Maximum Range of Radar Calculator

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Radar & Antenna Specifications

Radar Antennas Reception

Special Purpose Radars

✖Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals.ⓘ Transmitted Power [P_trns]			+10% -10%
✖Transmitted Gain is a parameter used to describe the ability of an antenna to concentrate and direct electromagnetic energy in a specific direction when it is used to transmit signals.ⓘ Transmitted Gain [G_trns]			+10% -10%
✖Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar.ⓘ Cross Section Area of Radar [σ]			+10% -10%
✖Effective Area of Receiving Antenna is a fundamental parameter that characterizes the ability of the antenna to capture electromagnetic radiation and convert it into an electrical signal.ⓘ Effective Area of Receiving Antenna [A_eff]			+10% -10%
✖Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor.ⓘ Minimum Detectable Signal [S_min]			+10% -10%

✖Target Range is defined as the distance from the radar site to the target measured along the line of sight.ⓘ Maximum Range of Radar [R_t]

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Formula

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Maximum Range of Radar

Formula

`"R"_{"t"} = (("P"_{"trns"}*"G"_{"trns"}*"σ"*"A"_{"eff"})/(16*pi^2*"S"_{"min"}))^0.25 `

Example

`"289.6204m"=(("100kW"*"657"*"25m²"*"17.5875m²")/(16*pi^2*"0.026W"))^0.25 `

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Download Radar & Antenna Specifications Formulas PDF

Maximum Range of Radar Solution

STEP 0: Pre-Calculation Summary

Formula Used

Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25
R_t = ((P_trns*G_trns*σ*A_eff)/(16*pi^2*S_min))^0.25
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Target Range - (Measured in Meter) - Target Range is defined as the distance from the radar site to the target measured along the line of sight.
Transmitted Power - (Measured in Watt) - Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals.
Transmitted Gain - Transmitted Gain is a parameter used to describe the ability of an antenna to concentrate and direct electromagnetic energy in a specific direction when it is used to transmit signals.
Cross Section Area of Radar - (Measured in Square Meter) - Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar.
Effective Area of Receiving Antenna - (Measured in Square Meter) - Effective Area of Receiving Antenna is a fundamental parameter that characterizes the ability of the antenna to capture electromagnetic radiation and convert it into an electrical signal.
Minimum Detectable Signal - (Measured in Watt) - Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor.

STEP 1: Convert Input(s) to Base Unit

Transmitted Power: 100 Kilowatt --> 100000 Watt (Check conversion here)
Transmitted Gain: 657 --> No Conversion Required
Cross Section Area of Radar: 25 Square Meter --> 25 Square Meter No Conversion Required
Effective Area of Receiving Antenna: 17.5875 Square Meter --> 17.5875 Square Meter No Conversion Required
Minimum Detectable Signal: 0.026 Watt --> 0.026 Watt No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_t = ((P_trns*G_trns*σ*A_eff)/(16*pi^2*S_min))^0.25 --> ((100000*657*25*17.5875)/(16*pi^2*0.026))^0.25

Evaluating ... ...

R_t = 289.620369423853

STEP 3: Convert Result to Output's Unit

289.620369423853 Meter --> No Conversion Required

FINAL ANSWER

289.620369423853 ≈ 289.6204 Meter <-- Target Range

(Calculation completed in 00.010 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 24 Radar & Antenna Specifications Calculators

Maximum Range of Radar

Go Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25

Minimum Detectable Signal

Go Minimum Detectable Signal = (Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Target Range^4)

N Scans

Go N Scans = (log10(1-Cumulative Probability of Detection))/(log10(1-Detection Probability of Radar))

Transmitted Gain

Go Transmitted Gain = (4*pi*Effective Area of Receiving Antenna)/Wavelength^2

Transmitted Frequency

Go Transmitted Frequency = Doppler Frequency*[c]/(2*Radial Velocity)

Power Density Radiated by Lossless Antenna

Go Lossless Isotropic Power Density = Maximum Radiated Power Density/Maximum Gain of Antenna

Maximum Power Density Radiated by Antenna

Go Maximum Radiated Power Density = Lossless Isotropic Power Density*Maximum Gain of Antenna

Maximum Gain of Antenna

Go Maximum Gain of Antenna = Maximum Radiated Power Density/Lossless Isotropic Power Density

Target Height

Go Target Height = (Range Resolution*Range)/(2*Antenna Height)

Radar Antenna Height

Go Antenna Height = (Range Resolution*Range)/(2*Target Height)

Probability of Detection

Go Detection Probability of Radar = 1-(1-Cumulative Probability of Detection)^(1/N Scans)

Cumulative Probability of Detection

Go Cumulative Probability of Detection = 1-(1-Detection Probability of Radar)^N Scans

Antenna Aperture Efficiency

Go Antenna Aperture Efficiency = Effective Area of Receiving Antenna/Antenna Area

Antenna Area

Go Antenna Area = Effective Area of Receiving Antenna/Antenna Aperture Efficiency

Effective Area of Receiving Antenna

Go Effective Area of Receiving Antenna = Antenna Area*Antenna Aperture Efficiency

Pulse Repetition Frequency

Go Pulse Repetition Frequency = [c]/(2*Maximum Unambiguous Range)

Maximum Unambiguous Range

Go Maximum Unambiguous Range = ([c]*Pulse Repetition Time)/2

Pulse Repetition Time

Go Pulse Repetition Time = (2*Maximum Unambiguous Range)/[c]

Target Velocity

Go Target Velocity = (Doppler Frequency Shift*Wavelength)/2

Doppler Frequency

Go Doppler Frequency = Doppler Angular Frequency/(2*pi)

Doppler Angular Frequency

Go Doppler Angular Frequency = 2*pi*Doppler Frequency

Radial Velocity

Go Radial Velocity = (Doppler Frequency*Wavelength)/2

Measured Runtime

Go Measured Runtime = 2*Target Range/[c]

Range of Target

Go Target Range = ([c]*Measured Runtime)/2

Maximum Range of Radar Formula

What is Minimum Detectable Signal?

A minimum detectable signal is a signal at the input of a system whose power allows it to be detected over the background electronic noise of the detector system

How to Calculate Maximum Range of Radar?

Maximum Range of Radar calculator uses Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25 to calculate the Target Range, The Maximum Range of Radar formula is defined by several parameters, including the size of the radar antenna and the frequency of the signal used. Target Range is denoted by R_t symbol.

How to calculate Maximum Range of Radar using this online calculator? To use this online calculator for Maximum Range of Radar, enter Transmitted Power (P_trns), Transmitted Gain (G_trns), Cross Section Area of Radar (σ), Effective Area of Receiving Antenna (A_eff) & Minimum Detectable Signal (S_min) and hit the calculate button. Here is how the Maximum Range of Radar calculation can be explained with given input values -> 289.6204 = ((100000*657*25*17.5875)/(16*pi^2*0.026))^0.25 .

FAQ

What is Maximum Range of Radar?

The Maximum Range of Radar formula is defined by several parameters, including the size of the radar antenna and the frequency of the signal used and is represented as R_t = ((P_trns*G_trns*σ*A_eff)/(16*pi^2*S_min))^0.25 or Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25. Transmitted Power is the amount of power the radar system is radiating into the environment to transmit radar signals, Transmitted Gain is a parameter used to describe the ability of an antenna to concentrate and direct electromagnetic energy in a specific direction when it is used to transmit signals, Cross Section Area of Radar also called radar signature, is a measure of how detectable an object is by radar, Effective Area of Receiving Antenna is a fundamental parameter that characterizes the ability of the antenna to capture electromagnetic radiation and convert it into an electrical signal & Minimum Detectable Signal represents the minimum power level of a signal that a radar can detect reliably above the noise floor.

How to calculate Maximum Range of Radar?

The Maximum Range of Radar formula is defined by several parameters, including the size of the radar antenna and the frequency of the signal used is calculated using Target Range = ((Transmitted Power*Transmitted Gain*Cross Section Area of Radar*Effective Area of Receiving Antenna)/(16*pi^2*Minimum Detectable Signal))^0.25. To calculate Maximum Range of Radar, you need Transmitted Power (P_trns), Transmitted Gain (G_trns), Cross Section Area of Radar (σ), Effective Area of Receiving Antenna (A_eff) & Minimum Detectable Signal (S_min). With our tool, you need to enter the respective value for Transmitted Power, Transmitted Gain, Cross Section Area of Radar, Effective Area of Receiving Antenna & Minimum Detectable Signal and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Target Range?

In this formula, Target Range uses Transmitted Power, Transmitted Gain, Cross Section Area of Radar, Effective Area of Receiving Antenna & Minimum Detectable Signal. We can use 1 other way(s) to calculate the same, which is/are as follows -

Target Range = ([c]*Measured Runtime)/2

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