Posts about: "Stagnation Point" [Posts: 6 Pages: 1]

Many years ago Barnes Wallis gave a talk at my school, some of which I still remember. I recall his comments about hypersonics being dependant on materials technology that could withstand the stagnation temperatures involved.
He mentioned Concorde, almost with a regret that the aluminium derivative chosen automatically set the operating limit of the airframe. Even if the Olympus engines were improved it would be of no advantage. Limit would also be around 60,000 ft as altitude temperate starts to rise again above that.

There was also a comment about US plans for M3+ airliner with a small joke about having to use heavier alloys for the higher temperatures and what with overpressure being proportional to mass, not many greenhouses would survive.

It feels strange now having sat through his comments at the birth of supersonic commercial aviation to think that it is possibly already over

1) Effectively it was (not the skin, but the TAT probe. The highest temp rise would be at the stagnation point so one can be confident that TAT is a realistic answer for max skin temp).

2) AFAIK pretty standard:

Q from pitots
S from statics
T from temp probe

Modified by ADC for position error. It's possible that ADC used beta inputs and I'm sure it used alpha inputs to achieve this.

Thanks Ex Wok but now I'm even more confused!

1) So there is a direct temp reading, from the TAT probe. But where is TAT probe? Is it in the needle nose probe that also measures pitot/static for the intake computers? And how many TAT sensors are there (failure of a single one if that's all there is would not be good)?

2) Mach comes from dynamic pressure (pitots), from static ports, and from temp. But what temp? OAT perhaps?

Er - no, the TAT probes measure just what they say Total Air Temperature.

They are mounted off the skin and in freestream, so they measure the same temperature as would a probe on the nose.

Somewhere near the nose (not exactly on it, as the aircraft flies with a small AoA) there will be a 'stagnation' streamline where the oncoming air is brought to rest. At this point the skin temperature will be equal to the stagnation temperature (TAT). Behind that it gets more complicated! The skin temperature would depend on SAT, local Mach No, local skin friction coefficient (Mach and Re dependent, so varies with distance from nose), amount of heat radiated into space (paint colour!) and the amount of structure available to conduct heat away from the skin into the fuel (so roughly varying with thickness/chord and fuel distribution perhaps?

Static temperature and total temperature are related by a simple expression:

TAT = SAT *(1+0.2m^2) all in deg K

So in the troposphere at ISA +5 and Mach 2, SAT = 222 and TAT = 400.

OK, so the skin temperature at the stagnation point will be equal to TAT. This can be taken as the hottest part of the aircraft (behind it, the skin temperature will be less than the TAT).

The temperature shown in the top window of the flight deck gauge is TAT, with the legend 'TMO 128C' beneath it. So the aircraft was flown with reference to TAT, and provided TAT was no greater than 128C then the skin rearward of the stagnation point would be <128C?

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 \xb0 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 \xb0 C, ISA -5 is -61.25 \xb0 C and ISA +5 is -51.25 \xb0 C.

MACH 0.5 . ISA -5: TAT = -50.6 \xb0 C . ISA: TAT = -45.3 \xb0 C. ISA +5 TAT = -40 \xb0 C
MACH 1.0 . ISA -5: TAT = -18.5 \xb0 C . ISA: TAT = -12.5 \xb0 C. ISA +5 TAT = -6.5 \xb0 C
MACH 1.5 . ISA -5: TAT = 34.8 \xb0 C . ISA: TAT = 42 \xb0 C. ISA +5 TAT = 49.3 \xb0 C
MACH 2.0 . ISA -5: TAT = 109.5 \xb0 C . ISA: TAT =118.6 \xb0 C. ISA +5 TAT = 127.6 \xb0 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. The Mach 2, ISA +5 case was particularly significant for Concorde, as it breached the 127 \xb0 C/400 \xb0 K airframe temperature limit (TMO) and Mach Number would therefore be automatically reduced by the autopilot. (An overspeed warning would be generated at TMO +7 (134. \xb0 C). Fortunately sustained ISA +5 or above conditions were relatively rare over the North Atlantic but not unheard of either.