What happens to MACH and TAS when climbing at constant CAS?

When climbing at a constant Calibrated Airspeed (CAS), the relationship between Mach Number (MACH) and True Airspeed (TAS) is influenced by altitude and temperature variations. As altitude increases during a climb, the air density decreases, which affects the true airspeed.

At a constant CAS, the aircraft's indicated airspeed will remain the same despite changes in altitude. As the aircraft climbs and the air becomes less dense, the TAS must increase. This is because TAS is the speed of the aircraft relative to the air mass, and a higher TAS is required to maintain the same CAS as altitude increases.

Moreover, MACH, which is the ratio of the aircraft’s true airspeed to the speed of sound, also increases as the climbing altitude rises. The speed of sound decreases with decreasing temperatures at higher altitudes, but the TAS increases enough that the MACH value rises as well.

So, in a climb at constant CAS, both MACH and TAS increase as a result of the decreasing density of air and the corresponding changes in the aircraft's speed profile.