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Guest Lecturer
"SmokeDog" Stu Moment
Stu Moment is an air show performer who also participates in many aviation education activities for kids and adults.
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“Simple Aerodynamics"
Part 4
copyright 1984, 2004, Sublogic Corporation 

SmokeDog's Note: Part 3 illustrated the generation of lift. This lesson will quantify the amount of lift you can generate and the trade-off between producing lift versus generating a new type of drag. This lesson will end by contrasting the lift generation/drag generation properties of two airfoils.

In Part 1 we were presented with a formula to calculate drag.

D=K x A x Vsquared where D=drag, K = co-efficient of resistance determined by experiment, A = area of plate in square feet, and V = velocity in miles per hour.

We also have a formula for lift.

Lift = (some) Coefficient X Area X Velocitysquared. (Area is the total wing area).
Early texts used "K" for coeffients but modern science uses "C" to denote coeffients. Since were about to show some modern charts, we’ll designate the coefficient of lift as ‘CL’ and the coefficient of drag as ‘Cd’.

The coefficient of lift will vary with angle of attack. The last lesson ended with a chart showing that lift increases with angle of attack until the stall is reached.

The following chart shows the coefficient of lift for a particular airfoil at different angles of attack. The lift coefficient line is the tallest one and is labeled ‘CL’. The numerical lift coefficient is shown just to the right of the chart.

A standard graph of coefficient of lift versus angle of attack. Lift Coefficient is just to the right of the graph. Angle of attack is on the bottom. The maximum coefficient of lift for an airfoil with this shape is 1.6. The maximum occurs at 22 degrees angle of attack. (This NACA 2312 airfoil is a very nice, general purpose airfoil for cruise speeds between 100 and 200 MPH.)

But there is another column of numbers to the right of the lift coefficients. It’s a column of “drag coefficients”. We discussed parasitic drag in the first two lessons. This was drag caused by a structure getting in the way of airflow. As you increased speed, this "parasitic" drag increased by Velocitysquared. The drag on the airfoil chart is a different type of drag. It is caused by the creation of lift (nothing comes for free). It is called "induced" drag.

Induced Drag
While creating lift, your airfoil changes the direction of airflow in many ways. You’re already familiar with downwash. This downward deflection of air changes the relative wind in the vicinity of the wing to a slighty downward direction. As a result, the true angle of attack is different from the apparent angle of attack. In the last lesson, we described this apparent angle of attack by stating that the relative wind is opposite the flight path. But the airfoil alters the relative wind. This is described in the following diagram as “induced relative wind.”

Lift is produced perpendicular to the real, induced relative wind direction. A relative wind in a slighty downward direction will give us a real lift vector with a component toward the rear. This rearward component is known as induced drag. The following figure illustrates the concept of induced drag.

Since higher angles of attack tilt the lift vector even further back, induced drag is increased when the angle of attack increases. Let’s repeat the chart that we showed earlier. Now, note the line showing the coefficient of drag ‘Cd’. Notice that it is not a straight line. ‘Cd’ increases quickly with an increase in angle of attack.

Let’s relate “angle of attack” to flight at different airspeeds. If weight, bank angle, and other factors are held constant, a slower airspeed demands a higher angle of attack to produce the same lift. Therefore, the slower the airspeed, the greater the induced drag. The next figure shows a graph of Induced Drag vs. Airspeed. Note that it is nonlinear. As velocity decreases, induced drag increases inversely proportional to the square of the velocity. This phenomenon can be explained when you remember that dynamic pressure from the airstream increases as the square of velocity. Greater dynamic pressure means more lift production capability. Drop your airspeed by one-half and you only get one-quarter the lift production capability. Therefore, you will need a large increase in angle of attack to produce the same lift, and induced drag will also increase dramatically.

Total Drag
Total drag equals parasitic drag plus induced drag. The next figure shows both parasitic and induced drag on the same graph. Total drag is simply both types of drag added together vertically on the graph.

This graphically-illustrated concept of total drag is important for proper aircraft control. Since you need thrust to oppose drag, think of the vertical axis as required thrust rather than drag. You’ll note that at airspeeds below the minimum drag point, more power is needed to sustain level flight than at the minimum drag point. Flying at airspeeds below the minimum drag point can cause problems for the novice pilot.

Different Airfoils for Different Purposes
We now know that ‘CL’ varies with angle of attack. It is interesting to note that different airfoils have different ‘CL’ charts.

We will compare a thin vs. a thick airfoil in the previous and next chart. Note the line on the charts labeled L/D (lift / drag). The peak of this curve is an efficient angle of attack for maximum flight duration. The NACA 0006 airfoil is very thin. After 3 degrees angle of attack, drag rises rapidly. The NACA 0018 airfoil is fat. It has more drag at low angles of attack but its ‘Cd’ does not rise as rapidly as the 0006 airfoil when you increase angle of attack. Also its coefficient of lift, ‘CL’ keeps on increasing up to 20 degrees angle of attack while the thin airfoil gave up at 14 degrees. Jet fighters usually use thin airfoils at low angles of attach (low drag but in a small range of angles of attack). Heavy transport aircraft use thick airfoils. They give up a narrow range of speed for a wide range of load carrying capability at various airspeeds.

We have discussed lift and 2 forms of drag. But there are four forces in balanced flight. Next lesson we will begin a discussion of thrust.

(continued next week)

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“Simple Aerodynamics"
Part 4
copyright 1984, 2004, Sublogic Corporation