Imagine an observer at a point Q on the Earth’s surface — Page 426, Lesson 388

Let’s start with the idea of twilight itself. Before sunrise and after sunset, there’s a period when it’s still light, even though the Sun is below the horizon. That period is called twilight. The reason it stays light is that the Sun’s rays are refracted — bent — by the atmosphere, so light reaches us even when the Sun itself is out of sight. That refraction is the whole reason twilight exists. To understand this properly, we need to be precise about what we mean by the horizon. Imagine an observer at a point Q on the Earth’s surface. His Sensible Horizon is the tangent to the Earth’s surface, ignoring terrain features. In other words, it’s the flat plane that touches the Earth at his position — the horizon that a spirit level would sense. That’s why it’s called “sensible” — it’s what an instrument would detect. Now, because of atmospheric refraction, the visual horizon — what your eye actually sees — sits below the sensible horizon by about 34 minutes of arc. That’s a small angle, but it matters. At sunset, when the top lip of the Sun passes below the visual horizon, the centre of the Sun is still another 16 minutes of arc below that — that’s the Sun’s apparent radius as seen from Earth. So the centre of the Sun ends up approximately 50 minutes of arc below the sensible horizon at sunset. Here’s the key conversion: 50 minutes of arc equates to 3 minutes of time. So at sunset, the centre of the Sun is already 3 minutes of time below the sensible horizon. The same argument applies at sunrise — the centre of the Sun is 3 minutes of time below the sensible horizon when it first appears. That’s why the length of day at the Equator is approximately 6 minutes longer than the length of night — 3 minutes gained at sunrise and 3 minutes gained at sunset. So twilight is that period before sunrise and after sunset when refracted light from the atmosphere gives us illumination. The amount of illumination isn’t constant — it varies with the Sun’s depression below the sensible horizon, and with atmospheric conditions. Now we come to the first specific type: Civil Twilight. Civil twilight occurs when the Sun’s centre is between 0° 50’ and 6° below the sensible horizon. During this period, illumination is such that you can carry out daytime tasks without additional artificial lighting — for example, a daytime visual approach is possible. And importantly, this is the only twilight period considered in the Air Almanac. Let me make sure the numbers are clear. The lower bound, 0° 50’, is that 50 minutes of arc we just talked about — the Sun’s centre at sunset. The upper bound is 6° of depression. So civil twilight spans from the moment the Sun’s centre is 50 minutes of arc below the sensible horizon, down to when it’s 6° below. That’s the window where you have enough natural light for normal daytime operations. One thing to note: the excerpt introduces civil twilight but stops mid-sentence — there are other twilight categories that follow, but for now, hold onto this: twilight is caused by refraction, the sensible horizon is the instrument-sensed tangent plane, the visual horizon sits 34 minutes of arc below it, and civil twilight is the 0° 50’ to 6° depression band that the Air Almanac uses.