geo-distance Verified Precision Tool
Earth Curvature Drop Calculator
Calculate vertical drop and hidden obstacle height over distance due to Earth curvature.
📍 Select World Location Presets or Custom Coordinates
WGS-84 EllipsoidPoint 1 Coordinates (Origin)
Observer & Target Parameters
Calculated Geodetic Solution
Horizon: 4.654 km | Drop: 7.85 m
Geometric Horizon Distance4.654 km
Curvature Drop over Target7.85 meters
Hidden Height Beyond Horizon2.24 meters
🗺️ Interactive Geographic Map & Geodesic Trajectory
Click anywhere on the map or drag pins to update coordinates live.
Map Data: © OpenStreetMap ContributorsWGS-84 Precision Geodesic Curve
Step-by-Step Mathematical Derivation
1. Given Input Coordinates:
- Eye Level Height: 1.7 m
- Target Distance: 10 km
2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km
3. Governing Geodesic Formula:
d_horizon = sqrt(2R*h + h²), Drop = R * (1 - cos(d/R))4. Variable Substitution:
R = 6,371,000m, h = 1.7m5. Interpretation & Practical Application:
For an observer at 1.7m height, the horizon is 4.654 km away. At 10 km, curvature causes a 7.85m drop.
Mathematical Formula
Drop = R * (1 - cos(d/R)) approx 8 inches per mile squared
Overview & Explanation
Calculates how many meters an object drops below the geometric horizon at a specified distance.
How It Works
- Applies circular arc drop formula over Earth radius.
Practical Applications
- Telecommunications tower height planning.
- Long-range vision checks.
Worked Example: 20 km distance
Calculate curvature drop.
1
Compute Drop
20km target distance
= Drop: 31.39 meters | Hidden: 18.2 meters
Frequently Asked Questions
What is the rule of thumb for Earth curvature drop?
The approximate rule of thumb is 8 inches per mile squared (0.667 feet * miles²).
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