What the airborne measurements show
Current combined findings: 15 globe preferences, zero flat, 38 unresolved. The qualified recovery adds three completed stretches, including an IMU8 recording, with full source-track details. All fifteen also favor the specified background-field globe. The wider recovery is running; partial fits are not yet added to the headline.
Preserved first-study findings
All 12 completed whole-stretch comparisons favor globe geometry under both processing assumptions. None favors the specified flat disc. This is a substantial empirical finding from NASA's archived aircraft measurements. It reports which model fits better, rather than how many calculations finished for each model.
At the end of the first study, 41 comparisons were numerically unfinished; they do not erase the completed results or establish equal support for flatness. The finding's statistical strength still needs validated uncertainty estimates and accounting for shared flights and instruments. Twelve stretches are not automatically twelve independent replications, and no calibrated significance level has yet been assigned.
All 12 also favor the globe candidate with the standard background rotation field over the zero-field globe. That comparison does not identify the field's physical cause.
Recordings and flight tracks
The measurements come from NASA's Operation IceBridge airborne lidar surveys over ice sheets and related terrain. An IMU (inertial measurement unit) measures turning and acceleration; GPS records the aircraft's track. Survey-grade Applanix systems supplied the IMU increments used to reconstruct motion for precision mapping. NSIDC describes ILVIS0 as an archive of raw IMU and GPS data.
The analysis screened all 232 retained recordings. It selected 53 complete, steady stretches totaling 424.3 minutes, each at least four minutes long with every supported receiver ground-speed reading at least 700 km/h. Selection was saved before model fitting. The eligibility record explains the motion, timing and completeness rules and links to exact filenames, source fingerprints, UTC intervals, durations and speeds. Several instruments recorded overlapping flight time; 53 stretches are not 53 independent flights.
The records contain Applanix Group-4 angle and velocity increments, with logged IMU types 8 and 21 decoded separately. All 12 first-pass completed comparisons are IMU21; the original unresolved group includes 39 IMU21 stretches and two IMU8 stretches. A successful IMU8 decoder check is not a hardware identification or calibration certificate for IMU21. The detailed recording and track tables and track positions preserve the source detail.
Complete comparisons
Each stretch receives six fits: rotating globe, still globe and stationary flat disc, under each of two processing cases. Both allow a constant gyro offset of ±1°/hour. One assumes no Earth-rate removal; the other fits a shared removal fraction. These checks allow for uncertainty in the logging system without changing the observations.
| Whole-stretch result | Stretches | Meaning |
|---|---|---|
| Globe | 12 | All required fits finished; the better globe fit beats the flat disc in both processing cases. |
| Flat | 0 | No complete comparison favors the flat disc. |
| Unknown | 41 | At least one required fit did not pass the numerical stopping checks. |
All 12 globe results also favor the rotating globe over the still globe in both processing cases. Shape is evaluated first; rotation is reported only after the complete shape comparison favors globe.
The completed group totals 87.6 minutes, with a median stretch duration of 7.3 minutes and median ground speed of 822.9 km/h. The unfinished group totals 336.6 minutes, with medians of 8.9 minutes and 834.7 km/h. Faster or longer stretches did not consistently make the numerical calculation easier in this already-fast selection.
What the unfinished comparisons say
An unfinished comparison is not a finding that globe and flat fit equally well. Of 318 individual fits, 188 passed the stopping checks and 130 did not. Most unfinished fits exhausted their numerical allowance. Convergence means the parameter adjustment finished; it does not mean the model fits the observations well.
Some unfinished stretches still supply a matched pair in which both calculations finished:
| Available comparison, across both processing cases | Globe fits better | Flat disc fits better |
|---|---|---|
| Rotating globe versus flat disc | 35 | 0 |
| Still globe versus flat disc | 30 | 26 |
The flat-favoring pairs are against the still globe. They do not establish that flat beats the globe family, which also includes the rotating globe. Every available finished rotating-globe/flat comparison favors the rotating globe. Where a required calculation is missing, the full outcome remains unknown. These pairs reuse recordings and are not independent votes. The saved-result review gives the numerical details.
Instrument quality and checks still outstanding
These are professional surveying instruments, not consumer phone IMUs. Their published capabilities support investigating the degree-per-hour signals predicted here. The instrument guide distinguishes recorded instrument types, published system performance and inferred hardware families.
The model observations are original IMU increments and receiver positions. The finished, fused navigation solution is used for decoder validation and motion screening only. "Raw" does not require the sensor to have had no internal calibration or filtering: ordinary noise filtering can preserve slow turning. Automatic zeroing or subtracting Earth rate is a different operation and can remove the signal. Exact legacy logging corrections are still being investigated; fitting successfully does not identify them.
Many fits reach permitted calibration or mounting limits, and some are sensitive to the integration clock. These are specific measurement-model checks, not evidence that flat Earth fits as well. The study reports model fit preferences; it has not assigned a validated probability of error or established that every fitted solution is the best possible solution. The original measurements, failures and numerical evidence remain available.
Pilot and next work
The earlier six-recording pilot reached complete comparisons for two recordings. Both favored globe and then rotation under all four tested cases. Two other recordings supplied globe-favoring partial pairs; two had no finished shape pair. None had a resolved flat preference.
A 12-fit matched solver trial is complete. It finished 10 fits compared with 11 in the original calculation, so it does not justify expanding the revised solver. The completed control still favors globe and rotation; the diagnostic stretch remains unfinished. Original results remain unchanged.
The saved-fit audit now compares calibration limits and residual errors. On the same 12 resolved stretches, median horizontal error is 0.068 m for rotating globe, 29.5 m for still globe and 47.1 m for flat disc. Calibration trade-offs and checks of residual behavior remain the next priorities.
The two-recording residual diagnostic now saves individual errors and reproduces the original calculations without refitting. It confirms the large error separation while exposing residual correlation and vertical sensitivity to timing. It leaves every original convergence label and model preference intact.
This page explains the results in plain language. The original audited report and its numerical records remain unchanged for reproducibility.