Altitude and TAS

[A.FLOOR]

Please help!

At what approximate altitude will you get the highest TAS for a given Mach number or IAS and why?

Thanks

[hawk37]

All things being approximate, and thus a standard atmosphere assumed, the answer to the first part is sea level
Mach 1, speed of sound, is solely dependent on temperature. Highest TAS is at highest temperature for a given mach, regardless of altitude.
Death valley, perhaps, in the real world.

Second part, highest tas for a given IAS (I'll assume no position error, so ias = cas). If we're talking a vessel capable of deriving lift from the atmosphere, then the space shuttle during reentry would represent this altitude. Very low cas, very high tas, at point where it begins to fly again.
Short answer, as high as possible.

Hawk

[FlexibleResponse]

A practical application of hawke37’s answer for your aircraft type would be to climb at maximum IAS (Vno) until you reach the altitude at which you attain your maximum Mach No (Vmo).

Alternately descend at Vmo until you reach the altitude at which you attain your maximum Vno.

The Flight Level (FL) of the intersection of Vmo/Vno will give the maximum TAS for your aircraft (in the range of FL150-300 for a sub-sonic a/c and at or above FL360 for a supersonic one).

Surprisingly, the relationship of FL/IAS/Mach No is such that given any two of the values the third is constant regardless of temperature.

If you fly the "Bus" (from your handle Alpha Floor), then M0.86/330 = FL298 (but you would already know this from your Emergency Descent practice in the Sim!)

Therefore, to obtain Maximum practical cruise TAS in the A330/340 model using M0.835 (Mach Crit Drag Rise is around M0.84) and 330 IAS = FL282.

For practical purposes say M0.835/325IAS = FL290.

Hope I twiddled my CR-4 properly!