Computing Radar Horizon

Computing Radar Horizon

Precomputed Radar Horizons

Ticonderoga CG AN/SPY-1 (50 ft above SL)

17~ nm vs target at 50 ft
95~ nm vs target at 5,000 ft
200~ nm vs target at 25,000 ft
283~ nm vs target at 50,000 ft
397~ nm vs target at 100,000 ft
713~ nm vs target at 328,000 ft (100 km)
1,800~ nm (3,336 km) vs target at 648 km (Thor ICBM Apogee)

AWACS (20,000 ft above SL)

179~ nm vs target at 50 ft
260~ nm vs target at 5,000 ft
368~ nm vs target at 25,000 ft
449~ nm vs target at 50,000 ft
563~ nm vs target at 100,000 ft
878~ nm vs target at 328,000 ft (100 km)
2,401~ nm vs target at 1,000 km (Apogee level for ICBMs)

Simplified Radar Horizon for Earth (English Units)

Radar_Horizon = 1.23 * sqrt (Height_Antenna)

Radar_Horizon = Distance to the Radar Horizon in Nautical Miles.
Height_Antenna := Height of Radar Antenna in Feet.

NOTE: This equation is inaccurate compared to the full radar horizon equation, but it yields results accurate enough for “back of the envelope” work.

EXAMPLE: You have a B-70 flying at 75,000 feet; what is the maximum radar horizon of a search radar on it?

1.23 (sqrt[75,000])

1.23 (273.86) = 336.86 nm

Simplified Radar Horizon For Earth (Metric Units)

Radar_Horizon = 4.124 * sqrt (Height_Antenna)

Radar_Horizon: Distance to the Radar Horizon in kilometers.
Height_Antenna: Height of Radar Antenna in meters.

NOTE: This equation is inaccurate compared to the full radar horizon equation, but it yields results accurate enough for “back of the envelope” work.

Complex Radar Horizon (Metric Units)

Radar_Horizon = sqrt (4/3) * sqrt (2 * Radius_Planet * Height_Antenna)

Radar_Horizon: Distance to the Radar Horizon in kilometers.
Height_Antenna: Height of Radar Antenna in meters.
Radius_Planet = Radius of the planet in kilometers. (Earth is 6,378 km)

Simplified Radar Horizon Against a Target at a Specific Height for Earth (English Units)

Radar_Horizon = 1.23 * ( sqrt [Height_Antenna] + sqrt [Height_Target])

Radar_Horizon = Distance to the Radar Horizon in Nautical Miles.
Antenna_Height = Height of Radar Antenna in Feet.
Height_Target = Height of Target in feet.

NOTE: This equation is inaccurate compared to the full radar horizon equation, but it yields results accurate enough for “back of the envelope” work.

EXAMPLE: You have a EC-121 flying at 25,000 feet; what is the maximum radar horizon of a radar on the EC-121 against a target at 5,000 feet?

1.23 * (sqrt[25,000] + sqrt[5,000]) = = 281.45 nm

Simplified Radar Horizon Against a Target at a Specific Height for Earth (Metric Units)

Radar_Horizon = 4.124 * ( sqrt [Height_Antenna] + sqrt [Height_Target])

Radar_Horizon = Distance to the Radar Horizon in kilometers
Antenna_Height = Height of Radar Antenna in meters.
Height_Target = Height of Target in meters.

NOTE: This equation is inaccurate compared to the full radar horizon equation, but it yields results accurate enough for “back of the envelope” work.