What is relationship between EAS, CAS, TAS & Mach number?

032 Aircraft Performance (Aeroplane) theory.
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CaptainMFT
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What is relationship between EAS, CAS, TAS & Mach number?

Postby CaptainMFT » 17 Jun 2016 02:57

EAS = Equivalent airspeed.
CAS = Calibrated airspeed.
TAS = True airspeed.
Mach = TAS/LSS (local speed of sound).
More on them discussed under 022 Instrumentation.


E=EAS, C=CAS, T=TAS and M=Mach 


If climbing use -ECTM+ 
If one amongst the speeds is kept constant, then the speeds to the right of it are continually increasing and to the left decreasing. If an inversion is suspected (involved) change over TAS and mach. If an isothermal layer is suspected (involved) then TAS and mach are coincident with one another. 


Conversely utilizing the same laws during a descent use +ECTM- 
A higher altitude at constant mass and mach number needs a positive (higher) angle of attack. a rising (increment) in altitude at constant mach number suggests that a reduction in EAS which implies the angle of attack is going to be greater. 


Let's test our knowledge with some exemplary questions below, shall we?

 

Example 1: an airplane climbs at constant TAS, should the CAS and mach number increase or decrease? 

CAS Decreases, mach number will increase. 


Example 2: an airplane climbs at constant TAS through an inversion, should the CAS and mach increase or decrease? 

CAS Decreases, mach number Decreases. 

Why does it happen, let's find out?

As we have a tendency to climb with increasing temperature the air density shall decrease, more than it would if the temperature were falling. If TAS is constant and density decreases more than it commonly does, then CAS have to decrease, more than it commonly does.. 
Mach number = TAS/LSS. LSS will increase with increasing temperature, TAS is constant, therefore mach should decrease, rather than increasing. 


Example 3: an airplane descends through an isothermal layer with constant TAS, what is going to happen to the CAS and mach number? 

CAS will increase, mach number remains Constant. 

Dynamic pressure = 1/2 rho V^2, V is constant and density is increasing therefore the CAS should increase. 
Mach number = TAS/LSS, TAS is constant, the LSS is constant as temperature is constant, therefore mach should be constant.
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Good luck,
CaptainMFT.

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