Compressibility of Airflow and Mach Number

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Compressibility of Airflow and Mach Number

Post  Admin on Tue Dec 01, 2009 6:37 am

These notes have little value for the recreational aviator, but are included for interest.
Except for a slight EAS correction to IAS/CAS, and the possible propeller effects, the compressibility/elasticity of airflow (i.e. the density change resulting from pressure disturbances) does not have any significant airframe aerodynamic effects for aircraft operating at velocities below about 250 knots TAS. Pressure disturbances, or waves, propagate through the atmosphere in all directions, at the speed of sound.

Mach 1.0 is the notation for the speed of sound. For aerodynamic purposes airflow speeds are classified within five ranges:

Hypersonic flow — airflows greater than Mach 5.0
Supersonic flow — airflows between Mach 1.5 and Mach 5.0
Transonic flow — airflows between Mach 0.8 and Mach 1.5
Subsonic flow — airflows between Mach 0.3 and Mach 0.8
Incompressible flow — airflows below Mach 0.3

The term 'incompressible flow' doesn't mean that air is incompressible; it just indicates that at flow speeds below Mach 0.3 (30% of the speed of sound or about 200 knots TAS), local density variations within the flow — due to compressibility — are insignificant; so aerodynamicists can assume constant density within the flow.

At subsonic velocities, significant density changes may occur in the airflow around wings, which will produce flow separation and a turbulent wake — wave drag. The associated drag coefficient builds rapidly at airspeeds above Mach 0.75 then reduces as Mach 1.0 is exceeded.

The speed of sound in the atmosphere varies with air temperature. The Mach number is the measure of an aircraft's TAS in relation to the ambient speed of sound. For example, Mach 0.6 indicates that the aircraft's true airspeed is 60% of the speed of sound.

The speed of sound is proportional to the square root of the absolute temperature. In the ISA, Mach 1.0 at sea level = 663 knots, and temperature at sea level = 15 °C [288 K]. Thus, if the temperature = −36 °C (237 K) then the ambient Mach 1.0 = 663 × √237/√288 = 601 knots. Thus, Mach 0.60 at 15 °C would be 398 knots TAS, while Mach 0.60 at −36 °C would decrease to 360 knots TAS. Below the tropopause — the speed of sound decreases as altitude increases.

A machmeter is an instrument that measures and compares the speed of the aircraft and the speed of sound, using the outside air temperature. It adjusts for actual air density but is still subject to the same position errors as the ASI. The machmeter is usually incorporated within an ASI; the numeric Mach appears in a small window within the ASI dial.

You may see references to design diving speed presented as 'Vd/Md' which indicates the speed may be expressed as IAS or Mach number. Other reference airspeeds are presented in similar fashion. For interest, the following table is the maximum permissable speed/altitude for a late 1940s/early 1950s piston-engined naval fighter — the Seafire 47:

Altitude feet Max. IAS knots Mach no. Approx. TAS
Sea level – 10 000 455 0.78 505
10 000 – 15 000 410 0.78 495
15 000 – 20 000 375 0.78 485
20 000 – 25 000 340 0.78 472
25 000 – 30 000 300 0.78 459
30 000 – 35 000 270 0.78 448
35 000 + 240 0.78 432

Subsonic jet transport aircraft are designed to cruise close to their maximum allowable speed — Vmo/Mmo. Vmo is the limiting indicated airspeed and Mmo is the limiting Mach number. Mmo is probably between Mach 0.80 and Mach 0.85. In normal operations the limiting airspeed is Vmo, up to a change-over pressure altitude (perhaps around 25 000 feet). Above this altitude Mmo becomes the limiting speed value because of compressibility problem restraints.

Vmo could be shown as a fixed red line on the ASI (or 'Mach/Airspeed Indicator') but, because the speed of sound decreases as altitude increases, Mmo can't be represented by a fixed marking on the indicator. So, a moving red-and-white striped pointer, the 'barber pole', shows the limiting Vmo/Mmo varying with altitude. It shows the IAS corresponding to the lower of Vmo or Mmo for the current altitude.

All information here is fully accredited to at

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