PLANFORM EFFECTS AND. AIRPLANE DRAG

EFFECT OF WING PLANFORM

The previous discussion of aerodynamic forces concerned the properties of airfoil sec­tions in two-dimensional flow with no consid­eration given to the influence of the planform. When the effects of wing planform are intro­duced, attention must be directed to the ex­istence of flow components in the spanwise direction. In other words, airfoil section properties, deal with flow in two dimensions while planform properties consider flow in three dimensions.

In order to fully describe the planform of a wing, several terms are required. The terms having the greatest influence on the aerody­namic characteristics are illustrated in figure

1.28.

(1) The wing area, T, 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.

(2) The wing span, b, is measured tip to tip.

(3) The average chord, c, is the geometric average. The product of the span and the average chord is the wing area (bXc=S’).

(4) The aspect ratio, AR, is the proportion of the span and the average chord.

AR=bjc

If the planform has curvature and the aver­age chord is not easily determined, an alternate expression is:

AK~b2jS

The aspect ratio is a fineness ratio of the wing and this quantity is very powerful in determing the aerodynamic characteristics and structural weight. Typical aspect ratios vary from 35 for a high performance sail­plane to 3.5 for a jet fighter to 1.28 for a flying saucer.

(5) The root chord, cT, is the chord at the wing centerline and the tip chord, ct, is measured at the tip.

(6) Considering the wing planform to have straight lines for the leading and trail­ing edges, the taper ratio, X (lambda), is the ratio of the tip chord to the root chord.

= Ctlcr

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 0.0.

(7) The sweep angle, A (cap lambda), 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-

(8) The mean aerodynamic chord, MAC, 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 airplane 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.

DEVELOPMENT OF LIFT BY A WING. In order to appreciate the effect of the planform on the aerodynamic characteristics, it is neces­sary to study the manner in which a wing produces lift. Figure 1.29 illustrates the three­dimensional flow pattern which results when the rectangular wing creates lift.

If a wing is producing lift, a pressure differ­ential will exist between the upper and lower surfaces, i. e., for positive lift, the static pres­sure on the upper surface will be less than on the lower surface. At the tips of the wing, the existence of this pressure differential creates the spanwise flow components shown in figure

1.27. For the rectangular wing, the lateral flow developed at the tip is quite strong and a strong vortex is created at the tip. The lateral flow—and consequent vortex strength—reduces inboard from the tip until it is zero at the centerline.

The existence of the tip vortex is described by the drawings of figure 1.29. The rotational pressure flow combines with the local airstream flow to produce the resultant flow of the trailing vortex. Also, the downwash flow field behind a delta wing is illustrated by the photographs of figure 1.29. A tuft-grid is mounted aft of the wing to visualize the local flow direction by deflection of the tuft ele­ments. This tuft-grid illustrates the existence of the tip vortices and the deflected airstream aft of the wing. Note that an increase in angle of attack increases lift and increases the flow deflection and strength of the tip vortices.

Figure 1.30 illustrates the principal effect of the wing vortex system. The wing pro­ducing lift can be represented by a series of

DOWNWASH FLOW FIELD BEHIND A DELTA WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AT

VARIOUS ANGLES OF ATTACK

FROM NACA TN 2674

Figure 7.29. Wing Three Dimensional Flow (sheet 2 of 2)

vortex filaments which consist of the tip or trailing vortices coupled with the bound or line vortex. The tip vortices are coupled with the bound vortex when circulation is induced with lift. The effect of this vortex system is to create certain vertical velocity components in the vicinity of the wing. The illustration of these vertical velocities shows that ahead of the wing the bound vortex induces an up – wash. Behind the wing, the coupled action of the bound vortex and the tip vortices in­duces a downwash. With the action of tip and bound vortices coupled, a final vertical velocity O-tv) is imparted to the airstream by the wing producing lift. This result is an inevitable consequence of a finite wing pro­ducing lift. The wing producing lift applies the equal and opposite force to the airstream and deflects it downward. One of the impor­tant factors in this system is that a downward velocity is created at the aerodynamic center (w) which is one half the final downward velocity imparted to the airstream (2w).

The effect of the vertical velocities in the vicinity of the wing is best appreciated when they are added vectorially to the airstream velocity. The remote free stream well ahead of the wing is unaffected and its direction is opposite the flight path of the airplane. Aft of the wing, the vertical velocity (2tv) adds to the airstream velocity to produce the down – wash angle « (epsilon). At the aerodynamic center of the wing, the vertical velocity (tv) adds to the airstream velocity to produce a downward deflection of the airstream one-half that of the downwash angle. In other words, the wing producing lift by the deflection of an airstream incurs a downward slant to the wind in the immediate vicinity of the wing. Hence, the sections of the wing operate in an average rela­tive wind which is inclined downward one-half the final downwash angle. This is one important feature which distinguishes the aerodynamic properties of a wing from the aerodynamic properties of an airfoil section.

The induced velocities existing at the aero­dynamic center of a finite wing create an aver­age relative wind which is different from the remote free stream wind. Since the aerody­namic forces created by the airfoil sections of a wing depend upon the immediate airstream in which they operate, consideration must be given to the effect of the inclined average rela­tive wind.

To create a certain lift coefficient with the airfoil section, a certain angle must exist be­tween the airfoil chord line and the average relative wind. This angle of attack is a0, the section angle of attack. However, as this lift is developed on the wing, downwash is in­curred and the average relative wind is in­clined. Thus, the wing must be given some angle attack greater than the required section angle of attack to account for the inclination of the average relative wind. Since the wing must be given this additional angle of attack because of the induced flow, the angle between the average relative wind and the remote free stream is termed the induced angle of attack, a*. From this influence, the wing angle of attack is the sum of the section and induced angles of attack.

a=ao+«t

where a—wing angle of attack

«0=section angle of attack induced angle of attack