NAVWEPS 00-801-80 BASIC AERODYNAMICS and high power, the dynamic pressure in the net produced by the is difference shaded area can be much greater than the free between the lifts on the upper and lower sur- stream and this causes considerably greater faces. The point along the chord where the lift than at zero thrust. At high power con- distributed lift is effectively concentrated is ditions the induced flow also causes an effect termed the "center of pressure, c.p. - The similar to boundary layer control and increases center of pressure is essentially the ''center of the maximum lift angle of attack. The typical gravity" of the distributed lift pressure and four-engine propeller driven airplane may have the location of the c.p. is a function of camber 60 to 80 percent of the wing area affected by and section . the induced flow and power effects on stall Another aerodynamic reference point is the speeds may be considerable. Also, the lift of -aerodynamic center, a.c. - The aerodynamic the airplane at a given angle of attack and air- center is defined as the point along the chord speed will be greatly affected. Suppose the where all changes in lift effectively take place. airplane shown is in the process of landing To visualize the existence of such a point, flare from a power-on approach. If there is notice the change in pressure distribution with a sharp, sudden reduction of power, the air- angle of attack for the symmetrical airfoil plane may drop suddenly because of the reduced of figure 1.21. When at zero lift, the upper lift. and lower surface lifts are equal and located The typical jet does not experience at the same point. With an increase in angle the induced flow velocities encountered in of attack, the upper surface lift increases while propeller driven airplanes, thus the only sig- the lower surface lift decreases. The change nificant factor is the vertical component of of lift has taken place with no change in the thrust. Since this vertical component con- center of pressure—a characteristic of sym- tributes to supporting the airplane, less aero- metrical . dynamic lift is required to hold the airplane Next, consider the cambered airfoil of in flight. If the thrust is small and the thrust figure 1.21 at zero lift. To produce zero lift, inclination is slight at maximum lift angle, the upper and lower surface lifts must be equal. only negligible changes in stall speed will re- One difference noted from the symmetrical air- sult. On the other hand, if the thrust is very foil is that the upper and lower surface lifts are great and is given a large inclination at maxi- not opposite one another. While no net lift mum lift angle, the effect on stall speed can exists on the airfoil, the couple produced by be very large. One important relationship the upper and lower surface lifts creates a nose remains since there is very little induced flow down moment. As the angle of attack is in- from the jet, the angle of attack at stall is creased, the upper surface lift increases while essentially the same power-on or power-off. the lower surface lift decreases. While a change in lift has taken place, no change in DEVELOPMENT OF AERODYNAMIC PITCHING MOMENTS moment takes place about the point where the lift change occurs. Since the moment The distribution of pressure over a surface about the aerodynamic center is the product is the source of the aerodynamic moments as of a force (lift at the c.p.) and a lever arm well as the aerodynamic forces. A typical example of this fact is the pressure distribution (distance from c.p. to a.c.), an increase in lift acting on the cambered airfoil of figure 1.21. moves the center of pressure toward the aero- The upper surface has pressures distributed dynamic center. which produce the upper surface lift; the lower It should be noted that the symmetrical air- surface has pressures distributed which pro- foil at zero lift has no about duce the lower surface lift. Of course, the the aerodynamic center because the upper and 47

Aircraft Technical Book Company (800) 780-4115 (970)-887-2207 http://www.ACTechBooks.com NAVWEPS 00--80T-80 BASIC AERODYNAMICS CAMBERED AIRFOIL UPPER DEVELOPING POSITIVE SURFACE LIFT LIFT NET LIFT

C. P.

-LOWER SURFACE LIFT

SYMMETRICAL AIRFOIL CAMBERED AIRFOIL AT ZERO LIFT AT ZERO LIFT UPPER SURFACE UPPER SURFACE LIFT LIFT .. 41/111W .40er

LOWER SURFACE 41! IOW LIFT LOWER SURFACE LIFT SYMMETRICAL AIRFOIL CAMBERED AIRFOIL AT POSITIVE LIFT AT POSITIVE LIFT I UPPER SURFACE LIFT 1-4-UPPER SURFACE LIFT

-way w 111111rmr. LOWER SURFACE LIFT LOWER SURFACE LIFT

4--CHANGE IN LIFT -4-CHANGE IN LIFT f t PITCHING MOMENT a.c. a.c.

Figure 1.21. Development of Pitching Moments

48 Aircraft Technical Book Company (800) 780-4115 (970)-887-2207 http://www.ACTechBooks.com NAVWEPS 00-801-80 BASIC AERODYNAMICS lower surface lifts act along the same vertical c,,,,,.e. versus lift coefficient for several repre- line. An increase in lift on the symmetrical sentative sections. The sign convention ap- airfoil produces no change in this situation and plied to moment coefficients is that the nose-up the center of pressure remains fixed at the aero- moment is positive. dynamic center. The NACA 0009 airfoil is a symmetrical sec- The location of the aerodynamic center of an tion of 9 percent maximum thickness. Since airfoil is not affected by camber, thickness, and the mean line of this airfoil has no camber, angle of attack. In fact, two-dimensional in- the coefficient of moment about the aerody- compressible airfoil theory will predict the namic center is zero, i.e., the c.p. is at the a.c. aerodynamic center at the 25 percent chord point The departure from zero occurs only as the for any airfoil regardless of camber, thickness, airfoil approaches maximum lift and the stall and angle of attack. Actual airfoils, which produces a moment change in the negative are subject to real fluid flow, may not have the (nose-down) direction. The NACA 4412 and lift due to angle of attack concentrated at the 63 1 -412 sections have noticeable positive cam- exact 25 percent chord point. However, the ber which cause relatively large moments about actual location of the aerodynamic center for the aerodynamic center. Notice that for each various sections is rarely forward of 23 percent section shown in figure 1.22, the cm..e. is constant or aft of 27 percent chord point. for all lift coefficients less than clmax. The moment about the aerodynamic center The NACA 23012 airfoil is a very efficient has its source in the relative pressure distribu- conventional section which has been used on tion and requires application of the coefficient many airplanes. One of the features of the form of expression for proper evaluation. The section is a relatively high coma, with only a moment about the aerodynamic center is ex- small cia.e. The pitching moment coefficients pressed by the following equation: for this section are shown on figure 1.22 along with the effect of various type flaps added to = qSc the basic section. Large amounts of camber where applied well aft on the chord cause large nega- tive moment coefficients. This fact is illus- Ma.c. = moment about the aerodynamic center, trated by the large negative moment coeffi- a.c., ft.-lbs. cients produced by the 30° deflection of a 25 percent chord flap. Cma.c. = coefficient of moment about the a.c. The cn, a, is a quantity determined by the q= dynamic pressure, psf shape of the mean-camber line. Symmetrical airfoils have zero cma and the c.p. remains at S= wing area, sq ft. the a.c. in unstalled flight. The airfoil with positive camber will have a negative c,„„, c= chord, ft. which means the c.p. is behind the a.c. Since the cma.c. is constant in unstalled flight a certain The moment coefficient used in this equation is relationship between lift coefficient and center the dimensionless ratio of the moment pressure of pressure can be evolved. An example of to dynamic pressure moment and is a function this relationship is shown in figure 1.22 for the NACA 63 1-412 airfoil by a plot of c.p. versus Ma.c. Cm c1 — qScqSc . Note that at low lift coefficients the center of pressure is well aft—even past the trailing of the shape of the airfoil mean camber line. edge—and an increase in c 1 moves the c.p. for- Figure 1.22 shows the moment coefficient, ward toward the a.c. The c.p. approaches the 49 Revised January 1965 Aircraft Technical Book Company (800) 780-4115 (970)-887-2207 http://www.ACTechBooks.com NAVWEPS 00-801-80 BASIC AERODYNAMICS

+0.1

SECTION LIFT COEFFICIENT, C1 .2 .4 .6 .8 1.0 1.2 1.4 16 1.8 0 i NACA 23012 NACA 0009 NACA 31-412 1-7z L.LJ NACA 4412 5 —0.1 s7C--)

0 i---z 25% NACA 23012 WITH SPLIT FLAP AT 30° 0 —0.2 2 0 ►s= 25°4 NACA 23012 WITH PLAIN FLAP AT 30° —0.3

2 5°41 1 1 NACA 23012 WITH SLOTTED FLAP AT 30°

—0.4

ehq CP POSITION FOR NACA 631-412 z 2.0 SECTION Cmac = —.075 w c.) 1 .8 1.6 'AMAX 0 1.4

Li 1.2 z 1.0 0 .8 (.3 .6 .4

.2 t-- 0 10 20 30 40 50 60 70 80 90 100 110 CP POSITION PERCENT CHORD AFT OF LEADING EDGE

Figure 1.22. Section Moment Characteristics 50 Revised January 1965 Aircraft Technical Book Company (800) 780-4115 (970)-887-2207 http://www.ACTechBooks.com NAVWEPS 00-80T-80 BASIC AERODYNAMICS

CHANGE IN LIFT CHANGE IN LIFT DUE TO UPGUST DUE TO UPGUST

(STABLE) (UNSTABLE)

a c. C.G.

LIFT

Ma.c.

C G. a c. WEIGHT

Figure L23. Application to Stability

a.c. as a limit but as stall occurs, the drop in aerodynamic center. This very necessary fea- suction near the leading edge. cause the c. p. to ture can be visualized from the illustrations of move aft. figure 1.23. Of course, if the airfoil has negative camber, If the two symmetrical airfoils are subject or a strongly reflexed trailing edge, the moment to an upgust, an increase in lift will take place about the aerodynamic center will be positive. at the a.c. If the c.g. is ahead of the a.c., the In this case, the location of the aerodynamic change in lift creates a nose down moment center will be unchanged and will remain at about the c.g. which tends to return the air- the quarter-chord position. foil to the equilibrium angle of attack. This The aerodynamic center is the point on the stable, "weathercocking" tendency to return chord where the coefficients of moment are to equilibrium is a very necessary feature in constant—the point where all changes in lift any airplane. If the c.g. is aft of the a.c., the take place. The aerodynamic center is an ex- change in lift due to the upgust takes place at tremely important aerodynamic reference point the a.c. and creates a nose up moment about and the most direct application is to the longi- the c.g. This nose up moment tends to displace tudinal stability of an airplane. To simplify the airplane farther from the equilibrium and the problem assume that the airplane is a is unstable—the airplane is similar to a ball tailless or flying wing type. In order for this balanced on a peak. Hence, to have a stable type airplane to have longitudinal stability, airplane, the c.g. must be located ahead of the the center of gravity must be ahead of the airplane a.c. 51

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