Page 46 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 33

How Airplanes Fly 33

The Scoop

Fig. 2.12. The scoop as a visualization tool.

speed. But what if the scoop were taken to a higher altitude The amount of air diverted by a
where the air has a lower density? If the air were half as dense wing is proportional to its area,
the scoop would divert half as much air for a given speed. the speed of the airplane, and
Thus, the amount of air intercepted by a wing is proportional the density of the air.
to its area, the speed of the airplane, and the density of the air.
Temperature and humidity also affect air density. An increase in
temperature causes the air to expand. An increase in temperature from
32°F (0°C) to 95°F (35°C) causes a reduction in air density of 10
percent. Humidity reduces the density of the air because water vapor
is almost 40 percent less dense than the air it displaces.
For the normal changes in angle of attack experienced in flight we
can make the statement that the amount of air diverted by the wing is
not dependent on the angle of attack of the wing. The amount of air
diverted also does not depend on the load on the wing, which affects
the angle of attack.
We said that the scoop is only a visualization aid, but it is a very
useful one in understanding how much air a wing diverts. It also gives
correct aerodynamic relationships such as how the lift goes with
speed, air density, angle of attack, and power. The relationships that
we derive using the scoop image are exact and not approximations.
Let us do a back-of-the-envelope calculation to see how
much air a wing might divert. Take, for example, a Cessna 172 Chuck Yeager became an ace in
that weighs about 2300 lb (1045 kg). Traveling at a speed of a day.
140 mi/h (220 km/h) and assuming an effective angle of attack