR is defined as the square of the wingspan b divided by the area S of the wing planform, which is equal to the length-to-breadth ratio for a constant chord wing. In symbols,

This equation is not to be used for the wing with geometry other than rectangle; such as triangle, trapezoid or ellipse; except when the span is redefined. At this point, only wing planform area is known. The designer has infinite options to select the wing geometry. For instance, consider an aircraft whose wing reference area has been determined to be 30 m². A few design options are as follows:

1.      A rectangular wing with a 30 m span and a 1 m chord (AR =30)

2.      A rectangular wing with a 20 m span and a 1.5 m chord (AR =13.333)

3.      A rectangular wing with a 15 m span and a 2 m chord (AR = 7.5)

4.      A rectangular wing with a 10 m span and a 3 m chord (AR = 3.333)

5.      A rectangular wing with a 7.5 m span and a 4 m chord (AR = 1.875)

6.      A rectangular wing with a 6 m span and a 5 m chord (AR = 1.2)

7.      A rectangular wing with a 3 m span and a 10 m chord (AR = 0.3)

8.      A triangular (Delta) wing with a 20 m span and a 3 m root chord (AR = 13.33; please note that the wing has two sections (left and right))

9.      A triangular (Delta) wing with a 10 m span and a 6 m root chord (AR = 3.33)

The effects of aspect ratio on various flight features such as aircraft performance, stability, control, cost, and manufacturability :

1.      From aerodynamic points of view, as the AR is increased, the aerodynamic features of a three-dimensional wing (such as CLmax, CDmin) are getting closer to its two-dimensional airfoil section (such as Clmax, Cdmin).

2.      as the AR is increased, the wing lift curve slope  is increased

3.      As the AR is increased, the wing stall angle is decreased toward the airfoil stall angle. For this reason, the horizontal tail is required to have an aspect ratio lower than wing aspect ratio to allow for a higher tail stall angle. This will result in the tail to stall after wing has stalled, and allow for a safe recovery. For the same reason, a canard is desired to have an aspect ratio to be more than the wing aspect ratio. For this reason, a high AR (longer) wing is desired.

4.      Due to the third item, as the AR is increased, the wing maximum lift coefficient (CLmax) is increased toward the airfoil maximum lift coefficient (Clmax).

5.      As the AR is increased, the wing will be heavier.

6.      As the square root AR is increased, the aircraft maximum lift-to-drag ratio is increased. Since

 

7.      As the AR is increased, the wing induced drag is decreased, since the induced drag  is inversely proportional to aspect ratio. For this reason, a low AR (shorter) wing is desired.

8.      As the AR is increased, the effect of wing tip vortex on the horizontal tail is decreased.

9.      As the AR increases, the aileron arm will be increased, since the aileron are installed outboard of the wing. This means that the aircraft has more lateral control.

10.  As the AR increases, the aircraft mass moment of inertia around x-axis will be increased. This means that it takes longer to roll. In another word, this will reduces the maneuverability of aircraft in roll

11.  If the fuel tank is supposed to be inside wing, it is desirable to have a low aspect ratio wing. This helps to have a more concentrated fuel system. For this reason, a low AR (shorter) wing is desired.

12.  As the aspect ratio is increased, the wing stiffness around y-axis is decreased. This means that the tendency of the wing tips to drop during a take-off is increased, while the tendency to rise during high speed flight is increased. In practice, the manufacture of a very high aspect ratio wing with sufficient structural strength is difficult.

13.  A shorter wing needs lower cost to build compared with a long wing. For the cost reason, a low AR (a shorter wing) is desired.

14.  As the AR is increased, the occurrence of the aileron reversal is more expected, since the wing will be more flexible. The aileron reversal is not a desirable phenomenon for a maneuverable aircraft. For this reason, a low AR (shorter) wing is desired.

15.  In general, a wing with rectangular shape and high AR is gust sensitive.

Several rectangular wings with the same planform area but different aspect ratio

5.     λ Taper Ratio

Taper ratio (λ) is defined as the ratio between the tip chord (Ct) nd the root chord (Cr). This definition is applied to the wing, as well as the horizontal tail, and the vertical tail.

The geometric result of taper is a smaller tip chord. In general, the taper ratio varies between zero and one. 

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The effect of wing taper can be summarized as follows:

1.      The wing taper will change the wing lift distribution. This is assumed as an advantage of the taper, since it is a technical tool to improve the lift distribution. One of the wing design objective is to generate the lift such that the spanwise lift distribution be elliptical. The significance of elliptical lift distribution will be examined in the next section. Based on this item, the exact value for taper ratio will be determined by lift distribution requirement.

2.      The wing taper will increase the cost of the wing manufacture, since the wing ribs will have different shapes. Unlike a rectangular planform that all ribs are similar; each rib will have different size. If the cost is of major issue (such as for homebuilt aircraft), do not taper the wing.

3.      The taper will reduce the wing weight, since the center of gravity of each wing section (left and right) will move toward fuselage center line. This results in a lower bending moment at the wing root. This is an advantage of the taper. Thus, to reduce the weight of the wing, more taper (toward 0) is desired.

4.      Due to item 3, the wing mass moment of inertia about x-axis (longitudinal axis) will be decreased. Consequently, this will improve the aircraft lateral control. In this regard, the best taper is to have a delta wing (λ = 0).

5.      The taper will influence the aircraft static lateral stability , since the taper usually generates a sweep angle (either on the leading edge or on quarter chord line).

The effect of the weep angle on the aircraft stability show in figure below

6.     Wing Area

Wing area is the projected area of the planform and is bounded by the leading edge and trailing edge and wing tips. The wing area is not the total surface area of the wing(total surface area includes both upper and lower surface). The Wing area is the projected area and is almost half of the total surface area.( take the reference wing area to be that of the trapezoidal portion of the wing projected into the centerline.)

7.     Twist

Wing twist is an aerodynamic feature added to aircraft wings to adjust lift distribution along the wing.

Often, the purpose of lift redistribution is to ensure that the wing tip is the last part of the wing surface to stall, for example when executing a roll or steep climb; it involves twisting the wingtip a small amount downwards in relation to the rest of the wing. This ensures that the effective angle of attack is always lower at the wingtip than at the root, meaning the root will stall before the tip.

Twist that decreases the local chord's incidence from root to tip is sometimes referred to as washout. Washout is used to control the spanwise development of the stall. Insufficient washout can cause dangerous roll-off at the stall.

Twist that increases the local incidence from root to tip is less common and is called wash-in. When the tip incidence and root incidence are not the same, the twist is referred to as geometric twist. However, if the tip airfoil section and root airfoil section are not the same, the twist is referred to as aerodynamic twist.

Wing twist can also, rarely, refer to the deflection of the wing when it is made of insufficiently stiff materials.

8.     Chord

 

          chord refers to the imaginary straight line joining the leading and trailing edges of an airfoil. The chord length is the distance between the trailing edge and the point on the leading edge where the chord intersects the leading edge. The point on the leading edge which is used to define the chord can be defined as either the surface point of minimum radius, or the surface point which will yield maximum chord length.

            The chord of a wing, stabilizer and propeller is determined by examining the planform and measuring the distance between leading and trailing edges in the direction of the airflow. (If a wing has a rectangular planform, rather than tapered or swept, then the chord is simply the width of the wing measured in the direction of airflow.) The term chord is also applied to the width of wing flaps, ailerons and rudder on an aircraft.

            Most wings do not have a rectangular planform so they have a different chord at different positions along their span. To give a characteristic figure which can be compared among various wing shapes, the mean aerodynamic chord, or MAC, is used. The MAC is somewhat more complex to calculate, because most wings vary in chord over the span, growing narrower towards the outer tips. This means that more lift is generated on the wider inner portions, and the MAC moves the point to measure the chord to take this into account.

9.     Span

The wingspan of an airplane is the distance from one wingtip to the other wingtip , is always measured in a straight line, independently of wing shape or sweep. For example, the Boeing 777 has a wingspan of about 60 metres (197 ft).

10.                        Basic theory wing

Wing is an aerodynamic structure that generates lift when comes into contact with moving air  molecules i.e. wind. The lift is generated due to the wing’s unique shape. It is curved on the upper surface and is almost flat on the bottom surface. This unusual form causes the air to go faster over the top than the bottom. This difference in speed results in a difference in pressure between the top and the bottom of the wing which exerts an upward net force on the wing. This upward force is called lift.

Each wing section has a certain airfoil that could be categorized as either laminar or conventional the difference between these two types of airfoils is discussed later in the section.

It was found that the elliptical shape gave tha uniform air deflection along the entire span, which minimize the induced drag. It was also determined that the relationship between span and lift was constant.

11.                        Basic theory wing mengacu pada elliptical wing, mengapa?

Menurut saya, itu dikarenakan bentuk elliptical ini membuat sayap mempunyai distribusi lift yang natural, yang mengurangi efek dari tip stall membuat defleksi udara pada span menjadi seragam yang menyebabkan berkurangnya induced drag. Hubungan antara span dan lift juga konstan. Bentuknya pun (elliptical) sangat indah untuk dilihat, terkesan sangat modis.

12.                        Span efficiency factor (e)

Span efficiency factor (e) measures the departure of the loading from its elliptic optimum for the inviscid induced drag of a finite wing, when e =1. The condition for e = 1 is only that the circulation distribution along the span be elliptic, which, for a wing with constant profile shape, can come from planform geometry or from wing twist.

This e may be referred to as the Oswald efficiency factor, or sometimes as the span efficiency, even though it is not the same as e in C_DI equation because it contains corrections not only from departures from elliptical loading δ but also from finite AR and from the presumed parabolic shape of the section lift–drag polar k.

Increase Span Efficiency (e) can reduced induced drag :

o   Wing Tips

§  Some Improvement possible (~ 5%)

o   Winglets and End Plates

§  Induced Drag Decreased

§  Parasite Drag Increased

§  Span Extension Usually Superior

o   Improve Wing Root Junction Flow

§  Poor Junction causes large loss of span efficiency