Chapter

13

High Speed Flight

Introduction			407
Speed of Sound . . . . . . . . . . . . . . . . . . . . . . . . .	. . . .		407
Mach Number			408
Effect on Mach Number of Climbing at a Constant IAS . . . . . . . . . .	. . .	.	. 408
Variation of TAS with Altitude at a Constant Mach Number . . . . . . . .	. . .	.	. 410
Influence of Temperature on Mach Number at a Constant Flight Level and IAS			410
Subdivisions of Aerodynamic Flow			411
Propagation of Pressure Waves . . . . . . . . . . . . . . . . . . .	. . .	.	412
Normal Shock Waves . . . . . . . . . . . . . . . . . . . . . . .	. . . .		414
Critical Mach Number			414
Pressure Distribution at Transonic Mach Numbers . . . . . . . . . . . .	. . .	.	. 416
Properties of a Normal Shock Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
Oblique Shock Waves			419
Effects of Shock Wave Formation . . . . . . . . . . . . . . . . . .	. . .	.	. 420
Buffet . . . . . . . . . . . . . . . . . . . . . . . . . . . .	. . .	.	. 427
Factors Which Affect the Buffet Boundaries . . . . . . . . . . . . . .	. . .	.	. 428
The Buffet Margin . . . . . . . . . . . . . . . . . . . . . . . .	. .	. .	432
Use of the Buffet Onset Chart . . . . . . . . . . . . . . . . . .	. .	.	. 432
Delaying or Reducing the Effects of Compressibility . . . . . . . . . . . .	. .	. .	434
Aerodynamic Heating . . . . . . . . . . . . . . . . . . . . . .	. . .	.	. 442
Mach Angle . . . . . . . . . . . . . . . . . . . . . . . . . .	. . .	.	. 443
Mach Cone . . . . . . . . . . . . . . . . . . . . . . . . . .	. . .	.	. 444
Area (Zone) of Influence . . . . . . . . . . . . . . . . . . . . . .	. .	. .	444
Bow Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		. .	. 444
Expansion Waves . . . . . . . . . . . . . . . . . . . . . . . .	. . .	.	. 445
Sonic Bang			447
Methods of Improving Control at Transonic Speeds . . . . . . . . . . . .	. .	. .	447

Continued Overleaf

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13 High Speed Flight

Sweepback - Fact Sheet				449
Questions . . . . . . . .	. . . . . . . . . . . .	. . . . . . . .	.	. 451
Answers . . . . . . . .	. . . . . . . . . . . .	. . . . . . . .	. .	.456

Flight Speed High 13

406

High Speed Flight 13

Introduction

During the preceding study of low speed aerodynamics it was assumed that air is incompressible, that is, there is no change in air density resulting from changes of pressure.

At any speed there are changes in air density due to ‘compressibility’, but if the speed is low, the changes are sufficiently small to be ignored. As speed increases however, the changes in air density start to become significant.

When an aircraft moves through the air infinitesimally small pressure disturbances, or waves, are propagated outward from the aircraft in all directions, but only the waves travelling ahead of the aircraft are significant for the study of high speed flight. These pressure waves ’signal’ the approach of the aircraft and make the air change direction (upwash) and divide to allow passage of the aircraft.

Speed of Sound

For the study of high speed flight we are interested in the speed at which the infinitesimally small pressure disturbances (waves) travel through the atmosphere. Pressure waves ‘propagate’ from their source, that is, each air molecule is rapidly vibrated in turn and passes on the disturbance to its neighbour. The speed of propagation of small pressure waves depends upon the temperature of the air ONLY. The lower the temperature, the lower the speed of propagation. Sound is pressure waves, and the speed of any pressure wave through the atmosphere, whether audible or not, has become known as ‘the speed of sound’.

The speed of sound at 15°C is 340 metres per second, or approximately 661 kt.

It can be shown that:		a = √			(Eq 13.1)
			γ R T
where	a = speed of sound			R	= the gas constant
	γ = a constant (1.4 for air)			T	= absolute temperature

Since γ and R are constants, the speed of sound is proportional only to the square root of the absolute temperature. For example, at 15°C (288 K):

a = √

1.4 × 287 × 288

(R = 287 J/kg K)

= 340 m/s

		The speed of sound changes
	a √ T
		with Temperature ONLY

High Speed Flight 13

407

13 High Speed Flight

Mach Number

Flight Speed High 13

As the speed of an aircraft increases, there is a decrease in the distance between the aircraft and the influence of the advancing pressure waves. The aircraft begins to catch up the pressure waves, so the air has less time to move from the aircraft’s path and upwash has a more acute angle.

At higher speeds there is also a change in the flow and pressure patterns around the aircraft.

Ultimately lift and drag, manoeuvrability and the stability and control characteristics will all be changed.

These effects are due to the compressibility of air, where density can change along a streamline, and the associated conditions and the characteristics which arise are due to ‘compressibility’.

It is vitally important that the flight crew know the speed of the aircraft in relation to the potential effects of ‘compressibility’. If the aircraft speed through the air (TAS) and the speed of sound in the air through which it is flying (the local speed of sound) is known, this will give an indication of the degree of compressibility. This relationship is known as the Mach number and Mach number is a measure of compressibility. (E.g. M 0.5 is half the local speed of sound).

Mach number (M) is the ratio of the true airspeed (V) to the local speed of sound (a)

M =	V	(Eq 13.2)
	a

Equation 13.2 is a good formula to remember because it allows several important relationships to be easily understood.

Effect on Mach Number of Climbing at a Constant IAS

•It is known that temperature decreases with increasing altitude, so the speed of sound will decrease as altitude is increased.

•It is also known that if altitude is increased at a constant IAS, the TAS increases.

•Therefore, the Mach number will increase if altitude is increased at a constant IAS. This is because (V) gets bigger and (a) gets smaller.

From a practical point of view: climbing at a constant IAS makes the distance between the aircraft and the influence of the advancing pressure waves decrease, which begins to change the flow and pressure patterns around the aircraft.

The lower the temperature

The lower the speed of sound

408

High Speed Flight 13

The International Standard Atmosphere assumes that temperature decreases from 15°C at sea level to -56.5°C at 36 089 ft (11 000 m), then remains constant. The speed of sound will therefore decrease with altitude up to the tropopause and then remain constant, Figure 13.1.

50
40				STRATOSPHERE
×
				TROPOSPHERE
30
I SA CONDITIONS
20
10				SPEED OF SOUND
				13
0				Flight
400	500	600	700	Speed
	SPEED OF SOUND - kt			High

Figure 13.1 Variation of speed of sound with altitude

Chapter 14 will fully describe VMO and MMO, the high speed (generally speaking) operational limit speeds. It has been stated that as an aircraft climbs at a constant IAS its Mach number will be increasing. It is clear that it is possible to exceed the maximum operating Mach number (MMO) in a climb at a constant IAS.

As the climb continues, an altitude will be reached at which the flight crew must stop flying at a constant IAS and fly at a constant Mach number, to avoid accidentally exceeding MMO. The altitude at which this changeover takes place will depend on the outside air temperature.

The lower the outside air temperature, the lower the changeover altitude.

409