Right, let's pick this up with the practical side of arc/time conversion — Page 393, Lesson 349

Right, let's pick this up with the practical side of arc/time conversion. We've been dealing with the theory, but now we're going to get our hands dirty with the actual calculation. The book recommends we use the dms function on a scientific calculator for these problems. dms stands for degrees, minutes, seconds. It's the button that lets you input an angle in degrees and minutes and then convert it. Let me walk you through the example: Convert 137°36’ of arc to time. The key relationship we're using is that 15° of arc equals 1 hour of time. So to convert arc to time, we divide by 15. On the Casio calculators that Oxford recommends, the dms button is marked with the symbols ° ’ ”. So you press 1, 3, 7, then the dms button. The display will show 137°. Then you press 3, 6, and the dms button again. Now the display shows 137° 36’. Then you press divide, 1, 5, and equals. The calculator will show 9°10°24, which reads as 9 hours, 10 minutes, and 24 seconds. That's your answer. The exact button sequence depends on your calculator model, but the principle is the same. And you can always check your answer against the arc/time table in the Air Almanac. Now, let's move on to Local Mean Time, or LMT. This is a fundamental concept. The Earth rotates daily around its geographic axis, anticlockwise if you're observing from above the North Pole. But it's often convenient to think of it the other way: consider the Earth as stationary and the Sun travelling around the Earth once a day in a clockwise direction. This fits our perception that the Sun rises in the East and sets in the West. So for our discussions, we'll use this alternative, and unless otherwise stated, the Sun we refer to is the 'mean' Sun. Here's the core definition: when the mean Sun transits, or crosses, a particular meridian, the Local Mean Time at all places on that meridian is 1200 hours, which is midday or noon. So the moment the mean Sun is directly over your meridian, it's 12:00 LMT for everyone on that line of longitude. Similarly, when the mean Sun transits the anti-meridian of a point—that's the meridian exactly 180° away—the LMT at that point is 0000 hours, or 2400 hours, which is midnight. There's a convention here: midnight of a particular night, say the night of the 6th/7th, is regarded as 2400 hours LMT on the 6th, or 0000 hours on the 7th. Both are correct; it just depends on which date you're referencing. Let me give you a concrete example to make this stick. Figure 25.1 illustrates the situation when the mean Sun is transiting the meridian of 45°E on the 16th of May. The date is just for illustration. So the LMT at all places on the 45°E meridian—that includes Baghdad, Aden, and Madagascar—is 1200 LMT on the 16th of May. Now, remember this key fact: it takes the Sun 1 hour to travel 15° of longitude. That's the same 15° relationship we used for the conversion. So let's work east from 45°E. At 90°E, which is approximately India, the LMT is 1500 hours on the 16th of May. Why? Because the Sun passed the meridian 3 hours ago. The difference is 45° of longitude, and 45 divided by 15 equals 3 hours. So it's 1200 plus 3 hours, which is 1500. At 135°E, approximately Japan, the LMT is 1800 hours on the 16th of May. That's 6 hours ahead of 45°E, because 90° of longitude divided by 15 equals 6 hours. At 180°E, which is the mid-Pacific in the Eastern hemisphere, the LMT is 2100 hours on the 16th of May. That's 9 hours ahead, because 135° divided by 15 equals 9. Now let's work to the west from the 045°E meridian. At 0°E/W, which is the Greenwich Meridian, the LMT is 0900 LMT on the 16th of May. That's 3 hours behind, because we're moving west and the Sun hasn't reached us yet. And here's an important term: LMT at the Greenwich Meridian is known as Greenwich Mean Time, or GMT, also called Zulu, denoted by the letter 'Z'. GMT used to be the Earth's standard time. The present standard time is called Coordinated Universal Time, or UTC, which for all practical purposes is the same as GMT. So when you hear UTC or Zulu time in aviation, it's essentially the time at Greenwich. Continuing west: at 45°W, which is Newfoundland, the LMT is 0600 LMT on the 16th of May. At 90°W, which is mid USA, the LMT is 0300 LMT on the 16th of May. At 135°W, which is Alaska, the LMT is 0000 LMT on the 16th of May. And this time can also be considered 2400 hours LMT on the 15th of May. That's the midnight convention we talked about earlier. So the pattern is clear: as you move east, time increases; as you move west, time decreases. And the rate is always 15° of longitude per hour. That's the foundation for all time calculations in navigation.