Let me define the sensible horizon first — Page 545, Lesson 542

I want to walk you through the twilight question first, because it's a classic definition trap. The question asks for the duration of civil twilight, and the correct definition hinges on two very precise terms: the sensible horizon and the visual horizon, plus the exact starting and ending moments. Let me define the sensible horizon first. The sensible horizon is the plane tangent to the Earth's surface at the observer's position — think of it as the geometric horizon you'd get if the Earth were perfectly smooth and there were no atmosphere. The visual horizon, by contrast, is what you actually see, and because of atmospheric refraction, the visual horizon appears slightly below the sensible horizon. That's the key contrast: refraction bends light, so the visible horizon is lower than the geometric one. Now, civil twilight. The correct definition is: from the moment when the centre of the Sun is on the sensible horizon until the centre reaches a depression angle of 6° from the sensible horizon. So the start is when the Sun's centre — not its tip — crosses the sensible horizon, and the end is when that same centre is depressed 6° below that same sensible horizon. The wrong answers try to trick you by swapping in the tip of the Sun, or by using the visual horizon instead of the sensible one. The tip disappears slightly later than the centre, and the visual horizon is lower, so both changes would shift the timing. The precise, correct answer is the one that uses the centre and the sensible horizon throughout. Now, moving on to question 140, which asks you to plot a position from the Connaught VOR/DME. Connaught is at 53°55'N, 008°49'W. You plot a radial of 048° magnetic and a range of 22 NM. The radial is the bearing from the station, and the range is the distance from the DME. So you start at Connaught, draw a line outbound on 048° magnetic, and mark a point 22 NM along it. That gives you the aircraft position. The correct coordinates are 54°07'N, 008°37'W. The other options are close, but they're shifted slightly in latitude or longitude — the key is to be precise with the 22 NM distance and the 048° radial. Question 141 is a great one for great-circle distance. You're given Point A at 35°43'N, 008°41'E and Point B at 54°17'N, 171°19'W. The shortest distance between two points on a sphere is along the great circle. Here, the longitudes are 008°41'E and 171°19'W — those are nearly 180° apart, which means the points are almost antipodal in longitude. The correct great-circle distance is 5400 NM. The other options — 6318, 6557, and 6000 — are all plausible-looking but wrong; they'd come from using a rhumb line or miscomputing the spherical triangle. Question 142 introduces the constant of the cone on a conformal chart. On a conformal (or Lambert conformal) chart, the standard parallels are the latitudes where the cone intersects the Earth's surface — here, 41°20'N and 11°40'N. The constant of the cone is a number that defines how the cone is wrapped around the Earth; it's essentially the sine of the mean latitude of the standard parallels, adjusted for the conformal projection. For these two standard parallels, the constant of the cone is 0.660. The other options — 0.202, 0.446, and 0.895 — are wrong because they don't match the geometry of these specific parallels. Question 143 is a wind-component calculation. You're given a runway direction of 083° magnetic and a surface wind of 045° at 35 knots. The effective headwind component is the component of the wind that acts directly against your direction of travel. The angle between the runway (083°) and the wind (045°) is 38°. The headwind component is the wind speed times the cosine of that angle: 35 × cos(38°), which gives approximately 27 knots. So the correct answer is 27 kt. The other options — 29, 31, and 34 — would come from using the wrong angle or the wrong trigonometric function. Question 144 gives you TAS = 375, Track = 335°(T), and W/V = 340°(T)/50. You need to find the heading and ground speed. The wind is almost directly behind you — 340° versus your track of 335° — so it's a tailwind, and it's blowing at 50 knots. The heading stays very close to the track, at 335°(T), and the ground speed is your TAS plus the tailwind component, which comes to 322 knots. So the correct answer is 335°(T) and 322. The other options either shift the heading slightly or give a ground speed that doesn't match the wind component. Finally, question 145 is a simple statement: lines of latitude on a chart are always... and that's where the excerpt ends. I'll stop there, but I want to make sure you've got the key ideas from this set: the sensible versus visual horizon distinction in twilight, the precise plotting from a VOR/DME, the great-circle distance calculation, the constant of the cone, and the wind-component math. Each of these is a building block for the navigation work ahead.