Local Level Lab

What do aircraft motion measurements reveal about Earth's shape and a background rotation field?

Local Level Lab analyzes NASA airborne survey recordings to investigate that question. The data come from professional inertial equipment and GPS receivers aboard research aircraft. A simpler, stationary crowdsourced experiment using smaller, less expensive IMUs is secondary work. The code, selection criteria and analysis records are open for review.

Forty-one of 53 selected stretches consistently favor globe geometry over the specified flat disc. None favor flat; 12 remain unresolved. This is a substantial empirical finding from professional airborne measurements. The completed numerical recovery adds twenty-nine to the original twelve while preserving the same observations, selected intervals and physical assumptions. Current findings and source tracks are available for review.

The opportunity is to test Earth's curvature through the aircraft's measured motion. Professional IMU recordings let anyone examine the gradual turning expected while crossing a curved surface, and compare competing explanations against the same data. The contribution is an open, reproducible airborne test of competing geometries. It builds on a long tradition of measuring Earth's figure, including Snellius's 1617 survey (English translation).

An IMU (inertial measurement unit) measures turning and acceleration. Its gyroscopes measure how it turns; its accelerometers measure forces associated with gravity and motion. GPS records where the aircraft went and when.

The project separates surface geometry, measured rotation and its physical explanation. A gyro measures the sensor's angular motion relative to an inertial reference—a reference that is not itself turning. Separating aircraft motion from a persistent background field is an analysis task. Identifying what produces that field is a further question, which these recordings alone do not settle. This project does not treat a gyro signal as proof of heliocentrism or any other cosmology.

Earth's shape and its place in the solar system are separate questions. Geocentric does not mean flat, and a globe result alone does not establish heliocentrism.

The idea

An aircraft staying level over a globe must gradually turn as it follows the curved surface: the direction of local down changes along its route. At 900 km/h, that curvature corresponds to roughly eight degrees of turning per hour. A background rotation field would add a different contribution. The analysis separates these terms from ordinary aircraft movements and instrument errors.

“Rotating globe” and “still globe” are names for these mathematical candidates. They compare a specified background angular-rate term with zero. They do not compare every proposed cause of rotation. A proposed stationary Earth with a nonzero inertial field is not represented by the zero-field “still globe” candidate. It would need explicit measurement predictions before it could be tested here.

The first question is globe, flat or unknown. All three models are fitted together, comparing the flat model with whichever globe model fits better. The background-field comparison is reported only after shape consistently favors a globe; it reuses the globe fits.

A persistent gyro reading alone proves little. Instrument offsets, aircraft motion and uncertain onboard corrections can imitate parts of the signal. Those effects must be allowed fairly across all models. This tests the specified models, rather than every possible description of a flat Earth.

Primary work: NASA airborne data

These recordings supported NASA's Operation IceBridge lidar surveys of ice sheets, glaciers and sea ice. LVIS, the Land, Vegetation, and Ice Sensor, measures laser returns from the surface. GPS locates the aircraft and the IMU tracks its orientation so those returns can become accurately positioned elevation maps. See NASA's LVIS description.

The raw recordings are source material underlying those finished survey products. Reliable survey maps depend on reliable measurements, calibration and processing. This project uses the archived IMU measurements themselves to compare Earth models, rather than using the survey's finished navigation answer as evidence.

The ILVIS0 archive contains survey-grade Applanix IMU recordings with embedded GPS. These instruments were built for precision airborne mapping and are far more capable than phone IMUs. Their published capabilities make slow turning at degrees per hour a credible measurement target. The reference instrument is a POS AV 510; other recorded configurations are decoded and assessed separately.

The analysis preserves original measurements and timestamps, checks packet integrity, and verifies units against the instrument's combined GPS/IMU navigation output. That combined output supplies decoder checks and motion context, rather than independent evidence about Earth's shape. The model fits use IMU increments and receiver positions.

The GPS positions come from the primary receiver's own recorded stream, separately from the combined IMU/GPS navigation solution. Applanix's interface specification identifies this as Group 10001. This avoids testing the instrument's finished navigation answer against itself. GPS latitude, longitude and height still use geodetic coordinate conventions, and the analysis assigns a declared geometry to each candidate. It is an explicit comparison of models with separate measurement streams, rather than a model-free measurement of curvature. The archive guide explains the distinction and the checks planned to isolate the IMU's contribution.

Here, raw means the recorded angle and velocity increments, before the finished navigation solution. It does not mean that the electronics applied no calibration or filtering. Ordinary noise filtering can preserve slow turning. Automatic zeroing or subtracting a presumed background rotation can remove it, so the analysis also tests possible upstream Earth-rate removal. Passing a numerical fit does not identify which onboard processing was used.

flowchart TD
    A[Check IMU and GPS recordings] --> B[Select complete, steady, fast stretches]
    B --> C[Save selection before comparing models]
    C --> D[Fit each whole stretch under all three models]
    D --> E[Report globe, flat or unknown]
    E -->|Resolved globe result| F[Compare background field with zero field]

The current selection requires four continuous minutes with every supported GPS ground-speed reading at least 700 km/h, plus limits on aircraft motion, gaps and instrument changes. Selection is fixed before examining model preferences. Each whole stretch is fitted jointly; shorter sections check consistency without becoming extra flights or receiving separate calibration fits.

The public selection record links to every eligible interval and every file's screening outcome. The complete table of all 53 stretches lists source recordings, dates, durations, speeds, courses, latitudes and current dispositions. See the methodology for the reasoning and the archive guide for instruments, decoding and remaining uncertainties.

A planned rotation-field follow-up will measure the background rotation freely before interpreting its cause. With longer records and sufficient precision, it will also test whether the measured rate distinguishes a sidereal day from a 24-hour solar day: about 15.0411 versus 15.0000 degrees/hour. That small difference needs separate calibration and timing checks; the current short-stretch results do not resolve it.

Current status

• Coverage: all 232 retained recordings have been screened. The first full run analyzed 53 eligible stretches, totaling 424.3 minutes.
• Shape: the preserved first study found 12 complete globe preferences. The completed recovery brings that to 41 globe, zero flat, 12 unresolved. Unfinished comparisons are not evidence for either shape.
• Background rotation: all 41 resolved stretches favor the specified rotation field over zero field. Its physical cause and a solar-versus-sidereal distinction have not been determined.
• Numerical recovery: the completed run finished 159 new fits. The subsequent precision recovery passed 83/86 fits, both controls and all twelve repeats, adding nine complete comparisons. Every reported recovery passed its full comparison and scheduled repeat.
• Current priority: continue the three fits that exhausted their small evaluation allowances, then address the other nine unfinished stretches separately. Earlier results and the completed timing, calibration and prediction checks remain preserved.
• Instrument coverage: completed comparisons now include both recorded IMU8 and IMU21 configurations, decoded separately under the same analysis rules.

The completed findings are substantial, but a validated statistical significance level has not yet been established. Some recordings overlap or share instruments, so the stretches cannot simply be counted as independent confirmations.

See current findings and source tracks, how the method works, method development and robustness checks, and the next steps.

Secondary work: a stationary crowdsourced experiment

Can people recover the same horizontal rotation field with independently owned IMUs at different latitudes? This experiment keeps the IMU on a solid, level surface.

Point a marked horizontal sensor axis approximately toward true north, record without touching it, then turn it 180° with the same face up and record again. An external horizontal rate changes sign; a constant sensor offset stays on the same axis. Repeated A–B–B–A blocks help separate a steadily changing offset.

The Android app guides these still blocks and saves original IMU data, timing, device information and participant-entered location/alignment. It needs no aircraft, flight details or continuous GPS. The initial setting is 30 minutes per block, about four hours for eight blocks; this is a development setting, not a guaranteed minimum. A simple holder with two opposite stops can make reversals repeatable.

The analyzer estimates a signed reversal rate without using latitude or an expected rotation value. A later geographic analysis would compare those estimates with cos(latitude), fitting the amplitude rather than assuming 15 degrees/hour. This tests the measured field before interpreting its cause. It does not establish Earth's shape on its own. Why the horizontal component depends on latitude.

The collection flow and preliminary diagnostic are implemented. Real consumer-device sensitivity, temperature behavior, alignment and uncertainty still need testing; geographic pooling and detection thresholds are not yet implemented. Longer averaging does not remove every systematic error or restore a signal erased by automatic zeroing. NASA results do not certify consumer IMUs.

See the stationary method, simple participant protocol, instrument checks and validation plan. Public upload requires consent; read the privacy policy.

Explore or contribute

Developer setup covers the app, Python analysis and upload server. Contributing explains how to help. Reviews of the physics, statistics, instrument behavior and explanations are welcome.

Code uses AGPL-3.0-or-later. Published participant recordings use CC0; third-party data retain their own terms. See data licensing. Local Level Lab is an Ars Astronomica project.