Page 49 - Understanding Flight

CH02_Anderson 7/25/01 8:55 AM Page 36

36 CHAPTER TWO

drag, which is a force against the motion of the airplane, would come
first and power would be given little consideration. That may be
appropriate for the design of an airplane, but it is less useful for the
understanding of its operation.
Power is the rate at which work is done. The power associated with
flight also relates to the demand placed on the engine and the limitations
on airplane performance. We will consider two types of power
requirements. The first is induced power, which is the power associated
with the production of lift. It is equal to the rate at which energy is
transferred to the air to produce lift. So when you see the word induced
with respect to flight, think of lift. The second power requirement we
need to consider is parasitic power. This is the power associated with the
impact of the air with the moving airplane. The total power is simply the
sum of the induced and parasitic powers.

Induced Power
Let us first look at the induced power requirement of flight. The wing
develops lift by accelerating air down. Before the wing came by, the
air was standing still. After the wing passes, the air has a downward
velocity, and thus it has been given kinetic energy. As stated in Chap-
ter 1, if one fires a bullet with a mass m and a velocity v, the energy
2
1
given to the bullet is simply ⁄2mv . Since the induced power is the rate
at which energy is transferred to the air, it is proportional to the
amount of diverted air times the vertical velocity squared of that air.
(Remember that in the rest frame of the observer on the
ground the direction of the downwash is down.) But since the
During an evacuation of a
lift of a wing is proportional to the amount of air diverted
Chinese village in 1942, 60
times the vertical velocity of that air, we can make a simplifi-
passengers were loaded on a
cation. The induced power associated with flight is propor-
DC-3 designed for 30. When the
tional to the lift of the wing times the vertical velocity of the air.
plane landed, there were 68
Now let us look at the dependence of induced power on the
passengers plus the crew of four.
speed of the airplane.
Eight were stowaways. One of the
We know that if the speed of an airplane were to double,
passengers was Brigadier General
the amount of air diverted would also double. So the angle of
James Doolittle, returning from
attack must be adjusted to give half the vertical velocity to the
his famous raid on Tokyo.
air, maintaining a constant lift. The lift is constant and the