katooie,
What you have to remember is that the Airspeed Indicator measures Impact Pressure, which is the total sum of Dynamic Pressure (related directly to EAS) and compressibility (related directly to Mach Number). It does not measure Density, which is related to Pressure and Temperature. In fact, all of the manometric instruments on your aircraft, the ASI, Mach-Meter, Altimeter, and VSI only sense Pressure. You, the pilot, have to apply Temperature to Pressure Height to find Density Height and True Altitude, and to CAS and/or Mach Number to find TAS.
During climb, with decreasing pressure, the aircraft must fly faster, i.e. a higher TAS, to achieve the same Impact Pressure, because you're at a constant CAS. This is so, even above the Tropopause where there is no change in temperature with change of Pressure Height. Because the aircraft is flying faster, compressibility increases, you are experiencing an increasing Mach Number. Note this - On a very hot day, your TAS will be higher due to the lower density AS WELL AS the lower Pressure, but this temperature factor puts you not one jot closer to the speed of sound, because at the higher temperature, the speed of sound (M1.0) is ALSO higher. Thus, the 'hot day effect' of a higher TAS than that due to pressure change alone, has no effect upon Mach Number whatsoever.
Consider the formula for CAS calibration -
Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)
Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)
The Left-most portion of the equation is the ‘f’ factor, the compressibility effect –
F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])
At altitude, the Static Pressure, P, is substituted for Po in the left-most radical.
Temperature does not even get a mention (except in establishing standard Sea Level Density for calibration purposes, and then it's a constant)!!!!!
Regards,
Old Smokey