Range

Calculating Range to Target

An operating field weather radar is “listening” most of the time. The few microseconds spent broadcasting each pulse is an extremely short period compared to the time following each transmission during which the radar system waits to receive returning energy.

The transmission of pulses of electromagnetic energy allows a radar system to determine the range to a target which can then be displayed on the PPI and RHI displays. The range to a target is given by the equation below where the divisor ‘2’ accounts for the round trip which the pulse must make before detection by the radar system. The equation is basically the fundamental equation of distance, Distance = Speed * Time. Although the pulse has traveled a distance c*t in time t, it has made a round trip from radar to target and back again. Therefore, to obtain the range, we need to divide by 2:

R = (c*t) / 2

R – Distance from radar to target (m) - Range
c – Speed of light (3*108 m/s)
t – Elapsed time since transmission of pulse (seconds)

In practice with modern digital processing systems, the received signal is sampled at regular intervals and assigned to the appropriate “range gate”. These “range gates” might be spaced at 250 m, 500 m or 1 km intervals depending on the operating requirements of the system.

The number of range gates available to a radar system will depend on the design of the signal processing system. The number of “range gates” together with the required operating range of the radar will determine the range gate spacing. For example, if the radar has 225 range gates available and it is necessary that the radar be able to scan a range of 225 km then the “range gate” spacing must be 1 km. This places obvious practical limits on the accuracy of the calculated range to a target. There is little benefit in the range gate spacing being less than the pulse length.

Maximum Unambiguous Range

Maximum distance that a radar pulse can travel out to and back again between consecutive pulses

Ru = (c * PRT) / 2 = c / (2 * PRF)

  • Ru – Unambiguous Range (m)
  • c – Speed of light (3*108 m/s)
  • PRF – Pulse Repetition Frequency (sec-1)

Suppose the radar emits a pulse that strikes a target and returns to the radar in time T:

  • If T < PRT then the return signal arrives before the next pulse has been emitted
  • If T = PRT then the return signal arrives exactly when the next pulse has been emitted
  • If T > PRT then the return signal arrives after the next pulse has been emitted and there is an ambiguity, ie the radar cannot tell whether the return signal has come from the first or second pulse.
  • Therefore Maximum Unambiguous Range Ru is the range for which T = PRT

The greater the PRF, the shorter the PRT and the shorter the Unambiguous Range of the radar


Note: Maximum Unambiguous Range for weather radars is generally greater than the Maximum Display Range (512km)

Unambiguous Range > Maximum Display Range because:

  1. Radar pulses tend to overshoot (pass over) precipitation targets at long ranges
  2. Errors in measured precipitation intensity increases at long range