13 High Speed Flight

Variation of TAS with Altitude at a Constant Mach Number

TAS

If M = a

then TAS = M × a

When descending at a constant Mach number IAS will be increasing

It can be seen from the equation that if an aircraft is flown at a constant Mach number:

•as altitude decreases the temperature will rise, local speed of sound will increase and TAS will increase.

•as altitude increases the temperature will drop, local speed of sound will decrease and TAS will decrease (up to the tropopause and then remain constant).

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When climbing at a constant TAS Mach number will be increasing, up to the tropopause, and then remains constant

Influence of Temperature on Mach Number at a Constant Flight Level and IAS

An aircraft normally operates at Indicated Airspeeds and the Mach number can be expressed in terms of IAS:

M =		IAS
									(Eq 13.3)
							P
		constant √P0
For IAS in knots: M =		IAS
									(Eq 13.4)
				P
		661	√P0

where: P = pressure altitude

P0 = pressure at sea level

This shows that at a constant pressure altitude (Flight Level), the Mach number is independent of temperature for a constant IAS.

This is because the speed of sound and the TAS, for a given IAS, both change as √ T

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Subdivisions of Aerodynamic Flow

M 0 4		M 0 75				M 1 2
LOW	HIGH
SUBSONIC			TRANSONIC			SUPERSONIC
ALL ML	< 1 0		SOME ML		< 1 0	ALL ML > 1 0
			OTHER ML		> 1 0
				COMPRESSIBLE FLOW
			MCRIT	M 1 0			MFS	(not	to scale)
	about	M 0 7 to M 0 8				(Aircraft	Mach number)
depending		on	individual	aircraft
	and angle of attack

Figure 13.2 Classification of airspeed

Figure 13.2 shows the flow speed ranges with their approximate Mach number values, where:

MFS = Free Stream Mach number: The Mach number of the flow sufficiently remote from an aircraft to be unaffected by it. (In effect, the Mach number of the aircraft through the air). This is the Mach number shown on the aircraft Mach meter.

ML	= Local Mach number: When an aircraft flies at a certain MFS the flow over it is accelerated
	in some places and slowed down in others.

Local Mach number (ML), the boundary layer flow speed relative to the surface of the aircraft, is subdivided as follows:

Subsonic	Less than Mach 1.0 (<M 1.0)
Sonic	Exactly Mach 1.0 (M 1.0)
Supersonic	Greater than Mach 1.0 (>M 1.0)

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Propagation of Pressure Waves

WEAK PRESSURE WAVE

M 0 2

r

(a)

M 05

r

(b)

M 075

r

(c)

	M 1 0
	r
	(d)
AIRFLOW	PRESSURE WAVE

KEY

= POSITION OF OBJECT WHEN PRESSURE WAVE GENERATED

= POSITION OF OBJECT WHEN PRESSURE WAVE REACHES RADIUS r

M = MACH NUMBER OF OBJECT

=PRESSURE WAVE EXPANDING FROM SOURCE AT LOCAL SPEED OF SOUND

Figure 13.3 shows a series of sketches which illustrate the basic idea of pressure wave formation ahead of an object moving at various Mach numbers and of the airflow as it approached the object. Pressure waves are propagated continuously, but for clarity just one is considered.

If we assume a constant local speed of sound, then as the object’s Mach number increases, the object gets closer to the ‘leading edge’ of the pressure wave and the air receives less and less warning of the approach of the object.

The greater the Mach number of the object, the more acute the upwash angle and the fewer the number of air particles that can move out of the path of the object. Air will begin to build up in front of the object and the density of the air will increase.

When the object’s speed has reached the local speed of sound (d), the pressure wave can no longer warn the air particles ahead of the object because the object is travelling forward at the same speed as the wave.

Figure 13.3

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Therefore, the free stream air particles are not aware of anything until the particles that are piled up right in front of the object collide with them. As a result of these collisions, the air pressure and density increase accordingly.

As the object’s speed increases to just above M 1.0, the pressure and density of the air just ahead of it are also increased. The region of compressed air extends some distance ahead of the object, the actual distance depending on the speed and size of the object and the temperature of the air.

At one point the free air stream particles are completely undisturbed, having received no advance warning of the approach of a fast moving object, and then are suddenly made to undergo drastic changes in velocity, pressure, temperature and density. Because of the sudden nature of these changes, the boundary line between the undisturbed air and the region of compressed air is called a ‘shock wave’, a stylized sketch of which is shown in Figure 13.4.

At supersonic speeds there is no upwash or downwash

SHOCK WAVE

(STYLIZED)

SUBSONIC

SUPERSONIC

AIRFLOW

APPROXIMATELY M 1 3

AIRFLOW

Figure 13.4 Stylized shock wave

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