Right, so we’re moving into the heart of time conversion in navigation — Page 422, Lesson 378

Right, so we’re moving into the heart of time conversion in navigation. This page is the conversion table for arc to time, and I want you to understand what it actually is before we read a single number. The whole idea is this: the Earth rotates 360 degrees in 24 hours. That means every 15 degrees of longitude corresponds to one hour of time. So if you know the longitude difference between two places, you can convert that arc — that angular distance — into a time difference. That’s the entire purpose of this table. It lets you turn degrees and minutes of arc into hours and minutes of time, which is exactly what you’ll need when you’re working out things like sunrise, sunset, or the time at a different meridian. Now, let me show you how to actually read this table, because it’s laid out in a very specific way. Look at the columns. Each column is headed with a label like “hour min” — that tells you the output is in hours and minutes. And at the very top of each column you’ll see a number like 0, 60, 120, 180, 240, or 300. Those are the degrees of arc. So the first column handles 0 to 14 degrees, the second column handles 60 to 74 degrees, the third handles 120 to 134, and so on up to 300 to 314 degrees. Here’s the trick: the left-hand number in each row is the degrees, and the two numbers to its right are the hours and minutes that correspond to that many degrees. So, for example, look at the very first row. The left column shows 0 degrees, and next to it you see 0 hours and 0 minutes. That makes sense — zero arc is zero time. Now go down to the row where the left number is 15. You’ll see 1 hour and 0 minutes. Fifteen degrees of arc equals one hour of time. That’s the fundamental relationship I mentioned. Now, here’s where it gets interesting. Look at the row for 1 degree. The table shows 0 hours and 4 minutes. One degree of arc equals 4 minutes of time. And that’s because 15 degrees is 60 minutes, so one degree is 60 divided by 15, which is 4 minutes. You’ll see that pattern repeat throughout the table. Two degrees gives you 8 minutes, three degrees gives you 12 minutes, and so on. Every single degree adds exactly 4 minutes. But the table doesn’t stop at whole degrees. Look at the row for 1 degree again — you’ll see it’s paired with a smaller number on the far left, and that’s the minutes of arc. So the table handles degrees and minutes of arc together. For example, 1 degree and 1 minute of arc converts to 0 hours and 4 minutes of time — wait, let me check that. Actually, look at the row where the left number is 1 and the next number is 0, then 0 hours and 4 minutes. That’s 1 degree exactly. Then the next row shows 1 degree and 1 minute of arc, and the time is 0 hours and 4 minutes — no wait, it shows 0 hours and 4 minutes for 1 degree, and then for 1 degree 1 minute it shows 0 hours and 4 minutes as well? Let me look more carefully. Actually, I need to be precise here. Look at the structure. The first column of numbers on the left is the degrees, and the second column is the minutes of arc. So when you see “1” and then “0” on the left, that’s 1 degree and 0 minutes. The time shown is 0 hours and 4 minutes. Then when you see “1” and “1”, that’s 1 degree and 1 minute of arc, and the time is still 0 hours and 4 minutes — because 1 minute of arc is only 4 seconds of time, which is too small to show in whole minutes. So the table rounds to the nearest minute. But here’s the key pattern you need to see. Look at the row for 15 degrees — it shows 1 hour and 0 minutes. Then 16 degrees shows 1 hour and 4 minutes. Seventeen degrees shows 1 hour and 8 minutes. Every degree adds 4 minutes, exactly as I said. And you’ll see this same pattern in every column. The column starting at 60 degrees: 60 degrees gives 4 hours and 0 minutes. Sixty-one degrees gives 4 hours and 4 minutes. Sixty-two gives 4 hours and 8 minutes. And so on. Now, why does the table start columns at 0, 60, 120, 180, 240, and 300? Because those are the multiples of 60 degrees, and each 60 degrees of arc equals exactly 4 hours of time. So the table is organized so you can quickly find any angle by locating the nearest multiple of 60, then adding the remainder. For example, if you need to convert 73 degrees, you go to the 60-degree column, find the row for 73, and read 4 hours and 52 minutes. Let me verify that from the table — yes, 73 degrees shows 4 hours and 52 minutes. And that makes sense: 60 degrees is 4 hours, plus 13 degrees at 4 minutes each is 52 minutes. Four hours and 52 minutes. Let me also point out the minutes of arc column more carefully, because that’s where students often get confused. Look at the leftmost pair of numbers in each row. The first number is degrees, the second is minutes of arc. So when you see “1” and “4”, that’s 1 degree and 4 minutes of arc, and the time is 0 hours and 4 minutes — because 4 minutes of arc is 16 seconds of time, which rounds down to 0 minutes. When you see “1” and “8”, that’s 1 degree and 8 minutes of arc, and the time is still 0 hours and 4 minutes. The minutes of arc only start to matter when they accumulate enough to push the time to the next minute. Now, the critical thing for you as a pilot: this table is your quick reference. In the exam, you won’t have time to calculate 4 minutes per degree from scratch every time. You’ll be expected to read this table fluently. So let me walk you through a few more examples to cement the pattern. Look at the row for 30 degrees. The table shows 2 hours and 0 minutes. Thirty degrees is twice 15, so it’s 2 hours. Correct. Now look at 45 degrees — that shows 3 hours and 0 minutes. Forty-five is three times 15, so 3 hours. And 90 degrees — that’s in the 60-degree column, row 90, showing 6 hours and 0 minutes. Ninety degrees is six times 15, so 6 hours. The pattern holds perfectly. Now, one more thing I want you to notice. Look at the very last row of the table that’s visible. It shows 326 degrees — wait, let me check. The last row I can see clearly shows 325 degrees and 21 hours and 40 minutes, and then 326 degrees with 21 hours and 44 minutes. Let me verify: 325 degrees divided by 15 is 21 hours and 40 minutes — yes, because 21 hours times 15 is 315 degrees, leaving 10 degrees, which is 40 minutes. And 326 degrees is 21 hours and 44 minutes — 21 hours for 315 degrees, plus 11 degrees at 4 minutes each is 44 minutes. Perfect. So the table goes all the way up to 360 degrees, which would be 24 hours — a full rotation of the Earth. That’s the complete cycle. Now, here’s the practical application you need to remember. When you’re navigating, you’ll often know the longitude of two points. The difference in longitude, expressed in degrees and minutes of arc, is what you convert to time using this table. That time difference tells you how much later or earlier the sun rises or sets at one point compared to the other. It’s also how you convert between local mean time and Greenwich Mean Time, or UTC. If you’re at 73 degrees west of Greenwich, your local time is 4 hours and 52 minutes behind UTC — that’s what the table just told us. One more critical detail: the table works for both east and west. The conversion is the same magnitude; the sign — whether you add or subtract — depends on whether you’re east or west of the reference meridian. East is ahead in time, west is behind. But the table itself just gives you the magnitude of the difference. So, to summarize what this table is and how to use it: it converts degrees and minutes of arc into hours and minutes of time, based on the Earth’s rotation of 15 degrees per hour. Each degree is 4 minutes. The columns are organized by multiples of 60 degrees for quick lookup. You find your angle, read across to the hours and minutes, and that’s your time difference. That’s the entire tool, and you’ll use it constantly in navigation calculations.