Radar Principles — Page 192, Lesson 176

Let's start with the core idea of radar distance measurement — the echo principle. I want you to picture a radar transmitter sending out a very short burst of energy, a pulse. That pulse travels out to an object, bounces off it, and comes back to the radar as an echo. The radar doesn't measure distance directly; it measures time. The distance to the object is found by timing the interval between the instant of the pulse's transmission and its return as an echo. That's the whole foundation — we time the round trip. Now, because the pulse has to go out and come back, it travels twice the distance to the object. That's the crucial "× 2" you'll see in every formula. The speed of the pulse is the speed of light, which we take as c = 300 000 000 m/s, or equivalently 162 000 NM/s. Let me give you a worked example so you see how the numbers fit. Suppose the echo time — the time between transmission and reception — is 500 microseconds. Remember, a microsecond is one millionth of a second, so 500 µs is 500 divided by 1 000 000 seconds. The distance in metres is: distance = 300 000 000 × 500 / (1 000 000 × 2). Let's read that carefully. We multiply the speed of light by the time in seconds, then divide by 2 because the pulse went out and back. That gives 75 000 metres, which is 75 km. If we work in nautical miles instead, using the speed 162 000 NM/s, we get distance = 162 000 × 500 / (1 000 000 × 2) = 40.5 NM. So the same 500 µs echo gives us 75 km or 40.5 NM — same physical distance, two unit systems. Now, there's a neat shorthand. Notice that 300 000 000 divided by 1 000 000 is 300. So the range in km can be written as range = 500 × 300 / 2 = 75 km. And if you want nautical miles, you can convert by dividing by 1852, because there are 1852 metres in a nautical mile: range = 500 × 300 / (2 × 1852) = 40.5 NM. There's also a very handy constant called the radar mile. A radar mile is defined as one nautical mile out and back — that is, the time for the pulse to travel one NM to the target and one NM back. That time is 12.36 µs. So if you know the echo time in microseconds, you can just divide by 12.36 to get the range in NM. Check it: 500 / 12.36 = 40.5 NM. Same answer, much faster. So remember that constant: one radar mile = 12.36 µs. Now let's move to the theoretical maximum range and its relationship to the pulse repetition frequency, the PRF. The PRF is the number of pulses transmitted in one second, measured in pulses per second, or pps. Here's the key constraint: each pulse must be allowed to travel to the most distant object planned before the next pulse is transmitted. Why? Because if you send the next pulse too soon, you can't tell whether an echo belongs to the first pulse or the second one. You'd have ambiguity — you couldn't relate a particular echo to a particular pulse. So the maximum range is directly tied to the PRF: the greater the range required, the lower the PRF used. Longer range means you need more time between pulses, so fewer pulses per second. Let me walk you through the worked examples so you see the logic. Example 1: we want a radar to measure a range of up to 187 km. What should the PRF be? First, the pulse must travel 374 km — that's 2 × 187, out and back — before the next pulse is transmitted. The time for that journey is T = D/S, distance divided by speed. So T = 374 000 / 300 000 000 seconds. That works out to 0.0012466 seconds, which is 1246 µs. That time is the pulse repetition interval, the PRI — the time between pulses. So the PRI is 1246 µs, and the PRF is the reciprocal of that. The maximum PRF is therefore 1 divided by 0.0012466, which is about 802 pps. So for a 187 km range, you can't transmit faster than roughly 802 pulses per second. The other examples follow the same pattern. Example 2: maximum PRR for a radar required to measure up to 200 NM. The pulse must travel 400 NM out and back. Using the speed 162 000 NM/s, the time is 400 / 162 000 seconds, which is about 2469 µs. So the maximum PRR is 1 / 0.002469, about 405 pps. Example 3: maximum range 170 km, so the pulse travels 340 km. Time = 340 000 / 300 000 000 = 0.001133 s, about 1133 µs. Maximum PRR is about 882 pps. Example 4: an AWR — that's an Airborne Weather Radar — has a PRR of 400 pps. We calculate the maximum range. The PRI is 1 / 400 = 0.0025 seconds, which is 2500 µs. Divide by the radar mile constant, 12.36 µs per NM, and you get about 202 NM. So a 400 pps radar can see out to roughly 202 NM before ambiguity sets in. Let me show you the figures that illustrate this. shows the distance measurement by timing the interval between transmission and echo return. And shows the pulse technique itself — the short burst of energy. So the takeaway: distance is measured by timing the echo, the pulse travels out and back so we always divide by 2, the radar mile is 12.36 µs per NM, and the maximum range is set by the PRF — the lower the PRF, the longer the range you can measure without ambiguity.