This tool is designed to calculate the maximum distance (range) that a radar can detect

Inputs

(linear)
 
 

Output

Meter (m)

Overview

The radar's maximum range is determined by several parameters, including the size of the radar antenna and the frequency of the signal used. This tool helps you determine the maximum range of a radar system given the required parameters. To use this tool, simply place the required values in the fields and press the "calculate" button. 

Equation

 

$$Range = \sqrt[4]{\frac{P_{r} \sigma c^{2} G_{r}^{2}}{(4\pi)^{3} f_{O}^{2} P_{min}}}$$

Where:

$$P_{r}$$ = power output of the radar (W)

$$\sigma$$ = radar cross section (m2)

$$c$$ = speed of light = 299, 792, 458 m / s

$$G_{r}$$ = radar antenna gain 

$$f_{0}$$ = radar signal frequency

$$P_{min}$$ = minimum detectable power (W)

Applications

The maximum radar range is one of the most important concerns for engineers, when constructing radar systems. There are three known factors that can limit the maximum range of a radar system. First is line of sight which depends on the radar antenna's height above ground. If the antenna cannot directly "see" the object to be detected, the radio path is blocked and must be cleared. Second is a parameter called "maximum non-ambiguous range". This is the distance the pulse is reflected and received before the next pulse is transmitted. Finally, radar sensitivity brought on by environmental conditions (rain, snow, etc) and radar cross section also limit the maximum range of the system. 

Further Reading

Textbook - Principles of Radio

Technical Article - Estimating Wireless Range

Worksheet - Fundamentals of Radio Communication

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