Let me start with the core calculation — Page 269, Lesson 248

I want to walk you through a practical technique for using airborne weather radar to estimate the height of storm cloud tops above your aircraft. This is a critical skill when you're trying to decide whether you can safely climb over a thunderstorm, and it relies on a simple geometric rule called the 1:60 rule. Let me start with the core calculation. The idea is that you take the recorded range to the edge of a cloud return — that's the distance in nautical miles from your aircraft to the leading edge of the storm echo on the radar screen. You then apply a correction based on your radar antenna's tilt angle and beam width to find the height of the cloud top above you, expressed in nautical miles. Here's the step-by-step logic. Your radar has a notional beam width — that's the angular width of the radar beam, typically a few degrees. In the example we're given, the notional beam width is 4°. When you tilt the antenna upward to make a cloud return just disappear — meaning the top of the beam is grazing the top of the cloud — you note that tilt angle. In the example, that tilt angle is +3.5° (positive meaning the antenna is tilted up). Now, to find the angle from the centre of the beam to the top edge of the beam, you take half the notional beam width. Half of 4° is 2°. So you subtract that 2° from your tilt angle: 3.5° minus 2° equals 1.5°. That 1.5° is the angle between the horizontal (level flight) and the top edge of the radar beam that just touches the cloud top. Now we apply the 1:60 rule. This rule states that at a distance of 60 nautical miles, an angle of 1° subtends a height of 1 nautical mile. More generally, the height in nautical miles equals the angle in degrees multiplied by the range in nautical miles divided by 60. So here: 1.5° times 40 nautical miles divided by 60 gives you 1 nautical mile. That's the height of the cloud top above your aircraft. Since 1 nautical mile is approximately 6000 feet, the cloud tops are 6000 feet above your current altitude of 20,000 feet. That puts the cloud top at about 26,000 feet. But the recommended minimum clearance when overflying a thunderstorm is 5000 feet. So to achieve that clearance, you'd need to climb to at least 31,000 feet — that's 26,000 plus 5,000. The excerpt gives a very important caution here: if you decide to climb, remember that in the time it takes your aircraft to climb and close the distance to the storm, the top of a very active storm cloud might itself have ascended to a higher altitude. So your estimate is only a snapshot. Now, what if your aircraft is not equipped with radar, or the radar is inoperative? In that case, the rule is simple: avoid by at least 10 miles any storm that, by visual inspection, is tall, growing rapidly, or has an anvil top — that flat, spreading top that signals a mature thunderstorm. Next, a procedural point: you should intermittently monitor long ranges on radar to avoid getting into situations where you have no alternative but to penetrate potentially hazardous areas. Unless the radar manufacturer instructs otherwise, you usually need to adjust both gain and tilt during this monitoring. The gain control affects the sensitivity of the receiver — how strongly it displays returns — and the tilt control adjusts the vertical angle of the antenna. You adjust these to ensure that new weather targets are not missed and that active clouds are continually tracked. There's also a specific warning about flying under a cumulonimbus overhang. That overhang is the part of the cloud that extends out ahead of the main updraft, often hiding severe weather. If you cannot avoid flying under it, you should tilt the antenna full up occasionally to try to determine whether precipitation — which may be hail — exists in or is falling from the overhang. Finally, a crucial note on accuracy: notwithstanding all the principles and guidance from radar manufacturers or instructors, always bear in mind that the result is only an estimate of the height of the storm cloud tops. The accuracy is limited by the geometry, the beam width, and the dynamic nature of the storm itself. Let me show you the diagrams that illustrate this radiation fog concept — though note that the diagrams in the book are for radiation fog, not radar, but they help visualise the inversion layer that often caps these clouds.