Page 53 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 40

40 CHAPTER TWO

tional to the lift of the wings times the vertical velocity of the down-
wash. Now if we were to double the load, maintaining the same
speed, we would have to double the vertical velocity of the air to
provide the necessary lift. Both the load and the vertical velocity of
the air have been doubled and the induced power has gone up by a
factor of 4. Thus, the induced power increases as the load squared.
It is easy to see why the weight of an airplane and its cargo is so
important. Figure 2.15 shows the data for the relative fuel con-
sumption of a heavy commercial jet as a function of weight. These
measurements were made at a fixed speed. From the data one can
estimate that at a gross weight of 500,000 lb (227,000 kg) and a
speed of Mach 0.6 about 40 percent of the power consumption is
induced power and 60 percent is parasitic power. In reality the air-
plane would cruise at a speed of around Mach 0.8, where the
induced power would be lower and the parasitic power consump-
tion would be higher. Unfortunately, at that more realistic
speed the details of the power consumption become more
The induced power increases as
complicated and it is more difficult to separate the parasitic
the load squared.
and induced powers from the data.

1.6
Fuel Consumption vs. Load

1.4
Fuel Flow (arb. units) 1.2

1.0
Constant Speed
Mach 0.6

0.8
300 350 400 450 500 550
Gross Weight (x 1000 lb)
Fig. 2.15. Fuel consumption vs. weight for large jet at a constant speed.