If an aircraft climbs in the standard atmosphere below the tropopause at a constant TAS, what will happen to the Mach number?

When an aircraft climbs in the standard atmosphere below the tropopause while maintaining a constant True Airspeed (TAS), the Mach number will increase. This phenomenon is primarily due to the relationship between TAS, altitude, and the speed of sound.

As altitude increases, the air density decreases, which also affects the temperature of the air. The speed of sound is dependent on the temperature of the air; it decreases with decreasing temperatures and increases with increasing temperatures. In the standard atmosphere, temperature tends to decrease with altitude up to the tropopause. Therefore, even though the aircraft's TAS is constant, the speed of sound decreases due to the lower temperature at higher altitudes.

Given this situation, since the denominator in the calculation of Mach number (which is the speed of sound) decreases while the numerator (TAS) remains constant, the result is an increase in the Mach number. This means that as the aircraft climbs, the relative speed of the aircraft compared to the speed of sound rises, leading to an increased Mach number.

Understanding this concept is crucial for pilots, as operating at different Mach numbers can have significant implications on performance and handling characteristics of the aircraft at high altitudes.