Page 82 - Aerodynamics for Engineering Students

Governing equations of fluid mechanics 65

measuring pressure. These would be completely unsuitable for use on an aircraft
where a pressure transducer is used that converts the pressure measurement into an
electrical signal. Pressure transducers are also becoming more and more commonly
used for laboratory measurements.
When the measured pressure difference is converted into air speed, the correct
value for the air density should, of course, be used in Eqn (2.19). This is easy enough
in the laboratory, although for accurate results the variation of density with the
ambient atmospheric pressure in the laboratory should be taken into account. At one
time it was more difficult to use the actual air density for flight measurements.
This was because the air-speed indicator (the combination of Pit&-static tube and
transducer) would have been calibrated on the assumption that the air density took
the standard sea-level International Standard Atmosphere (ISA) value. The (incor-
rect) value of air speed obtained from Eqn (2.19) using this standard value of
pressure with a hypothetical perfect transducer is known as the equivalent air speed
(EAS). A term that is still in use. The relationship between true and equivalent air
speed can be derived as follows. Using the correct value of density, p, in Eqn (2.19)
shows that the relationship between the measured pressure difference and true air
speed, u, is

Ap = -PU 12 (2.25)
2
whereas if the standard value of density, po = 1.226 kg/m3, is used we find
1
AP = p.2, (2.26)

where UE is the equivalent air speed. But the values of Ap in Eqns (2.25) and (2.26)
are the same and therefore
1
1
-pod =pd (2.27)
2
or

(2.28)

If the relative density 0 = p/po is introduced, Eqn (2.28) can be written as
UE = vfi (2.29)

The term indicated air speed (IAS) is used for the measurement made with an actual
(imperfect) air-speed indicator. Owing to instrument error, the IAS will normally
differ from the EAS.
The following definitions may therefore be stated: IAS is the uncorrected reading
shown by an actual air-speed indicator. Equivalent air speed EAS is the uncorrected
reading that would be shown by a hypothetical, error-free, air-speed indicator.
True air speed (TAS) is the actual speed of the aircraft relative to the air. Only when
0 = 1 will true and equivalent air speeds be equal. Normally the EAS is less than
the TAS.
Formerly, the aircraft navigator would have needed to calculate the TAS from
the IAS. But in modem aircraft, the conversion is done electronically. The calibration
of the air-speed indicator also makes an approximate correction for compressibility.