Radar Horizon Calculator

Radar Height (\( h_r \)):

Target Height (\( h_t \)):

Radar Horizon (\( d_r \)):

Target Horizon (\( d_t \)):

Total Distance (\( D \)):

1. What is Radar Horizon Calculator?

Definition: This calculator computes the radar horizon distances for both the radar (\( d_r \)) and the target (\( d_t \)), as well as the total distance (\( D \)), based on the heights of the radar and the target, accounting for atmospheric refraction.

Purpose: It is used in radar systems to determine the maximum distance at which a radar can detect a target, considering the curvature of the Earth and atmospheric effects.

2. How Does the Calculator Work?

The calculator uses the modified radar horizon formulas:

Radar Horizon Formula: \[ d_r = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot h_r} \] Target Horizon Formula: \[ d_t = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot h_t} \] Total Distance Formula: \[ D = d_r + d_t \] Where:

\( d_r \): Radar horizon distance (cm, m, km, in, ft, yd, mi)
\( d_t \): Target horizon distance (cm, m, km, in, ft, yd, mi)
\( D \): Total distance (cm, m, km, in, ft, yd, mi)
\( h_r \): Height of the radar (cm, m, km, in, ft, yd, mi)
\( h_t \): Height of the target (cm, m, km, in, ft, yd, mi)
\( 6,371.009 \): Earth's radius (km)
\( \frac{4}{3} \): Atmospheric refraction correction factor

Unit Conversions:

Height (\( h_r \), \( h_t \)): cm (1 cm = \( 10^{-5} \) km), m (1 m = \( 10^{-3} \) km), km, in (1 in = 2.54e-5 km), ft (1 ft = 0.0003048 km), yd (1 yd = 0.0009144 km), mi (1 mi = 1.60934 km)
Distance (\( d_r \), \( d_t \), \( D \)): cm (1 cm = \( 10^{-5} \) km), m (1 m = \( 10^{-3} \) km), km, in (1 in = 2.54e-5 km), ft (1 ft = 0.0003048 km), yd (1 yd = 0.0009144 km), mi (1 mi = 1.60934 km)

Steps:

Enter the radar height (\( h_r \)) and target height (\( h_t \)), and select their units.
Convert heights to km.
Calculate the radar horizon: \( d_r = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot h_r} \).
Calculate the target horizon: \( d_t = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot h_t} \).
Calculate the total distance: \( D = d_r + d_t \).
Convert each result to its selected distance unit (cm, m, km, in, ft, yd, mi).
Display the results, using scientific notation for values less than 0.001, otherwise with 4 decimal places.

3. Importance of Radar Horizon Calculation

Calculating the radar horizon is crucial for:

Military Applications: Determining the detection range of enemy aircraft or ships in radar systems.
Aviation: Ensuring safe navigation and surveillance by understanding radar coverage.
Weather Monitoring: Estimating the range of weather radar systems for tracking storms.

4. Using the Calculator

Examples:

Example 1: For \( h_r = 9,150 \, \text{m} \), \( h_t = 122 \, \text{m} \), distances in km:
- Convert: \( h_r = 9,150 \times 10^{-3} = 9.15 \, \text{km} \), \( h_t = 122 \times 10^{-3} = 0.122 \, \text{km} \)
- Radar Horizon: \( d_r = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot 9.15} \approx 394.3 \, \text{km} \)
- Target Horizon: \( d_t = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot 0.122} \approx 45.53 \, \text{km} \)
- Total Distance: \( D = 394.3 + 45.53 = 439.8 \, \text{km} \)
Example 2: For \( h_r = 30,000 \, \text{ft} \), \( h_t = 400 \, \text{ft} \), distances in mi:
- Convert: \( h_r = 30,000 \times 0.0003048 = 9.144 \, \text{km} \), \( h_t = 400 \times 0.0003048 = 0.12192 \, \text{km} \)
- Radar Horizon: \( d_r = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot 9.144} \approx 394.0 \, \text{km} \), in mi: \( 394.0 \times 0.621371 \approx 244.8 \, \text{mi} \)
- Target Horizon: \( d_t = \sqrt{2 \cdot \frac{4}{3} \cdot 6,371.009 \cdot 0.12192} \approx 45.5 \, \text{km} \), in mi: \( 45.5 \times 0.621371 \approx 28.3 \, \text{mi} \)
- Total Distance: \( D = 394.0 + 45.5 = 439.5 \, \text{km} \), in mi: \( 439.5 \times 0.621371 \approx 273.1 \, \text{mi} \)

5. Frequently Asked Questions (FAQ)

Q: What is the radar horizon?
A: The radar horizon is the maximum distance at which a radar can detect a target, limited by the curvature of the Earth and the heights of the radar and target.

Q: Why is the refraction factor \( \frac{4}{3} \) used?
A: The \( \frac{4}{3} \) factor accounts for atmospheric refraction, which bends radar waves slightly downward, effectively increasing the radar horizon compared to a straight-line calculation.

Q: Can the radar detect a target beyond the total distance \( D \)?
A: Generally, no, unless other factors like radar wave reflection, terrain, or advanced technology (e.g., over-the-horizon radar) are involved.