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-   top surface streamlines
~   bottom surface streamlines
b) RoU-up of trailing vortices
Fig.1.33   Development oftrailing -vortices.
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34                 PERFORMANCE, STABfUTY, DYNAMICS, AND CONTROL
Largc Aircraft
]fig.1.34   Effect ofwake vortices.
are caused by a large aircraft and the aircraft that flies into them is a small aircraft.
This condition can be hazardous if an encounter occurs close to the ground and
the roll rate required to counter the induced roll rate is beyond the capability of
the small aircraft
     A number of accidents have happened at the time of takeoff and landing when
one aircraft enters into the field of tip vortices left behind by another aircraft. To
minimize such mishaps, a safe separation distance or time between a leading and
 a following aircraft is specified by aviation regulatory authorities. This separation
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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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
　
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