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In the question What makes 21st century fairings so valuable that they'd potentially be recovered and re-used? I said:

21st century fairings are much more than passive rooftop boxes to "keep the wind off of the customer's stuff."

In the discussion in comments below this answer, the criteria for a safe altitude for fairing ejection was discussed. I did a quick check of five SpaceX webcast videos and their corresponding press kits, and found that the five fairing deployments were tightly clustered around an altitude of about 110 km, independent of (ground) speed or time after secondary engine start.

I've included an estimate of the target inclination. With that and the latitude at deployment, the actual air speed could be estimated, but I'm really looking only for rough ballpark numbers.

MISSION Ground speed (m/s) Gr. s. (km/h) Altitude (km) Post 2nd stage ignition (sec) Inclination (estim.)
ORBCOMM-2 1571 5657 111 13 45°
THAICOM-8 2536 9131 111 51 ~0°
Eutelsat/ABS 2517 9061 111 47 ~0°
JCSAT-16 2459 8852 110 48 ~0°
Iridium-1 2034 7322 107 40 86°
Echostar XXIII 2847 10248 114 38 ~0°

The atmosphere is quite rarified at 110 km; I estimate about $2 \cdot 10^{-6}$ of sea level's pressure using $exp(\frac{\text{-110 km}}{H})$ with a scale height $H$ of 8.4 km.

Satellites are built to endure huge g-forces during launch, but those forces on each component are proportional to the mass of the component. So any given section of all that light weight (Kapton or Mylar?) film wrapping the satellite may not experience a very large g-force in terms of newtons, but once the fairing deploys, some surfaces will be exposed to very low pressure but very high velocity winds.

In addition to the force of the wind (momentum transfer) there is also energy transfer, and that will scale faster with velocity than the momentum transfer. So even if the bulk mechanical forces turn out to be low, there can be local drag-induced heating, and things that conduct heat poorly (like thin polymer films for example) could develop hot spots.

Further, considering that 110 km is between the E and F layers of the ionosphere, there will be a substantial electron and ion wind, which might also cause trouble.

Thus:

Question: How strong and "hot" is the wind on the payload after the fairing is deployed at ~110km?

enter image description here

Above: Photo from Spaceflight Insider's Sierra Nevada delivers final 11 ORMCOMM OG2 satellites for launch.

No Nonsense
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uhoh
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    You have all you need. It's just ${1\over 2}\rho v^2$. – Mark Adler Feb 03 '17 at 02:14
  • @MarkAdler edit: "How strong and "hot:*... – uhoh Feb 03 '17 at 02:40
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    You added that. In this rarefied flow, you can estimate the heat flux with ${1\over 2}\rho v^3$. – Mark Adler Feb 03 '17 at 03:42
  • @MarkAdler I'll generate an answer if nobody else does. I can do the math, but there may be more relevant and interesting information that someone more knowledgeable can add. – uhoh Feb 03 '17 at 03:44
  • @RussellBorogove I'm wondering if I should change my question to something like "what are the considerations involved in choosing the optimal time for fairing separation" but that may bring a host of other considerations. They would be interesting to discuss, but I'm just after the "wind" related ones. I don't understand your comment - is it humor? – uhoh Feb 03 '17 at 04:37
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    Oh, I was completely misreading the question -- because you started with discussion of the recoverability of fairings, I thought you were asking about the stresses on the fairing rather than the payload. Sorry about that. – Russell Borogove Feb 03 '17 at 05:35
  • @RussellBorogove Oh no problem! Actually you have made me think about the question, do I want to expand to all the considerations involved in choosing an optimal altitude, or just consider the various stresses and potential degradation the payload may experience. – uhoh Feb 03 '17 at 05:38
  • For atmospheric density at this altitude, see http://space.stackexchange.com/questions/18223/atmospheric-density-vs-altitude/ – Hobbes Feb 03 '17 at 12:56
  • @Hobbes I've been there, and also looked around at http://ccmc.gsfc.nasa.gov/modelweb/models_home.html but couldn't find something simple to use. I have the feeling I could download code, or submit a job, but that's obviously overkill. Ditto for here as well: http://ccmc.gsfc.nasa.gov/modelweb/models_home.html But as I noted there, here is some tabulated pressure and density data from the 1976 standard atmosphere http://ccmc.gsfc.nasa.gov/modelweb/models_home.html – uhoh Feb 03 '17 at 13:40
  • Can you find ambient air temperature at that altitude? Knowing that I'll be able to give you the "hot" resulting from speed. – SF. Mar 28 '17 at 06:55
  • @SF. this one is on my "personal to-do" list (as opposed to this space exploration to-do list) . I can probably do this calculation, and probably should. Thanks for the reminder! – uhoh Mar 28 '17 at 07:14
  • @uhoh: in that case - the keyword is "ram rise". – SF. Mar 28 '17 at 08:14
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    Density at 110 km is 7.1 E-8 bar, temp is 240 K, according to the table in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539.pdf – Hobbes Mar 28 '17 at 09:22
  • @Hobbes yep, and mass density on the same Z=110,000 line on page 68 is 9.7E-08 kg/m^3. Using H=110,000 makes only a relatively small difference. Thanks! – uhoh Mar 28 '17 at 09:51
  • At 8km/s the temperature on flat "wind facing" surface will be of order of 25,000K. – SF. Mar 28 '17 at 11:34
  • @SF. cite your source. Is that a slab of material, or the some component of the plasma temperature? Is it even in equilibrium? All kinds of parameters can be assigned an effective temperature. A plasma can have an electron, ion and a neutral temperature associated with kinetic energy, and the electronic excitation states of the atoms/ions might even have another, considering the high velocity and low density. Without more info, one temperature number doesn't mean much. – uhoh Mar 28 '17 at 11:51
  • @uhoh: wait, at the fairing separation, following the telemetry from a stream, speed is around 2200m/s. That corresponds to only about 1900K. Calculation of TAT for that speed. For flat surface going straight against the air stream, RAT=TAT. – SF. Mar 28 '17 at 11:57
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    I'm not sure how much this would help, but from the launch vehicle manuals I've glanced through fairings are jettisoned at a time where free molecular aerothermal flux is less than 1135 W/m^2. Mark Adler gives the right formula for the heat flux. – awksp Dec 10 '17 at 01:35
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    It won't be a complete answer, since I can only answer the "how hot" part of the question, but it's something? – awksp Dec 10 '17 at 17:17

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Launch vehicle operators (or at least the major ones) all seem to drop their fairings such that the heat produced by the remaining atmosphere remains below 1135 W/m$^2$. Not all the operators provide details on how heat is calculated, but those that do say that the heat flux is calculated using a free molecular flow through a plane perpendicular to the direction of travel, so I suspect that this is more or less a standard definition.

Sources:

The Vega User's Manual, page 3-14

The nominal time for jettisoning the fairing is determined in order not to exceed a maximum instantaneous flux of 1135 W/m$^2$. This flux is calculated as a free molecular flow acting on a plane surface perpendicular to the velocity direction ($\frac{1}{2}\rho V^3$).

The Falcon 9 Payload User's Guide, page 32:

The payload fairing will nominally be deployed when free molecular aero-thermal heating is less than 1,135 W/m$^2$.

The Ariane 5 User's Manual, page 3-11:

The nominal time for jettisoning the fairing is determined in order to not exceed the aerothermal flux of 1135 W/m$^2$. This flux is calculated as a free molecular flow acting on a plane surface perpendicular to the velocity direction, and based on the atmospheric model US66, latitude 15° North.

The Delta IV Launch Services User's Guide, page 3-19:

Unless otherwise requested, fairing jettison for Delta IV missions will occur shortly after the 3-sigma high theoretical free molecular heating for a flat plate normal to the free stream drops below 1135 W/m$^2$ (360 Btu/hr ft$^2$) based on the 1962 United States Standard Atmosphere.

The Delta II Payload Planners Guide, page 4-13:

Unless otherwise requested, fairing jettison will occur shortly after the theoretical free molecular heating for a flat plate normal to the free stream drops below 0.1 Btu/ft$^2$-sec (1135 W/m$^2$) based on the 1962 U.S. standard atmosphere.

The Atlas V Launch Services User's Guide, page 3-27:

PLF [payload fairing] jettison typically occurs when the 3-sigma maximum free molecular heat flux decreases to 1,135 W/m$^2$ (360 Btu/hr-ft$^2$).

The Arianespace Soyuz User's Manual, page 3-15:

The nominal time for jettisoning the Fairing is determined in order to not exceed the aerothermal flux of 1135 W/m$^2$. This flux is calculated as a free molecular flow acting on a plane surface perpendicular to the velocity direction and based on the atmospheric model US 66, latitude 15° North. After Fairing jettisoning, the aerothermal flux varies from 1135 W/m$^2$ to less than 200 W/m$^2$ within 20 seconds.

The Proton Launch System Mission Planner's Guide, page 3-6:

The PLF [payload fairing] is jettisoned at approximately 340 to 350 seconds into flight (at an altitude of 121 to 125km or more), and the maximum FMHF [free molecular heat flux] does not exceed 1135 W/m$^2$ at any time following PLF jettison.

awksp
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    That's a surprising degree of consistency! I wonder what the source of this value is. I notice it's slightly more than the sunlight flux at ground level, but I doubt there's any direct connection there. – Russell Borogove Dec 10 '17 at 17:43
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    It's more of a traditional value than anything else – pericynthion Dec 10 '17 at 17:57
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    It looks like the single digit round number 0.1 Btu/ft22-sec may be the original source of the funky 1135. This is a really great answer! There's a lot to read here. – uhoh Dec 10 '17 at 18:16