EFLIGHT 2015 – 20 March 2015 Total
Solar
Eclipse
An Amazing Flight into The
Darkness of the
Lunar Umbral Shadow
From the Pristine, Dark, Cloud-Free
Free Skies > 37,000 feet AMSL
Dr.
Glenn Schneider
Astronomer and EXCEDE Project Principal Investigator
Steward Observatory and the Department of Astronomy
933 North Cherry Avenue
The University of Arizona
Tucson, Arizona 85721 USA
Telephone: 520-621-5865
email: gschneider@as.arizona,edu
URL:
http://nicmosis.as.arizona.edu:8000
~ 3m 45s ± ~ 10s of
prolonged
Greatest-Eclipse Totality @ 63.4° N Latitude
Launched from Dusseldorf, Germany to
the point of "Maximum Eclipse"
A COLLABORATIVE ADVENTURE OFFERED BY:
TOP 10 REASONS FOR A HIGH LATITUDE
STRATOSPHERIC
TSE 2015 ECLIPSE FLIGHT
DEPLOYMENT/RELOCATION FLEXIBILITY
To Find
the BEST Spot(s) in the
Area of Operations for Observing
|
CLOUD OBSCURATION AVOIDANCE
High Latitude Stratosphere
Stratosphere: 99.99% -- Virtually Assured
|
TOTALITY PROLONGATION FOR MAXIMUM ECLIPSE
Aircraft
Speed Extends the
Duration of Totality
|
SKY TRANSPARENCY
Significantly
Improved -- Low
Particulate Scattering
|
SKY DARKNESS
Much
Higher Contrast Coronal
Visibility and to Larger Circumsolar Distance
|
IMPROVED ASTRONOMICAL SEEING
"r_naugh"
Decreases with
Increasing Altitude
|
REDUCED ATMOSPHERIC TURBIDITY
Vorticity
& Sheer Decline
in Power Above Tropopause
|
PANCHROMATIC
VISIBILITY
IR and
UV "Windows" Open Up or
are Extended
|
UNPARALLELED HORIZON REACH &
OBSERVATION VISTA
Apparent
horizon 377 km
distant, depressed 3.4° (at 37,000 ft)
|
ESTHETIC, ETHEREAL EXPERIENCE
There is
nothing quite like
it...
|
THE TSE
2015 PATH OF TOTALITY
A truly remarkable, but
geographically remote, total solar eclipse
(TSE) will occur on 20 March 2015 with the Sun on the
celestial equator at the vernal equinox, as
the Moon's umbral shadow traverses a narrow path for 1 hour and 5
minutes over the North Atlantic and Arctic Oceans, spectacularly ending
with a blackened sunrise at the geographic North Pole. The
path of
totality, the region on the Earth's surface where the Sun will be
totally obscured by the Moon, begins at sunrise over the cold waters of
the north Atlantic Ocean 650 km east of Newfoundland where the eclipse
centerline then at 09:13 UT is 600 km is south of the southern tip of
Greenland. The path then sweeps north eastward passing, but
missing,
the east coast of Iceland in route, literally, to the "top" of the
world at the North geographic pole.
|
|
The TSE
2015 path of totality (left: blue arc, right: gray arc) with our
planned point of "to the max" mid-eclipse intercept indicated (red
markers).
(Maps: left - adapted from Espenak and Meeus 2006, 5MCSE; right
- adapted from HMNO)
TSE 2015 finds landfall only on two north Atlantic island locations.
The first, to the south-east of the centerline of the path of totality,
on the Faroe
Islands (latitude 62° N) where the Sun will fall into total eclipse
for a maximum duration of off-centerline totality of 2m 25s on the
western side of the tiny island of Mykines. The second, as the
centerline of the path of totality traverses Svalbard/Spitzbergen
(latitude ~ 79° N) giving rise to a nearly equal maximum
on-the-ground duration
of on-centerline totality 2m 26s from the island's north coast.
Both island locations,
while wonderful locations to visit and explore, are very likely
contra-indicated as eclipse viewing sites in mid-March due to the
strong prevalence of clouds and precipitation (e.g., see here
and here)
with high probabilities of obscuration with
the Sun at low elevation angles above the local horizons. Some eclipse
chasers will undoubtedly make the attempt, and we wish them great luck
– but the virtually-assured solution for TSE 2015 observers is to take
to the
skies above
the prevailing weather.
The point of greatest eclipse, 250 km north of the Faroe
Islands in the Norwegian Sea between Iceland and Norway, is
where the Moon's shadow is very nearly simultaneously moving most
slowly
across the Earth and the duration of totality is at a maximum anywhere
along the path of totality (2m 47s). Further north, after
passing over Svalbard/Spitzbergen, the Moon's shadow
streaks northward to the geographic North Pole where at 10:17 UT with
(from sea-level) the horizon bifurcating the fully-eclipsed Sun as it
very slowly rises and the Pole is plunged into a prolonged total
eclipse induced twilight for 1m 55s.
EFLIGHT
2015 MAX ... TO THE MAX!
The ideal location on Earth for eclipse-chasers to observe TSE 2015
would be at (or very close to) at the point of greatest eclipse,
if the twin,
daunting, concerns
of weather (high probability of cloud cover) and lack-of-accessibility
(in the frigid waters off the east coast of Iceland) could be
overcome. Our now-planned TSE 2015 eclipse observation
flight, "EFLIGHT 2015 MAX"
removes these dual obstacles, and this rare opportunity is now enabled
for
high-flying umbraphiles.
For TSE
2015 we have planned a spectacular airborne eclipse
expedition to simultaneously satisfy the goals and objectives of
umbraphiles called by the siren's
song of "duration, duration, duration" while obviating concerns of very
high-probability cloudy weather miles below on the Earth's
surface. EFLIGHT 2015 MAX
will stretch the duration of totality to ~ 3m 45s, with our
aircraft immersed centrally in the lunar umbra at mid-eclipse from a
sky-high venue > 11 km above the surface of the Earth. EFLIGHT
2015 MAX will launch from Dusseldorf, Germany with optimal
eclipse
viewing as the driving requirement for defining all details of the
flight plan of our Air Berlin Boeing 737-800 aircraft. During
totality, the
eclipsed Sun will be
positioned "straight out" the main cabin passenger
windows for optimum viewing of the corona enshrouded Sun and umbral
shadow on the sea/ice below and eclipse-darkened sky above from an
altitude of >
37,000 ft AMSL where we will be above any
obscuring clouds and otherwise disturbing weather below.
Viewing a total solar eclipse, and the sweep of the Moon's
umbral shadow as it races across (and above) the Earth, as seen from
such a lofty height as enabled by our EFLIGHT aircraft, is magnificent
beyond description. As
seen from 37,000 feet above the surface of the Earth, the apparent
horizon is 377 km (234 miles) away and depressed by 3.4° compared
to
sea level. Looking along the apex of the lunar umbral
cone
toward the
eclipsed Sun at mid-totality, or along its outer periphery as the
shadow sweeps over the aircraft coincident with the instants of second
or third
contacts, the curvature and grandeur of the umbral
shadow boundary (i.e., the "shadow ellipse") is stunningly apparent.
See HERE for
a graphic illustration of
the Sky at Totality and the movement of the umbral shadow on the
Earth. At
near-polar latitudes in mid-March, the
high reflectivity of the polar ice and/or cloud tops far below
accentuates the stark
contrast between the eclipse-darkened regions within umbral shadow, and
those illuminated by the Sun beyond the shadow's edge. Being above more
than 3/4 of the Earth's atmosphere, the corona of the Sun is presented
with contrast and clarity in the rarefied air incomparable to
ground-based venues at the bottom of a bubbling pool of atmospheric
turbulence. See below, shadow and corona photos taken from our
predecessor TSE 2008 flight;
similarly executed over the Arctic Ocean.
Stunning stratospheric views (and
photographs) of the 01
August 2008 Total Solar Eclipse, at 82° N latitude, 11
km above the Arctic Ocean, were uniquely obtained on board
our then-chartered AirBerlin (LTU) A330-200 EFLIGHT
2008 aircraft (above by Dan McGlaun, Bill Kraemer, Glenn
Schneider). In planning EFLIGHT 2015 MAX we drew
significantly in detail upon the successes of this historical
predecessor
implemented also in partnership with AirEvents/Deutsche
Polarflug under the experienced guidance and technical leadership
of Dr.
Glenn Schneider (Steward Observatory, The University of Arizona)
and in collaboration with TraveQuest
International.
EFLIGHT
2015 MAX will be aboard an Air Berlin provided and operated Boeing
737-800,
eclipse-suitable,
narrow-body jet aircraft, providing the best and most
cost-effective viewing-window to seat-count ratio, to
be used to centrally intercept the
Moon's shadow at a point within ± 1/20th second of the duration
of the greatest (globally maximum) eclipse at
(nominally) 37,000 AMSL.
With an at-altitude mid-eclipse occurring at 09h 43m 30s UTC, the
duration
of totality will be
stretched to approximately 3m 45*s ± 10s, a
minute longer
than
would be possible from a hypothetical Ocean-going vessel 11 km below,
and appx. a minute and a half longer than will be seen from the
Faroe Islands (should clouds below us cooperate for ground-based
observers located there). *Duration with with no wind
at Mach 0.78 (@ 37,000 ft), so a
nominal ground speed of 447.4 nm/h.
|
Schematic Representation of the
End-to-End Flight Plan
exclusive of planned contingency maneuvering to mitigate risks of
ground or outbound cruise delays.
|
With a planning-baseline max-eclipse intercept point of (63.39154°
N, 7.56084° W; see below "Why This
Location?"), the fully-eclipsed Sun will stand 18.8° above
the astronomical horizon (22.2° above the apparent horizon)
allowing very easy and comfortable viewing out the aircraft
sun (right) side passenger cabin windows, individually or shared with a
window-viewing
partner.
For those who want the maximum possible duration of totality EFLIGHT
2015 MAX, this appx 5 hour round-trip flight, is it!
THE
"WEATHER"
(acuna matata)
At |latitudes| > 60°, such as our MAX point of
mid-eclipse intercept, the tropopausal boundary between the troposphere
below (where "weather occurs") and the
stratosphere has typical equinoctial heights of < 9–10 km. Polar
stratospheric (nacrecous) clouds are extremely
rare and only form at
very
low temperatures (< -78° C) during the deep polar winter, making
the
probability of cloud-free eclipse viewing nearly 100% at our
equinoctial
flight
altitude of 37,000 ft (~11.3 km) at our chosen observing
location. Of course, we will have flexibility for in
situ retargeting (with a small trade in totality duration) of our
viewing locations if that is required for any
reason, however unlikely.
At this altitude and latitude, aerosol scattering of
sunlight by
airborne particulates is usually extremely low, giving rise to an
exceptionally
dark sky during totality, enabling eclipse viewing with significantly
enhanced image contrasts. Moreover, the airmass along
the line-of-sight to the Sun is significantly reduced (by
~
75% compared to sea level), resulting in
exceptional sky transparency, greatly reduced atmospheric turbidity,
and better astronomical "seeing".
At 63° N, east of Iceland, the possibility of
high-altitude volcanic ash originating in Iceland while statistically
small is non-zero. Thus, for further (but intrinsically very-low) risk mitigation, we have
designed our EFLIGHT 2015 MAX plan
with
sufficient flexibility to reach higher latitudes (with somewhat reduced
maximum duration of totality) where such particulates are very unlikely
to be transported given normal sub-polar wind circulation patterns.
THE
AIRCRAFT and ON-BOARD ECLIPSE-VIEWING
We will be using an Air Berlin
Boeing B737-800
(aka "738")
aircraft, normally used for more "conventional" commercial service,
from the Air Berlin fleet, with all economy class seating throughout
the entire cabin as shown schematically below.
Sun-side eclipse-viewing windows ONLY will be openly offered
for no more than 27 seating rows
on the aircraft (first come first serve).
Sun-side eclipse-viewing windows may (later on booking) be reserved
for
individual exclusive use, or shared with an adjacent seat-mate partner
with a per-person pricing plan (details
available from TravelQuest
Tours).
The
passenger cabin windows on the right side of the aircraft will
be used
for eclipse viewing and photography. Seat offerings, and
on-board
operations
during the eclipse-viewing phase of the flight, have been designed to
provide an optimal eclipse observing experience. All rows offer
at least one window suitable for eclipse viewing* with those numbered
in green as annotated on the figure below fully unobscured with seat
backs in upright positions.
(*Row 11 with one window, and Row 13 with two, have window edges
marginally obscured as shown).
The locations of the windows on the cabin wall with respect to each of
the passenger seat rows are illustrated in the figure below. To
maximize the utility of all windows accessible to any seat row without
interference to adjacent rows, seat backs in some specific rows may be
tilted backwards to provide partial to full access to the window
nearest the adjacent passenger seat (those identified in light blue)
without compromising the useful window(s) in the seat row behind.
EFLIGHT 2105 MAX seat rows and their windows.
Further utility of the windows identified in light blue (only) can be
gained by their exposure by seat back reclining.
Additional photographs, by row number,
of the seat/window configurations, may be seen in photos --> HERE.
WINDOW METROLOGY
Flight participants can
individually, or as partners sharing a seat-row, assess their needs for
using their seat-row window(s) as a viewing and/or photography
portal. All windows are rectangular in shape, 25 cm (9.8" wide)
by 34 cm (13.4") high, with rounded corners imposed by the cabin wall
framing -- see pictures below. The center of the windows are 94
cm (37") from the main cabin floor. The inter-window spacing
(cadence) is 50 cm (19.7") for all windows except for a "missing"
window between rows 11 and 12 (see photos above), and w.r.t. the
windows in the emergency row doors (rows 14 and 15; whose window shade
tabs protrude from the bottom rather than the top).
ABOUT THE
AIRCRAFT WING AND OUTBOARD (VERTICAL) WINGLET
EFLIGHT 2015 OPERATIONS AND LOGISTICS
(1) Early Preparations: Detailed photographs and measurements of
all seat rows and windows will be made available to eclipse viewers far
ahead of the flight, to allow informed preparations by photographers,
those using optical aides, and or planning window-sharing with a
seat-row partner (see above).
(2) At Dusseldorf International Airport: our
flight will be given first priority by Air Berlin's handling,
ground operations, flight planning and in-flight will also be
communicated as
priority 1 towards Air Traffic Control and for inter-flight
coordination.
(3) Our Outbound Flight Plan: is baselined for a 45 minute earlier
than critically required take-off time, providing built-in contingency
time against the possibility of a take-off delay or strongly
unfavorable outbound head-winds.
(4) Windows Quality/Frost Risk Mitigation: The specific Air Berlin
B737-800 we will use will be one of the very newest in their aircraft
fleet with very fresh windows with minimal scratches or sleeks that
could otherwise act as frost-formation centers. Cabin air will be
pre-conditioned to reduce the potential and minimize the (unlikely)
risk of frosting, and the aircraft will then remain at high altitude
prior to totality (no descents for "flightseeing") to keep the relative
humidity on potential frost-forming surfaces low. Additionally, not all
available seat-rows with eclipse viewing windows will be offered to
keep several in reserve for viewing position exchange, in the unlikely
event of individual anomalous window frosting elsewhere in the aircraft.
(5) No Extraneous Passengers: This is a dedicated eclipse-viewing
flight. No seats will be
offered on the anti-sun side of the aircraft for others to "fill" the
aircraft. No potential over-crowding, no unintentional
interference or
distractions during the totality run to eclipse-viewers.
(6) During the Totality Run: Eclipse observing will be conducted
without any intra-eclipse "seat swapping/rotation" of positions with
excess passengers (obviated by (5)) otherwise disturbing/interfering
with same, or adjacent row eclipse-viewers. This
"exclusive" or pre-planned partner-shared use only of the windows will
enable an atmosphere much more conducive to concentrated and
uninterrupted eclipse
viewing.
(7) Throughout All Flight Planning and in situ until CIII on the
Aircraft: Dr. Glenn Schneider will act actively as the consulting
expert with the mission planners and flight crew to assure the smooth
execution of the totality run and
mid-eclipse intercept per the baseline plan and in response to any
in-flight deviations.
(8) Post-Totality: Upgraded catering and celebratory
imbibement after collecting solar coronal photons to revel in our
successes.
EFLIGHT 2015 MID-ECLIPSE (ME) INTERCEPT FOR MAXIMUM
DURATION
BASELINE PLANNING ASSUMPTIONS:
Flight Level = FL 37,000 ft
No Wind, TAS = Ground Speed
=
Mach 0.78 @ FL 37,000 ft
Delta-T: 67.8 seconds
(current
IERS prediction for March 2015)
Geodetic Coordinate
Reference
Frame: WGS84
KEY FLIGHT/INTERCEPT
PARAMETERS:
AIRCRAFT
B737-800
PROFILE
CONCEPT
LONGEST
DURATION
LAUNCH POINT
(LP)
DUSSELDORF INT. AIRPORT
DESIGNATION
DUS
(EDDL)
LAUNCH POINT
LOCATION
51.28944° N, 6.76666°
E
OUTBOUND CONTINGENCY
"BUFFER" 45
minutes
FLIGHT
LEVEL
37,000 ft (11,278 m)
AMSL
MID-ECLIPSE (ME)
INTERCEPT
[a] 63.39 154° N, 7.56084° W
UTC ME
INTERCEPT
09:43:30
UTC
G.C. DISTANCE FROM LP to
ME 859.69
nm
BASELINE TAS = GROUND SPEED
[b] 447.4 kts (Mach 0.78)
GROUND TRACK AZIMUTH @
ME [c]
43.3°
DURATION OF
TOTALITY [d] 3m
45.1s
ME SOLAR ALTITUDE
ANGLE [e]
18.8°
ME SOLAR AZIMUTH
ANGLE
133.3°
SURFACE-OBSERVER
DURATION 02m
46.8s
TOTALITY RUN
TIMESPAN [f] -9, +6
minutes
BASELINE TOTALITY RUN:
TR-START TIME
UTC
09:34:30
UTC
TR-START
LOCATION
60.15964° N, 13.62041° W
TR-ME INTERCEPT
UTC
09:43:30
UTC
TR-ME
LOCATION
63.39154° N, 7.56084° W
TR-END TIME
UTC
09:49:30
UTC
TR-END
LOCATION
65.77103° N, 3.64945° W
|
NOTES:
[a] For initial
baseline
planning a "no wind" condition is assumed. So,
GROUND SPEED (GS) = TRUE AIR SPEED (TAS). This is tunable with
predicted winds aloft.
[b] LONGEST DURATION
ME
remains constant +/- 0.05 seconds over an an on-centerline
distance of 45.78 nm starting at the location indicated for baseline ME
as follows:
UTC Intercept Duration Intercept
Location GC to ME
09:43:30.0 3m 45.1s 63.39154°N,
7.56084°W 859.69 nm <ME START
09:44:18.0 3m 45.1s 63.69695°N,
7.03965°W 865.60 nm <ME CENTRAL
09:45:05.0 3m 45.1s 63.99930°N,
6.53004°W 872.35 nm <ME EXIT
ME
START selected for baseline intercept within this window to reduce
total flight
distance from Dusseldorf without impact on maximum possible
duration of totality.
[c] Aircraft Ground
Track
to orient sun at ME orthogonal to ("straight out")
the sun (right) side PAX windows. Heading tunable based on actual
winds aloft.
Ground track (with winds aloft) should be maintained.
[d] As corrected
for
topocentric lunar limb profile (complete photospheric extinction).
[e] Above the
astronomical
(true) horizon.
[f] Totality-Run
Timespan:
Centered on UTC of ME.
• Totality Run Start (TR-START) at
indicated UTC/LOCATION to commence
at
UTC of ME minus 9 minutes.
• Aircraft MUST then be at this location and flying straight-and-level
on
indicated course to TR-END.
• Totality Run End (TR-End) at indicated UTC/LOCATION to end at UTC of
ME
minus 6 minutes.
• Post C3, TR may be extended beyond TR-END at pilot's discretion.
|
The
track,
geometry, and location of the path of totality, and the time-correlated
UTCs of key eclipse events (e.g., start, end, and middle of totality)
that ultimately constrain an end-to-end eclipse-observation flight
plan, as seen from a
moving aircraft, will depend in detail on the aircraft
altitude above mean sea level and its velocity vector (ground speed and
direction) as modified by winds aloft. Baseline (Phase 1) eclipse-flight
planning (as discussed and presented here) makes assumptions for later
(Phase 2) optimization and refinement within constrained margins with
dependencies on in situ
conditions that may be parametrized in final computations. A baseline flight plan is developed
to provide a framework to be refined for an executable flight mission
subject to refinements and constraints levied by aircraft performance
and operations factors. Phase 2 "fine tuning" of the flight plan
(e.g., in light of statistically anticipated and actual winds aloft) is
later expected.
|
|
Eclipse
circumstances are dependent upon observer's height above mean sea
level (AMSL). The time-correlated position (centerline track) of the
Moon's shadow shifts in latitude and longitude with topocentric
altitude AMSL. This is illustrated by example for TSE 2015 with the
difference in centerline topographic coordinates at 37,000 ft compared
to sea level.
|
The speed of
the Moon's shadow projected on the surface of the Earth varies
significantly along the path of totality. Where slowest, the
duration of totality is near maximum. The shadow speed can
advantageously be reduced, prolonging totality, with an aircraft moving
in the direction of the lunar velocity vector.
|
For EFLIGHT 2015 baseline
planning purposes, here we adopt a flight
altitude for the eclipse-observing phase of the flight (and nominal
out/inbound cruise phases) of 37,000 ft AMSL. Here (for initial
planning), a no-wind condition is assumed and a TAS of Mach 0.78
(i.e., ground speed equals
airspeed) during at-altitude cruise. We designate a "Totality
Run" as that portion of the
flight devoted to the observation of the total phase of the eclipse.
The Totality Run is planned so the aircraft has assumed
straight-and-level flight (nominally) at constant speed at and
throughout the totality
and
during pre/post flanking intervals closely prior to and after
totality.
The point (time correlated location and UTC) of "mid eclipse" (ME)
intercept is the instant at which the aircraft is concentrically
located in the Moon's umbral shadow. The totality run is planned
so the aircraft heading is the solar azimuth at ME minus 90 degrees, so
the
Sun will present itself "straight out" the sun-side passenger
windows. This is the
right
(starboard) side of the aircraft, so enabling an aircraft velocity
vector component in
(not against) the
velocity vector of the Moon's shadow with a resulting increase in the
duration of totality as seen from the moving aircraft.
In practice, small compensating adjustments to the derived totality run
(and pre-totality run flight plan) based upon:
(a) TBD (Phase 2) statistically most-likely, and/or
in situ actual winds-aloft,
(b) different (faster is better for longer totality) TAS during the
totality run within
operating limits, and
(c) different (higher is better for sky clarity)
flight level to the limit of the service ceiling with trade of
achievable ground speed.
Such parametrically defined
variations to the baseline flight plan, subject to aircraft operational
and performance constraints, will be reviewed and discussed with the
aircraft flight operations and planning personnel, and are readily
(re)-computatble as needed. (See here an overview of the
EFLIGHT
planning S/W [20
MB PDF file], developed and used by G. Schneider for many prior
successful EFLIGHTs.
The baseline flight plan presented here is of
sufficient fidelity
for the
(presumed nominal) parametric conditions assumed that, if
rigorously followed, will successfully result in a highly
viewing-optimized and geometrically precise time-correlated mid-eclipse
intercept with the aircraft concentrically located along the apex of
the lunar umbral shadow cone.
N.B.:
All timings and correlated locations, and maps presented here are
(in detail) valid ONLY for the specific set of baseline assumptions
used here. Later recomputation of the eclipse observation
plan (and
thus to a small degree end-to-end) flight plan, based upon
parameterization a-c above, is expected and anticipated.
The totality run (TR) is entered (nominally) at the completion of a
heading
re-alignment maneuver (with a constant-radius turn onto the TR track)
at the requisite UTC,
location, altitude, TAS, and heading. Once on the TR track,
before the start of totality (C2 = "second contact"), small
adjustments to the aircraft speed may be made to compensate for
winds-aloft or turn-exit navigation errors to maintain the desired
mid-eclipse flight profile.
N.B.: The specific pointg of mid-eclipse intercept results in a
totality duration appx 0.05s (insignificantly) shorter than the
absolute
theoretical maximum (for this set of flight parameters) for this
eclipse. This was arrived at from a cost/benefit trade to reduce
the overall flight distance R/T from Dusseldorf while retaining
in-flight contingency margins,
BASELINE
EFLIGHT and ECLIPSE-OBSERVATION ("Totality Run") PLANNING
The detailed definition of the EFLIGHT 2015 MAX baseline flight plan was
developed
to optimize the observing opportunity while minimizing to near-zero
risks that are otherwise high-probability at ground-based locations.
The nominal
(baseline) flight plan is built around an
eclipse-viewing "totality run" (TR) constrained by celestial mechanics,
aircraft operational considerations, and a need to maintain in situ
flexibility to implement contingency alternatives. For baseline
planning and logistical purposes we build from: (1) a flight altitude
for eclipse-viewing of 37,000 feet AMSL, with (2) a ground speed of 447.4 nm/hr and (3)
no wind (so ground speed = air speed, and heading = course).
Detailed pre-eclipse flight planning, and in-flight execution, will
incorporate and allow for the full range of possible flight levels, air
speeds, and wind-vectors that may be encountered in flight to
re-optimize the totality runs in situ
as may be necessary or desired.
We define the baseline totality run such that the aircraft is
centrally located at the apex of the lunar umbral shadow (but corrected
for the irregular lunar-limb profile) at the topocentric instants of
"maximum eclipse" at the chosen intercept point. We also define
the baseline totality run so that the aircraft velocity vector at
mid-eclipse places the Sun "straight out" the right-side windows of the
aircraft passenger cabin to provide optimum out-the-window viewing and
utilization. This
orientation also provides an optimal orientation to prolong
the duration of totality to a theoretical maximum anywhere along the
path of totality by using the aircraft's speed to (partially) keep pace
with the lunar shadow. With these constraints, we compute, and
tabulate below, three key time correlated waypoints for the totality
runs that define the lunar shadow intercept and crossing by the
aircraft designated C2 (eclipse contact II), MAX (corresponding to the
UTC instant of maximum eclipse), and C3 (eclipse contact III).
MAX, in both UTC and lat/long, will depend upon the aircraft altitude
AMSL. C2 and C3 will also depend upon the aircraft ground speed
and track (i.e., airspeed and winds aloft).
The (earlier) start of the pre-totality leg of the totality run is be
defined by a pre-totality time-correlated waypoint nine minutes before
mid-eclipse. The aircraft is initially positioned on the
MAX-eclipse intercept track at the requisite course/heading, distance,
and flight-time from the intercept point allowing for airspeed
adjustment in the run up to the C2 time-correlated waypoint to
compensate for deviations due to actual (vs. predicted) winds aloft
(holding the MAX intercept time-correlated waypoint invariant).
After C3 the aircraft will remain on the MAX-to-C3 heading for 6
minutes following mid-eclipse to allow viewing of the recession of the
Moon's shadow
before returning back to Dusseldorf.
End-to-End BASELINE FLIGHT PLAN
TIME-CORRELATED
WAYPOINTS and ECLIPSE CIRCUMSTANCES FOR EFLIGHT 2015 MAX
Flight scenario: FL 370, Mach 0.78 (TAS
447.4 nm/hr). No statistical winds assumed.
(Details
Subject to Change)
##
|
FLIGHT
PLAN PHASE/DESCRIPTION
|
U.T.
|
Long.
|
Lat.
|
Bearing°
|
Dist
dist(nm)
|
Leg
time
|
Alt° |
Az° |
01
|
NOMINAL
Wheels-Up
Dusseldorf
|
06:51:07
|
6.76666°
E |
51.28944°
N |
328.3
|
0.0
|
|
|
|
02
|
ASCENT:
Est.
Climb to FL 370 (TBD)
|
|
|
|
|
156.0
|
24m
00s
|
|
|
03
|
START
OUTBOUND CRUISE
|
07:15:31
|
4.48331°
E
|
53.47821°
N |
326.5
|
|
|
|
|
04
|
Outbound Cruise
|
|
|
|
|
690.7
|
1h
32m 38s
|
|
|
05
|
Contingency Buffer Start
|
08:48:09 |
At pilot's discretion / direction in
response to in situ conditions
|
45m
|
|
|
06
|
Contingency Buffer End
|
09:33:09
|
|
|
07
|
END
OUTBOUND CRUISE and START
PRE-TR CONSTANT RADIUS TURN
|
09:33:09
|
9.20690°
W
|
62.42545°
N
|
|
|
|
|
|
08
|
86.6°
Constant Radius Right Turn
Center
TBD: 25° bank, 1.35 min, Rad: 6.4 nm |
|
9.04412°W
|
62.50048°
N
|
|
9.7
|
1m 21s
|
|
|
09
|
Totality
Run Start (ME - 9 min) - Mach 0.78
|
09:34:30 |
9.21557°
W |
62.57147°
N |
41.8 |
|
|
17.9
|
129.2
|
10
|
WANING
SOLAR CRESCENT VIEWING
|
|
|
|
|
52.7
|
7m
05s
|
|
|
11
|
2nd Contact (C2)
|
09:41:35
|
7.92106°
W |
63.21854°
N |
43.0
|
|
|
18.6
|
132.4
|
12
|
TOTALITY
|
|
|
|
|
14.3
|
1m
55s
|
|
|
13
|
Mid-Eclipse (Umbral Axis
Intercept)
|
09:43:30
|
7.56084°
W |
63.39154°
N
|
43.3
|
|
|
18.7 |
133.3 |
14
|
TOTALITY
|
|
|
|
|
13.8
|
1m
51s
|
|
|
15
|
3rd
Contact (C3)
|
09:45:21
|
7.20902°
W |
63.55765°
N |
43.6
|
|
|
18.9
|
134.2
|
16
|
WAXING SOLAR
CRESCENT VIEWING
|
|
|
|
|
30.9
|
04m
09s
|
|
|
17
|
Totality
Run End (ME + 6 min) |
09:49:30
|
6.40478°
W |
63.92706°
N |
44.7
|
|
|
19.2 |
136.1 |
18
|
100.2°
Constant Radius Right Turn
Center
TBD: 25° bank, 1.56 min, Rad: 6.4 nm |
|
6.23351° W
|
63.85217° N
|
|
11.2
|
1m 34s
|
|
|
19
|
START
INBOUND CRUISE
|
09:51:04
|
6.03594°
W
|
63.91317°
N
|
|
|
|
|
|
20
|
Inbound Cruise
|
|
|
|
145.8
|
710.7
|
1h 35m 18s
|
|
|
21
|
End
Inbound
Cruise and Start Descent
|
11:26:22
|
5.110876°
E |
53.57091°
N |
|
|
|
|
|
22
|
DESCENT
from FL 370
|
|
|
|
|
150.0
|
24m
00s
|
|
|
23
|
Wheels-Down
Dusseldorf
|
11:50:22
|
6.76666°
E |
51.28944°
N |
155.4
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
TOTAL TIME and DISTANCE
|
|
|
|
|
1840.0
|
4h 59m 15s |
|
|
|
Notes:
(1) Totality run to place the Sun "straight out" the main
cabin windows at
mid-eclipse.
(2) No statistical (i.e., anticipated seasonal average) wind vectors
have been (yet) been assumed.
(3) Constant radius turns onto/off the TR track assume a bank angle
(and thus derived turn radius/duration) of 25°
(4) Ascent and Descent profiled durations and ground-track distances
are to-be-verified
(5) Geodetic co-ordinate reference frame is WGS84
(6) Delta-T: 67.8 seconds (Current IERS derived prediction for March
2015) |
The
end-to-end (wheels up to wheels down) flight planning seamlessly
merges into the immutable (but tunable based on actual flight
conditions) Totality Run. Most critical is entering the
pre-planned Totality Run exactly as specified with minimal error.
Any "delay" and the Moon's shadow will pass over the location where the
aircraft should have been and totality will be missed. This MUST,
and will be, be avoided.
(1) Take-off. To mitigate against the operational possibilities
"time-critical" take-off delay from DUS for any reason, an earlier than
time-critical wheels-up time for a central intercept at the
chosen mid-eclipse intercept point is planned. This is 45
minutes. See item (4) below on "Buffer" time.
(2) Ascent (and Descent). This phase of the flight must be
defined in detail by the aircraft flight planners. For Phase 1
planning an estimated climb to FL 370 consuming 24 minutes of time and
covering 156 nm (ground track), and descent over 150 nm in 24 minutes.
(3) Cruise and Totality Run Speeds. An "most economical"
TAS cruise speed of Mach 0.78 is suggested (and used) for initial
planning. This, importantly, provides some leverage to invoke higher or
lower cruise speeds (within performance limits) to allow mitigation
against unfavorable head or tail winds that would otherwise result in a
too-early or too-late arrival at the TR start point, or during
time/position decorrelation during the TR itself. Performance
options that may be invoked are to be discussed with the flight crew
and operations planners.
(4) Buffer Time. In the event of an on-schedule (prudently
planned) earlier than time-critical, takeoff , this "extra" (i.e.,
"buffer") time programmed into the flight plan to otherwise compensate
for a delay must be consumed by either maneuvering enroute,
and/or flying at a slower TAS to the time-critical TR start
point. This is a detail of the flight planning that will
necessarily worked in concert with the flight crew and flight planners
(given airspace and other operational constraints) at a later date
closer to eclipse time. A placeholder for this outbound
navigational contingency "buffer" is stipulated in the end-to-end plan,
and implementation details will be worked later in Phase 2 planning
with the pilot in command and flight planners.
CONTINGENCY
MITIGATION FOR DELAYED TAKE-OFF
AND/OR
UNFAVORABLE WINDS ALOFT
The baseline end-to-end flight plans
are designed to allow for delays
in reaching their time-invarient totality-run start points, beyond
those that can be accommodated by the adjustment range of the aircraft
speed, by up to 45 minutes. The NOMINAL baseline plan defines an
earlier than critical wheels-up take-off time from Dusseldorf [00].
Margin is provided to accommodate for such delays with a pre-allocated
contingency in-flight maneuvering "buffer" of variable duration [05-06]
of up to 45 minutes after reaching outbound cruise [03] prior to a
UTC-correlated entry onto the totality run [09]. The specific
maneuvering required to consume this buffer will depend upon the actual
take-off time. Two generic scenarios are suggested here,
but left to the discretion of the pilot in command with a requirement
to re-merge onto the nominal flight plan at item [09] for the start of
the time-critical totality run:
(1) (Conceptually) flying "zig-zags" traversing the outbound
cruise leg. This provides maximum flexibility against an
arbitrarily long take-off delay without the necessity of retargeting
for a different (less optimal) mid-eclipse intercept point within
reachable limits.
(2) Repositioning the heading re-alignment maneuver following the
outbound cruise phase to a point earlier time, and thus to a location
to the south-east of the totality run start point. I.e.,
establishing earlier a straight-and-level approach to totality run
start point and effectively extending the pre-totality portion of the
totality run. This presents a "lower risk" of navigation error by
placing the aircraft in situ within the path of totality for a longer
duration before totality begins. Pre-planned contingency, and/or
in situ, repositioning will be aided and enabled through the use of G.
Schneider's EFLIGHT eclipse flight optimization and navigation software.
INTERESTED? QUESTIONS ON
TECHNICAL/OPERATIONAL/LOGISTICAL DETAILS?
Contact: Dr. GLENN SCHNEIDER
at gschneider@mac.com
Who is Glenn Schneider? SEE HERE (eclipse
context). SEE HERE
(astronomical context).
Please
note, I myself am an
astronomer, and I am not in (nor do I
intend to be) in the aviation, or tour business. Here,
for
EFLIGHT 2015, as for all previous EFLIGHTS I have motivated and
designed, I
serve to facilitate the enabling, technical planning, implementation
and execution. I am happy to take any technical, operational, or
logistical questions regarding this flight. Questions about, or
requests for, flight bookings should be directed to TravelQuest
International
(1-800-830-1998 toll free in the USA or +1 928 445 7742 elsewhere).
UPDATES,
CONTACT,
AND ADDITIONAL INFORMATION
I will endeavor to keep all who are interested appraised of
any/all new developments through this web page as the EFLIGHT
2015 MAX implementation plan is further matured in collaboration with
the Air Berlin flight planning/operations groups and our flight
crew. Please check back again at
this
page's URL. Additional links will later be provided as
appropriate/necessary. I can be contacted by my email address
gschneider@mac.com, with also the additional/alternate contact
information:
Dr. Glenn Schneider
Astronomer and EXCEDE Project Principal Investigator
(Member: IAU Div. 2 Working Group on Solar Eclipses)
Steward Observatory and the Department of Astronomy
933 N. Cherry Avenue
The University of Arizona
Tucson, Arizona 85721 USA
email: gschneider@as.arizona.edu
Telephone: 520-621-5865
URL: http://nicmosis.as.arizona.edu:8000
last update: 14 September
2013