Author

Topic: Rounding DR Lat

Gary Rose

posted December 28, 2004 07:21 AM
I'm reworking my home study Celestial Navigation course and have a question about rounding DR Lat. Some of the problems in my book have a DR lat of 45 degrees 30 min North. My question is why is the DR Lat rounded down to 45 degrees not up to 46 degrees in these problems? 30 min of lat is 50% and normally you would round up at 50%. Please explain! Is there something I have missed  a rule I forgot?
Thank you


David Burch

posted December 28, 2004 04:09 PM
If we were choosing an assumed Lat, it would not matter if we rounded down or up. The rule there is choose the one that is closest to your DR, and with it right in the middle it would not matter.
The convention that halfway between values rounds up is not applicable here. In some other cel nav procedures, we must indeed always choose the lower (base) value to enter tables looking for corrections, even when we might be dealing with angles of say 45° 50'.
With that said, we can go on to some details:
If you did have a DR at say 25° 30.0' and you then chose an assumed Lat of 26° and completed the problem, and then found that your fix latitude was say 25° 14', then you could be better off to then redo the sight reduction choosing 25 instead of 26. This would be especially the case if any avalues ended up being greater than say 50' or more.
In cases with large avalues, we can begin to push the mathematical limits of the procedures and thus introduce errors of as much as a mile or so for avalues greater than 60 or 70', and even larger errors for larger avalues.
The general rule is this. Choose the assumed position according to the standard rules using your best estimate of the DR position at the time of the sights. Then do the fix correcting for vessel motion etc. Then compare the fix with the assumed position you used. If they differ by more than 30 miles or so, I would consider changing the DR position to the fix position and choose another assumed position based on these new values.
This can improve your accuracy in some cases.
Now on to the real answer to your question. In our selected tables data, we have sight reduction tables only for 45° Lat, not for 46 nor 43, so we must round to 45 in all practice problems to use these selected tables.
Of course, if you have your own sight reduction tables, or use those on our cel nav CD (or download them from the Internet) then you could use 46 for the 45 30 DR positions. You will get different avalues, very similar Zn values but should get the actual fix positions very close, pending the notes and possible corrections mentioned above.
From: Starpath, Seattle, WA


Gary Rose

posted December 29, 2004 05:32 PM
Thanks for trying to clear up the muddy waters.
After studying your reply I worked out the 2 problems in question using the NAO Tables, using both 45 and 46 degrees for the assumed latitude. I then plotted all the sight reductions on one sheet. The resulting fixes are one minute or less different in both latitude and longitude, which is not too bad since I’m working with a sheet that 3 inches = 60 nautical miles and a 0.5mm mechanical pencil that its lead is about 0.333 nautical miles wide.
I just had to prove this to myself. Yes a little OCD.


