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

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.

**** SpaceX - data estimated from telemetry in webcasts and press kits ****

MISSION         ground speed  altitude  post 2nd stage   inclination
m/s    km/hr    km      ignition (sec)   deg (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 2E-06 of sea level using exp(-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?

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

• You have all you need. It's just ${1\over 2}\rho v^2$. Feb 3 '17 at 2:14
• You added that. In this rarefied flow, you can estimate the heat flux with ${1\over 2}\rho v^3$. Feb 3 '17 at 3:42
• 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. Feb 3 '17 at 5:35
• Density at 110 km is 7.1 E-8 bar, temp is 240 K, according to the table in ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539.pdf Mar 28 '17 at 9:22
• 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. Dec 10 '17 at 1:35

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

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.

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.

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.

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 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 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.

• 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. Dec 10 '17 at 17:43
• It's more of a traditional value than anything else Dec 10 '17 at 17:57
• 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