A jet airplane is flying at 0.72 MACH with an OAT of -40 degrees C. What is the TAS?

To determine the true airspeed (TAS) of a jet airplane flying at a specific Mach number and outside air temperature (OAT), you can use the relationship between Mach number, temperature, and TAS. Mach number represents the ratio of the aircraft's speed to the speed of sound at the given temperature.

In this instance, the process involves a few steps:

1. Calculate the speed of sound: The speed of sound in air decreases as the temperature drops. The formula for the speed of sound (in knots) is approximately:

Speed of sound (knots) = 39.37 x √(Absolute Temperature in Rankine)

First, convert the outside air temperature from Celsius to Rankine. The conversion is done as follows:

• Absolute temperature in Kelvin = -40 + 273.15 = 233.15 K

• Absolute temperature in Rankine = 233.15 K × 1.8 = 420.71 °R

Now apply the speed of sound formula:

Speed of sound = 39.37 × √(420.71) ≈ 39.37 × 20.53 ≈ 810 knots (approximately).

2. Calculate TAS: