We know there is a Max-Q point1 during a launch, have an approximate altitude, equations for it's pressure value and suspect it lies very near the apex of a rocket's nose.

But is there a "Max-T" point where a rocket is most likely to get the hottest during ascent through the atmosphere due to aerodynamic heating?

If so, where would it likely be on the rocket, and at what altitude would it occur? Is it likely to happen at the same time as Max-Q or earlier or later?

I am curious mostly of the max temperature on the body of stage 1 and stage 2.

I've added the Falcon-9 tag as a reference point but if there is more information from a different but somewhat similar launch vehicle that would be fine.

1further reading on Max-Q:

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    $\begingroup$ See some of the non-sunlit screenshots in this question and also see What causes those curtain-like hot and cool spots in the 2nd stage nozzle of this Electron ELaNa 19 launch? $\endgroup$ – uhoh Oct 27 '20 at 1:54
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    $\begingroup$ Have a look at my edit and see if you think it still captures your intention. I made some adjustments in style and included a little bit of research. $\endgroup$ – uhoh Oct 27 '20 at 13:15
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    $\begingroup$ Thanks. I am curious mostly of the max temperature on the body of stage 1 and stage 2 $\endgroup$ – Joe Jobs Oct 27 '20 at 15:51
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    $\begingroup$ Feel free to edit and clarify your question further. $\endgroup$ – uhoh Oct 27 '20 at 15:52

Source: am aerospace engineer, have worked on multiple launch vehicles

Great question, and I think you should do some more investigation into what you actually want to know and why (currently it's not well-posed but I'll try to answer all the questions you could be asking). Keep in mind MaxQ is a load condition, and frankly, engineers don't care so much about temperatures as heat rates (thermal loads). Things can be a lot of different temperatures.

Assuming you're asking only about the ascent portion of the trajectory:

If you're asking about what location on the rocket, that is almost always going to be on the base of the rocket, just above the engine - this is especially a concern for multi-engine stages, such as Saturn V: The heating from expanded rocket plumes impinging on the base is extreme to say the least - check out the Saturn V Base Heating Handbook, 600 pages of some of the coolest engineering you can find (you can also find it just be googling "Saturn V base heating"): https://ntrs.nasa.gov/citations/19720023245

If you're only interested in the body temperature of the vehicle, you have to ask yourself why you're interested in this value - most large vehicles (F9 included) use their tanks as the rocket body, so that would stay approximately as cold as the LOX itself - cryogenic in that case. This differs a lot based on which part of the body you're interested in (fairing, booster body, raceway, etc)

If you're asking about what point on its ascent trajectory (like maxq), the reason there's not an easy answer to that question is because temperatures don't really matter - heat rates matter. Differeny things (metals, composites, etc) heat up at different rates and for different reasons. Overall, it varies based how fast the vehicle moves in which portion of the atmosphere, but it also matters where on the vehicle something is. Peak temps on different parts may happen at different times, the "temperature" of a rocket isn't something that's tracked.

If you're asking about aerodynamic heating on F9 specifically, that definitely happens during reentry:

You can get a much more intuitive understanding of aerodynamic heating by looking at reentry vehicle aerothermal profiles - for example, with a high ballistic coefficient, the peak heat RATE is higher, but the net heat LOAD is lower, whereas this is flipped for a lower ballistic coefficient. This relationship is flipped when it comes to the atmospheric entry angle - how much time you spend at which portion of the atmosphere going at what speed determines heat rate and heat load - two subtly different concepts. This is an awesome resource: https://www.faa.gov/about/office_org/headquarters_offices/avs/offices/aam/cami/library/online_libraries/aerospace_medicine/tutorial/media/iii.4.1.7_returning_from_space.pdf

  • $\begingroup$ The question does clearly specify aerodynamic heating so perhaps at least a bit of the "so if you're asking"-ness of the wording can be reduced? I think your answer to the question as written is "I don't know but you shouldn't want to know either" and that's not the optimal style for a Stack Exchange answer. All that said, you do provide plenty of helpful perspective to the topic. Welcome! $\endgroup$ – uhoh Nov 2 '20 at 1:56
  • $\begingroup$ Very useful Information there. Shall I ask separate questions for fairing, body, base? What is a raceway btw? Are you sure the body is not getting much hotter on the outside? $\endgroup$ – Joe Jobs Nov 2 '20 at 1:58
  • $\begingroup$ My answer isn't so much "you shouldn't care" so much as "the question doesn't make complete sense" which is completely ok! Most of the effort in a space engineering project is trying to figure out what the right question even is to ask, Elon makes a specific point about this in one of his talks. A Max-T as described in the post doesn't have a definition because temperature is a 4-dimensional function for any given part. Max-Q is a single, meaningul scalar value that represents something physical. JoeJobs, asking this question for a fairing is VERY meaningful - continued on my next comment $\endgroup$ – AEngineer Nov 2 '20 at 3:19
  • $\begingroup$ As you can see on F9 images, the fairing (white, composite) has a metal piece just at the very tip. This gets more to the sources of aerodynamic heating - most of the body is feeling skin friction - this comes from a boundary layer, which is always subsonic, even if the vehicle is traveling > mach 1. This is because of the no-slip boundary condition and generates some heat. Read about supersonic boundary layers to learn more about that! On the fairing, the heating comes from a shock wave, which generates a ton of heat, enough to potentially melt the composite on ascent or Fairing recovery $\endgroup$ – AEngineer Nov 2 '20 at 3:24
  • $\begingroup$ A raceway is something that travels up the outside of the vehicle, routing tubes, fluids, wires, etc. They're covered in smooth aerodynamic things (also usually called fairings) so that 1) the random shapes dont cause extra drag/get ripped off, or 2) melted off. Sharp corners in supersonic or hypersonic flows have extreme thermal and physical loads - heat can be generated from shocks, skin friction, or chemical reaction if the vehicle travels fast enough. Raceways are the black things in this pic: raceways cover external tubes, valves: i.imgur.com/bpcZdwY.jpg $\endgroup$ – AEngineer Nov 2 '20 at 3:28

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