Steward Observatory and the Department of Astronomy, The
University of Arizona
*A Collaborative Undertaking and Flight Project Planned and
Implemented by:
(U. Arizona), Tim Todd (
A total solar eclipse
(TSE) is, unequivocally, one of nature’s grandest spectacles and most awe-inspiring
events that we can see with our own eyes! But, the elusiveness of the path of totality for TSE 2021 (Figure
1) has left many eclipse-chasers fretting and asking “how
the heck am I going to get there?”
We now can answer as we have planned and are vigorously
pursuing a unique opportunity to view the eclipse from
two high-altitude jetliners in a near-sunrise moonshadow
rendezvous, above the otherwise high-probability
occurrence of clouds below.
Figure 1. TSE 2021 path of totality and
EFLIGHT 2021-SUNRISE circumstances tabulation.
Yellow
“+
” marks the
location of our on-centerline Mid-Eclipse Intercept
(MEI) for our ex-Punta Arenas Airbus A321-200 eclipse-flight
charter.
By comparison, on the Earth
’s
surface, at the much more distant point of greatest duration (
GD) eclipse, totality is
only 9 seconds longer than will be seen from our aircraft.
See
HERE
for the representative extent of circum-Antarctic sea-ice
extrusion for early December.
The “Sunrise”
Mid-Eclipse Intercept (07:02:14 UTC)
The Moon’s umbral shadow touches
down on the Earth’s surface along our planet’s night/day
terminator nearly due east of Punta Arenas. This,
serendipitously, is both the closest launch point (along
with Ushuaia, which we considered but declined) and
shortest flight-time for a charter flight to reach
centerline, and in particular the MEI target-point for our
“sunrise” EFLIGHT. At this location, and instant of time,
the trajectory of the lunar umbral shadow stretching back
approximately
400,000 km into space will emanate from the
totally-eclipsed Sun on the astronomical horizon
(everywhere 90° from the zenith). Second-by-second, during
the 1m 45s of our airborne totality as the surface
projection of the shadow rapidly decelerates, the lunar
umbra will horizontally sweep around, over, and then
engulf the aircraft in darkness like a broad
darkness-inverted searchlight beam. Those who have seen a
similar phenomenon from the ground (e.g., Figure 3) have
described the effect there as “God’s bowling alley”. This
will be even more accentuated with the 390/380 km distant
terrestrial horizon at 39,000/37,000 ft depressed by
3.5°/3.4° from the astronomical horizon (coincident with
the origin of the shadow) as we fly at Mach 0.78
(approximately 447 kts true air speed) centrally through
the darkness of the Moon’s umbral shadow.
Figure
3.
“God’s bowling alley” (TSE 2002 December 04 UTC) as photographed by Carter Roberts at sea level from
Lyndhurst, South Australia.
The eclipsed Sun is 4° above the
at-sea-level-coincident astronomical and terrestrial
horizons.
For our EFLIGHT 2021-SUNRISE the totally
eclipsed Sun will be ON the astronomical horizon, but
with the apparent (terrestrial) horizon depressed by
3.5°.
While the “big
show”, of course, is totality, the proximity of Punta
Arenas to the sunrise line at umbral touchdown on the
Earth provides a unique opportunity to observe TSE 2021
totality with the rapidly decelerating shadow cone grazing
tangentially along the surface of the Earth (e.g., see
Figure 3 with a similar geometry at mid-eclipse). From our
lofty EFLIGHT venue our SUNRISE aircraft will provide some
of the most esthetically stunning views of the opening
terrestrial traverse of the lunar umbra.
Our
“Totality Run” (TR) approach to the MEI (where at MEI itself
the center of the lunar umbra first and fully obliquely
touches down on the Earth at 39,000/37,000 ft AMSL) begins
25.2 minutes prior to mid-total eclipse. At that “TR
Start” time (06:37:02 UTC) the lower limb of the Sun
in partial eclipse will touch and then rise over the
-3.5°/-3.4° depressed terrestrial horizon (see Figure 4).
The increasingly partially-eclipsed Sun then ascends
toward totality with a diminishing solar photospheric
crescent fully obscured by the Moon at the end of the C2
diamond ring at 07:01:23, heralding the start of 1m 45s of
totality.
Figure 4. Schematic depiction
of Sun rising during partial eclipse ingress from 39,000 ft as
seen from EFLIGHT 2021-SUNRISE with the Sun’s lower limb on the terrestrial
horizon at the start of the Totality Run.
Though only the “opening
act” preceding totality, this proximal MEI location
to Punta Arenas and within the MPN ETOPS60 circle permits
us to program an approach for the SUNRISE totality run
track that will initially present a 47% (obscured by area)
partially eclipsed Sun at lower-limb sunrise. The partially-eclipsed sunrise also marking
the start of our “totality
run”, like totality itself, will be visible from the left side of the aircraft*.
(*Due to the low elevation angle of the eclipse, from a few seat rows flanking the third
emergency exit door the aircraft wing itself will block this view,
and the view of totality as well. Thus, these few specific rows
will not be used for eclipse viewing.)
At this extreme
line-of-sight sunrise viewing geometry, as the Sun ascends
the apparent horizon, its partially-lunar-occluded disk
may take on an oblate or even more extreme morphologically
distorted shape due to differential atmospheric refraction
with the possibility of a partially-eclipsed
omega
effect, or even more
extreme
distortions and/or a green
flash while rising in partial-eclipse.
At our 07:02:14 MEI, thanks
to the aircraft altitude, the totally eclipsed Sun will gloriously stand approximately 3.5°, i.e., 14 solar radii, above
the depressed terrestrial horizon and “straight
out” the left-side passenger windows. There, the
umbral axis will lie in the horizontal plane parallel to
surface of the Earth with the Moon’s
conical shadow stretched out and over the astronomical
horizon as seen in perspective sweeping over a distance of
nearly 400 km, framing the Sun’s
magnificent corona as it circumscribes and enshrouds the
ashen lunar disk for a stunning, ethereal 1m 45s of
totality.
This will be a TSE viewing flight of an entirely
different flavor!
CENTERLINE and Mid-Eclipse-Intercept (MEI)
The total phase of TSE 2021
is optimally viewed from along the “centerline” of the
PoT midway between the northern and southern path
limits. The very center of the Moon’s shadow, which traces out the centerline of
the PoT, is where (for any location along the path)
the totality duration is longest, the sky is darkest (amazingly so at 39,000/37,000 ft*), and the view of totality is optimal. (*At their high-level eclipse-viewing altitudes
both aircraft will be above
approximately
80% of the Earth’s atmosphere
and will put us into the tropopause, where the concerns of
sub-polar weather (and clouds) will remain in the
troposphere below.) Our
EFLIGHT is
designed to be precisely on centerline just as the
Moon’s shadow axis reaches that centrally-located
position of the aircraft, i.e., this is the UTC
time-correlated point of “Mid-Eclipse Intercept” (MEI)
around which the rest of the flight is planned.
The centerline of the path of
totality, for all practical purposes, may be expressed
as a (UTC) time-correlated set of waypoints (latitude,
longitude) that maps out the central position of the
Moon’s umbral shadow as it traverses the Earth. In
principle, totality may be seen (where accessible and
not cloudy on the ground) anywhere along that path.
The TSE 2021 eclipse geometry and local circumstances
guide us in selecting our MEI location in concert and
in conformance with normal aircraft performance
characteristics and ETOPS60 operational limitations –
and (most importantly!) above otherwise potentially
problematic sub-polar cloudy weather.
BASELINE
End-to-End Plan
Routing: The EFLIGHT 2021-SUNRISE flight plan can
be best described as an
approximately
5-1/2 hour round-trip flight to/from the same originating
location, Punta Arenas, with the inclusion of an
additional critically-defined approximately half-hour leg
called the “Totality Run” (TR). It is from there that for
1m 45s, totality centered on 07:02:14 UTC will be observed
with the aircraft concentrically located along the axis of
the Moon’s
umbral cone at the instant of mid-eclipse. The turn onto
the totality run is immediately preceded by a contingency,
real-time tunable, “circle and hold” (C&H) segment for UTC ground-track synchronization of
the start of the TR in the event of a delayed take-off
from Punta Arenas. The end-to-end basically “triangular”
EFLIGHT plans PUQ→eclipse→PUQ can then be described as:
- take-off (“wheels-up” not
push-back)
- airport pattern departure and
ascent to top-of-cruise (TOC)
- outbound cruise toward totality
run
- contingency circle and hold for
up to 45 minutes for UTC synchronization
- release onto totality run at
UTC-correlated TRSTART waypoint (lower-limb sunrise at
TRSTART)
- totality run (inclusive of, and
anchored on, the UTC-correlated MEI point)
- inbound return to
start-of-descent (SOD)
- descent and pattern approach
- landing
where (1 – 3) and (7 – 9) are as usual
on any flight, but here with (4 – 6) augmenting the usual
“point-to-point” plan with the inclusion of the
time-critical Totality Run.
Aircraft:
We have proceeded with our baseline planning for our
chartered Airbus A321-200, ETOPS60 rated aircraft, as we are
fine-tuning the operational details of their joint flight
plan with our aircraft provider/operator, LATAM Airlines.
We predicate our baseline plans for a true air speed (TAS)
of 447 kts (Mach 0.78) for the Totality Run in particular,
also assumed as cruise speed for other pre- and
post-requisite flight segments in straight-and-level
flight.
Flight
Duration (with 45-minute in-air contingency margin):
For baseline plan definition and tolerance with in-segment
flight-time variation for actual winds aloft we assume no
winds, but provide margins in the end-to-end plan to
compensate for actual winds aloft in flight. With these
baseline assumptions we estimate the end-to-end duration
as closely proximate to 5.5 hours. Preliminary estimated
time of departure (ETD) = 03:39 UTC ex-Punta Arenas (to be
updated/confirmed).
BASELINE
Totality Run
Predicated by the MEI UTC and location
for EFLIGHT
2021-SUNRISE flight, the end-to-end baseline totality run
may be represented in simple parametric form with three
key time-correlated waypoints defined by their start, MEI,
and end. We enter the TR run track 25.2 minutes prior to
MEI (allowing for pre-totality sunrise viewing). The TR
ends 6 minutes after MEI.
Totality Run Waypoint
|
UTC (hh:mm:ss)
|
Aircraft Longitude
|
Aircraft Latitude
|
TRSTART
|
06:37:02
|
W04806.112
|
S5006.932
|
MEI
|
07:02:14 |
W05110.202
|
S5234.421
|
TREND
|
07:08:14
|
W05157.054
|
S5308.783
|
(all coordinates WGS84
referential datum)
CLICK HERE
for a
multi-parametric tabulation of this Totality Run with 1
minute time granularity w.r.t. MEI after ETOPS60-limited
TRSTART (START).
CLICK HERE for an explanation of the multi-parametric
tabulation.
TIMING
CONTINGENCIES (pre-planning for success)
The PUQ→eclipse→PUQ EFLIGHT plan
is designed with more than sufficient time to execute all
flight segments. In the unlikely event of a take-off delay, or
with unfavorable outbound winds, our pre-planned,
expendable,
C&H leg provides an additional in-flight margin of up to 45 minutes for the
successful attainment of the MEI exactly as planned.
Beyond this margin, we have further contingency
flexibility to modify the TR if necessary, maintaining the
same MEI by shortening the length of its pre-C2 TR segment
by up to approximately 20 additional minutes.
COMPARATIVE RISK
ASSESSMENT - TSE 2021
Ground-based (including
sea-going) TSE observations are inherently “risky”
due to the ever-present possibility of uncooperative
weather. This is the case, in particular, from sky cover
obscuration due to clouds, fog, or precipitation that
differ from eclipse to eclipse and with location. E.g., for statistical expectations and
discussion specifically germane for TSE 2021 see HERE.
Therein the risk of cloud cover obscuring totality for
locations reachable by ship is summarized by
eclipse-weather expert Jay Anderson as “Over the oceans, cloud cover
averages more than 90% {!}”
When path access is limited (as extremely so for
TSE 2021) but not impossible, and nature conspires against
us with high risk of obscuring clouds, some will nonetheless (grudgingly) accept such risks when
no other alternatives are presented.
Such high-risk scenarios,
however, are eliminated by employing a high-altitude jet aircraft as a
platform for eclipse observations. Risk is never
entirely mitigated, but typically can be reduced to at
most a few percent. E.g., while the statistical
expectation of opaque cloud above 39,000/37,000 ft is
vanishingly small for a sub-polar eclipse such as TSE 2021
where we plan to intercept, it is non-zero due to other
remote possibilities. E.g., one could posit various,
but highly unlikely, reasons the point-of-departure
airport could shut down due to low-probability events, but
the percentage
“chance”
of that occurring at requisite take-off time is counted
generously on fingers far less than on one hand.
In the case of our EFLIGHT 2021-SUNRISE
scenario, the risk of not seeing totality is somewhat “high”
by airplane expectations (but extremely low compared to anything
else!). That risk is about 4%, and potential flight
participants must understand (and accept) this risk.
This risk comes about from the
necessity to plan a requisite contingency ETOPS60
diversion landing return specifically at the Royal Air
Force (UK) Mt. Pleasant airport (MPN) in the Falkland
(Malvinas) Islands. MPN is the only existing
facility for such planning that allows us to boot-strap
with an ETOPS60 hop to the path of totality (see Figure
2). During the months of November and December
(climatologically representative of the December 4 eclipse
time of year), approximately 4%* of the time, MPN
experiences a high-wind phenomenon known as “rotor
winds” – severe low-level turbulence causing a
temporary closing of the runway until subsidence.
(*Based on prior year NOTAMS
(Notice to Airmen) statistics; e.g., in 2018 MPN was
closed to air traffic for a total of 61 hours out of
1464.) While we do not plan at all to land at MPN,
it must be available (open) to us while we are in the air.
Thus, if the MPN runway closes for this reason (or is
forecast/predicted to close) during that time, we would
not be permitted to take off from PUQ. To put in
perspective in comparison to the “next
best” option by ship, the statistical expectation of
the likelihood of success by deploying into a cloud-free
sky with EFLIGHT 2021-SUNRISE is
approximately
96%, whereas the “odds”
of successfully viewing the eclipse on the ocean are <
10% (per quoted reference from J. Anderson, above).
WINDOW-SHARING
and
ECLIPSE-VIEWING
Probably the
most often asked questions related to the aircraft windows
for eclipse viewing are:
- “What are the aircraft windows like?”
- “Could I share a window in an eclipse-viewing
seat row with a partner to watch the eclipse?”
From our many past
experiences we can answer as follows:
1a) QUALITY:
Commercial aircraft windows are not research-grade optics.
Nonetheless, if not optically degraded in some fashion,
such windows are typically more than well suited for
visual and/or binocular viewing of TSEs, and for wide- to
intermediate-field photographic imaging and even
low-resolution spectroscopy. Several examples are
offered below. This, of course, depends upon the window
quality. LATAM is aware to provide us with the best -
i.e., typically the newest - two A321-200
’s in their fleet that they
possibly can, with defect-free, distortion-free, and
scratch/sleek-free windows being a top priority. Aircraft with more than a minimal number of
such window artifacts will be rejected from our
consideration. Window cleanliness (free of dust, dirt,
oils, or any other light-scattering materials or
particulates), of course, is also essential; and
well-proven protocols for pre-EFLIGHT window cleaning
(without leaving residual streaks) are called out in a
technical annex to our charter requirements.
Though no photographs can come close to reproducing the
magnificent views captured on our retinas and interpreted
by our visual cortices, here are a few images taken on
prior EFLIGHTs through their aircraft windows indicative
of their suitability for TSE observing.
Wide-Field
Imaging:
View from EFLIGHT 2015 March 20 UTC over the Norwegian
Sea at Second Contact, 35,000 ft.
Canon
EOS 5D Mark III Digital SLR at ISO 1600, 1/60th sec,
14mm EFL f/2.8 Rokinon IF ED UMC Ultra Wide-Angle Lens
used at f/4.
Glenn Schneider and Geoff Simms
Coronal
Imaging
from EFLIGHT
2015 over the Norwegian Sea, 35,000 ft.
Inner
Corona
|
Mid+Outer
Corona
|
|
|
Nikon
D3000 + 300 mm f/5.6 VR lens (ISO 800) – handheld. Left:
single frame, right: 5 frame stepped exposure time
composite.
Glenn Schneider
Click HERE
for some remarkable HDR coronal imaging from EFLIGHT
2003 November 23-24 UTC by Miloslav Druckmüller and
David Finlay – Antarctica, 35,000 ft.
Totality Time-Resolved
Coronal Ramp Up/Down Imaging from EFLIGHT 2010 July 11 UTC –
South Pacific, 39,000 ft.
Nikon
DX3 camera at ISO 200 and VR 80-400 mm lens at 400 mm
f/5.6. (Double-click on the image mosaic to view at
larger scale.)
Glenn Schneider
Near-Infrared (0.7 to 1.0
micron)
Chromospheric “Flash” Spectrum at C2 from EFLIGHT 2019-MAX
(July 2) – 1,100 km N. of Easter Island, 41,000 ft.
1b) METROLOGY.
Below is an annotated photograph that shows the Airbus
A320-family window metrology. This particular photo was
actually taken from our EFLIGHT 2010 aircraft, which was
an Airbus A319 CJ/LR. The window metrology and spacing,
however, is identical
to the A321-200
’s we will
use for EFLIGHT 2021-SUNRISE (except where
exit row doors interrupt the otherwise uniform spacing of
the windows).
C
= 53 cm Inter-window
centerline distance
(most
windows; a few have larger inter-window spacings)
L = 30
cm Clear-area with trim gasket
window-length
W = 21
cm Clear-area with trim gasket
window-width
T = 114 cm
Top of window to floor vertical distance
B = 86
cm Bottom of window (actual surface,
not trim) to floor vertical distance
D = 0
cm Top of window protrusion distance
vertical to cabin floor edge [a]
θ = 14 deg
Tilt angle (top inward) of window with respect
to vertical [b]
[a]
The right panel figure indicates a downward projection
of the window top onto the floor is inboard (by a
distance D) of bottom of the actually slightly curved
wall.
This is typically actually
zero, but the cosmetic wall floor panel may be different
in our charter aircraft.
[b] The windows themselves, as mounted on the aircraft
fuselage, are tilted inward at the top by approximately
14°.
2) WINDOW SHARING.
The low vertical angle of the Sun (on the horizontal
plane, 3.5°/3.4° above the terrestrial horizon at
39,000/37,000 ft) will greatly facilitate “window sharing” for those contemplating an observing
partner, which can be much more problematic (and
contorting!) for high-solar-elevation-angle eclipse
flights. To aid in visualization, we have a
high-fidelity window template from Airbus that, if you
print to actual size, you can tape to a wall following
the dimensions above and try for yourself. Click HERE
for that template. So the answer to this second question is –
yes. Note that the number of windows accessible
to any seat row will vary from 1.0 to 2.0, with some
rows providing partial access to a second
window. As a result, some seat rows are more
amenable to window-sharing than others.
The EFLIGHT 2021-SUNRISE TEAM – Points of
Contact and Pedigree