Page 51 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 38

38 CHAPTER TWO

The parasitic power varies as the have a speed squared due to the energy given to each mole-
speed cubed. cule and a single speed term due to the collision rate. This
yields the result that the parasitic power varies as the speed
cubed. The parasitic power as a function of speed is also graphed in
Figure 2.13 by the dashed line.
The fact that the parasitic power goes as the airplane’s speed cubed
has an important consequence for the performance of an airplane at
its cruise speed, where it is limited by the parasitic power. In order for
an airplane to double its cruise speed, it would have to increase the
size of its engine by eight times! So when an airplane owner upgrades
to a larger engine, there is an improvement in the rate of climb and
turn of the airplane but only a modest increase in cruise speed. To
substantially increase the speed of the airplane, the parasitic power
must be decreased. Such design features as retractable landing gear,
smaller fuselage cross sections, and an improved wing design
accomplish this.

The Power Curve
As stated above, the total power is the sum of the induced and para-
sitic powers. The solid line in Figure 2.13 shows the total power as a
function of speed. At low speed the power requirements of the air-
plane are dominated by the induced power which goes as 1/speed. At
cruise speeds the performance is limited by the parasitic power which
goes as speed cubed. This graph of total power as a function of speed
is known as the power curve. Flying at slow speeds where the total
power requirement increases with decreasing speed is what pilots
refer to as flying the backside of the power curve.
One might ask how an increase in altitude would affect the power
curve. This is illustrated in Figure 2.14, which shows the power curves
for altitudes of 3000 ft and 12,000 ft (about 900 m and 3600 m). With
an increase in altitude, there is a decrease in air density. Thus, the
wing diverts less air and the angle of attack must be increased in order
to maintain lift. As stated before, as the density of the air is reduced,
the angle of attack, and the vertical velocity of the downwash, must
be increased to compensate. Thus, the induced power would be
increased. A 10 percent reduction in air translates to approximately a