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distance or time depends on the'gross weight of the aircraft. Generally, air traffic
controllers maintain a minimum of three minutes separation for an aircraft like a
Boeing 757, which has an approximate gross weight of 240,000 lb.
irplane
Fig.135    Induced rolling motion because of wake vortices.
REVIEW OF BASIC AERODYNAMIC PRfNCIPLES                 35
1.9   Flow of a Compressible Fluid
    Infinitesimal disturbances in fiuid propagate at a velocity equal to the speed of
sound in that medium. The speed of sound depends on the nature of the fluici and
its temperature. In a stationary fiuid, the pressure disturbances travel in concent.ric
circles as shown in Fig. 1.36a. For a two-dimensional flow, these circles are cross
sections of a cylinder and, for a three-dimensional fiow, they are cross sections of
a sphere. However, if the object that creates these pressure disturbances moves,
the picture changes as shown in Figs. 1.36b-1.36d.
    When the speed of the body is subsonic (Uoo < a), pressure pulses traveling
at the speed of sound a will always be ahead of the body. These pulses would
crowd in front, of the body and spread out behind it. As the speed of the body  Uoo
approaches the speed ofsound a, the crowding in front ofthe body becomes intense
until at Uw - a; the pressure pulses merge to form a moving front, which is called
a Mach wave, When the speed of the body Uoo exceeds the speed of the sound a,
the body will be ahead of the moving wave front as shown in Fig. 1.36d. All the
disturbances emitted by the body are confined into a narrow region, which is called
a) Stationary fluid
Mach Waw
Pressure Pulses
b) Body moving at subsonic speeds
c) Body moving at sonic speed        d) Body moving at supersonic speed
Fig.1.36    Propagation ofdisturbances in a fluid medium.

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'a
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  . 't
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't:.:
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36               PERFORMANCE, STABIL17Y, DYNAMICS, AND CONTROL
Fig. 1.37    Zone of action and zone ofsilence.
the Mach wedge (two-dimensional flow) or the Mach cone (three-dimensional
flow), obtained by drawing a tangent to the circles representing the propagation of
pressure pulses. The zone inside the Mach cone (or wedge) is called the zone of
action, and that outside the Mach cone (or wedge) is called the zone of silence.
      An interesting example of the zone of silence and the zone of action is the flight
of a supersonic aircraft past an observer stationed on the ground. The observer
looking at the aircraft will not hear any sound emitted by the aircraft until the
aircraft flies past and the observer comes within the Mach cone as schematically
 shown in F,gT1.37. If this aircraft were subsonic, the observer would have heard
the sound long before the aircraft flies past him.
    The semi-included angle of the Mach cone is called the Mach angle U and is
given by
siny = U
              1
     := N
    M
1.10   Aerodynamic Forces in Supersonic Flow
(1.53)
(1.54)
   In supersonic flow, fiuid particles are not aware of the existence of the body
downstream because this information is confined only to that region that is within
the Mach cone of the body. Therefore, a fluid particle comes to know of the
existence of the body only when it stnikes it abruptly and comes within its Mach
REVIEW OF BASIC AERODYNAMIC PRINCIPLES               37
                 a) Subsonic flow
Attachd Shock Wavc
               -" ~:::-
 M_ ~
b) Supersoruc flow over a sharp leading-edge body
--t
 M
    >
 ~
c) Supersonic flow over a bluntleading-edge body
Fig.138   High-speed flow over streamlined bodies.
cone. As a result  a fiuid particle cannot adjustitself to flow smoothly over the body
as it would ha've done if the flow were subsonic.ln subsonic flow, the streamlines
　
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