The planform is the geometrical shape of the wing when viewed from above. It largely determines the amount of lift and drag obtainable from a stated wing area and has a pronounced effect on the value of the stalling angle of attack.
We will mainly discuss the low-speed effects of variations in wing planforms. The terms having the greatest influence on the aerodynamic characteristics are illustrated shown below
- Wing Area, ‘S’. It is simply the plan surface area of the wing. Although a portion of the area may be covered by fuselage or nacelles, the pressure carryover on these surfaces allows legitimate consideration of the entire plan area.
- Wing Span, ‘b’. It is measured tip to tip.
- Average Chord, ‘c’. It is the geometric average. The product of the span and the average chord is the wing area (b X c = S) e.g. mean chord of 1.78 m for the hawk and 4.56m for mirage 2000 and 3.3 for the MiG 29.
- Aspect Ratio, ‘AR’. It is the ratio of the span and the average chord, i.e. AR=b/c. If the planform has curvature and the average chord is not easily determined, an alternate expression is: AR= b² / S. The aspect ratio is a fineness ratio of the wing and this quantity is very powerful in determining the aerodynamic characteristics and structural weight. Typical AR vary from 35 for a high performance glider to 3.5 for a jet fighter to 1.28 for a flying saucer.
- Taper Ratio λ. Considering the wing planform to have straight lines for the leading and trailing edges, the taper ratio, λ (lambda), is the ratio of the tip chord to the root chord. λ=CT/CR. The taper ratio affects the lift distribution and the structural weight of the wing. A rectangular wing has a taper ratio of 1.0 while the pointed tip delta wing has a taper ratio of 0.
- Sweep Angle, ‘Λ’ (Cap Lambda). It is usually measured as the angle between the line of 25 percent chords and a perpendicular to the root chord. The sweep of a wing causes definite changes in compressibility, maximum lift and stall characteristics
- Mean Aerodynamic Chord, ‘MAC’. It is the chord drawn through the centroid (geographical center) of plan area. A rectangular wing of this chord and the same span would have identical pitching moment characteristics. The MAC is located on the reference axis of the aeroplane and is a primary reference for longitudinal stability considerations. Note that the MAC is not the average chord but is the chord through the centroid of area. As an example, the pointed-tip delta wing with a taper ratio of zero would have an average chord equal to one-half the root chord but an MAC equal to two-thirds of the root chord.
The aspect ratio, taper ratio, and sweepback of a planform are the principal factors which determine the aerodynamic characteristics of a wing. These same quantities also have a definite influence on the structural weight and stiffness of a wing.
The aspect ratio (AR) of a wing is found by dividing the square of the wing span by the area of the wing. Thus if a wing has an area of 25 square meter and a span of 10 meter, the aspect ratio is 4. Another wing with the same span but with an area of 15 square meters would have an aspect ratio of 6.66. Another method of determining the aspect ratio is by dividing the span by the mean chord of the wing. For example, a span of 12 meter with a mean chord of 1.2 meter gives an aspect ratio of 10. From the preceding examples it can be seen that the smaller the area or mean chord in relation to the span, the higher is the aspect ratio. A rough idea of the performance of a wing can be obtained from knowledge of the aspect ratio.
Effect of Aspect Ratio on Induced Drag
The effect of aspect ratio on the induced drag is the principal effect of the wing planform. The value of induced drag is determined by the formula:
Di = CDI ½ ρ v2 S Where CDI is the coefficient of induced drag
The relationship between CDi and AR is given by the formula:
CDi = K CL²/ π AR
The effect of aspect ratio on the lift and drag characteristics is shown in Fig below for wings of a symmetrical aerofoil section. The basic aerofoil section properties are shown on these curves and these properties would be typical only of a wing planform of extremely high (infinite) aspect ratio. When a wing of some finite aspect ratio is constructed of this basic section, the principal differences will be in the lift and drag characteristics, the moment characteristics remain essentially the same. The effect of decreasing aspect ratio on the lift curve is to increase the wing angle of attack necessary to produce a given lift coefficient. The difference between the wing angle of attack and the section angle of attack is the induced angle of attack, αi = K CL / π AR which increases with decreasing aspect ratio. The wing with the lower aspect ratio is less sensitive to changes in angle of attack and requires higher angles of attack for maximum lift. When the aspect ratio is very low (below 5 or 6) the induced angles of attack are not accurately predicted by the elementary equation for αi and the graph of CL versus α develops distinct curvature. This effect is especially true at high lift coefficients where the lift curve for the very low aspect ratio wing is very shallow and CL max and stall angle of attack are less sharply defined. The effect of aspect ratio on wing drag characteristics may be appreciated from inspection of Fig . The basic section properties are shown as the drag characteristics of an infinite aspect ratio wing. When a planform of some finite aspect ratio is constructed, the wing drag coefficient is the sum of the induced drag coefficient, CDi = K CL² / π AR, and the section drag coefficient. Decreasing aspect ratio increases wing drag coefficient at any lift coefficient since the induced drag coefficient varies inversely with aspect ratio. When the aspect ratio is very low, the induced drag varies greatly with lift and at high lift coefficients, the induced drag is very high and increases very rapidly with lift coefficient.
Aspect Ratio and Stalling Angle
A stall occurs when the effective angle of attack reaches the critical angle. Induced downwash reduces the effective angle of attack of a wing. Since induced drag is inversely proportional to aspect ratio it follows that a low aspect ratio wing will have high induced drag, high induced downwash and a reduced effective angle of attack. The low aspect ratio wing therefore has a higher stalling angle of attack than a wing of high aspect ratio.
The reduced effective angle of attack of very low aspect ratio wings can delay the stall considerably. Some delta wings have no measurable stalling angle up to 40° or more inclination to the flight path. At this sort of angle the drag is so high that the flight path is usually inclined downwards at a steep angle to the horizontal. Apart from a rapid rate of descent, and possible loss of stability and control, such aircraft may have a fairly high nose up attitude with respect to the horizon and this can be deceptive. This condition is called the super stall or deep stall, although the wing may be far from a true stall and still be generating appreciable lift.
Use of High Aspect Ratio
Aircraft types such as gliders, transport, patrol and anti-submarine demand a high aspect ratio to minimize the induced drag (High performance gliders often have aspect ratios between 25 and 30). While the high aspect ratio wing will minimize induced drag, long thin wings increase weight and have relatively poor stiffness characteristics. Also the effects of vertical gusts on the airframe are aggravated by increasing the aspect ratio. Broadly it can be said that the lower the cruising speed of the aircraft, the higher the aspect ratios that can be usefully employed. Aircraft configurations which are developed for very high speed flight (especially supersonic flight) operate at relatively low lift coefficients and demand great aerodynamic cleanness. This usually results in the development of low aspect ratio planforms.
Use of Low AR Wings & Caution
While the effect of aspect ratio on lift curve slope and drag due to lift (lift dependent drag) is an important relationship, it must be realized that design for very high speed flight does not favor the use of high aspect ratio planforms. Low aspect ratio planforms have structural advantages and allow the use of thin, low drag sections for high speed flight. The aerodynamics of transonic and supersonic flight also favour short span, low aspect ratio surfaces. Thus, the modern configuration of aeroplane designed for high speed flight will have a low aspect ratio planform with characteristic aspect ratios of two to four. The most important impression that should result is that the typical modern configuration will have high angles of attack for maximum lift and very high drag due to lift at low flight speeds. This fact is of importance to the Military Aviator because the majority of pilot-error accidents occur during this regime of flight-during takeoff, approach, and landing. Induced drag predominates in these regimes of flight.
THE EFFECTS OF TAPER
The aspect ratio of a wing is the primary factor in determining the three-dimensional characteristics of the ordinary wing and its drag due to lift. However, certain local effects take place throughout the span of the wing and these effects are due to the distribution of area throughout the span. The typical lift distribution is arranged in some elliptical fashion.
The natural distribution of lift along the span of the wing provides a basis for appreciating the effect of area distribution and taper along the span. If the elliptical lift distribution is matched with a planform whose chord is distributed in an elliptical fashion (the elliptical wing), each square foot of area along the span produces exactly the same lift pressure. The elliptical wing planform then has each section of the wing working at exactly the same local lift coefficient and the induced downflow at the wing is uniform throughout the span. In the aerodynamic sense, the elliptical wing is the most efficient planform because the uniformity of lift coefficient and downwash incurs the least induced drag for a given aspect ratio. The merit of any wing planform is then measured by the closeness with which the distribution of lift coefficient and downwash approach that of the elliptical planform.
The effect of the elliptical planform is illustrated in Fig below by the plot of local lift coefficient cl / CL to wing lift coefficient, against semi-span distance. The elliptical wing produces a constant value of cl / CL = 1.0 throughout the span from root to tip. Thus, the local section angle of attack, αo, and local induced angle of attack, α1 are constant throughout the span. If the planform area distribution is anything other than elliptical it may be expected that the local section and induced angles of attack will not be constant along the span.
A planform previously considered is the simple rectangular wing which has a taper ratio of 1.0. A characteristic of the rectangular wing is a strong vortex at the tip with local downwash behind the wing which is high at the tip and low at the root. This large non-uniformity in downwash causes similar variation in the local induced angles of attack along the span. At the tip, where high downwash exists, the local induced angle of attack is greater than the average for the wing. Since the wing angle of attack is composed of the sum of α1 and αo, a large local α1 reduces the local αo creating low local lift coefficients at the tip. The reverse is true at the root of the rectangular wing where low local downwash exists. This situation creates an induced angle of attack at the root, which is less than the average for the wing, and a local section angle of attack higher than the average for the wing. The result is shown by the line B in the graph of Fig 10-5 which depicts a local coefficient at the root almost 20% greater than the wing lift coefficient.
The effect of the rectangular planform may be appreciated by matching a near elliptical lift distribution with a planform with a constant chord. The chords near the tip develop less lift pressure than the root and consequently have lower section lift coefficients. The great non-uniformity of local lift coefficient along the span implies that some sections carry more than their share of the load while others carry less. Hence, for a given aspect ratio, the rectangular planform will be less efficient than the elliptical wing. For example, a rectangular wing of A = 6 would have 16% higher induced angle of attack for the wing and 5% higher induced drag than an elliptical wing of the same aspect ratio.
Lift Distribution and Stall Patterns
At the other extreme of taper is the pointed wing which has a taper ratio of zero. The extremely small area at the pointed tip is not capable of holding the main tip vortex at the tip and a drastic change in downwash distribution results. The pointed wing has greatest downwash at the root and this downwash decreases toward the tip. In the immediate vicinity of the pointed tip an upwash is encountered which indicates that negative induced angles of attack exist in this area. The resulting variation of local lift coefficient shows low cl at the root and very high cl at the tip. The effect may be appreciated by realizing that the wide chords at the root produce low lift pressures while the very narrow chords towards the tip are subject to very high lift pressures. The variation of cl / CL throughout the span of the wing of taper ratio 0 is shown as curve E in the graph of Fig 10-5. As with the rectangular wing, the non-uniformity of downwash and lift distribution result in inefficiency of this planform. For example, a pointed wing of A = 6 would have 17% higher induced angle of attack for the wing and 13% higher induced drag than an elliptical wing of the same aspect ratio.
Between the two extremes of taper will exist planforms of more tolerable efficiency. The variations of cl / CL for a wing of taper ratio 0.5 (curve C in the graph of Fig 10-5) are similar to the lift distribution of the elliptical wing and the drag due to lift characteristics are nearly identical. A wing of A = 6 and taper ratio = 0.5 has only 3% higher induced angle of attack and 1% greater CDi than an elliptical wing of the same aspect ratio.
The elliptical wing is the ideal of the subsonic aerodynamic planform since it provides minimum induced drag for a given aspect ratio. However, the major objection to the elliptical planform is the extreme difficulty of mechanical layout and construction. A highly tapered planform is desirable from the standpoint of structural weight and stiffness and the usual wing planform may have a taper ratio from 0.45 to 0.20. Since structural considerations are important in the development of an aeroplane, the tapered planform is a necessity for an efficient configuration. In order to preserve the aerodynamic efficiency, the resulting planform is tailored by wing twist and section variation to obtain as near as possible the elliptic lift distribution.
An additional effect of the planform area distribution is on the stall pattern of the wing. The desirable stall pattern of any wing is a stall which begins at the root sections first. The advantages of the root stall first are that ailerons remain effective at high angles of attack, favourable stall warning results from the buffet on the tailplane and aft portion of the fuselage, and the loss of downwash behind the root usually provides a stable nose-down moment to the aircraft. Such a stall pattern is favoured but may be difficult to obtain with certain wing configurations. The types of stall patterns inherent with various planforms are illustrated in Fig 10-5. The various planform effects are separated as follows:
- Elliptical Planform. The elliptical planform has constant lift coefficients throughout the span from root to tip. Such a lift distribution means that all sections will reach stall at essentially the same wing angle of attack and the stall will begin and progress uniformly throughout the span. While the elliptical wing would reach high lift coefficients before an incipient stall, there would be little advance warning of a complete stall. Also, the ailerons may lack effectiveness when the wing operates near the stall and lateral control may be difficult.
- Rectangular Wing. The lift distribution of the rectangular wing exhibits low local lift coefficients at the tip, and high local lift coefficients at the root. Since the wing will initiate the stall in the area of highest local lift coefficients, the rectangular wing is characterized by a strong root stall tendency. Of course, this stall pattern is favorable since there is adequate stall warning buffet, adequate aileron effectiveness, and usually strong stable moment changes on the aircraft. Because of the great aerodynamic and structural inefficiency of this planform, the rectangular wing finds limited application only to low cost, low speed, light planes.
- Moderate Taper Wing. The wing of moderate taper (taper ratio = 0.5) has a lift distribution which is similar to that of the elliptical wing. Hence the stall pattern is much the same as the elliptical wing.
- Highly Tapered Wing, The highly tapered wing (taper ratio = 0.25) shows the stalling tendency inherent with high taper. The lift distribution of such a wing has distinct peaks just inboard from the tip. Since the wing stall is started in the vicinity of the highest local lift coefficient, this planform has a strong “tip stall” tendency. The initial stall is not started at the exact tip but at the station inboard from the tip where the highest local lift coefficients prevail.
- Pointed Tip Wing. The pointed tip wing (taper ratio = 0) develops extremely high local lift coefficients at the tip. For all practical purposes the pointed tip will be stalled at any condition of lift unless extensive tailoring is applied to the wing. Such a planform has no practical application to a subsonic aircraft.
- Swept Back Wing. The effect of sweepback on the lift distribution of a wing is similar to the effect of reducing the taper ratio. The full significance of sweepback is discussed in the following paragraphs.
Effect of Sweep back and Variable geometry in next article…