What is the TAS at MACH 0.78 and -32 degrees C?

To find the True Airspeed (TAS) at a specific Mach number and temperature, we utilize the relationship between Mach number, temperature, and airspeed.

At -32 degrees Celsius, we first need to convert the temperature from Celsius to Kelvin for accurate calculations, which is done by adding 273.15. This gives us approximately 241.15 K.

Next, we use the formula for the speed of sound (a) in air, which is approximately given by:

[ a = 20.05 \times \sqrt{T} ]

where ( T ) is the temperature in Kelvin. Plugging in our value:

[ a = 20.05 \times \sqrt{241.15} ]

Calculating this gives a figure around 67.51 m/s or equivalently in knots, we find the speed of sound at this temperature.

To find the True Airspeed at Mach 0.78, we multiply the speed of sound (a) by the Mach number:

[ TAS = Mach \times a ]

Substituting the calculated speed of sound and the Mach number into the equation ultimately provides us with the TAS.

Completing this calculation leads to a True Airspeed of approximately