Example preset
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Inputs
Common settings (earth radius/refraction coefficient)
“Tangential drop” is the difference between the starting point tangent and the ground surface (so-called “8 inches/mile²”). "Sagitta" is the maximum center difference for the string.
Results
| Target horizon distance (ground distance) | — |
|---|---|
| Effective earth radius R_eff | — |
| Observer's straight line distance (tangential length) | — |
| Straight line distance of object (tangential length) | — |
| Determination of comparative distance | — |
| Visible margin distance (based on comparison distance) | — |
| required target height at that distance | — |
| Hidden height (approximate) |
| Approximate d²/(2R) | — |
|---|---|
| central angle θ | — |
| distance covered by opponent | — |
|---|---|
| Effective earth radius R_eff | — |
Schematic diagram
A schematic diagram will be displayed as you input.
Assumptions & limits
- The calculation is an approximation of a spherical (effective Earth radius) model. Terrain, obstacles, and uneven sea surfaces are not handled.
- The refractive coefficient k varies with the environment. Default is k=0 (no refraction).
- At high altitude conditions (approximately over 20 km), the reliability of the refraction approximation with k constant decreases.
- Horizontal distance is mainly displayed as ground distance (arc length), and straight line distance is a reference value.
- At long distances, model simplification (no consideration of terrain or weather) has a greater influence than approximation.
How to use this calculator effectively
This guide helps you use Horizon distance & earth curvature calculator (with refraction k) in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.
How it works
The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.
When to use
Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.
Common mistakes to avoid
- Changing multiple parameters at once, which hides the true cause of output movement.
- Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
- Comparing with another tool without aligning defaults, constants, and rounding rules.
- Using rounded display values as exact downstream inputs without re-checking precision.
Interpretation and worked example
Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.
See also
FAQ
Is there a difference between ground distance (arc length) and straight line distance?
The difference is usually small but not zero. This calculator mainly shows ground distance (arc length).
What is the refractive coefficient k?
k approximates atmospheric refraction by adjusting Earth's effective radius. Weather can change refraction, so treat k as a guide.
What does “8 inches/mile²” correspond to?
It corresponds to tangent drop from the start point. The sagitta at the same distance is about one quarter of that value.
What does "hidden height (approximate)" indicate?
At comparison distance dc, it is the extra target height needed for visibility at observer height h1 compared with the input height h2. Terrain and weather are not included.
Are mountains, buildings, and weather conditions considered?
Not considered. If necessary, combine it with visual analysis using terrain data.
How to use Horizon distance & earth curvature calculator (with refraction k) effectively
What this calculator does
This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.
Input meaning and unit policy
Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.
Use-case sequence
A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.
Common mistakes to avoid
Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.
Interpretation guidance
Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.
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- Solar altitude, direction, sunrise/sunset, day length (ES-002)
- Tidal/diurnal cycle: sunrise/sunset + moon phase + tide (data linkage) (ES-021)
- Noise: dB addition/distance attenuation (simple) (ES-009)
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