Apparent time

[Rumata]

Gentlemen, hope  you  can help  me in  this  little  "predicament."

At  first ,  a few  general  terms:
 
1. Apparent time is a  measure of  the  sun'  true  position.  To  get  Greenwich  apparent  time at  any  instant  we just  convert GHA  of the  sun  into time (hh/min/ec).,  We  need  apparent  time  to  find  when  the  sun  will  be  on  the  observer's  meridian. Local  apparent  noone,  when  the  observations  for  latitude  are  made. We  know  that  it is  different  for  each meridian,  and  unless two  places  are  on  the  same  meridian- apparent time  is  different.

2. On  the  Mercator  chart  every  parallel  is expanded in  the  ration of  the secant of  its latitude.
To  avoid  local  distortion every  meridian  of  a  Mercator  chart must also  be  expaned  in  the  vicinity of  each  parallel by  multiplying  it by  the secantr  of  the  latitude of  the  parallel.

My  question:

When  the  vessel  is  located  above let's say  50 deg Lat. and  we are  trying  to find  LAN the  natural  curvature  of  meridians  would  make  GHA slightly  shorter  than  Mercator  chart  projections (  straight,  parallel  lines). And  it  means  LAN  calculated  would  be  different  from  LAN  real ,  considering expansion  ratio  of scant  of  the  latitude.  And  it means  the  moment  we  are catching  the  sun  in a sextant  is not exactly  the time  the  sun  is in Zenith.  Difference  should  not  be  significant,  but  I just  want  your  expert  opinion about  it.

Please,  advice.

Thank  you

[P.Rutherford]

Rumata,

My thought is that the moment of LAN as observed in your sextant is correct but this must be qualified by the following;

- Sextants and ship movement combine to effect imprecise determination of LAN.

- Making a series of observations before MP and after MP based on equal altitudes will mitigate inaccuracies but not exactly.  Equal Altitudes, of course, will give you longitude and an imprecise latitude.  Plotting these observations and then drawing a curve through them can provide a fair assessment of latitude.

These things kept in consideration, a plot isn't necessary to determine LAN- just get zenith and do the calculations to obtain latitude.  

See here- https://thenauticalalmanac.com/Formulas....e_Latitude

Yes, the lines of longitude converge is a problem which can be accounted for by adjusting the amount on the UPS (Universal Plotting Sheet) between the lines of latitude.  At 50°, as you mentioned, it's not that much....but it is an amount that can be easily measured.  Again, this isn't a problem of determining LAN- it would be relative to determining longitude. 

Oh, the UPS, generally, is only laid out in 1° lines of latitude and, of course, 1° lines of longitude.  And at the Poles it's a real mess since the lines of longitude are so close on the UPS.

Anyone have another idea?

Paul

[Rumata]

Thank you, Paul. Will follow. Re: UPS. Tried a few times to construct a specific area of a chart using meridional parts method. It is much more precise and a lot of headache with calcs and proper scales for longs and lat. At least I tried it. Will I use it? Don't think so.

[pabrides]

Ive never tried to ascertain longitude or latitude with a noon shot, but I am aware that LAN is not always LAN. The sun, as I recall, is sometimes advanced or retarded of clock noon if I'm thinking about this correctly. The difference between zenith and clock noon is shown in the daily pages as equation of time or Meridian passage.

A plotting chart has a true compass rose and is also marked in degrees of latitude. Draw a line from the center out to your latutude along the circle. Using dividers pick off miles from the meridian (central vertical line), then lay it along the diagonal you drew. Draw a vertical line down to the parallel and thats the equivalent short longitude. Im at 10 degrees north so there is only a slight difference between equatorial and local divisions, but I draw the diagonal every time just so I don't get lazy. I guess this might be termed the graphic method. Works for me.

First thing I do with a plot sheet is draw in my dr bracketing meridians to either side of the circle intersecting the latitudes north and south. Then I draw the diagonal as mentioned which scales minute and second for that latitude. I never use the associated longitude scale.

I hope were all talking about the same thing. Lol

I'd like to know more about meridional parts and how to use them.

BTW - sometimes to assist accuracy I rescale the ups to reflect half degrees both lat and long... it makes the mile tick marks into half mile. With some planning you could even quarter or double the ups. My ups are all 8.5x11. Rescaling saves me the expense of large plotting sheets.

Cheers.