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 fundamental skill for all time problems in navigation, so let's build it properly from the ground up. The core idea is beautifully simple. The Earth rotates 360 degrees in 24 hours. That single fact gives us our conversion factors. Let me lay them out for you, because you'll use these constantly. 360 degrees equals 24 hours. From that, we get 15 degrees equals 1 hour. Then, 1 degree equals 4 minutes. Going smaller, 15 minutes of arc equals 1 minute of time. And 15 seconds of arc equals 1 second of time. So the ratio is always 15 to 1. Fifteen of any angular unit equals one of the corresponding time unit. Now, a practical note before we dive into examples. In the exam, you're only required to work to the nearest minute of time. You don't need seconds. That's your accuracy target. There's a tool for this. The Air Almanac has an arc-to-time conversion table, reproduced at the end of this chapter. It converts angular arcs from 0 to 360 degrees into hours and minutes of time. The first five columns handle the degrees, and the final column converts minutes of arc into minutes and seconds of time. Let me show you how it works with an example. Convert 137 degrees 36 minutes of arc to time. Using the table, 137 degrees of arc converts to 9 hours 08 minutes. Then, 36 minutes of arc converts to 2 minutes 24 seconds. Adding those together gives 9 hours 10 minutes and 24 seconds. Rounding to the nearest minute, the answer is 9 hours 10 minutes. Now, you might not have that table available. In that case, you calculate it. And in most cases, the arc of longitude will be in whole degrees, which makes it easier. Let me walk you through the calculation method with two examples. Example 1: Convert 127 degrees of arc into time. Divide 127 by 15. That gives you 8.4667 hours. The answer is now in hours and decimal hours, but the question might want hours and minutes. So convert the decimal part, .4667, to minutes by multiplying by 60. .4667 times 60 equals 28. So the answer is 8 hours 28 minutes. Example 2: Convert 096 degrees 17 minutes of arc into time. This one has minutes, so first express the arc in decimal form by dividing the minutes by 60. 17 divided by 60 equals .283. So the arc is 096.283 degrees. Now 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. .4189 times 60 equals 25 minutes, to the nearest minute. So the answer is 6 hours 25 minutes. So you see the pattern. Divide degrees by 15 to get hours, multiply the decimal remainder by 60 to get minutes. And if you have minutes of arc, convert them to decimal degrees first by dividing by 60. That's the complete arc-to-time conversion process. You've got the table method and the calculation method, and you know your target is the nearest minute.