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At cruise altitude (~ 33,000 ft) and cruise airspeed (~ 500 mph) how much do present-day airliners heat up due to air friction during their journey? Probably not much because there's still ice on the window outside when you're at cruise altitude, but by how many degrees is the plane's hull warmer than in case the plane stood still at that altitude (therefore, compared to the minus 56°C at the tropopause)?

I'm also curious about the Concorde which flew up to 60,000 ft high and at more than 1300 mph. To the air friction there also comes the heating due to supersonic flight, so all in all how much warmer did the Concorde get during its supersonic cruise?

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Based on the formula already shown in this answer, we can calculate the TAT (true air temperature), which is the temperature reached at the stagnation point1, from the SAT (static air temperature) and Mach number:

$$ \frac{\text{TAT}}{\text{SAT}} = 1 + \frac{\gamma - 1}{2} M^2 = 1 + \frac{1}{5} M^2 $$

The resulting plot of TAT vs. Mach number at the SAT of -56.5°C (ISA tropopause) is shown below:

TAT

As you can see, a subsonic airliner (I assumed Mach 0.85) will still experience temperatures below freezing. Concorde however was reaching temperatures of around 120°C at cruise speed of Mach 2.02. This was already close to the limit:

Maximum Total Temperature (TMO): 127 Degrees Celsius (on nose)

(Concorde Performance)


As requested in the comments, here is a larger speed range including the SR-71:

TAT

The temperature could reach almost 400°C at Mach 3.2 (What is the true top speed of the SR-71?), but note that the SR-71 used fuel to cool the skin (the windscreen was the hottest part at 316°C according to Wikipedia.


1The TAT is measured by the aircraft with a probe that brings the air to rest w.r.t. to the aircraft (stagnation). The kinetic energy of the air is therefore converted into thermal energy, raising the temperature. The surface temperature of the aircraft at points where no stagnation occurs will be at a lower temperature. Thanks to Peter Kämpf for pointing this out.

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  • $\begingroup$ Shouldn't the SR-71 be included as a data point, just because Cool!? $\endgroup$
    – FreeMan
    Mar 18 at 16:04
  • $\begingroup$ @FreeMan Actually even more examples would be cool to mention on this diagram, such as the X-planes. $\endgroup$
    – Giovanni
    Mar 18 at 16:48
  • $\begingroup$ Thank you for adding the Blackbird. $\endgroup$
    – Giovanni
    Mar 19 at 5:54
  • $\begingroup$ That's a very large temperature rise, I'm honestly surprised. Why don't we do something with it? $\endgroup$
    – Abdullah
    Mar 21 at 5:39
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    $\begingroup$ Please add that the temperature shown is only reached at the stagnation point. Most of the surface experiences much lower temperatures and those come from friction heat, not stagnation. $\endgroup$ Mar 21 at 12:52
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The temperature change is relatively minor, but total air temperature is always much less than the static air temperature in flight, due to surface friction.

I have been able to increase fuel temperature in outboard tanks, when fuel recirculation wasn't enough to increase the fuel temp at northern latitudes, by increasing cruise speed by a small margin. It's interesting to see the results. The change isn't rapid or great, but enough to keep the fuel temperature off the lower limit (where gelling occurs), in certain cases.

Typically, TAT (total air temperature) will be about 30 degrees C warmer, than the static outside air temperature (SAT), for typical transport category aircraft (not supersonic), operating at the base of the transonic range (.80 M1 or higher).

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