Page 29 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 16

16 CHAPTER TWO

Daniel Bernoulli did not derive trailing edge. Since the wing has a hump on the top, the air
the “Bernoulli equation.” His going over the top travels farther. Thus it must go faster to
friend Leonid Euler did. rejoin at the trailing edge. The description is complete.
This is a tidy explanation and it is easy to understand. But
one way to judge an explanation is to see how general it is. Here one
starts to encounter some troubles. If this description gives us a true
understanding of lift, how do airplanes fly inverted? How do
symmetric wings (the same shape on the top and the bottom) fly?
How does a wing flying at a constant speed adjust for changes in load,
such as in a steep turn or as fuel is consumed? One is given more
questions than answers by the popular description of lift.
One might also ask if the numbers calculated by the popular
description really work. Let us look at an example. Take a Cessna 172,
which is a popular, high-winged, four-seat airplane. The wings must
lift 2300 lb (1045 kg) at its maximum flying weight. The path length
for the air over the top of the wing is only about 1.5 percent greater
than the length under the wing. Using the popular description of lift,
the wing would develop only about 2 percent of the needed lift at 65
mi/h (104 km/h), which is “slow flight” for this airplane. In fact, the
calculations say that the minimum speed for this wing to develop
sufficient lift is over 400 mi/h (640 km/h). If one works the problem
the other way and asks what the difference in path length would have
to be for the popular description to account for lift in slow flight, the
answer would be 50 percent. The thickness of the wing would be
almost the same as the chord length.
Though enthusiastically taught, there is clearly something seriously
wrong with the popular description of lift. The first thing that is wrong
is that the principle of equal transit times is not true for a wing with lift.
It is true only for a wing without lift. Figure 2.1 shows a computer
simulation of the airflow around a wing. Periodically simulated smoke
has been introduced to show the changes in the speed of the airflow.
The first thing to notice is that the air going over the top of the
The principle of equal transit wing reaches the trailing edge before the air that goes under the
times is not true for a wing wing. In fact, the air that passed under the wing has a
with lift. somewhat retarded velocity compared to the velocity of air
some distance from the wing. Without the principle of equal