An aeroplane is in steady descent. If the total temperature remains constant, what happens to the Mach number?

In a steady descent, if the total temperature of the aeroplane remains constant, the dynamic conditions affecting the Mach number must be examined. The Mach number is defined as the ratio of the aircraft’s true airspeed to the speed of sound in the surrounding air.

As an aircraft descends, the static pressure increases, which leads to an increase in the static temperature if the airplane remains in a constant total temperature scenario. However, as the aircraft descends, it also moves through denser air, which effectively means that at a constant total temperature, the true airspeed will decrease relative to the increasing speed of sound due to the increasing static pressure and temperature.

Consequently, the Mach number will decrease. In this scenario, even though the total temperature is constant, the corresponding changes in static pressure and density reduce the true airspeed relative to the speed of sound, resulting in a decreased Mach number. This relationship illustrates how the dynamics of airspeed, density, and pressure interact to affect the Mach number during a steady descent.