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Flight planning topic 5.

Finding TAS from Mach Number


You will have to find the TAS given a Mach number and temperature in the ATPL Flight Planning, and Navigation exams. You may be given true Outside Air Temperature (OAT), or Total Air Temperature (TAT). Either way, TAS can be found quickly on your circular navigation computer. There is just two steps.
Below are some examples.

Example 1. Given Mach 0.60    TAT -20C  CT1.0

a. TAS
b. Ram Rise Temp
c. True OAT


Step 1. Set Mach 0.60 in the Mach window.

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Step 2. Align the green CT1.0 recovery co-efficient line with the intersection of the dark black spiral line, and the TAT -20C curved line as shown.
Follow the green line down to read TAS of 355 kt in the TAS window (answer a).

Follow the green line down further to find out the ram temperature rise occurring at this Mach number. It is 16 degrees C (answer b).

The true outside air temperature will always be equal to or colder than TAT. In this case the true OAT is -46C (answer c).

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Ram temperature rise causes the cockpit temperature gauge to indicate that it is warmer outside than is actually the case. This happens at high speeds/altitudes because of the compression heating of the thin, high speed air against the temp probe, plus frictional heating of the probe also.

A quick approximate of the TAS for high flying aircraft is to multiply the Mach number by 6.
Eg: Mach 0.60 = TAS 360 kt approx.      Mach 0.80 = TAS 480 kt approx.

It could be that the question quotes true OAT,  rather than TAT. A different set-up is used for this. Refer to example below.

Example 2. Given Mach 0.71    OAT -50C 

Find: TAS


Step 1. In the True Airspeed window, set the true OAT of -50C against the Mach index arrows as shown.

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Step 2. Opposite Mach 0.71 on the inner scale, read TAS of 411 kt (answer)

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The 6 times the Mach number approximate TAS is about 420 kt. A good gross error check. A TAS of 411 kt is a plausible one !

Hopefully this helps you define the methods used to find TAS when TAT, or OAT are quoted. Remember that with TAT you must set the temperature in the large "Indicated Temp" window. With OAT you set the true OAT given against the Mach index double arrows in the "Airspeed window", and read around the outside of the scale opposite Mach number to get TAS.

Remember: Pilots are the ultimate professionals ... strive to be one !

This topic is covered in detail in the training text called "Airspeed/Altimetry/ETP/PNR", that is readily available from most pilot supply shops around Australia, and through the "SHOP" portion of this website.
Good luck with your exams !

Best regards

Rob Avery

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