1. What is the Horizon Distance Equation?

The horizon distance equation calculates how high an observer needs to be to see a certain distance to the horizon, accounting for Earth's curvature. It's derived from geometric principles of a spherical Earth.

2. How Does the Calculator Work?

The calculator uses the horizon equation:

Where:

• \( h \) — Observer height above surface (meters)
• \( d \) — Distance to horizon (converted to meters)
• \( R \) — Earth's radius (default 6,371,000 meters)

Explanation: The equation approximates the height needed to see a given distance to the horizon, assuming a perfect sphere without atmospheric refraction.

3. Importance of Horizon Calculation

Details: This calculation is important for navigation, aviation, radio communications, and understanding visibility limitations in various fields.

4. Using the Calculator

Tips: Enter distance to horizon in kilometers and Earth's radius in meters. Default values are provided for standard calculations.

5. Frequently Asked Questions (FAQ)

Q1: Why is Earth's radius needed?
A: The calculation depends on Earth's curvature, which is determined by its radius. The standard value is 6,371 km.

Q2: How accurate is this calculation?
A: It's a geometric approximation. Real-world visibility is affected by atmospheric refraction, observer eyesight, and terrain.

Q3: What's the typical horizon distance?
A: For an observer at 1.7m height, horizon is about 4.7km away. At 10km visibility, height needed is ~7.85m.

Q4: Does this account for atmospheric refraction?
A: No, this is a pure geometric calculation. Refraction typically increases visible distance by about 8%.

Q5: Can this be used for other planets?
A: Yes, by changing the radius value to that of another celestial body.