Maximum Unambiguous Range (Rmax)

The primary reason for sending out discrete pulses of E-M energy at given time intervals is that this allows for target ranging. The listening period is the time from when the radar finishes transmitting the first pulse to when it begins transmitting the second pulse. This period allows the first pulse to travel a certain round trip distance. This distance when divided by 2 yields the maximum unambiguous range (Rmax) of a radar. Rmax can be expressed mathematically as

 
Equation 6.  Rmax (Maximum Unambiguous Range).  Click for long description.
 
(Equation 1)

    where c = speed of light (~ 3 x 108 ms-1)
    and greek symbol tau = listening period (s) time difference between transmission of a pulse and receipt of backscattered energy from the same pulse.

Equation (1) can take on two forms (by substitution of definitions of PRF and PRT)
 
Equation 7.  Rmax.  Click for Long Description.
 
(Equation 2)
or
 
Equation 8.  Rmax.  Click for long description.
 
(Equation 3)
    where PRF = pulse repetition frequency (s-1)
    and PRT = pulse repetition time (s) = 1/PRF

The typical "listening time" for the WSR-88D is around 1000 microseconds (but for some VCPs can at maximum be 3067 micro second)s. Substitution into Equations (1 through 3) yields an Rmax = 230 km for the WSR-88D.

Targets which lie beyond Rmax will be incorrectly displayed at ranges too close to the radar. This phenomenon is called range folding.