I cannot model skip trajectories or trajectories that change angle during entry. I can only model straight-in entries at constant angle below local horizontal. I am using the old H. Julian Allen scale height entry model (ref. 1), updated to include plasma radiation heating (ref. 3).
Sources on-line differ in the exact numbers given for most
vehicles, Apollo and Orion
included. I did the best I could, with what I could find. Figure 1 was a convenient
comparison. Because the shapes are
similar, I presumed the same Rn/D
ratio, and the same blockage-area-basis hypersonic
drag coefficient CD (ref. 4).
Assuming the load of samples could be heavier, I increased the mass a bit to increase the
ballistic coefficient β slightly.
Figure 1 – Source Data for Entry Models of Apollo and Orion
I simply presumed speed at entry interface of 10.95 km/s
returning from the moon. Entry angles
were 2.0 degrees (Figure 2), 1.5
degrees (Figure 3), 1.0 degrees (Figure
4), and 0.7 degrees (Figure 5). Entry interface altitude was 140 km, per the Justus & Braun scale height model
of Earth’s “typical” atmosphere (ref. 2). (Apollo modeled at 2 degrees.)
Figure 2 – Estimate for Orion at 2.0 Degrees Below Local
Horizontal
Figure 3 – Estimate for Orion at 1.5 Degrees Below Local
Horizontal
Figure 4 – Estimate for Orion at 1.0 Degrees Below Local
Horizontal
Figure 5 – Estimate for Orion at 0.7 Degrees Below Local
Horizontal
I accumulated these annotated data from the figures, figured some heat shield pressures with
them, and cross-plotted the results as a
function of the constant average entry angle.
Peak deceleration gees vs entry angle is plotted in Figure 6.
Peak decelerating force is simply entry mass times peak gees
times the standard acceleration of gravity at Earth. Average pressure on the heat shield is that
decelerating force divided by the capsule blockage area. The peak pressure at the stagnation point is
about 4/3 of the average pressure. This peak
pressure estimate is plotted in Figure 7, along with a reported limiting pressure for
the kind of Avcoat used on Apollo.
The entry spreadsheet model figures both convective and
plasma radiation heating rates per unit area at stagnation, and it totals them, for the peak stagnation total heating. These total heating values are plotted in Figure
8, along with one reported max
heating limit value, for the kind of
Avcoat ablative heat shield that was used on Apollo.
That Apollo material was hand-gunned into a reinforcing fiberglass
hex already bonded to the capsule exterior.
So, too, was the heat shield used on the original
Orion flight test (EFT-1). The version
of Avcoat used on the Orion for both Artemis-1 and Artemis-2, was bonded tiles machined from blocks of cast
Avcoat, without any reinforcing hex.
Figure 6 – Peak Deceleration Gees Vs Constant Entry Angle
(Apollo 10-11 near 2)
Figure 7 – Peak Pressure on Heat Shield Vs. Constant Entry
Angle (Apollo ~ 0.56 near 2)
Figure 8 – Peak Stagnation Heating Vs. Constant Entry Angle
(Apollo ~ 380 near 2)
Orion flies entry at some modest angle of attack, to generate
lift force perpendicular to the oncoming wind. This is for fine trajectory shaping and
control, accomplished by rolling the
capsule to point the lift vector in the desired direction. This has been done since Gemini in the
mid-1960’s. It was done with Apollo.
This shifts the stagnation point on the heat shield away
from center, toward the rim on one
side, which reduces the angle seen
between the wall and the separated flow boundary and plasma sheath coming off
the rim of the heat shield. That can
lead to attached flow with higher “scrubbing action” and heating rate, on a swatch of the capsule lateral wall, on that side.
The crew’s windows must be on the other side, where such extra heating cannot occur because
of the larger separation angle forcing local separation.
One cannot just rescale the total stagnation heating to
different locations around the capsule,
because convection and radiation rescale differently.
For regions away from stagnation but with attached
flow, my ballpark estimate for
convection is stagnation/3, and my
ballpark estimate for the separated wake region is stagnation/10.
For regions away from stagnation but with attached
flow, my ballpark estimate for plasma
radiation is stagnation (because the plasma sheath is still quite nearby), and my ballpark estimate for separated wakes
is stagnation/3 (because the plasma sheath is more remote). Some have claimed that radiation heating has proven higher than initially expected, in those separated wake zones.
I roughed out the numbers from the annotated data in the
spreadsheet plots, and plotted them vs
entry angle in Figure 9. I then depicted
them around the capsule in Figure 10.
Bear in mind that these illustrations are not to scale, and the angle of attack (AOA) is shown
somewhat exaggerated.
It should be quite clear that lateral capsule surfaces with
attached flow will need more heat shield thickness than regions that always stay
separated. Heating in regions with
attached flow is really not very far below that at stagnation, since the radiation heating is still quite
near stagnation values.
Figure 9 -- Estimated
Heating Rates for Stagnation, Attached,
and Separated Flow
Figure 10 – Rough Ballpark Heating Distributions Around the
Capsule
We cannot make conclusions about the adequacy of the
Artemis-2 heat shield relative to the damages seen on the Artemis-1 heat shield,
from data like this! That will take good photographs of both
capsules side-by-side. Such have not yet
been released as of this writing. But
one place to look, besides the main base
heat shield, is very clearly the lateral
side away from the windows, where
attached flow is likely to occur while flying entry at angle of attack. Too little thickness there risks a
burn-through, at one or another
level.
I cannot model the difference between the “skip trajectory”
of Artemis-1, and the “non-skip” or
“reduced-skip” used by Artemis-2, except
to say that the “non-skip” trajectory is similar to steeper angles below
horizontal, as modeled here. The heating numbers are higher, the steeper the angle. And that is as true for attached flow on a
lateral side, as it is on the
main base heat shield.
I did hear it claimed during the televised entry coverage
that the crew of Artemis-2 experienced something like only 4 or 5 peak gees
during entry. That is unlike the 10-11
gees experienced by Apollo crews returning from the moon. So, it
is likely that the “best” model among those shown here, for the Artemis-2 entry, would lie somewhere near my constant 1 degree
model. That corresponds to heating
rates well below that of Apollo,
suggesting in turn that the max heating rate limit for the unreinforced
Avcoat is below that of Apollo’s.
References as indicated above:
#1. H. J. Allen and
A. J. Eggers, “A Study of the Motion and
Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at
High Supersonic Speeds”, NACA Technical
Report 1381, 44th Annual
Report of the NACA 1958, Washington D.C.
1959. (unclassified) – this has the scale height atmosphere model and the
relationship between altitude and velocity,
plus the convective stagnation heating correlation.
#2. C. G. Justus and
R. D. Braun, “Atmospheric Environments
for Entry, Descent, and Landing”,
MSFC-198, June, 2007.
– this has the same Allen and Eggers entry model, and scale height atmosphere model as Allen
and Eggers, but goes beyond just Earth. Atmospheres for Mars, Titan,
and Venus were obtained from here.
#3. SAE, “Aerospace Applied Thermodynamics
Manual”, 1969. (hardbound) – this had a simple plasma radiation
heating model that was modified and added to the spreadsheet embodying the
Allen and Eggers technique.
#4. Sighard
Hoerner, “Fluid Dynamic Drag”, self-published by the author, 1965.
– drag data for many shapes into the low hypersonic range are in this
reference.
Note that the spreadsheet used for this study was described
in an earlier posting to this site: “Entry By Hand”, 1 May 2026. A related study comparing probes at both
Earth and Mars entry conditions, plus
Apollo at Earth, was posted as “Entry
Study”, 1 June 2026.
-----
Search code DDMMYYYY format 01072026
Search keywords
aerothermo, space program
-----
