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**Lift and Drag Curves- Level 3**

As the amount of lift varies with the angle of attack, so too does the drag. Hence drag is the price we pay for lift. Thus, although it is desirable to obtain as much lift as possible from a wing, this cannot be done without increasing the drag. It is therefore necessary to find the best compromise.

The lift and drag of an airfoil depend not only on the angle of attack, but also upon:

The shape of the airfoil

The plan area of the airfoil (or wing area)—S.

The square of the velocity (or true airspeed)—V^{2}.

The density of the air—.

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

The symbols C_{L} and C_{D} represent the **lift
coefficient and drag coefficient **respectively. They depend on the shape of the airfoil
and will alter with changes in the angle of attack and other wing appurtenances.

The **lift-drag ratio **is used to express the relation between lift
and drag and is obtained by dividing the lift coefficient by the drag coefficient, C_{L}
/ C_{D}.

The characteristics of any particular airfoil section can conveniently be represented by graphs showing the amount of lift and drag obtained at various angles of attack, the lift-drag ratio, and the movement of the center of pressure.

Notice that the lift curve (C_{L}-yellow curve) reaches its
maximum for this particular wing section at 18 degrees angle of attack, and then rapidly
decreases. 18 degrees angle of attack is therefore the stalling angle.

The drag curve (C_{D}-blue curve) increases very rapidly from 14
degrees angle of attack and completely overcomes the lift curve at 22 degrees angle of
attack.

The lift-drag ratio (L/D-green curve) reaches its maximum at 0 degrees angle of attack, meaning that at this angle we obtain the most lift for the least amount of drag.

The Center of Pressure(CP-red cross) moves gradually forward until 12 degrees angle of attack is reached, and from 18 degrees commences to move back.

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 information in the first half of this section has been extracted from several sources. Those sources have been contacted and permission to use their material on our site is pending. However, the format in which this material has been presented is copyrighted by the ALLSTAR network.

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: March 12, 2004**