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A Simplified Chart for Determining Mach Number and True Airspeed from Airspeed Indicator Readings

By Donald D. Beale and Virgil s. Ritchie
SUMMARY

The determination of flight Mach number fromameaeure—
ments of indicated airspeed and pressure altitude is shown
to be relatively simple and leads to direct and accurate
computation of true airspeed. A simplified chart is pre—
sented for determining flight Mach number and true airspeed
for a range of values of indicated airspeed, pressure
altitude, and air temperature. A table'of standard atmos—
pheric values is included. -

INTRODUCTION

The pitot—static type of airspeed indicator in dur—
rent use does not measure airspeed directly. but measures
a pressure difference between a total— and a static—
pressure tube. The instrument calibration expresses this
differential pressure.in terms of airspeed for scarlevel
standard conditions. In order to determine true airspeed
for conditions other than sea—level standard. corrections
must be applied tO'the indicated—airspeed readings.
Installation and instrument errors are assumed to be
included in the airspeed—indicator calibration.

In order to determine true airspeed for low—speed
,flight conditions at altitude, the usual density—ratio
correction for incompressible flow is sufficient; for-
high—speod flight at altitude, however. the incompressible—
flow relations do not apply and an added factor must be
considered. At high speeds, the ratio of the differential
pressure between a total— and a static—pressure tube to
the dynamic pressure is greater than unity and is a func-
tion of the flight Mach number. -Because the speed of
sound varies with altitude; the flight Mach number for a
given true airspeed will correspondingly vary and a
3

”correction will be reauired; Neglect of this correction

will produce errors in the determination of true airspeed
of the order of 5 percent for high—speed flight at alti—

tude.

The determination of the compressibility correction.
is difficult and its physical significance is obscure.
An analysis by simple compressible—flow relations. as
pointed out in reference 1, provides a more direct compu—
tation of true airspeed through the evaluation of flight
Mach number. A simple chart has been developed for the
direct determination of flight Mach number and true air-
speed for standard atmospheric conditious. Provisions
for obtaining true airspeed for conditions other than
standard have been included in the chart.

EQUATIONS FOR DETERMINING FLIGHT MACH NUMBER '

AND TRUE AIRSPEED

By simple compressible—flow relations, the pressure
difference between a total— and a static—pressure tube
can be shown to be a function of only two variables, flight
Mach number and static pressure; that is,