Pilot Training - Theory of Flight: Airfoils

 35. Airfoil characteristics.-A particular airfoil, that is, one of specific dimensions, is characterized by the following properties:

a. Lift Coefficient.

b- Drag coefficient.

c- Lift-drag ratio.

d. Center Of pressure position.

In lieu of center of pressure position some equivalent property may be used, such as the moment of aerodynamic force about the leading edge- These quantities are collectively known as airfoil "characteristics".

36. Lift coefficient.--a. For any angle of attack the lift coefficient value of an airfoil is obtained from the fundamental equation of lift.

Since the lift must equal the weight of the airplane to satisfy conditions of equilibrium in unaccelerated or steady flight.

Both the weight of a given airplane and the area of its wings are constant quantities. The air density r varies with the altitude. Assuming the flight to occur at a constant value of r, it is evident that the lift coefficient varies inversely with the airspeed, or

b. For a particular airplane, it is possible to spot in airspeeds for corresponding lift coefficients and angles of attack as illustrated in figure 34. This shows conclusively that for unaccelerated flight there is one airspeed and only owe for a given angle of attack and vice versa.

c. The curve, it will be noted, is practically a straight line throughout the flight range. It crosses the zero ordinate at a small negative angle of attack which represents the vertical dive attitude. As it approaches its maximum value the slope changes rapidly indicating that with speed variations near the stall, relatively large changes in angle of attack are necessary to maintain the requisite lift. This flattening of the curve with increase in angle of attack is due to turbulence which eventually becomes so pronounced as to bring about an actual reduction in lift coefficient.

(1) These characteristics will vary with change in angle of attack of the airfoil since they depend on forces which vary in this manner. It is, therefore, convenient to plot them to definite scale against angle of attack. The resulting curves are termed the "characteristic curves" of the airfoil and are illustrated in figure 33 by a typical example.

(2) Results of wind tunnel tests on a large number of airfoils show that while the characteristic curves vary for the different shapes, they follow, in general, the same trend with corresponding values differing only in degree.

(3) The effect of turbulence is illustrated in figure 35.

d. The, lift coefficient attains a maximum value at an angle of attack in the neighborhood of 15°. This maximum is termed the "burble point." The angle of attack for maximum C_L, is designated as the "critical" or "stalling" angle since above this angle of attack the lift afforded is insufficient to support the weight of the airplane.

37. Drag coefficient.-a. The drag coefficient for any angle of attack is obtained from the fundamental formula for drag:

b. Obviously the drag coefficient curve illustrated in figure 36 will never attain a zero value regardless of the shape of the airfoil or its angle of attack.

c. It must be remembered that the drag coefficient curve indicates the variation of the airfoil drag alone with varying angles of attack and does not take into account the resistance offered by the remainder of the airplane. While a similar condition exists with regard to the lift coefficient, the remainder of the airplane contributes so little to the lift that no account is taken of it.

38. Lift-drag ratio.-The ratio of the lift to the drag of an airfoil at any angle of attack is a measure of its "effectiveness," for, in the airplane the former is the useful force, or the one required to support the weight while the latter is the unbeneficial one which must be

accepted to obtain sustentation. This ratio, termed the L/D ratio, will vary considerably with angle of attack as shown in the curve of figure 37. The curve is determined by plotting against angle of attack lift values divided by corresponding drags or it may be derived from the curves of C_L and C_D. For any angle of attack the C_L value divided by the C_D value will give the L/D for that angle. That this is correct can be shown by dividing the equation for lift by that for drag:

Since r/2, S, and V are common:

From a zero value for the angle of attack of zero lift, the curve rises to a maximum at an angle of attack ranging ordinarily from 1° to 4°. Thereafter it falls off more gradually and in a variety of ways for different airfoils.

While the maximum value of L/D for the airfoil is in the neighborhood of 20, that for the complete airplane is somewhat less than half this -alue. This is due to the fact that for the airplane -

The parasite drag, or drag of the airplane exclusive of the wings, varies comparatively little with change in angle of attack. Hence the L/D curve, besides having much lower values, will have a flatter peak with maximum probably somewhat shifted as shown in figure 37. The angle of attack for this maximum value will be that for the best glide without power as will be demonstrated.

For the wings alone, it is obvious that, other things being equal, the airfoil having the best maximum L/D will be the most acceptable.

39. Center of pressure.-Bearing in mind the variation in pressure distribution along the chord with change in angle of attack, the point of application of the resultant, that is, the center of pressure, shifts correspondingly. Throughout most of the flight range, there is a backward movement of the center of pressure with decrease in angle of attack as evidenced in figure 38. The most forward position is generally about 0.3 of the chord abaft the leading edge and obtains, as a rule, somewhat below the "critical" angle. The backward shift from this position becomes abrupt as low angles are reached and the center

of pressure finally runs off the trailing edge, approaching infinity for the tingle of attack of zero lift. This travel of the center of pressure on an airfoil is said to be unstable for, with it in equilibrium at any angle of attack, a disturbance will produce a moment which will augment the effect of such a disturbance rather than one which will tend to restore the, airfoil to its previous attitude once the disturbance subsides.

This is illustrated in figure 39. In A the airfoil is at an angle of attack a₁, and in equilibrium with respect to the vertical forces for L=W and there is no moment of lift. An upgust forces the airfoil to a new angle of attack a₂ as shown in B.

The lift must move forward but the weight will remain at the assumed center of gravity. A clockwise moment L x 1 is thus exerted tending further to stall the airfoil. This unstable travel of the center of pressure is characteristic of practically all airfoils employed. Without horizontal tail surfaces, a primary function of which is to impose counteracting moments, no conventional airplane would long remain in flight.

40. Airfoil dimensions.-The characteristics of an airfoil are influenced by the proportions of the plan view and by the amount of curvature of the section. The plan form of an airfoil is characterized by its span, chord length, aspect ratio, and contour of the wing tips.

a. Span is defined as being the distance between the wing tips, including ailerons.

b. The chord is the line of a straight edge brought in contact with the lower surface at two points or, in the case of an airfoil having double convex curvature, the line between the leading and trailing edges. (For the double convex section the edges may be defined as being the two points in the section that are farthest apart.) The method used in determining the chord must be stated in cases where ambiguity might exist.

41. Camber.-This quantity is the convexity or rise of an airfoil section above the chord. At any point the camber is expressed as a percentage of chord length and is a distance perpendicular to it. The coordinates and scheme of designating the section are shown in figure 40. The chord length is either the length of the straight line drawn between the leading and trailing edges as in A or is the distance between perpendiculars dropped from the leading and trailing edges to the chord as in B. The abscissa of any point is designated in percentage of the chord length, x/c, using the intersection of the chord with the leading edge as origin. The camber is the ordinate expressed in percentage of the chord as a/c and b/c.

42. Airfoil profiles.--a. Airfoil profiles may be considered as made up of a certain profile thickness form disposed about a mean line. The major shape variables then become two, the thickness form and the mean line form. The thickness form is of particular importance from a structural standpoint. On the other hand, the form of the mean line determines almost independently some of the most important aerodynamic properties of the airfoil section, e.g., the angle of zero lift and the center of pressure travel.

b. In wide use today are airfoil profiles developed as the result of Systematic investigation by the N. A. C. A. The airfoils of this series are designated by a number of four digits; the first indicates the camber of the mean line in percent of the chord, the second the position of the maximum camber of the mean line in tenths of the chord from the leading edge; and the last two, the maximum thickness in percent of the chord. Thus N. A. C. A. 2215 airfoil has a maximum camber of the mean line of 2 percent of the chord at a position 0.2c from the leading edge, and a maximum thickness of 15 percent of the chord.

c. An additional family of profile shapes developed about a mean line of different camber distribution has been tested by the N. A. C. A. Some of these profiles have excellent aerodynamic characteristics and find favor with designers. The, profiles of this series are designated by a number of five digits. Thus N. A. C. A. 22015 airfoil has a maximum camber of the mean line of 2 percent of the chord at a position 0.2c from the leading edge; a maximum thickness of 15 percent of the chord; and the shape of the curve of the mean line is from a family designated by the digit 0.

d. Different types of airplanes require widely varying wing sections. An airplane whose sole purpose is the transportation of heavy loads for relatively short distances may employ a wing section to give maximum lift without much consideration for drag. A racing airplane, on the other hand, may employ a thin section to permit a low resistance. The military airplane should have the weightcarrying capacity of a condor, the speed of a blue goose, and the maneuverability of a bat. It is necessary for the designer to sacrifice some of the desired characteristics and select a wing section that will satisfy the most important conditions.

43. Aspect ratio.-a. The span of an airfoil is the maximum transverse dimension normal to the relative wind, or the distance between the wing tips. The span therefore determines the amount of air acted upon and hence is an important factor in the production of lift by a given wing area. For an airfoil of rectangular plan form the ratio of span to chord is termed "aspect ratio." Thus an airfoil having a span of 30 feet and a chord of 6 feet would have an aspect ratio of 5. Very seldom however is an airfoil rectangular in plan form due to the employment of tapered wings, center section cut-outs, and various tip shapes. Consequently the aspect ratio is defined as span squared divided by area or

Aspect ratio= b²/S

b. The influence of aspect ratio on the airfoil and its characteristics hinges on the variations in airflow and pressure distribution with change in plan form. Were the airfoil of infinite span the airflow would be direct from leading to trailing edge for there would be no way for the streamlines below the surface to flow from this area of relatively high pressure to that of reduced pressure above. Since the airfoil is of finite area and span, air on the under side will seek the low pressure region above by "spilling" over the tips. Vortices or

.

eddies are thus formed at the tips, and the streamlines above and below the airfoil are deflected transversely as shown in figure 42.

The streamlines on the under side bend toward the tips, while those above bend toward the center owing to the pressure gradient produced. The "tip vortex" increases the drag on account of the turbulence created which absorbs energy.

They, furthermore, cut down the lift by destroying the section forces of the airstream above the airfoil close to the tips. Since these eddies are unavoidable, the only recourse is to reduce their effect as much as possible. This is accomplished by increase in aspect ratio. For a given airfoil area the tip vortices will be felt for an appreciable distance in from the tips. In figure 44 this distance is represented by x. The airfoil area is the same in each case. In A the area suffering from tip losses is 2cx and is much greater than in B where the value of c₂ is smaller and very much greater than in C where c³ is Still less.

c. Besides reducing the effect of tip vortices, increase in aspect ratio is directly beneficial to lift. This is due to the fact that the greater the aspect ratio the greater the mass of air to be given a downward momentum. Hence the lift coefficient will be greater, or for a given lift the amount of downward deflection can be reduced, thus lowering the drag.

d. To summarize, the airfoil characteristics are influenced as follows by increase in aspect ratio:

(1) The maximum value of C_L is increased.

(2) C_D values will be lower throughout the flight range. This is most marked at high angles of attack.

(3) The L/D is increased, with values particularly improved at high angles of attack.

e. From the foregoing it would appear that as high an aspect ratio as possible would give the most efficient airfoil. There are limitations in high aspect ratio in that too long a wing will require a larger amount of external bracing causing an increased drag and embracing more weight. In the case of the cantilever wing the root section must be of heavy construction and the necessity for increased material may offset the gain in lift. For these reasons aspect ratios have an upper limit of about 10 at the present. Improvements in metals may permit longer wings in the future. With increased aspect ratio the slope of the lift curve is steeper, indicating greater changes of lift with change in angle of attack and that the burble point is reached somewhat sooner.

f. It is interesting to note that some American racing airplanes and and fast low wing fighting airplanes employ a relatively low aspect ratio (5) - This permits better control in landing, for the stall is less abrupt and the drag is not much affected by a low aspect ratio at low angles of attack.

44. Induced drag.---a. By application of hydrodynamic theory, the following equation, for induced drag has been derived:

where C_D1, is the coefficient of induced drag and C_D0, is the coefficient of profile drag.

b. The relationship between lift, profile drag, and induced drag is shown in figure 45. This curve is a "polar curve". It will be observed that

(1) When the lift is zero the induced drag is zero.

(2) At small angles of attack the induced drag is small in comparison to the profile drag.

(3) At large angles of attack the induced drag is large in comparison to the profile drag.

(4) The profile drag coefficient is nearly constant throughout most of the flight range.

c. Another method of plotting the aerodynamic characteristics of an airfoil is becoming widely used. (Fig. 46.) In this method, C_D0 is plotted against C_L and C_D1 is computed. The total drag coefficient is therefore

The angle of attack for infinite aspect ratio a₀, is also plotted against C_L, and the angle of attack a  for any particular wing computed as follows:

45. Taper.--a. An airfoil is said to be tapered when a gradual decrease has been given to one or more of its dimensions in progressing from the plane of symmetry, or centerline, to the tip. The airfoil section at the centerline or, as in the case of a lower wing, at the fuselage is called the "root" section; that at the tip, the "tip" section. By maintaining the chord length constant and decreasing the camber, taper in thickness is obtained. By maintaining the camber constant and reducing the chord length, taper in plan form is produced. It is usual to employ taper in both plan form and thickness if employed at all.

b. Tapering a wing presents certain aerodynamic advantages. These advantages are offset by the fact that the tapered wing presents structural difficulties. The spars must be tapered and all ribs must be built in different jigs. Both these considerations increase

the cost of production and the designer must exercise judgment as to whether the aerodynamic advantages justify the increased cost.

c. The distribution of area is such that the resultant force is relatively close to the center line and hence a lighter structure is permissible. Furthermore, flight tests have shown tapered wings to be more easily controlled in flight by proper arrangement of angles of incidence along the span.

d. As compared with a rectangular airfoil of equivalent aspect ratio, a pronounced taper in plan form influences the airfoil characteristics as follows:

(1) Higher maximum C_L results.

(2) Lower values of C_D obtain, especially at low angles of attack.

(3) L/D is higher throughout the flight range, and especially so at high angles of attack.

(4) A somewhat greater movement of the center of pressure results with change in angle of attack.

e. Pronounced taper in thickness, say with the tip 60 percent that of the root, gives the following results in comparison with an airfoil of constant section equal to the average or mean section of the tapered Wing:

(1) The maximum C_L is greater with the peak of the characteristic curve flattened since the various sections attain their maxima at different angles of attack.

2) The C_D values are lower with the most pronounced decrease at small angles of attack.

(3) The maximum L/D is higher and values of L/D at small angles of attack are larger.

(4) The center of pressure movement is somewhat less for changes in angle of attack.

f. A proper employment of taper both in plan form and thickness will give an airfoil having characteristics which take advantage of the benefits of each kind.

46. Airfoil tip contours.-a. The types of airfoil tip contours are

(1) Rectangular.

(2) Elliptical.

(3) Positively raked.

(4) Negatively raked.

b. Figure 48 illustrates the types and shows the contour lines of pressure distribution for an angle of attack close to the stall. It should be noted that the positively raked tip is the one having the trailing edge longer than the leading edge.

c. The influence of tip contour on the airfoil characteristics is slight, any change from the rectangular giving some increase in both C_L and L/D and a decrease in C_D. The improvements are most marked in the elliptical tip and that with negative rake of approximately 30°.

d. The tip with positive rake, as also that of rectangular form, shows a relatively uneven distribution of pressure and high load concentration. These dictate a stronger structure and present the possibility of aileron flutter at high speed. In consequence, the elliptical type is usually favored.

e. The most commonly employed airfoils of today are of medium thickness employing negative or convex lower camber. This type gives a good lift-drag ratio, low resistance, and slight movement of the center of pressure. It also permits relatively high speeds with the available horsepower and wings thick enough for an efficient structure.

47. Airfoil selection.-In the selection of the proper airfoil for a particular airplane type, the factors to be considered will in many cases conflict, necessitating compromises. Principal among these factors are

a. Airfoil characteristics.

b. Airfoil dimensions.

c. Stability of airflow about the airfoil.

d. Adaptability of the airfoil to construction.

e. Operating limitations.

With very complete data available on hundreds of airfoils it would appear to be a hopeless task to select any particular one for a given purpose. However, whole groups of airfoils can be almost immediately discarded as evidencing undesirable qualities. Further analysis then quickly narrows the field to a very few acceptable shapes.

48. Lift coefficient criteria.-An airplane should have as low a landing speed as possible. For a given "'wing loading" this is fixed by the maximum lift coefficient. Wing loading is the ratio of the weight of the airplane in pounds to the wing area in square feet and varies but slightly for a particular type. The landing speed is then quickly determined from the formula

The higher the maximum lift coefficient the lower will be the landing speed for a given wing loading. If, on the other hand, the landing speed and weight are fixed by specifications, the higher the maximum lift coefficient the smaller the necessary wing area. A lift coefficient curve with a sharp peak or an unstable region at C_{L max} is undesirable as such an airfoil contributes to loss of control at stalling speeds.

49. Drag coefficient criteria.-The total drag on an airfoil is composed of induced drag and profile drag. Induced drag is that part of the total which results from deflection of the airstream and which would be the total drag were the air a nonviscous fluid and hence not subject to eddies. Profile drag is that part of the total which is due to skin friction and turbulence. It will vary only with the airfoil section employed, whereas the induced drag will vary with angle of attack and the aspect ratio of the airfoil. A low minimum drag is of vital importance to high speed airplanes, and in general the lower the minimum drag coefficient the greater is apt to be the high speed attainable.

50. L/D ratio criteria.-To determine the wing drag of an airplane of given weight at any angle of attack it is only necessary to divide the weight by the L/D ratio for that angle, or

This is obvious from the condition that the lift must equal the weight in steady flight. For a given weight, then; the greater the L/D ratio the smaller the drag at the particular angle of attack. While a good L/D ratio is desirable in the racer, minimum drag is of paramount importance. Where good climb and long range are the controlling factors, a high L/D ratio is essential owing to the economy afforded. This is due to the relatively low thrust required which in turn permits lower engine power and so a smaller fuel consumption.

51. Center of pressure criteria.-The distribution of load between the front and rear spars of an airplane wing as also that in its lift truss varies with movement of the center of pressure. Consequently the members must be built to withstand the worst loads to which they are subjected, which are bound to be greater than if the center of pressure were stationary. Other things being equal, then, the airfoil exhibiting the smallest center of pressure travel will be the lightest for a given strength. A second consideration in regard to center of pressure travel is its effect upon stability. With a fixed center of pressure the moment of lift would always be restoring and the moment arm small. The greater the travel of center of pressure, the greater will be the moment arm variation and instability of the wing.

52. Aspect ratio limitations.-a. In spite of the benefits accruing from increase in aspect ratio, seldom is it feasible to employ a value greater than 9, owing to structural and parasite drag limitations. Again, owing to the aerodynamic disadvantages of low aspect ratios a minimum value of 4 is the limit except in a few unconventional types. As the value is increased above this minimum the weight of the structure will increase for

(1) The bending moment will increase since the center of pressure on either side is farther from the wing hinges.

(2) The spar depths will decrease owing to the reduction in chord and less efficient and heavier spars must be employed for the requisite strength.

b. In the case of the cantilever monoplane these influences may eventually dictate abondonment of the cantilever type, but the addition of lift struts augments the parasite resistance which increases as these struts are lengethened to accommodate higher aspect ratios. The angle which these struts make with the wing will eventually become so flat as to lose rigidity of the truss unless undue weight is carried. Consequently, even a change from cantilever to semicantilever construction will not permit employment of abnormal aspect ratios.

c. The same elements are at work with the biplane. The internally braced type will first give way to single-bay trussing with an accompanying parasite drag of struts and wires. As the aspect ratio increases somewhat above 6, the wire pull angles become so flat that rather than increase weight unduly to aid rigidity and take care of bending, a two-bay truss is utilized instead. This must eventually give way to a three-bay truss but at just what point this and the preceding variations will occur depends upon such factors as the airfoil section used, the type of construction, the wing loading, etc.

d. A final consideration with regard to aspect ratio is that the greater its value the greater the span which dictates a longer fuselage, to place the tail advantageously for directional stability and control. This lengthening of the fuselage adds weight which must be taken into account when balancing the advantages and disadvantages of increased aspect ratio.

53. Airflow stability.-Airfoil sections of certain types show instability of airflow over their surfaces as evidenced by pressure distribution irregularities. They are very sensitive to changes in curvature which may come about from slight structural damage, loose fabric, flexure and torsion under flight loads, ice formation, and the like. Other sections show no such tendency, that is, their contours may be strongly modified without appreciable change of characteristics. Obviously, other things being equal the section showing the more stable airflow is the one to employ.

54. Structural adaptability.-The airfoil section chosen from careful study of characteristics must be suitable for the type of construction to be employed. A section clearly acceptable for a biplane may prove unsuitable for a monoplane owing to insufficient thickness to house spars of efficient section. Top and bottom cambers may be so formed as to dictate spar locations at points detrimental to utilization of the wing interior. The type of construction is bound to eliminate certain airfoils which are aerodynamically superior.

55. Operating limitations.-Of the, many operating limitations, that of landing speed is the most important. The size of landing fields offers a first limitation. The arresting gear of the aircraft carriers and launching speeds of catapults offer others. The added weight accompanying great span may dictate a change from monoplane to biplane construction or if not this then excessive hangar space is required and more elaborate handling facilities. These and many other operating limitations must not be overlooked when making the selection of the proper airfoil.

56. Airfoil sections.-Airfoil sections are classified as "thin", "'medium", or "thick". A thin section is one having a maximum thickness less than 10 percent of the chord. Medium thickness covers a range of 10 to 15 percent, and those above are thick sections. Generally speaking, a medium section is a good compromise. It does not have as low a drag as the thin section nor as high a lift as the highly cambered sections. It does, however, possess lift drag ratios approaching the maximum available.

57. Monoplane vs. biplane.-Were aerodynamic considerations paramount in the design of airplanes, all would be unbraced cantilever monoplanes with tapered wings on the basis of the superior aerodynamic performance of that type. That such considerations are not paramount is evidenced by the large number of biplanes in use and under construction at the present time. Airplanes with more than two sets of wings were employed in earlier times but were eliminated soon by the demonstrated superiority of the simpler types. The cantilever monoplane remained impractical until a deep airfoil section and more efficient materials were developed, since reasonable structural strength and rigidity could not be secured with the thin sections used in biplanes. Even where strength and rigidity were sufficient in the monoplane, structural efficiency, visibility, maneuverability, and other military features have dictated the use of biplanes in many cases.

58. Biplane pressure distribution.-The airflow between the wings of a biplane combination will differ considerably from what it would be if they were not in close proximity. Interference of the streamlines will exist which reduces the relatively low pressure on the upper surface of the lower wing. This interference is due to the air always wanting to flow from a region of high pressure to one of low pressure. The net result is that, while the lift of both wings is impaired, that of the lower suffers the most, for suction contributes the great percentage of lift. Unfortunately there is no reconciling reduction in drag, the lower wing contributing its portion. While the upper wing carries the greater load the percentage will be dependent on the values of gap-chord ratio, stagger, and decalage employed. These influencing factors will be discussed in succeeding paragraphs.

59. Biplane center of pressure.-The natural conclusion drawn from consideration of the pressure distribution of a biplane is that the resultant lift will be the sum of the lift of each wing and its line of action will be somewhere between the two centers of pressure. The point of application of the lift, however, must be assumed. It is said to be on the, mean aerodynamic chord of the combination. This mean aerodynamic chord is the chord of an assumed airfoil section having such a chord length, angle of attack, and so located in the side elevation of the airplane both vertically and horizontally that its airfoil would give the, same pitching moments as the combination at all angles of attack. In brief, it is essentially the chord of the equivalent monoplane wing, and will lie somewhere between the chords of the upper and lower wings as indicated in figure 49.

60. Gap-chord ratio.-The distance between the leading edges of the upper and lower wings of a biplane, measured perpendicular to the longitudinal axis of the airplane, is called "gap." This distance is not as a rule employed directly. Rather it is expressed as the gap-chord ratio. The method of measuring gap is shown in figure 51. The lower the gap-chord ratio, the greater will be the interference effects of the airflow and vice versa. However the practical variation of G/c from the value of unity is slight.

61. Stagger.-a. Stagger is the amount which one wing is set ahead of the other. It is positive when the upper wing is in advance of the lower and vice versa. It is measured parallel to the longitudinal reference axis of the airplane, usually between the 1/3 chord points of the mean aerodynamic chords of the individual wings as shown in figure 51. The wide employment of stagger is not due to

its aerodynamic benefits which are relatively small. Rather it is due to one or more of the following reasons:

(1) Improvement of vision.

(2) Affording of better free gun angles.

(3) Provision for better access to cockpits.

b. Some positive stagger may be necessary to place the pilot's eye in the chord line of the upper wing to minimize the "blind angle"

forward. With this position fixed, the farther aft the lower wing is moved, that is, the greater the positive stagger, the better will be the vision forward and downward. Negative. stagger, on the other hand, may be employed to obtain better gunfire angles forward and downward. Figure 53 illustrates these points.

c. Finally weight and balance considerations may require placing the forward cockpit between the wings of a two seater. By employ

ing positive stagger, and possibly by cutting away the trailing edge of the center section, access to the cockpit is improved as also exit therefrom in case of a forced jump. On the other hand gunfire angles from the rear seat might dictate the employment of negative stagger.

62. Decalage.-Decalage is defined as being "the difference between the angular settings of the wings of a biplane," or the acute angle between the extended chords of the upper and lower wings. The N. A. C. A. says that decalage is positive when the upper wing has the greater angle of incidence. When air is passing the wings of a biplane it is deflected downward. If the chord of the upper and lower wings were parallel, the downwash of the upper wing would have the effect of decreasing the angle of attack of the lower. In order properly to distribute the lift between the two wings it is then necessary to set the lower wing at a greater angle. Upper and lower wings being at different angles of attack, the pressure distribution between the wings will be altered. With positive decalage the upper Wing will receive an increase in load percentage which is most pronounced at high speed. Negative decalage throws an increased percentage on the lower wing. Since the wings reach their burble points at different angles of attack, the peak of the lift curve for the combination will be flattened and consequently the stall will be less abrupt.

63. Landing speed.-The minimum or stalling speed for the average aircraft is about one-third or two-fifths the maximum speed. This indicates landing speeds approaching 100 miles per hour for fast transports and military airplanes. High landing speed presents a disadvantage in an airplane, first because of the inherent danger in fast landing craft and second, the scarcity of large airports when an emergency landing is in order.

From the fundamental formula for landing speed

it is evident that landing speeds can be reduced only by increasing the area of wings or by increasing the maximum lift coefficient.

64. Variable wing area.-Variation in wing area while aerodynamically sound is fraught with structural difficulties. The rigidity of the wing must not be impaired, the necessary additional weight of operating mechanism must not be excessive, the strength of the wing must be maintained, and the shape of the section cannot be detrimentally affected by the variation. While telescoping wings are under experiment there is grave doubt of their ever completely satisfying the above structural requirements.

65. Variable camber.-a. The alternative to variation of area is that of variation of lift coefficient. One expedient is to change the airfoil section or camber in flight. Operation on the section as a whole to increase the camber has as great if not greater structural objections than has the variation of area, There remains then the variation of camber by turning down leading and trailing edges of the wing. Increased curvature or camber will result from turning down either one or both of these edges. This will improve the lift of the airfoil, but naturally not as much as if the curvature were gradual. The drag, of course, is increased, being particularly marked with the trailing edge well down. The rear flap in this position thus constitutes an effective airbrake which affords a steeper descent for landing without increase in airspeed. This is of great advantage in entering a small field over obstructions as illustrated in figure 54.

b. The combination of leading and trailing edge flaps is rarely used. The trailing edge flap, of which there are many variations, is in use to a great extent and is at present the most popular "highlift" device.

(1) The plain flap is similar to ailerons except that the flaps on both sides are lowered simultaneously. The normal plain flap installation on a monoplane is inboard of the ailerons and in a biplane on one wing with ailerons on the other. The plain flap is heavy, hard to operate, and rather inefficient. Its possible applications are limited.

(2) The plain split flap is normally housed flush with the under surface, of the wing just forward of the trailing edge. It is simply a flat metal plate hinged along its forward edge. Tests have shown it to be fairly light and effective, but the hinge, moments are large and it is difficult to operate.

(3) Zap or Alfaro, flaps are similar to the plain split flaps when retracted but the hinge axis is moved aft as the flap is opened to keep the trailing edges of the flap and wing on a line normal to the chord. Zap flaps are more effective and easier to operate than plain flaps.

c. Types of flaps are shown in figure 55. At normal speeds, the flaps being in the up or retracted position, there is no effect upon the lift characteristics of the wing. When the flaps are lowered for landing the lift coefficient curve for the airfoil shows an increase for similar angles of attack of the basic airfoil. The maximum lift coefficient is increased about 70 percent depending upon the type of flaps employed. This is illustrated by the curve in figure 56. In addition to the increased lift there is an increased drag when the flap is down. This increase in drag permits and requires a steeper glide to maintain the reduced flying speed. This increased drag also acts as a brake when the airplane is rolling to a stop on the field.

As a hint to pilots, as the airplane approaches to land and the speed is reduced to permit lowering the flaps, the increased drag as the flaps are lowered may further reduce the speed and permit the airplane to stall. The stall can he prevented by care on the part of the pilot. Also in landing, the stall is rather abrupt due to the high drag as the airplane is leveled off for landing. The high drag reduces speed so rapidly that the airplane is likely to "pancake" unless the pilot is decisive in his landing procedure.

d. The flap in recent use does not entirely satisfy the requirements of a high lift device. Its advantages stated briefly are

(1) Higher lift coefficient permits a lower speed in landing.

(2) Acting as "airbrakes" the flaps permit a shorter run on the ground in stopping the airplane.

(3) A steeper gliding angle without increase of speed permits clearing of obstructions in landing and also makes spot landings easier.

(4) The use of flaps prevents the tapered wing from stalling at the tip first which is a dangerous characteristic of this very valuable wing plan form.

e. The disadvantages of flaps are such as the following:

(1) The use of flaps requires a particular pilot technique.

(2) Owing to the high drag when increasing the angle of attack it is difficult to control the flight path.

(3) There is always added weight and the possibility of mechanical failure.

(4) The flap is not automatic in operation and the control constitutes another "gadget" to occupy the pilot.

(5) The flap, extending as it usually does along the trailing edge between the ailerons, will, when at full throw, interfere with the functioning of the latter to impair seriously lateral control. Cross wind landings cannot, therefore, be undertaken with impunity.

1. It may be of interest to note that, in the application of flap devices to biplanes, flaps on the lower wing only give a greater increase in maximum lift than flaps on the upper wing only, and that flaps on both wings give a much greater increase in maximum lift than the sum of the two increases, upper and lower. However, when installing flaps on only one wing of a biplane, it is customary to install them on the upper wing since the change in balance of the plane is less.

66. Automatic slots.-a. Another way of increasing lift and consequently reducing landing speeds is by preventing the wing from burbling until a greater angle of attack is reached. The automatic slot accomplishes this. It consists of an auxiliary airfoil housed in the leading edge of the wing at low angles of attack but free to move

forward a definite distance therefrom at high angles to form a flat nozzle or slot through which a portion of the airstream flows to be deflected along the upper surface. The effect of this diverted stream upon the airflow as a whole and consequently the advantage of the device are indicated in figure 57.

b. The auxiliary airfoil section, derived from the trace of a highly cambered airfoil, is on the leading edge of a normal wing. Were it not free to move, the airflow would be the same as for the normal wing as shown in A and B. It is, however, free to move on a system of linkages supported by the front spar. Considered alone, the,

airflow about it would be as in C. When advanced from the wing at high angle of attack to form the slot, the air will flow through the slot as is obvious from a, consideration of the relatively low pressure above the wing. Being deflected along the upper surface of the wing by the shape of the slot, this inflow of air will postpone the breakdown of streamline flow with increase in angle of attack. The burble point, in fact, will not be reached until the angle of attack is nearly double that of normal stall where the slot is well designed and functioning properly. This is shown in figure 58.

c. It is evident from the diagram that the lift is improved at angles where the slot is open and the maximum C_L is not only larger but occurs at a much higher angle of attack. Consequently, the airplane with the slotted wings will have a much lower stalling speed than one, not so equipped. But this is not all. The slotted wing is an effective agent for securing lateral stability and avoiding unintentional spins.

d. The automatic functioning of the slot depends upon the pressure distribution with change in angle of attack. It will be remembered that the leading edge is subjected to downloads at low angles of attack and to increasing suction with increase in angle. As long as there is a download the slot will necessarily remain closed. With increase in suction on the auxiliary airfoil, the resultant of all forces on it will finally attain a value and direction sufficient to move it on a properly designed mechanism.

e. For all its advantages the automatic slot imposes disadvantages. Additional weight and moving parts are unavoidable. Weight is further added by the necessity of having longer landing gear struts or oleo legs to eliminate tail skid landings otherwise imposed upon landplanes by the increased angle of attack at the stall.

f. If the slots are not properly fitted or do not operate with equal freedom at opposite wing tips their value is destroyed. They are located on the portion of the wing subjected most strongly to ice formation which, if occurring, will prevent their functioning. With an unbalance from any of the above causes, pernicious spinning may result once it is started and lateral control is difficult.

g. It is, therefore, important that a device, be available to lock poorly functioning slots in the closed position. Furthermore, the increased lateral stiffness afforded by the slots makes it advisable to lock them when performing violent manuevers Such a locking device, controlled from the cockpit, has been developed which adds materially to the service value of the airplanes on which they are installed.

h. In some instances airplanes are equipped with a combination of slots and flaps. This type of installation has many advantages. It permits a, much lower landing speed, better control of the flight path, and helps to eliminate nose heaviness caused by the use of flaps alone. The stalling angle of attack differs little from that of the basic airfoil and hence the length of the landing gear legs may remain unchanged.

67. Viscosity.-Viscosity is the tendency of a fluid to stick to surfaces and to resist relative motion by a shearing stress in the fluid itself. The unit of viscosity m is the force required to move two flat plates relative to each other, each plate being of unit area and unit distance apart.

The laws of air resistance thus far discussed are based on the assumption that the forces are due to the scale of the model L. the velocity V, and the density of the air r. Forces due to viscosity have been neglected as being so small as to result in no serious error.

The forces due to viscosity give rise to "skin friction," which in cases such as the resistance of airship hulls is a factor that may be

larger than the, dynamic forces. The laws of skin friction are quite different from the laws governing dynamic resistance.

68. Reynold's number.-a. By application of the theory of dimensions, it can be shown that the quantity Vl r/m (Reynold's number) is the factor that may be taken as a measure of the effects of viscosity. This is also referred to as "scale effect." V is in ft./sec., l in feet (customarily the chord of an airfoil) and r/m (for standard air) =6,380. sec./sq. ft. Thus the Reynold's number for an airplane with a chord of 10 feet at a velocity of 180 m. p. h. (264 ft./sec.) is

R. N. = 6,380 x 10 x 264 = 17,000,000   (40)

b. If wind tunnel data are to be useful to the airplane designer, the Reynold's number of the wind tunnel test must be of the same general magnitude as the Reynold's number of the full scale airplane. If a small scale model is used in the wind tunnel, one way of keeping the Reynold's number constant is to increase the density of the air as is done in the National Advisory Committee for Aeronautics variable density wind tunnel where tests are run at densities as high as 20 times the standard density.

c. In applying wind tunnel test data obtained from small models to full scale airplanes, the following effects can usually be expected:

(1) Lift coefficients are not materially affected by scale effects (except C_{L max})

(2) The drag of the full scale airplane will be considerably less than predicted.

(3) Center of pressure travel is not materially affected.

(4) C_Lmax and the shape of the lift curve at C_Lmax may be materially affected by the Reynold's number.

(5) The appearance of unstable airflow and the change from streamline flow to turbulent flow are greatly influenced by Reynold's number.

(6) Parasite resistance is greatly affected by Reynold's number, in general being less than predicted with increase in RN.

(7) Profile drag coefficient C_D, decreases with increase in RN.

69. Boundary layer effects.-a. Mathematicians imagine an ideal frictionless fluid which slips past solid surfaces with perfect ease. The real fluid, air, cannot slip past in this way. Due to its viscosity, it sticks to the surface of solid bodies and its velocity falls

to zero as the solid surface is approached. The layer of fluid surrounding the solid surface, in which this velocity fall takes place, is called the "boundary layer", and with large bodies of good streamline form moving fast it is relatively thin. Skin friction is the drag force which depends upon what happens within the boundary layer. It is due to the viscosity of the fluid.

b. The form taken by the boundary layer about a wing does not differ greatly from the boundary layer upon a flat surface which has been extensively studied both experimentally and theoretically. Figure 63 indicates a boundary layer on a flat surface, the vertical scale being greatly exaggerated. The thickness of the boundary layer and the amount of drag incurred in it remain very small for some distance from the leading edge of the surface. In this forward Part of the layer, the flow is called "laminar", that is, separate sheets, or laminae, of air overlie the solid surface and slide over one another without mixing. At the transition point, relatively rapid thickening of the boundary layer begins, the flow within the layer becomes irregular (turbulent), there is a thorough mixing of air from different levels, and the resulting drag is relatively large. Beneath the turbulent part of the boundary layer is an exceedingly thin viscous sublayer within which the velocity gradient is very great and the airflow returns nearly to the laminar form. The importance of this viscous sublayer lies in that it appears that, provided the roughness on the surface over which the air flows does not protrude beyond the viscous sublayer, it has no effect upon the turbulent outer parts of the boundary layer through which drag is conveyed from the main stream, and hence

it has no effect upon the skin friction. When a surface is sufficiently rough that the projections on it penetrate beyond the viscous sublayer, the main turbulent layer is increased and with it the skin friction. Surface irregularities such as rivet heads, lapped joints and spot welds may increase wing drag sufficiently to have important adverse effects on high speed airplane performance. This is the more readily understood if it is realized that the thickness of the laminar sublayer may be on the order of 0.0002 inch at the Reynold's number of maximum speed in flight, so that irregularities which project farther from the surface than this value will increase the drag due to skin friction.

c. In figure 64 is a representation of the boundary layer and wake of a wing in flight, together with the points of transition from laminar to turbulent flow and curves showing the drag incurred in the boundary layer up to each point on the profile. The dotted line indicates the skin friction drag which would be incurred if turbulent flow could be suppressed so that, skin friction drags would occur in an entirely laminar boundary layer. It is apparent from the diagram that any factors which will postpone transition

to turbulent flow to a point farther along the profile from the leading edge will result in greatly decreased profile drags. The location of the transition point is affected by several variables, among which are the Reynold's number, turbulence of the free air, curvature of the surface, and the roughness of the surface.  It is known that the free air is remarkably free from turbulence on a scale tending to transform the laminar flow of the boundary layer to turbulent flow, and that it is possible to postpone the transformation to turbulent flow to points sufficiently far from the leading edge of wings that large reductions in profile drag occur. Since at low angles of attack the greater part of the wing drag is profile drag, marked increase in high speed performance accrues from all measures which result in delaying the transition from laminar flow to turbulent flow in the boundary layer.