SAT, TAT and OAT?

[M2dude]

TAT/SAT and Mach Number

I was answering a post on the 'Concorde Question' thread, and thought that I could help clear this one up a bit too:

For a given gas, TAT varies with the square of Mach Number and SAT, and although all temperatures for calculation purposes are obviously ABSOLUTE temperature, they are 'converted back' to °C here. So shown below are a range of TATs shown at four different Mach numbers and three specific SATs (or OAT if you prefer). Altitudes can be assumed as being in the lower stratosphere (ie. above tropopause) and ISA relates to International Standard Atmosphere. ISA is of course -56.25°C, ISA -5 is -61.25°C and ISA +5 is -51.25°C.

MACH 0.5. ISA -5: TAT = -50.6°C. ISA: TAT = -45.3°C. ISA +5 TAT = -40°C
MACH 1.0. ISA -5: TAT = -18.5°C. ISA: TAT = -12.5°C. ISA +5 TAT = -6.5°C
MACH 1.5. ISA -5: TAT = 34.8°C. ISA: TAT = 42°C. ISA +5 TAT = 49.3°C
MACH 2.0. ISA -5: TAT = 109.5°C. ISA: TAT =118.6°C. ISA +5 TAT = 127.6°C

Hopefully it all makes a little more sense with some 'real' numbers. You can see that as Mach Number increases the gap between SAT and TAT increases hugely. As a matter of interest the Mach 2, ISA +5 case was particularly significant for Concorde, as it breached the 127°C/400°K airframe temperature limit and Mach Number would therefore be reduced. Fortunately sustained ISA +5 or above conditions were relatively rare over the North Atlantic but not unheard of either.