Celestial Navigation – Local Hour Angle

Boy today’s study has got me dusting off the cobwebs of my brain. I don’t like maths, and with the added complication of degrees, minutes and seconds… arraggh!

So Local Hour Angle – LHA… “What is that!?” I hear you cry. Well let’s find out together…

You will recall from one of my previous posts that we can work out the ground position of the sun at any particular time by using the Sun Almanac. The position we are given in the tables is the GHA (Greenwich Hour Angle) and Declination. If you can’t remember what that was all about then you might want to pop back for a quick read by clicking here.

The Local Hour Angle – or LHA is the angle between our assumed boat meridian position and the meridian of the sun. (Remember meridians are the lines of longitude) So in other words the difference between our longitude and the sun’s GHA.

We need to know this angle to work out our position.

The Local Hour Angle is a measurement of how far the sun is to the West of the boat’s assumed position. So we have to relate the sun’s position relative to our own DR position. Click here if you want to refresh your knowledge on Dead Reckoning positions.

Remember that the sun rises in the east and sets in the West. So any afternoon sights of the sun will be to the west of us, but any morning sights will have the sun in the east. But LHA measures the angle of the sun to the West of us – i.e. just about all the way around the world. See example 2 below.

Boat with a Western Longitude

So in the picture below. Imagine we are hovering above the north pole looking down on the earth. Our DR longitude is 120ºW. The sun’s GHA is 140º (which we got from the Almanac based on the UTC time we took our sight)

  • So if the Sun’s GHA is 140º and we are at 120ºW then the LHA is 20º
  • GHA – Longitude West = LHA or 140º – 120ºW = 20º

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So if we take all our sights in the afternoon, then the sun is going to be West of us. But what if we take the sight in the morning?

Check out example #2 in the picture above. Remember LHA is the measurement of how far the sun is to the West of us, so in this example our DR Longitude is 120ºW and the sun’s GHA is 100º. If we subtract the GHA from the Longitude then we get a negative number, so we simply add 360º.

  • GHA 100º + 360º = 460º
  • 460º – DR Longitude 120ºW = LHA 340º

Boat with an Eastern Longitude

GHA follows the sun all the way around the world and is counted towards the West. However when you are in the Eastern Longitudes things get just a little bit more confusing.

So if you are in the East, you add the GHA and Longitude East (instead of subtracting as in the Western examples above) If the result is greater than 360º then you simply subtract 360.

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Example # 3 – So if your boat’s DR Longitude is 80ºE and the sun’s GHA is 10º then you add them both together to get the LHA of 90º

Example # 4 – If your DR Longitude is still 80ºE and the sun’s GHA is 340º then we add those two together to get 420º and then subtract 360º to get our LHA of 60º

So on our sight reduction form, we will need to put the GHA and declination that we obtained from the tables, and then our assumed longitude in box 9.a below, and then work out the LHA as per these examples.

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When we are using the Sight Reduction Tables, we need a round figure for our LHA, because only round numbers are offered in the tables.

So if we are in a Western Longitude then we should adjust our Assumed Position to have the same number of minutes and seconds as the GHA figure.Because then when we do the subtraction then we end up with a round figure for the LHA.

If we have an Eastern Longitude remember we are adding the GHA and the Assumed Longitude, so we should use an Assumed Longitude with a number of minutes that will make the GHA’s minutes add up to 60. So if we have a GHA of 20º 10′ we will want to adjust our Assumed Longitude’s minutes to be 50′ and then when we add them together we get 60′ or = one extra degree.

Confused? Yes me too, but have another read and hopefully it will sink in – we are basically adjusting the number to get a nice round figure for our LHA with no pesky minutes and seconds to worry about.

Check out this video to learn more:

OK I think I get this now. I find it easier to draw it out as in the examples above. Let’s do some exercises. In the examples below, we are working out the LHA including minutes and seconds, but remember that when we are using the Sight Reduction Tables, we only need a whole round number.

Anyway it is good practice for my non-mathematical brain…

Question 1

  • GHA 165º 12.8′
  • Longitude 120º 59.3′ W
  • Is it morning or afternoon?

So when the Longitude is West we take the GHA and subtract the Longitude.

Answer: 165º 12.8′ – 120º 59.3′ W = LHA 44º 13.5′ afternoon

Question 2

  • GHA 18º 53.8
  • Longitude 97º 12.9’W
  • Is it morning or afternoon?

So when the Longitude is west we take the GHA and subtract the Longitude. If the GHA is lower than the Longitude we can add 360 and then do the subtracting.

Answer: 18º 53.8′ + 360º = 378º 53.8 – 97º 12.9 W = LHA 281º 40.9 morning

Question 3

  • GHA 205º 42.6′
  • Longitude 26º 51.3’E
  • Is it morning or afternoon?

So when the Longitude is east we add the GHA and the Longitude.

Answer: 205º 42.6′ + 26º 51.3’E = LHA 232º 33.9′ morning

Question 4

  • GHA 272º 49.3′
  • Longitude 174º 29.8′ E
  • Is it morning or afternoon

So when the Longitude is east we add the GHA and the Longitude, and if the total is over 360 then we subtract 360º

Answer: 272º 49.3 + 174º 29.8′ = 447º 19.1 – 360º = LHA 87º 19.1′ afternoon

OK are you still with me? Any thoughts on LHA? I promise that in the next couple of posts things are all going to come together a bit more!

 

3 thoughts on “Celestial Navigation – Local Hour Angle

  1. Pingback: Celestial Navigation – Putting it all Together | Astrolabe Sailing

  2. Pingback: Ocean Yachtmaster | Astrolabe Sailing

  3. Pingback: Celestial Navigation – Azimuth & Sight Reduction Tables | Astrolabe Sailing

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