RADAR Detection Range
Equation:

 R4    =     ((Pav x G2  x λ2 x δ x Td x Pg) / ((4 x pi)3x K x Teff x S/N x L))0.25

(Nach W.M. Hall)
Explanation:

Pav   = transmitter average RF power (Watt)
G     = antenna gain (figure not dB)
  λ    = wavelength (m)
 δ     = Radar Cross Section (sq. m)
Td    = time dwell (sec.)
          LOPAR:  14, 22, 44 milliseconds   
          HIPAR: 19, 28 milliseconds
Pg   = processing gain
K    = 1.38-23
Teff  = effective noise temperature
           LOPAR 1600°
           HIPAR 1100° 
           TTR  2000°)
S/N   = Signal to Noise ratio
L       = Loss
Td      = n x PRT                   
n       = number of hits (target echos)
n       = ( BW° x PRF ) / (6 x RPM)
BW°   = radar Beamwidth (degree)
PRF    =  Pulse Repetition Frequency
RPM    =  Revolutions Per Minute
PRT    = Pulse Repetition Time
Example for n:      beamwidth (BW°) LOPAR = 1.4°, PRF = 500 PPS, RPM = 5, 10 and  15

 (1.4 x 500) / (6 x 5)   =  23  (n) Hits at 5 RPM
  (1.4 x 500) / (6 x 10) =  11  (n) Hits at 10 RPM
  (1.4 x 500) / (6 x 15) =    7  (n) Hits at 15 RPM
Example for n:     beamwidth (BW°) HIPAR = 1.2° , PRF 420 PPS, RPM = 6.7 and 10

(1.2 x 420) / (6 x 6.7) = 12  (n) Hits at 6.7  RPM
(1.2 x 420) / (6 x 10) =    8  (n) Hits at 10   RPM
Example for PRT:  1 / PRF

 PRF LOPAR  = 500   Pulses Per Second (PPS)
  PRF HIPAR  = 420   (PPS)
then

 LOPAR  PRT = 2000  microseconds (usec)
 HIPAR  PRT = 2380  usec
Td  = n x PRT
 
LOPAR = 5 RPM   23  x 2000 usec = 46 milliseconds (msec)
            10 RPM   11 x  2000 usec = 22 msec
            15 RPM     7 x  2000 usec = 14 msec

HIPAR =     6.7  RPM  12 x 2380 usec  =  28 msec
                  10  RPM    8 x 2380 usec  =  19 msec
 Example: R4  =  ((Pav x G2 x  λ2 x δ x Td x Pg) / ((4 x pi)3 x K x Teff x S/N x L))0.25

 Variables : LOPAR
Pav 500 Watt
G2 32 dB (2 511 886)
 λ2 0.094 m (0.008836)
δ RCS 10 sq. m
Td 0.022  seconds
Pg 0 dB (1)
pi 1984.4
K 1.38 x 10-23
Teff 1600
S/N 3 dB (2)
L 20 dB (100)
Use the Microsoft Calculator (or any other) and don`t forget to type in the brackets!
 Klick the x^y key then type the exponent 0.25.
 R =  ((500 x 2 511 886 x 0.008836 x 10 x 0.022 x 1)

        /   (1984.4 x 1.38-23 x 1600 x 2 x 100))0.25


 R =  (2441452.71656   /   8.76311104-15)0.25
Under the above conditions  the target could be detected at  129 195.5 m  =  129.2 km or  80.3 mi
 1 km    = 0.62 miles

It`s a lot easier with a HP 48! The problem is you have to program the maschine. ;-)