TEMPERATURE HAS NO EFFECT!
One of the basic tenets of manometry is that the relationship between CAS (or EAS) and Mach Number depends only upon Static Pressure (Ps). Temperature has no effect whatsoever upon the CAS/EAS/Mach relationship, only Ps, end of story.
I believe that the original quote that spawned this thread was a mis-quote. As an aircraft passes from a cold mass of air to a warm mass of air, the CAS, EAS, and Mach Number will all initially fall due to reduced thrust. After thrust has been adjusted to regain the original target speed, whether it be a CAS or a Mach Number, both will again be in complete agreement with each other. The TAS and TAT will be higher. An example for an aircraft at 300 CAS at 30,000 feet, and ISA-25°C moving to an ISA+25°C air mass is as follows -
ISA-25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 439.75 : TAT = -44.0°C
ISA+25°C : CAS = 300 : EAS = 285.00 : Mach = 0.7905 : TAS = 490.76 : TAT = +12.3°C
Now that was one
HUGE longitudinal temperature gradient that I chose to prove the point, but even with this ridiculous temperature gradient, the CAS, EAS, and Mach Number have not budged by a 10,000th of a decimal place. TAS and TAT have risen very significantly.
TAS is a very significant value to aviation, it is of extreme importance in navigation, and in aerodynamics, TAS is 'the'
V that we consider in the highly important 1/2 Rho V squared formulae applied to both Lift and Drag calculations. TAS is so important that it's possible to be blinded by it when considering manometry, the measurement and calibration of speed measuring instruments.
Consider this, If we measured our speed as CAS, we need Pressure Height and Temperature to calculate TAS. If we measured our speed as a Mach Number, we need only Temperature to calculate TAS. If we now put it into very simplistic terms, we would have 2 formulae, namely -
TAS = CAS X A function of Ps X A function of Temperature, and
TAS = Mach X A function of Temperature.
Now, putting the two formulae together to calculate Mach from CAS (or vice versa), and as both equal TAS, we have -
Mach X A function of Temperature = CAS X A function of Ps X A function of Temperature
Now, as "A function of Temperature" appears on both sides of the equation, it is
SELF CANCELLING, leaving us with -
Mach = CAS X A function of Ps
Wot! No Temperature?
Before I'm accused of over-simplification, take a look at the formulae by which the Airspeed Indicator and the Machmeter are calibrated -
Vc = SQR((Y/(Y-1)) X Po/Qc X ((Qc/Po + 1)^((Y-1)/Y) - 1) X SQR (2 X Qc/Rho0)
M = SQR (5 X (Qc/Ps + 1)^((Y-1)/Y) - 1)
(NOTE - For flight at altitude, substitute Ps for Po in the Vc formula).
Where -
Vc = Calibrated Air Speed, ft/sec
M = Mach Number
Y = A constant, being the ratio of specific heat of air at constant
pressure to the specific heat of air at constant
volume = 1.4
Po = Sea Level Air Pressure
Ps = Static Pressure
Qc = Impact Pressure
Rho0 = Standard Sea level air density
Where is the temperature for either equation? It simply isn't there.
The only time that Temperature came into play was in establishng the STANDARD Sea Level Air Density (.0023769 Slugs per cubic foot), in other words, the standard temperature at Sea Level was used in establishing a
CONSTANT for calibration purposes.
As a parting remark, temperature, again, has absolutely no effect upon the Change-Over height from CAS to Mach for a given speed schedule. In other words, if your Climb speed schedule was, for example, 320 CAS / M 0.84, the Change-Over height will be 30,107 feet every day of the year, Winter, Summer, Spring and Fall, over the Arctic, the Sahara Desert.........Everywhere
The FAA guy made a mis-quote..... It's been done before
Regards,
Old Smokey