SmokeDog's
Note: Part 3 illustrated the generation of lift. This lesson
will quantify the amount of lift you can generate and the
tradeoff 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 = coefficient 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 onehalf and you only get onequarter 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 graphicallyillustrated
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 
