Calculator inputs
Formula used
Combined range: dtotal = √(2kRhr + hr²) + √(2kRht + ht²)
Required height: h = √((kR)² + d²) − kR
Curvature drop: y = kR[1 − cos(s ÷ kR)]
The calculator models Earth as a selected reference sphere. Atmospheric refraction changes the effective Earth radius. Larger k-values usually extend the theoretical radar horizon considerably.
Radar and target horizon legs are calculated separately. Their tangent distances are added for combined visibility. This method assumes a clear path between both endpoints.
How to use this calculator
Choose a preset or enter both endpoint heights. Select units, Earth radius, and atmospheric refraction. Then calculate to review every range and clearance result.
Use desired range for reverse height calculations. Enter frequency for a midpoint Fresnel-zone estimate. Add instrument range to identify the operational limiting factor.
Selected distance controls curvature and angle analysis. Clearance allowance creates a conservative endpoint-height reduction. Always compare outputs with terrain and system specifications carefully.
Example data
| Scenario | Radar height | Target height | Refraction factor | Typical purpose |
|---|---|---|---|---|
| Coastal station | 35 m | 12 m | 1.3333 | Ship approach monitoring |
| Airport radar | 25 m | 1,000 m | 1.3333 | Aircraft surveillance |
| Aircraft radar | 10,000 m | 10 m | 1.3333 | Surface target horizon |
| Drone detection | 20 m | 120 m | 1.0000 | Conservative line-of-sight |
| Marine navigation | 15 m | 5 m | 1.3333 | Nearby vessel awareness |
Radar horizon versus optical horizon
The optical horizon uses geometric Earth curvature directly. Radar waves often bend slightly within the atmosphere. Effective-radius modeling approximates that bending with a k-factor conveniently.
Standard conditions commonly use four-thirds effective Earth radius. Real atmospheric gradients can produce different propagation behavior. Ducting may extend signals far beyond simple horizon estimates.
Limitations and assumptions
Actual detection also depends on transmitter power and gain. Receiver sensitivity and target radar cross-section remain important. Weather, clutter, terrain, and processing can change results substantially.
The Fresnel result is a simplified midpoint estimate. Radar paths may cross complex atmospheric layers or obstructions. Use surveyed profiles for safety-critical engineering and operational decisions.
Frequently asked questions
What is the radar horizon?
It is the farthest curvature-limited line-of-sight distance. Antenna and target heights both affect this boundary. Atmospheric refraction can extend the apparent horizon beyond geometry.
Why use a four-thirds Earth radius?
Standard refraction bends many radio paths slightly downward. The four-thirds model approximates this effect conveniently. It remains an estimate rather than a fixed condition.
Does frequency change the horizon distance?
Basic geometric horizon distance does not require frequency. Frequency influences propagation, diffraction, and Fresnel-zone dimensions. Those effects can significantly change practical radar detection performance.
What does the instrument range limit mean?
It represents the radar system's configured measurable range. The calculator compares it with geometric visibility. The smaller value becomes the practical limiting estimate here.
Can this calculator include terrain?
It does not model detailed terrain profiles directly. Clearance allowance reduces endpoint heights conservatively. Surveyed elevation data provides a more reliable obstruction analysis.
What is curvature drop?
Curvature drop measures surface departure below a tangent. It increases rapidly as surface distance becomes larger. Refraction-adjusted drop uses the chosen effective Earth radius model.
What is slant distance?
Slant distance is the direct endpoint-to-endpoint straight line. It differs slightly from the surface arc distance. Both values meet closely under tangent horizon conditions here.
How are required heights calculated?
The known endpoint supplies its available horizon leg. The remaining desired distance becomes the unknown leg. The horizon equation is then solved for height directly.
What does sub-refraction mean?
Sub-refraction bends the radar path less than standard. The effective Earth radius becomes comparatively smaller. This generally shortens the expected radio horizon distance accordingly.
What does super-refraction mean?
Super-refraction bends signals more strongly toward the surface. It creates a larger effective Earth radius. The theoretical radar horizon may therefore become longer overall.
Can this predict guaranteed target detection?
No geometric calculator can guarantee target detection alone. Radar power, clutter, target size, and processing matter. Use system performance models for dependable operational planning decisions.