What is the true airspeed at MACH 0.80 and -40 degrees Celsius?

To determine the true airspeed at a given Mach number and temperature, it's important to understand the relationship between Mach number, speed of sound, and temperature.

Mach number is a dimensionless unit used to express the speed of an aircraft relative to the speed of sound in the surrounding medium. The speed of sound varies with temperature; it decreases as temperature decreases. At -40 degrees Celsius, the speed of sound can be calculated using the formula:

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

First, convert -40 degrees Celsius to Kelvin by adding 273.15, which results in 233.15 K. Then, the speed of sound would be:

Speed of sound = 39.37 * sqrt(233.15) ≈ 39.37 * 15.27 ≈ 602.7 ft/s.

To convert this value to knots (since 1 knot is approximately 1.68781 ft/s),

Speed of sound in knots ≈ 602.7 ft/s ÷ 1.68781 ≈ 357.5 knots.

Now, to find the true airspeed at MACH 0.80:

True airspeed = Mach number * speed of