Page 47 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 34

34 CHAPTER TWO

A Cessna 172 at cruise is of 5 degrees, we get a vertical velocity for the air of about 11.5
diverting about five times its mi/h (18 km/h) right at the wing. If we assume that the
own weight in air per second to average vertical velocity of the air diverted is half that value,
produce lift. we calculate from Newton’s second law that the amount of air
diverted is on the order of 5 tons/s. Thus, a Cessna 172 at
cruise is diverting about five times its own weight in air per second to
produce lift. Think how much air is diverted by a 250-ton Boeing 777.
So how big is the scoop? If for simplicity we take the scoop to be
rectangular for the calculation, with a length equal to the wingspan of
36 ft (14.6 m), we get a height of about 18 ft (7.3 m). This is a lot of
air. One should remember that the density of air at sea level is about
3
3
2 lb/yd (about 1 kg/m ). As implied by the shape of the scoop in
Figure 2.12, the lift is greatest at the root of the wing tapering to the
wingtip. Thus the air is diverted from considerably farther above the
root of the wing than the 18 ft calculated here.
The popular description of lift, and to a lesser extent the
mathematical description of lift, discusses the effect of the wing on
the air only very near its surface. This gives the false impression that
lift is a very local effect involving a small amount of air. Our back-of-
the-envelope calculation of the amount and extent of the air involved
in the lift of a wing shows that this is not true. A great deal of air is
involved in the production of lift.
This large amount of diverted air causes the lower wing of a biplane
to interfere with the lift of the upper wing. The air diverted by the
lower wing reduces the air pressure on the bottom of the upper wing.
This reduces the lift and efficiency of the upper wing. Thus,
many biplanes have the upper wing somewhat forward of the
A Boeing 747-400 flying at
lower wing, or at least the root of the upper wing is moved
maximum range is 45 percent
forward to reduce this interference.
fuel, by weight, at takeoff.

Putting It All Together

You now know that the lift of a wing is proportional to the amount of
air diverted times the vertical velocity of that air. The amount of air
diverted by the wing is proportional to the speed of the wing and the
density of the air. The vertical velocity of the downwash is proportional