What is the TAS at MACH 0.76 and -27 degrees C?

To determine the true airspeed (TAS) at a specific Mach number and temperature, you need to understand the relationship between Mach number, the speed of sound, and temperature.

Mach 0.76 indicates that the aircraft is traveling at 76% of the speed of sound. The speed of sound in air is affected by temperature, and at -27 degrees Celsius, the speed of sound can be calculated using the formula:

Speed of sound (a) = 39.37 * sqrt(Temperature in Kelvin)

To convert -27 degrees Celsius to Kelvin, you add 273.15, resulting in approximately 246.15 K.

Now, using this temperature in the formula for speed of sound, we find:

Speed of sound (a) = 39.37 * sqrt(246.15) ≈ 39.37 * 15.7 ≈ 618.5 feet per second.

Next, to find the true airspeed at Mach 0.76, multiply the speed of sound by the Mach number:

TAS = Mach number × Speed of sound

TAS = 0.76 × 618.5 feet per second ≈ 469.86 knots.

When rounded, this value is closest