Radar Principles — Page 192, Lesson 178

Let’s start with the range of primary radar. I want you to think of the radar as a transmitter that sends out a pulse, and then listens for the echo that comes back off a target. The maximum range of that radar is set by the strength of the returning pulses, because that strength decides how well the target shows up on the PPI — the Plan Position Indicator, which is the circular display you see on a radar screen. Now, several factors affect that range, and I want to walk you through each one carefully. First, transmission power. A radar signal gets weaker as it travels away from the transmitter — we say it attenuates with distance. But here’s the key point: the signal has to go out to the target and then come all the way back. So the power/range relationship is not a simple one. The power available is proportional to the fourth power of range. Let me make that concrete: to double the range, the power has to increase by a factor of 16. That’s because the signal is spreading out on the way out, and then spreading out again on the way back — so the loss compounds. That’s why doubling range is so expensive in power. Second, the characteristics of the reflecting object. Metals reflect the transmitted signal far more efficiently than wood does. The size and shape of the object make a considerable difference to the effective range — a big flat metal surface gives you a strong echo, a small or irregular one gives you a weak echo. And the aspect of the object matters too. Aspect means the angle at which the object presents itself to the radar. A manoeuvring aircraft presents various aspects, and those different aspects can affect the polarization of the reflected waves. Polarization is the orientation of the electric field of the wave — and if the reflecting surface rotates that orientation, the echo can be weakened. The practical rule here: the side of the fuselage gives a better aspect than the nose of the aircraft. So a broadside aircraft is much easier to detect than one pointing straight at you. Third, the height of the aircraft and the height of the radar head. Radar transmissions, because of their frequency bands, travel in straight lines. That means they give line-of-sight ranges — plus a little extra due to atmospheric refraction, which bends the path slightly around the earth. But the curvature of the earth itself puts much of the surface into shadow. So a higher-flying aircraft is more likely to be detected, because it rises above that shadow. Intervening high ground also screens low-flying aircraft from detection. And the higher you can position the radar head, the greater the radar’s range, and the less effect intervening high ground has on stopping the signal and reducing range. There’s a formula for the maximum theoretical radar range, and I want you to note it exactly. Maximum theoretical range in nautical miles equals 1.23 multiplied by the sum of the square root of HTX plus the square root of HRX. So: Max. Theoretical range (NM) = 1.23 × (√HTX + √HRX). Here HTX is the height of the radar station in feet above mean sea level — AMSL — and HRX is the height of the target in feet AMSL. So you take the square root of each height, add them, and multiply by 1.23 to get the range in nautical miles. Notice both heights are measured from mean sea level, not from the ground. Finally, wavelength and attenuation by raindrops. Rain absorbs and scatters radar energy, and the amount of attenuation depends on the wavelength of the signal. There’s a graph for this — Figure 11.6 — which plots attenuation against wavelength on a logarithmic scale, with wavelength in centimetres from 0.03 up to 10. The key idea is that shorter wavelengths are attenuated far more heavily by raindrops than longer ones. So a radar operating at a very short wavelength will lose a lot of its range in rain, while a longer wavelength will punch through the weather much better. So, to summarise the whole picture: the maximum range of a primary radar is governed by transmission power — with that fourth-power relationship — by the reflecting characteristics of the target, by the heights of both the radar and the target through that 1.23 formula, and by wavelength-dependent attenuation from raindrops. Each of these factors feeds into the strength of the returning pulse, and that strength is what determines the quality of the target depiction on the PPI.