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The energy factors at the upper surface of a wing, as we have said, are velocity and pressure—higher velocity, lower pressure. If the velocity of the relative wind is normally very high during cruising flight of an airplane, it is not necessary for its wings to have much camber. This is one of the reasons why fighter-type military aircraft have thin wings. At slower speeds, such as during takeoffs or landings, the loss of induced lift because of the low camber is compensated for by using a high angle of attack. As you can see, this high angle of attack causes an increase in the dynamic lift. Even so, the airplane with low-camber airfoils must use much higher takeoff and landing speeds than the more conventional airplane.

To further illustrate these points, note in the top portion of Figure 4-4 that we have two examples of airfoils with the same relative wind velocity and the same dynamic lift. However, by thickening and increasing the camber of the wing, wing B's total lift is increased because of the increased induced lift.

In the lower portion of Figure 4-4, you are looking at two wings which are producing the same mount of total lift even though one wing has less amber than the other. Both wings are at the same angle of attack so they have the same amount of dynamic lift for any given airspeed (velocity of the relative wind). The only way to make the thin wing produce as much lift as the thick wing is to speed it up, and this is what we attempt to show in the figure. Wing C's relative wind is ten miles per hour faster than D's relative wind, this additional speed is needed to increase both the dynamic and induced lift so that its total lift can equal that of Wing D. We want you to understand that the examples in Figure 4-4 are just that.

We have discussed the atmosphere and how airfoils produce lift because of their movement through the atmosphere. We also mentioned that lift is the force that counteracts the force of gravity to allow flight. At this point, you may have concluded that lift and gravity are the only forces involved with flight. Actually there are two others, thrust and drag, which complete the three-dimensional forces acting upon an aircraft in flight. Figure 4-5 shows the basic directions of all four forces when an aircraft is in straight and level flight at a constant speed. Now, you should be able to see that, in this situation, the four forces are in balance. The force of total lift equals the force of total weight, so there is no upward or downward movement. The force of thrust equals the force of drag, so there is no increase or decrease in the speed of the airplane. You should also be able to see that the moment one of these forces becomes stronger or weaker than the others, some type of reaction must take place.

The lift and drag of an airfoil depend upon several parameters:

The shape of the airfoil which is translated into coefficients
C_{L} and C_{D}; the planform area of the wing—S; the square of the velocity (or true airspeed)—V^{2};
and the density of the air—.

Thus, the lift (L) and drag (D) of an airfoil can be expressed as follows:-

The coefficients C_{L} and C_{D} represent the
**coefficient of lift and coefficient of drag **respectively. They change with the
shape of the airfoil and with the angle of attack and other wing additions
such as wing flaps.

The **lift-to-drag ratio **gives the relation between lift and
drag and is defined as L / D or equivalently C_{L} / C_{D}.

For each wing cross-section these parameters C_{L} , C_{D}
and L / D can conveniently be represented by graphs as functions of the
change in angle of attack. Also the movement of the center of pressure can
be plotted there as well.

Where the lift curve (C_{L}curve) reaches its maximum
for this particular wing section is called the stalling angle. As the
angle of attack increases, you will see a rapid drop in C_{L }and an increase in the drag, represented by
C_{D}

The lift-drag ratio (L/D curve) has a maximum at 0 degrees angle of attack. There you get the most lift for the least drag.

The graphs shown above represent data for one airfoil or wing cross-section. Different airfoils with different camber and airfoil thickness produce different looking curves. These curves are obtained normally by experimental work using wind tunnel tests. Many tests were run by the NACA, the predecessor to the NASA, and a booklet, NACA Report 824 (1945) was created to give the relation of coefficient of lift, coefficient of drag, pressure and moment coefficients (not shown above) for many different types of airfoil. We find that the coefficients of lift, drag and moment depend upon the angle of attack, the mach number and the Reynolds number.

For subsonic speeds, normal airfoils have a linear relationship between angle of attack and coefficient of lift until just before stall occurs (the airfoil or wing experiences a loss of lift). For higher speeds, when the mach number is higher than 0.3 (mach number is the velocity of the aircraft divided by the velocity of the sound), then the coefficient of lift is

C_{L} = C_{Lo} / (1 - M^{2})^{1/2}

where

C_{Lo}= the coefficient of lift at low speed

M = the mach number in the free stream

This correction for the mach number effect is based on Glauert
who proposed it in 1928. Von Karman and Tsien proposed a more complicated
equation (not shown here). Note that the coefficient of lift at low speed, C_{Lo},
is the value that is normally obtained experimentally. The above equation holds
true even for mach number values less than 0.3, but the effect on the
coefficient of lift is minimal.

Finally, we said that the lift coefficient is also dependent on Reynolds
number, R_{N}, where

R_{N} = rVd/m

Here, the Greek letter, r, represents the density of the fluid--air; V is the velocity of the free-stream airflow; d is the characteristic length of the airfoil and, the denominator, given by the Greek symbol, m, represents the fluid viscosity. Actually, the Reynolds number determines the type of flow (whether laminar or turbulent), which, in turn, determines where the flow separates from the airfoil or wing. This, in turn, affects the lift, drag and moment coefficients, as explained above. We note that as Reynolds number increases, the maximum lift coefficient increases. But this does not occur indefinitely; when flows become very turbulent, the maximum lift coefficient begins to drop and so does the overall lift coefficient.

The first portion of the page is given from the Civil Air Patrol student guide. Airplane Aerodynamics, by D.O. Dommasch, S.S. Sherby and T.V.Connolly , Pitman Press, Fourth edition, pp. 106-120 (1967) is the source for the last half of this page. The material has been summarized, paraphrased and presented by the ALLSTAR network.

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**Updated:
December 23, 2008**