We're starting a new topic now: converting arc, or angle, into time — Page 393, Lesson 347

We're starting a new topic now: converting arc, or angle, into time. This is the foundation for every time problem you'll solve in navigation, so let's build it properly from the ground up. The core idea is simple but powerful: because the Earth rotates 360 degrees in 24 hours, we can turn any angular measurement into a time measurement. Let me give you the exact conversion factors you must know cold: - 360° = 24 hours - 15° = 1 hour - 1° = 4 minutes - 15 minutes of arc = 1 minute of time - 15 seconds of arc = 1 second of time Notice the pattern: 15 of anything in arc equals 1 of the same unit in time. That's because 360 divided by 24 is 15. So 15 degrees of arc is one hour, 15 minutes of arc is one minute of time, and 15 seconds of arc is one second of time. Now, an important practical note: you're only required to work to the nearest minute of time. So when you do these conversions, you round your final answer to the nearest minute—you don't need seconds in your final answer. There's a tool for this: the arc-to-time table on the last page of the Air Almanac extract, reproduced at the end of this chapter. It converts angular arcs from 0° to 360° into hours and minutes of time in its first five columns. The final column converts minutes of angular arc into minutes and seconds of time. Let me walk you through an example using that table. Say we want to convert 137°36' of arc to time. First, take the whole degrees: 137° converts to 9 hours 08 minutes. Then take the minutes of arc: 36' converts to 2 minutes 24 seconds. Add them together: 9 hours 08 minutes plus 2 minutes 24 seconds gives 9 hours 10 minutes and 24 seconds. But since we round to the nearest minute, the answer is 9 hours 10 minutes. Now, you might not have that table available. In that case, you calculate the conversion by hand. In most cases, the arc of longitude will be in whole degrees, so let's start there. Example 1: Convert 127° of arc into time. Divide 127 by 15, which gives 8.4667 hours. That's the answer in hours and decimal hours, but the question may want hours and minutes. So convert the decimal part—0.4667 hours—to minutes by multiplying by 60. 0.4667 times 60 equals 28 minutes. So the answer is 8 hours 28 minutes. Example 2 is trickier because we have minutes of arc included: convert 096°17' of arc into time. First, express the arc in decimal form by dividing the minutes by 60. So 17 divided by 60 equals 0.283. Now the arc is 096.283 degrees. Divide that by 15 to get decimal time: 096.283 divided by 15 equals 6.4189 hours. Then convert the decimal hours back to minutes: 0.4189 times 60 equals 25 minutes, to the nearest minute. So the answer is 6 hours 25 minutes. Let me make sure you see the method clearly. When you have minutes of arc, you first convert them to a decimal of a degree by dividing by 60. Then you divide the total degrees by 15 to get hours. Then you take the decimal part of those hours and multiply by 60 to get minutes. Round to the nearest minute, and you're done. That's the whole conversion process. You'll use this constantly when you work with longitude and time, so make sure these steps feel natural.