Navigation question regarding longitude

[Brian D]

I am playing around with determining local noon and using Arc to Time tables to determine my longitude. I already know it based on many sources as being:

117° 15' 47.34"

Based on research I found that the sun will cross my meridian at 11:52:50.

Assuming I do not know my longitude, I want to extrapolate where I am based on knowing GMT and my local noon time. So, I did all that and ended up at:

118° 12' 30"

So where did I go wrong? Here is all my math as I understand it.

LMT 12:00:00 (My time when the sun crossed my meridian)
GMT 19:52:50

Delta = 7:52:50 (between me and GMT)

From the time to arc table in the National Almanac:

7 hr = 105°
52m = 13° 0'
50s = 12' 30"

I add and get the 118° 12' 30" answer.

Did I do something wrong or not take something into consideration? I do not have the National Almanac but found the tables on the internet in an older Bowditch book. So I copied the tables to a spreadsheet. Maybe I made a mistake when I copied them.

Professional help is requested. Thanks

 

[Dave Groshong]

If I'm remembering correctly from my Navy days, determining longitude that way isn't exact, and you are reasonably close. I'm looking for a old Arthur Piver book I know I have somewhere that's really simple and good. I'll let you know if I can find it. Here's a link you may have seen:

http://sv.berkeley.edu/VI/worksheet_longtutorial.html

Your math looks correct to me.

 

[Ed Schenck]

Without checking the math I wonder about "Based on research I found that the sun will cross my meridian at 11:52:50". To me that is the hard part, getting that crossing right. How certain are you?

 

[Brian D]

I used these methods, Ed.

1. (Local sunrise + Local sunset)/2
Local sunrise was 6:53 and local sunset was 16:54 came out to local noon of 11:53:00

2. USNO site based on Lon of your location gave local noon as 11:53
Begin civil twilight 6:26 a.m.
Sunrise 6:53 a.m.
Sun transit 11:53 a.m.
Sunset 4:54 p.m.
End civil twilight 5:21 p.m.

3. Software that tracks the sun showed the meridian crossing at 11:52:50

Those were my three sources.

 

[Brian D]

Found the error of my way. If you've been following this thread and wonder what I did wrong, I did not account for a Table of Equation of Time. This is a table that calculates if the sun is moving fast or slow (I'm still reading to understand) on a given day.

So, based on my readings from yesterday's Local Noon, I had to account of -3m 40s. With that, my corrected time is:

11:52:50
00:03:40
11:49:10 (delta of 7:49:10)

and the longitude based on that is:

117° 17' 30" (calculated)
117° 15' 47" (GPS)

That's close enough for a single siting. Now... to purchase a sextant and continue on with my education in celestial navigation. Thanks Dave for the link. It answered my question.

 

[Seattle Scott]

So Brian, is the difference in the final numbers about a 6 nm difference?

 

[Bill Roosa]

Equation of time

The sun is fast or slow based on the following:
The earth spins on its axis at an almost constant rate
The earth orbits the sun at a non constant rate.
That means that the earth moves faster or slower in its orbit as it progresses from apogee to perigee. If the earth was in a truly circular orbit it would turn once on its axis (360 degrees) in 23 hours, 51ish minutes The extra time to get 24 hours is needed to turn through the angle the earth moved in its orbit. But since that is not constant, the sun is either slow or fast from where it would be if the orbit was truly circular.
A non technical means of calculating local noon is to stick a rod in the ground and note when the shadow is the shortest. this also ends up being true south if you need a check on your compass. To find where the shadow will be shortest prior to it actually happening mark the top of the rod's shadow around 9:00 in the morning and wait an hour. mark the top of the rod's shadow again and connect two of the points. You can extend the line so that you can drop a perpendicular from the rod tops line to the rod itself. BTW the rod shadow top line is also a true East west line.

 

[Ross]

Brian the conflict resides in the difference between solar time and civil time. At present LAN is before civil noon by your location plus the adjustment made for convenience of civil time. I have a pole that casts a shadow on a nail at local noon LAN my watch tells me the the sun is fast by several minutes later in the year 12 noon EDT will be long gone when the shadow hits the nail and the sun wil be slow. You can also get a sense of this by the GHA (greenwich hour angle) at 1200 UT.

 

[Brian D]

Scott. I just found another error that I injected into the math. So basically, my new value shows about 2 nm off.

Ross, Bill, I am now just learning that. I've learned in the past about sidereal time and day and understand that concept. But not in the context of navigation. These are things we never think about until it is time to, well, think about them. I'd rather think about them while I am feet dry and not while feet wet.

 

[ChuckThomas]

if you are looking for a serious sextant check out this site.
http://landandseacollection.com/id2.html

 

[Brian D]

Chuck, going with a Davis Mark 15 until I am ready for a serious sextant. I'll keep your link handy, thanks.

 

[Ed Schenck]

Fun stuff Brian. I used to take my Davis sextant down to the beach along with my GPS. Take some sightings and see how close you can come to the GPS latitude. I was never able to get much closer than two nm. But I figure from there I might see land.

 

[Dave Groshong]

I think the name of the Arthur Piver book is actually "Noon Position", hopefully I can find it at home!

 

[Ross]

Brian, I have a Davis mark 3 that will resolve 2 minutes on the arc. With a noon sight I can get within 4 miles if my watch is correct.
You know of course that for a noon sight you take a sight before LAN and at the same ho after LAN and subtract the times and divide by 2 and add those minutes to the first sight for the time of LAN. You can't determine the exact moment of noon with observations.