Radar Principles — Page 192, Lesson 178

Let's pick this up right where the radar picture starts to get practical — the range of a primary radar. I want to walk you through what actually limits how far a primary radar can "see" a target, because that's the heart of this section. First, the core idea: the range of a primary radar depends on the strength of the returning pulses. That returning signal strength is what determines the quality of the target depiction on the PPI — the Plan Position Indicator, which is the circular display you see on a radar screen. So the stronger the echo that comes back, the better and more clearly the target shows up on that display. Now, several factors affect that range, and I want to take them one by one. The first is transmission power. A radar signal attenuates — that means it weakens — with increasing distance from the transmitter. And here's the crucial part: because the signal has to travel out to the target and then all the way back, the power/range relationship is not a simple one. The power available is proportional to the fourth power of range. Let me make sure you feel what that means. If you want to double the range of a radar, you don't double the power — you have to increase the power by a factor of 16. That's 2 to the fourth power. So doubling the range requires sixteen times the transmitted power. That's why radar range is so expensive in terms of power. The second factor is the characteristics of the reflecting objects. Metals are more efficient than wood at reflecting the transmitted signal — that's a straightforward contrast. But also, the size and shape of the detected object make a considerable difference to the effective range. A big, flat metal surface gives you a much stronger echo than a small or irregular one. And then there's the aspect of the object — the angle at which you're looking at it. This is really important for aviation. A manoeuvring aircraft presents various aspects, and those different aspects can affect the polarization of the reflected waves. In plain terms, the way the aircraft is turned relative to the radar changes how the wave bounces back. The side of the fuselage has a better aspect than the nose of the aircraft. So a broadside view of an aircraft gives a much stronger return than seeing it head-on. The third factor is aircraft height and the height of the radar head. This is a big one, so listen carefully. Radar transmissions, because of their frequency bands, travel in straight lines. They give line-of-sight ranges, plus a little extra due to atmospheric refraction — the bending of the wave as it passes through the atmosphere. But because they travel essentially in straight lines, the curvature of the earth causes much of the surface to be in shadow. Think of it this way: the earth curves away from the radar beam, so anything below that line of sight is hidden. Therefore, higher flying aircraft are more likely to be detected because they are above that shadow. And intervening high ground will also screen low flying aircraft from detection — a hill or mountain between the radar and the aircraft blocks the signal just like the earth's curvature does. That's why the height of the radar head matters so much. The higher the radar head can be positioned, the greater that radar's range, and the less effect intervening high ground will have on stopping signals and reducing its range. Put the antenna on a tall hill or a tower, and you push that line of sight out further. Now, there's a formula for this, and I want you to know it precisely. The maximum theoretical radar range in nautical miles is given by: Max. Theoretical range (NM) = 1.23 × (√HTX + √HRX) Let me define those symbols for you. HTX is the height of the radar station in feet AMSL — that's Above Mean Sea Level. And HRX is the height of the target in feet AMSL. So you take the square root of the radar station's height, add it to the square root of the target's height, and multiply the whole thing by 1.23. That gives you the maximum theoretical range in nautical miles. Notice it's called "theoretical" — it's the ideal line-of-sight limit, before you start losing range to the other factors we talked about, like power and target characteristics. The fourth and final factor is wavelength and attenuation by raindrops. Attenuation means the weakening of the signal as it passes through something. Raindrops absorb and scatter the radar energy, and how much they attenuate the signal depends on the wavelength of the transmission. I want you to picture the relationship: on a logarithmic scale of wavelength in centimetres, from about 0.03 up to 10, the attenuation by raindrops is not constant — it changes dramatically with wavelength. Shorter wavelengths are attenuated much more heavily by rain. So a radar operating at a very short wavelength will lose a lot of its signal in heavy rain, which cuts into its effective range. That's a real operational consideration — weather can literally eat your radar signal. So let me pull it all together. The range of a primary radar is set by the strength of the returning pulses, and that strength is governed by four things: the transmission power, with that punishing fourth-power relationship; the characteristics of the reflecting object, including its material, size, shape, and aspect; the heights of both the radar head and the target, which set the line-of-sight limit through that 1.23 formula; and the wavelength, which determines how badly raindrops attenuate the signal. Each one of these is a lever on how far you can see, and in real operations you're always balancing them.