One pressure where Vmo and Mmo are the same point
The subsonic compressible pitot relation connects CAS, Mach, and ambient pressure, independent of temperature. From Vmo as a CAS you get an impact pressure qc; from Mmo you get the ratio qc/p; the ambient pressure that satisfies both is p = qc / ((1 + 0.2 Mmo²)3.5 − 1). Inverting the U.S. Standard Atmosphere 1976 pressure profile then gives the pressure altitude of crossover. For 350 KCAS and M 0.80 that altitude is about 23,230 feet. The published AFM/POH marks, not this educational solve, are the limits you fly.
Temperature changes TAS at that altitude but not the CAS–Mach–PA relationship, so the crossover is quoted as a pressure altitude (or a flight level). For the underlying pitot identities and a TAS at a chosen altitude, use the true airspeed calculator; to express the result as a flight level, see flight level and transition.
Sources
- Subsonic pitot-static formula as used on this site’s true-airspeed page (γ = 1.4, a0 = 340.294 m/s, p0 = 101,325 Pa).
- U.S. Standard Atmosphere, 1976, pressure–altitude inversion.
- AFM / FAA concept of Vmo and Mmo (the published mark always wins).
Frequently asked questions
Does temperature change the crossover altitude?
Not in this model. CAS, Mach, and pressure altitude are linked by impact pressure, which does not need OAT. TAS at the crossover does.
What if the page returns nothing for my pair?
If Vmo already corresponds to a Mach greater than Mmo at sea level — or the solved pressure would be off the standard-atmosphere scale — there is no crossover in the atmosphere this page models.
Is this the altitude I should change from IAS to Mach on climb?
It is the altitude at which the two published limits coincide. Your SOP or AFM may specify a changeover slightly different from that exact figure.