The qantas/croydon total Solar Eclipse Flight 23 November 2003 ut




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4/23/16

The QANTAS/CROYDON Total Solar Eclipse Flight
23 November 2003 UT
Mission Planning & Definition Overview
REQUIREMENTS for Assisted Real-Time Computation and Navigation

Dr. Glenn Schneider, Ph D.

Associate Astronomer & NICMOS Project Instrument Scientist

Steward Observatory, The University of Arizona

Tucson, Arizona 85750 USA
Contact email: gschneider@as.arizona.edu, gschneider@mac.com

URL: http://nicmosis.as.arizona.edu:8000



Abstract
No total solar eclipse has ever been observed from Antarctica both because of the infrequency of occurrence and the logistical complexities associated with Antarctic operations. This paradigm of elusivity regarding Antarctic eclipses in the historical record of science and exploration is about to be broken. The next total solar eclipse, which occurs on 23 November 2003 U.T., the first in the Antarctic since 12 November 1985, will be very largely unobserved due to the geographic remoteness of the path of totality. Yet, interest in securing phenomenological observations of, and associated with, the eclipse by members of the scientific research communities engaged in solar physics, astrodynamics, aeronomy and upper atmospheric physics, as well as educators and amateur astronomers has been extremely high. The development of a flight concept to enable airborne observations, with a dedicated aircraft chartered from QANTAS Airlines, will permit the previously unobtainable to be accomplished. To do so successfully requires detailed preparatory planning for the execution of such a flight. The technical groundwork to achieving this goal has been pursued with diligence over the past four years and is predicated on a legacy and computational infrastructure capability founded on more than three decades of eclipse planning for ground, sea, and airborne venues. Here, given the geometrical circumstances of the eclipse, the uncertainties associated with weather, and the constraints of operations of the Boeing 747-400 aircraft, the requirements for the successful execution an intercept flight with the base of the Moon’s shadow over the Antarctic are reviewed. The unequivocal need for real-time, in-situ re-computation of an executable flight plan in response to in-flight conditions is discussed. The mechanism for fulfilling that need, through the expert operation of EFLIGHT, a well-tested highly specialized software package of unique pedigree designed specifically for this purpose by the author of this report, working in concert with the flight crew on the flight deck is elaborated upon in the specific context of the requirements of this flight.

The 23 November 2003 Antarctic Total Solar Eclipse
On the long-term average, a total solar eclipse is visible somewhere in the world about once every sixteen months. However, the overlap between the "cycles" of solar eclipses is complex. The next total solar eclipse occurs on 23 November 2003 and its immediate predecessor, the 4 December 2002 total solar eclipse, occurred only 354 days earlier. The next one (which has a maximum total phase duration of only 42 seconds) will not happen until 08 April 2005. Also on average, any given spot on the Earth will see a total solar eclipse about once every 360 years. However, eclipse paths can cross specific locations more frequently (e.g., the 2001 and 2002 eclipse paths crossed in South Africa, and those living in the right location saw both of them). The last total solar eclipse in the Antarctic occurred on 12 November 1985, but was unobserved.
The 23 November 2003 total solar eclipse (TSE2003) will be visible only from a small portion of the Eastern Antarctic. The "path of totality", the region on the Earth's surface which will be swept by the Moon's umbral shadow, and where the total phase of the eclipse can be seen, begins off the coast in the Antarctic (Great Southern) Ocean. The umbral shadow will "touch down" on the Earth at 22h 24m Universal Time (U.T.). At that time, the total phase of the eclipse becomes visible at sunrise at a latitude of 52.5°S, southeast of Heard Island and the Kerguelen archipelago. The lunar shadow then moves southward toward Antarctica, and traverses an arc-like sector of the continent from approximately longitudes 80E to 15E where it will "lift off" into space only 51 minutes later at 23h 15m U.T.

Fig. 1 – TSE2003 visibility. Partial eclipse seen in the region of the overlaid grid. Total eclipse seen within gray arc over Antarctica (path of totality). Ellipses indicate instantaneous surface projection of umbral shadow.



Total solar eclipses in the Polar Regions can have unusual geometries, and TSE2003 is no exception. In this case, the Moon's shadow passes "over the pole" before reaching the Earth. So the path of totality advances across Antarctica opposite the common direction of the Earth's rotation and the lunar orbit. The eclipse occurs in the hemisphere of the Earth which, except at southern polar latitudes, is experiencing nighttime. Hence mid-totality occurs very close to local midnight. Antarctic total solar eclipses are infrequent, but not particularly rare, the last occurring (but unobserved) eighteen years earlier in 1985 (the Saros predecessor to TSE2003).
Accessibility to, and mobility in, the path of totality on the Antarctic continent is severely limited and generally inaccessible inland. A Russian icebreaker will be making way to the coast with eclipse observers, but the coastal weather at the location and time of year of the eclipse is often cloudy, accompanied by high winds and ice fog. A ground-based expedition to the Russian Antarctic station at Novolazarevskaya, very close to the end of the eclipse path and sunset, is planned, but the Sun will be very close (only a degree) above the horizon and obscuration by blowing snow or white-out conditions is a strong possibility. Until this juncture in time and technology Antarctic total solar eclipses have been elusive targets, and never before has one been observed. If ever there was a clear-cut case for the necessity of using an airborne platform to observe a total solar eclipse, however, TSE2003 is it.
The QANTAS/Croydon Boeing 747-400 Total Solar Eclipse Flight
The upcoming opportunity to conduct high-altitude airborne observations of the 23 November 2003 (UT) total solar eclipse over Antactica is unique in the history of science, and indeed of humanity. To this day no total solar eclipse has ever been witnessed from the Antarctic. To fill this void in the experience base of humankind, while enabling compelling and otherwise unobtainable observations furthering a wide variety of astronomical, solar dynamical, and aeronomic studies, a truly unique Qantas B747-400 flight will depart Melbourne, Australia on 23 November 2003 (Universal Time). After a poleward journey to a latitude of ~ 70S, the flight will rendezvous with the base of the Moon’s shadow, nominally at 22:44:00 UT at an altitude of 11 km above the Earth’s surface, as the shadow rapidly and obliquely sweeps over the eastern end of the White Continent.
Sightseeing flights over the Antarctic have been implemented over the past decade on a fairly regular basis by Croydon Travel, an Australian based company, in concert with QANTAS Airlines. Croydon periodically charters a B747-400 aircraft from QANTAS for this purpose, and has done so with great success 40 times over the past decade. Given this experience base, the concept of developing an eclipse observation flight was a natural “variant”, but with many special needs and requirements, which are absent on Antarctic sightseeing flights.
Additional general information on the 23 November 2003 eclipse and the QANTAS B747-400 flight concept may be found in Appendix A of this document.
Shadow Dynamics and the Duration of Totality
The dynamics of the eclipse are driven by the inexorable laws of Newtonian celestial mechanics, as naturally applied to the orbital configurations of the Earth/Moon/Sun system. The long slender conic of the TSE2003 lunar umbral shadow, 1/2° in angular extent at the distance of the moon, is only 34 nautical miles in radius at 11 km above the Earth’s surface and tapers to a geometrical point below. The umbral shadow slices through the Earth’s atmosphere at very high speed with a non-linear acceleration profile (see Figure 2), decelerating to its slowest instantaneously velocity of 2109 Nm/hr with respect to the rotating surface of the Earth at 22:49:17 UT. At that instant, the instant of “greatest eclipse”, a ground-based observer concentrically located along the shadow axis would experience 1m 59s of totality, the maximum possible for this eclipse. Elsewhere within the path of totality the achievable ground-based duration is reduced. Time in totality is a highly precious commodity. Given the intrinsically short maximum duration of TSE2003, and the very limited opportunities to position observers within the path of totality, extreme care must be taken in the planning and execution of an airborne shadow intercept to avoid unnecessarily shortening the achievable duration due to targeting and/or navigation errors.

Fig. 2 – Instantaneous speed (blue) and radius (red) of the umbral shadow as a function of time.


The maximum duration along centerline declines very slowly (except near the points of sunrise and sunset) but reduces significantly and non-linearly (to zero) across the direction of the shadow’s velocity vector at the extrema of the shadow. For a ground-based observer, the duration of the total phase as seen at some particular location within the umbral shadow declines, to first order, as (1-[1-abs{x/R}]2)1/2 / D ; where R is the radius of the umbral shadow where it intersects a surface of constant elevation, x is distance of the observer from the shadow axis perpendicular to its instantaneous direction of motion, and D is the duration of totality on centerline at the same Universal Time of mid-eclipse. The duration of totality for an airborne observer, with three degrees of positioning freedom (X, Y and Z [or longitude, latitude and altitude]), is shown in Figure 3 as a function of the (X2+Y2+Z2)1/2 displacement of the aircraft from the shadow axis in a plane perpendicular to the axis.

Fig. 3 – Duration of totality for perpendicular off-axis position displacements along the path of totality.


The Modifying Effects of the Aircraft Velocity Vector
For simplicity, Figure 3 does not consider the effect of the aircraft’s velocity vector on the absolute achievable duration of totality and is directly applicable for a stationary (Earth co-rotating) observer. For any aircraft trajectory the duration of totality will decline with an aircraft/shadow axis centration error as illustrated in Figure 3, but the duration will additionally be modified by the aircraft’s motion relative to the lunar shadow.
The nominal at-altitude cruise speed of the B747-400 (with a no-wind condition) is 470 Nm/hr. The lunar shadow, then, moves across the Earth with a minimum speed (near the point of greatest eclipse) approximately 4-1/2 times faster than the aircraft’s speed. Hence, with the aircraft properly positioned at the critical time the lunar shadow will overtake the aircraft, but, depending upon the aircraft heading, more slowly than for a stationary observer. An increase in the duration of totality is realized for an aircraft with a net velocity component in the direction of motion of the lunar shadow axis. Without the necessary consideration of other constraining factors, a maximum theoretical gain of 37s may be realized for an aircraft with a ground speed of 470 Nm/hr following the trajectory of the lunar shadow axis and precisely co-aligned with axis at the instant of greatest eclipse. Such an optimal trajectory for the aircraft may not be sustainable, or even desirable, as the goal of maximizing the duration of totality cannot be taken in isolation.
Primary Factors for Simultaneous Optimization
A) AXIAL CONCENTRICITY: At the selected instant of mid-eclipse, the aircraft must be concentrically located along the lunar shadow axis. To the requisite degree of targeting precision, (discussed below) this is complicated because the photocentric location (i.e., the “center of figure”) of the Moon’s shadow is not coincident with its dynamical center (i.e., its “center of mass”) due to irregularities along the lunar limb (selenographic features such as mountains, ridges, and valleys). It is these features that give rise to the “diamond ring” and “Baily’s Beads” phenomenon at second and third contacts). The “lunar limb profile” (for example see Figure 4), changes with topocentric physical and optical librations and will differ with an observer’s latitude, longitude, and altitude along and across the path of totality, and hence, must be applied dynamically (and differentially) with changes in aircraft position and targeting.

Fig. 4 – Representative lunar limb profile for mid-eclipse at 22:40 UT for an observer at sea level on centerline. The scale-height of the features along the lunar limb as seen at this location has been vertically amplified for illustrative purposes. Note that one arcsecond at the distance of the moon is approximately 1.8 kilometers.


B) MID-ECLIPSE APPROACH/DEPARTURE SYMMETRY: Observation and analyses of the spectrally decomposed brightness and “color” gradients of the sky, illuminated by light scattered into the umbral shadow by upper atmospheric particulates, will provide unique insights into the bulk aerosol content over the Antarctic. In-situ measures by Antarctic ground stations rely on back-scattered LIDARs, whereas aerosol scattering of sunlight into the lunar shadow is uniquely front-scattered and can be used to break the degeneracies in particle scattering models applied to the upper atmosphere. Quantitative calibration of aeronometric studies of the bulk physical properties of the upper atmospheric, particularly due to airborne contaminants, require sampling the scattering properties of the atmosphere in a symmetrical manner with respect to concentric shadow illumination, and hence immersion and emersion of the aircraft’s penetration through the umbral shadow.
(A) and (B), above, define a temporal shadow concentricity/symmetry requirement for the aircraft trajectory, i.e., how close to the geometrical shadow axis the aircraft must be at the instant of mid-eclipse, and where it must be positioned as it transitions through the umbral boundary at second and third contacts. An offset in time would produce a time and position error not only reducing the duration of totality but causing a temporal shift in the expected contact times of the eclipse which is counter to the needs of planned imaging and photographic experiments to be conducted.
C) MID-ECLIPSE HEADING ALIGNMENT: For the purpose of observing, photographing, and providing a proper field-of-view for those on-board the aircraft observing the eclipse, the line-of-sight to Sun through the cabin windows should be in very close to a plane perpendicular to the aircraft heading. I.e., to provide an unimpeded, and near optimal viewing opportunity through the cabin windows. Such orientations will generally yield crossing-geometries with respect to centerline, and thus will preclude a full maximization of the duration of totality. The heading alignment and duration must be simultaneously optimized.
D) MINIMIZE INTER-TOTALITY RUN HEADING RE-ALIGNMENTS. The azimuth of the Sun varies continuously depending upon the time and aircraft position. To fully optimize (C) would require near-continuous differential course corrections, which cannot be accommodated at high temporal cadence due to CDU/FMS granularity and operational procedures constraints. Larger discrete corrections during totality would cause a sudden displacement in the positioning of the Sun with respect to the line-of-sight, which should be avoided.
Derived Navigation Requirements and Error Tolerance
Taken together, and applied to the topocentric circumstances of the eclipse, the following navigational precision requirements to meet the goals of (A) – (D), above, emerge:
TABLE 1

REAL-TIME NAVAGATION/TARGETING REQUIREMENTS
1) Absolute Position Error Tolerance:

a)Maximum Aircraft lateral (cross track) position error

±1 km at mid-eclipse, contact II, and contact III

b)Maximum Aircraft vertical position error ± 100 meters


2) Absolute Timing Error Tolerance : ± 6s in time w.r.t.

U.T. predictions* at CII and CIII.


3) Heading Constraint: Portside Orthogonality:

Absolute: ± 1.5° from mid-eclipse ±5 minutes

Differential: ± 0.5° from mid-eclipse ±5 minutes
4) CDU/FMS Way Point Input Updates During Totality Run:

a)Precluded within 2 minutes of mid-eclipse, except for

mid-eclipse update

b)Avoided if possible within 5 minutes of mid-eclipse

c)Desired Granularity: 5 minute intervals at relative

mid-eclipse times of –15, –10, -5, (0), +5 minutes


5) Aircraft Altitude: Maximum possible altitude for least

air-mass along line of sight to Sun.


* Exclusive of delta-T correction based upon pre-eclipse IERS updates

(see: http://www.iers.org/iers/ )

The Boeing 747-400 is exceptionally well suited to this task given the operational capabilities and chacteristcs of the aircraft. The experience base of the QANTAS flight crews conducting previous Antarctic overflights, though less demanding in navigational specificity and compliance than the 23 November 2003 flight, is unparalleled in commercial aviation. Hence, the choice of QANTAS B747-400 platform for this purpose was unequivocally clear.
External Influences and Parametric Variation
The requirements for previous QANTAS Antarctic flights, carried out with great success, were driven by the more casual needs to provide a suitable downward looking venue for sightseeing. These flights were unconcerned with the specific and highly demanding external constraints imposed by the unique needs of a solar eclipse intercept. For the 23 November 2003 eclipse flight the necessary responsiveness to uncontrollable, but anticipated, atmospheric variables (Table 2A) will be fettered and constrained by defining astrodynamical geometry of the eclipse (Table 2C) and coupled to the performance restrictions of the B747-400 aircraft (Table 2B/D).
TABLE 2

PRIMARY FLIGHT DEFINITION VARIABLES, CONSTRAINTS & RESTRICTIONS
A ATMOSPHERICS: METEROROGICAL CONDITIONS

Local obscuration by cloud: monolithic and multi-layer

along the line-of-sight to the Sun.

Wind speed and direction and vector gradients

Atmospheric turbidity along the line-of-sight to the Sun

Flight-level turbulence (platform stability)


B AIRCRAFT PERFORMCE CONSIDERATIONS

Take-off or In-flight delay

Maximum service ceiling for gross weight at eclipse intercept
C ASTRO-DYNAMICS: TIME/POSITION DEPENDENT FUNDEMENTAL GEOMETRY

Non-linear motions (absolute & relative) of Earth, Moon, and Sun

Shadow Velocity and instantaneous acceleration profile

Shadow axis (X,Y,Z) position loci as functions of altitude

above geodial surface (MSL), differentially corrected through

atmospheric refraction models based upon Temperature/Pressure

scale-height profiles.

Shadow boundary loci as a functions topocentric lunar

limb profile and atmospheric refraction corrections.

Conic shadow projection on the elevated oblate geoidal surface


D AIRCRAFT OPERATIONS CONSIDERATIONS

Minimum/Maximum Airspeed

FMS Targeting Compliance (input granularity and precision)


A “Baseline” Flight Concept for Plan Evaluation
Maintaining flexibility in the execution of the shadow intercept, within the previously delineated constraints, is paramount to permit the critical optimization of the spatial and temporal positioning of the aircraft to allow an unprecedented set of observations to be conducted to the greatest possible advantage that the circumstances of the eclipse will allow. In a decoupled sense, the outer envelopes of the flight definition parameter spaces can (and has) been evaluated and were used to define “baseline” or “nominal” flight intercept profiles for evaluation and early planning purposes. The “baseline” totality run intercept calls for a mid-eclipse intercept at 22:44:00 U.T, flight altitude of 35,000 ft, direction of flight to orient the sun orthogonal to the port-side windows, and waypoint pre-loads into the 747 CDU/FMS requiring no more frequent than 5 minute updates. This “baseline” plan, which was developed for planning purposes, is shown graphically in Figure 5 and tabulated in Table 3.

Fig. 5 – Schematic representation of the “baseline” flight used for planning purposes. Dotted red line: Centerline at 35,000 ft in 30-second intervals (1 minute annotation). Solid red lines: PROJECTION of the shadow conic major axis extrema onto a geoidal surface of 11 km constant elevation. Blue arrows: Lines of sight to Sun.


This particular point of mid-eclipse intercept and its corresponding baseline flight trajectory of approach and recession simultaneously satisfy the optimization criteria previously discussed. In particular, this scenario if executed in this form would achieve: (a) a 2m 34.7s extended duration totality, 36s longer than on the ground at he same mid-eclipse U.T. and only 0.6s shorter than the theoretical maximum for this eclipse, (b) a LOS viewing angle deviating by only (+0.3°, -0.1°) throughout the totality run, and (c) a solar elevation at mid-eclipse only 0.2° lower than theoretically possible. Additionally, at this point the lunar shadow velocity (2115 nM/hr) is very nearly at its minimum for this eclipse (2109 nM/hr) providing a greater temporal margin for tolerable positioning error than most other locations along the path of totality.
TABLE 3

BASELINE INTERCEPT PROFILE FOR PLAN EVALUATION
=============================================================================================================

U.T. Intercept: 22:44:00 TOTALITY DURATION = 2m 34.7s

Flight Altitude: 35000ft

Heading: 198.80° Cnt hh:mm:ss.f Alt° Az° P° Cnt Cnt hh:mm:ss.f Alt° Az°

Air Speed: 470.0nm/h 2ND 22:42:42.7 +14.8 109.0 109.3 3RD 22:45:17.4 +15.0 108.6 289.7

Wind Speed: 0.0nm/h LATITUDE: -069° 49' 09.4'' LATITUDE: -070° 08' 17.2''

Wind Direction: 0.0° LONGITUDE: +093° 09' 59.0'' LONGITUDE: +092° 51' 6.8''

=============================================================================================================

HMMSS UMbra Lon UMbra Lat WidKM Uaz° Ual° AC Long AC Lat Mid∆T Mid∆D LOS Bearng ACaz Acal

222900 9321.788E 6031.704S 541.8 113.7 10.2 9442.029E 6807.104S -900s 117.5nm +0.3 197.22 108.5 14.6

222930 9334.818E 6053.937S 540.9 113.4 10.5 9438.915E 6810.838S -870s 113.6nm +0.3 197.27 108.5 14.6

223000 9346.587E 6115.758S 539.9 113.1 10.8 9435.783E 6814.571S -840s 109.7nm +0.3 197.32 108.5 14.6

223030 9357.178E 6137.205S 538.8 112.7 11.0 9432.635E 6818.303S -810s 105.8nm +0.3 197.37 108.5 14.7

223100 9406.659E 6158.313S 537.6 112.4 11.3 9429.470E 6822.034S -780s 101.8nm +0.3 197.42 108.5 14.7

223130 9415.088E 6219.109S 536.3 112.2 11.5 9426.287E 6825.764S -750s -97.9nm +0.3 197.47 108.5 14.7

223200 9422.514E 6239.618S 535.1 111.9 11.8 9423.086E 6829.493S -720s -94.0nm +0.3 197.52 108.5 14.7

223230 9428.976E 6259.863S 533.7 111.6 12.0 9419.868E 6833.221S -690s -90.1nm +0.3 197.56 108.5 14.7

223300 9434.508E 6319.862S 532.4 111.4 12.2 9416.632E 6836.947S -660s -86.2nm +0.2 197.62 108.6 14.7

223330 9439.140E 6339.632S 531.0 111.1 12.4 9413.378E 6840.673S -630s -82.3nm +0.2 197.67 108.6 14.7

223400 9442.892E 6359.188S 529.6 110.9 12.6 9410.106E 6844.398S -600s -78.3nm +0.2 197.72 108.6 14.7

223430 9445.786E 6418.544S 528.1 110.7 12.8 9406.815E 6848.122S -570s -74.4nm +0.2 197.77 108.6 14.7

223500 9447.834E 6437.712S 526.7 110.5 13.0 9403.507E 6851.845S -540s -70.5nm +0.2 197.82 108.6 14.8

223530 9449.051E 6456.701S 525.3 110.3 13.1 9400.179E 6855.567S -510s -66.6nm +0.2 197.87 108.6 14.8

223600 9449.442E 6515.523S 523.8 110.1 13.3 9356.833E 6859.287S -480s -62.7nm +0.2 197.92 108.6 14.8

223630 9449.013E 6534.185S 522.4 109.9 13.4 9353.468E 6903.007S -450s -58.8nm +0.2 197.98 108.6 14.8

223700 9447.769E 6552.695S 521.0 109.8 13.6 9350.084E 6906.725S -420s -54.8nm +0.2 198.03 108.6 14.8

223730 9445.707E 6611.060S 519.6 109.6 13.7 9346.681E 6910.442S -390s -50.9nm +0.2 198.08 108.6 14.8

223800 9442.827E 6629.286S 518.2 109.5 13.9 9343.258E 6914.158S -360s -47.0nm +0.2 198.13 108.6 14.8

223830 9439.124E 6647.379S 516.8 109.3 14.0 9339.816E 6917.873S -330s -43.1nm +0.1 198.19 108.7 14.8

223900 9434.591E 6705.344S 515.4 109.2 14.1 9336.354E 6921.587S -300s -39.2nm +0.1 198.24 108.7 14.8

223930 9429.218E 6723.185S 514.0 109.1 14.2 9332.872E 6925.300S -270s -35.3nm +0.1 198.30 108.7 14.8

224000 9422.996E 6740.906S 512.7 109.0 14.3 9329.370E 6929.011S -240s -31.3nm +0.1 198.35 108.7 14.9

224030 9415.910E 6758.510S 511.4 109.0 14.4 9325.847E 6932.722S -210s -27.4nm +0.1 198.41 108.7 14.9

224100 9407.947E 6816.000S 510.1 108.9 14.5 9322.305E 6936.430S -180s -23.5nm +0.1 198.46 108.7 14.9

224130 9359.087E 6833.379S 508.8 108.8 14.6 9318.742E 6940.138S -150s -19.6nm +0.1 198.52 108.7 14.9

224200 9349.314E 6850.648S 507.5 108.8 14.7 9315.157E 6943.845S -120s -15.7nm +0.1 198.57 108.7 14.9

224230 9338.603E 6907.811S 506.3 108.8 14.7 9311.552E 6947.551S -90s -11.8nm -0.0 198.63 108.8 14.9

224300 9326.933E 6924.866S 505.1 108.8 14.8 9307.926E 6951.255S -60s -7.8nm -0.0 198.69 108.8 14.9

224330 9314.278E 6941.816S 503.9 108.8 14.9 9304.278E 6954.958S -30s -3.9nm -0.0 198.73 108.8 14.9

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