TOTAL SOLAR ECLIPSE 20 MARCH 2015   
PLANNING PHASE 1: BASELINE FLIGHT PROFILES
PREPARED: 09-12 JULY 2013

PRELIMINARY & FOR INTERNAL PLANNING USE ONLY (NOT FOR REDISTRIBUTION)
Subject to Review/Revision

Dr. Glenn Schneider
Astronomer and EXCEDE Project Instrument Scientist
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

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 presume (for both flight scenarios under development) 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.  These are the right (starboard) side, 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 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. 

The baseline flight plan (for both flights) 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.

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 derived prediction for MArch 2015)

The offsets in UTC and position of respective mid-eclipse intercepts for the two aircraft assures no interference (airspace intrusion) or mutual line-of-site obscurations of the eclipse as illustrated  in the graphic below.  Flight #2 (shortest great circle distance to mid-eclipse centerline from Dusseldorf and without airspace intrusion with Flight #1) will reach its Totality Run start location at 09:30:37 UTC at which time it will then commence on a track for a mid-eclipse intercept at 09:39:27 UTC.  Flight #1 (maximum totality duration) will reach its Totality Run start location at  09:34:40 UTC at which time it will then commence on a track for a mid-eclipse intercept at 09:43:30 UTC.  As Flight #1 begins its totality run, Flight #2 will at the same instant of  time be on its intercept track 85.2 nm to the southwest.  The two aircraft (nominally traveling at the same speed) will then maintain this distance until they complete, and sequentially, turn off of their respective totality run tracks to return to Dusseldorf.

The second-by-second details of the baseline Totality Runs for both aircrafts, and "local" (moving topocentic) circumstances for the eclipse are tabulated at the bottom of this page with key elements in UTC and position illustrated with accompanying graphics.  In practice, a small sub-set of UTC-correlated Aircraft location (waypoints) will be selected and programmed into the aircraft FMS to define the track to be followed.  Likely only four will be needed (tabulated below in green) with the two at the extrema at the beginning and end of the totality run. It is suggested that the two "most central" waypoints be selected at 1 minute prior second contact and one minute after third contact (tabulated below in blue) - not during totality.  This will provide sufficiently accurate mid-eclipse targeting without the aircraft executing a (small) track-following maneuver with then a potentially small instability with overshoot and correction that can cause a momentary dither (displacement) in the relative (otherwise stable) position of the Sun w.r.t. the line-of-sight.  For information (only) the tabulations also highlight the circumstances of the instants of contacts 2 and 3 (in red) and mid-eclipse (in purple).  These data are used in the development of the end-to-end flight plan.

The end-to-end (wheels up to wheels down) flight planning MUST seamlessly merge 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 be avoided.

(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.

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 for flight #1 and up to 30 minutes for flight #2.  For each aircraft, the NOMINAL baseline plan defines an earlier than critical wheels-up take-off time from Desseldorf [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 45/30 minutes (flight #1/#2, respectively) 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) flying "zig-zags" traversing the outbound cruise leg (schematically represented by the gray path in the figure below).  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 manuever 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 as illustrated in  (green lines) in the figure below.  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.

N.B.: If either option is executed, this may require "altitude stacking" of the two aircraft to assure mutual airspace intrusion avoidance. 

In the event of a maximum, fully buffer-consuming take-off delay or strong head winds, the aircraft would proceed directly by great circle route from start of its outboard cruise to the totality run start point, as schematically illustrated (purple line) for Flight #1 in the graphic below.

Flight #1 End-to-End BASELINE FLIGHT PLAN

Flight scenario: FL 370, Mach 0.78 (TAS 447.4 nm/hr).  No statistical winds assumed.

EFLIGHT 2015 #2 (B738) — 20 MARCH 2015 TOTAL SOLAR ECLIPSE — BASELINE FLIGHT PLAN

Flight #2 Baseline Totality Run