Earth Curve Calculator With Refraction

Earth Curve With Refraction Formula:

\[ Drop = \frac{d^2}{2 \times R_{eff}} \] \[ R_{eff} = \frac{R}{1 - k} \]

Drop:

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1. What is Earth Curve Calculation With Refraction?

Earth curve calculation with refraction accounts for atmospheric refraction when calculating the drop (hidden height) due to Earth's curvature over a given distance. Refraction bends light, making objects appear higher than they actually are, reducing the apparent drop.

2. How Does the Calculator Work?

The calculator uses the Earth curve with refraction formula:

\[ Drop = \frac{d^2}{2 \times R_{eff}} \] \[ R_{eff} = \frac{R}{1 - k} \]

Where:

\( d \) — Distance in miles
\( R \) — Earth radius (3959 miles)
\( k \) — Refraction coefficient (typically 0.143)
\( R_{eff} \) — Effective Earth radius accounting for refraction

Explanation: The refraction coefficient effectively increases the Earth's radius, reducing the calculated drop compared to the standard Earth curve formula.

3. Importance of Refraction in Earth Curve Calculations

Details: Atmospheric refraction is crucial for accurate calculations in surveying, navigation, and observational astronomy. It explains why distant objects remain visible when pure geometry suggests they should be hidden by Earth's curvature.

4. Using the Calculator

Tips: Enter distance in miles, Earth radius (default 3959 miles), and refraction coefficient (default 0.143). All values must be positive, with k between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: Why include refraction in Earth curve calculations?
A: Refraction bends light around Earth's curvature, making objects appear higher and reducing the actual drop. Ignoring refraction leads to overestimation of hidden height.

Q2: What is the typical value for refraction coefficient?
A: The standard value is approximately 0.143, though it can vary with atmospheric conditions, temperature, and pressure.

Q3: How does refraction affect long-distance observations?
A: Refraction allows objects to be visible at greater distances than pure geometry would allow, particularly over water or flat terrain.

Q4: When is refraction most significant?
A: Refraction effects are most noticeable at dawn and dusk, over large bodies of water, and in temperature inversion conditions.

Q5: Can refraction values change?
A: Yes, refraction coefficient can vary from 0.11 to 0.25 depending on atmospheric conditions, though 0.143 is the standard average value.