Download your PDF
Earth Curvature Geometry Comparator result sheet — free, supported by sponsors. Your download button appears in 20 seconds.
This free download is supported by sponsors — continuing in
20
Your file is generated in your browser when you choose Download — nothing is uploaded. If this calculator returns enough numeric data, the export also includes its best-fit chart alongside the readable table.
WorldCalculate result export
Earth Curvature Geometry Comparator — result sheet
Compare the exact spherical-surface drop below a local tangent plane with the small-distance approximation and a flat-plane zero-drop reference.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Exact spherical drop = R − √(R² − x²); small-distance drop ≈ x²/(2R); central angle = asin(x/R); surface arc = R·asin(x/R). The flat-plane reference has zero curvature drop.
The page frames the flat-versus-round comparison as geometry: a local tangent plane and a spherical cross-section receive the same horizontal-distance input. It reports the exact circular-section drop, a common short-distance approximation, the surface arc, and the flat reference without adding terrain, refraction, or visual claims.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Local tangent-plane distance — km; minimum 0; maximum 20000
- Sphere radius — km; minimum 100; maximum 100000
Worked example
| Input | Value |
|---|---|
| Local tangent-plane distance | 10 |
| Sphere radius | 6371 |
For a 10 km tangent distance and a 6,371 km radius, the exact spherical drop is about 7.848 m; the short-distance approximation is about 7.848 m as well.
Assumptions and limits
- The spherical model uses a constant radius and a two-dimensional cross-section.
- Distance is measured along the local tangent-plane direction from the starting point.
- The exact expression requires distance smaller than the sphere radius.
- The flat reference is a mathematical plane with zero curvature drop by definition.
- Terrain, elevation, refraction, optics, and ellipsoid corrections are outside the model.
- The calculator is a geometry worksheet and does not settle an observational question by itself.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
No saved result was found. Please run the calculation first, then choose Download again.