- frozen lake or very flat water crossing with ~6–10 km clear line of sight
- auto level, theodolite, or survey-grade leveling setup
- printed targets with a visible center gap (Bedford 1.85 m row + Tangent row)
- GPS or differential GNSS for waypoint logging (phone GPS is approximate only)
- camera or scope for photo documentation
- notebook or this page's field log for observations
Experiment
Rainy Lake Curvature Field Test
Over a long frozen-lake sightline, do Bedford and Tangent target rows match globe hidden-height predictions better than a flat-plane expectation?
Materials Needed
Setup Steps
- Mark an observer position and three or more targets along a straight ice path, the Bislin Rainy Lake layout uses Bedford targets at 1.85 m and Tangent targets scaled for a 3.91 m observer.
- Record waypoint coordinates and GNSS or tape-measured distances; note weather, refraction, and whether the crosshair sits in each target gap.
- Log observer height (Bedford 1.85 m or Tangent 3.91 m preset) and whether each target appears full, partial, or hidden.
- Compare each sightline with the Curvature Calculator using the same distance, heights, and refraction mode.
- Treat this lite protocol as educational, not a substitute for professional survey, and repeat on a clearer day if heat shimmer or inversion layers dominate.
Expected Calculation
dobs=√
dbeyond=max(d − dobs, 0)
hidden=dbeyond22Reff
sagitta=Reff (1 − cos(d2Reff))
clearance=max(targetHeight − hidden, 0)
On a sphere, the Bedford row should curve below a 1.85 m observer while the Tangent row should stay near eye level for a 3.91 m observer when refraction is accounted for. A flat plane predicts the opposite pattern for the two rows.
Graphic
What to Observe
- Bedford targets drop below eye level with distance while Tangent targets stay much closer to the leveled line for the higher observer.
- Hidden amounts grow with distance in a way that matches spherical geometry when refraction is included.
- Raising the observer or switching from Bedford to Tangent mode restores more of the distant structure.
Interpretation
When predictions from the same curvature math are logged beside field observations, the Rainy Lake pattern matches a convex Earth much better than a flat-plane plus ad hoc refraction story. Credit for the original 2018 field test: George Hnatiuk (design and construction), Jesse Kozlowski (GNSS surveying), Soundly (imaging), and Walter Bislin (analysis and published data).
Sources
- Walter Bislin: Rainy Lake Experiment: Primary reference and public-domain write-up. Original team: George Hnatiuk, Jesse Kozlowski, Soundly, and Walter Bislin (2018).
- Walter Bislin: Rainy Lake WGS84 Calculator: Shows how survey-grade ECEF/GNSS vectors differ from a lite educational waypoint sheet.
- USGS FAQ: Curvature drop over distance: Independent geometric hidden-height reference used by the on-site Curvature Calculator.
- NWS JetStream: Atmospheric Refraction: Why long water/ice sightlines need a refraction note alongside geometric curvature.
Evidence Card
Claim
Over a ~10 km frozen-lake baseline, a Bedford target row at 1.85 m should curve below a 1.85 m observer while a Tangent row should stay near eye level for a 3.91 m observer, the classic predict-vs-observe split between flat and globe models.
Model Used
Bislin-inspired Rainy Lake lite protocol: GNSS-referenced waypoint distances on Rainy Lake MN, Bedford/Tangent observer and target heights, and the same hidden-height pipeline as the Curvature Calculator with optional standard or custom refraction.
Formula
dobs=√
dbeyond=max(d − dobs, 0)
hidden=dbeyond22Reff
sagitta=Reff (1 − cos(d2Reff))
clearance=max(targetHeight − hidden, 0)
Last Verified
2026-06-30
Assumptions
- Waypoint coordinates are an educational preset aligned to published Bislin GNSS distances, not a differential-GNSS survey deliverable.
- Field log observations are user-entered paraphrases; photos are not hosted on this page.
- Refraction is logged as a note because Bislin measured k ≈ 0.17 during the original experiment.
What Would Falsify This Page
If logged Bedford/Tangent observations over the preset distances matched flat-eye-level predictions for both rows while sphere+refraction predictions failed across all three targets, the globe framing on this page would be weakened.