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Another mathematical genius required!

Discussion in 'General Discussion' started by Mike53, 7 Dec 2018.

  1. Mike53

    Mike53

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    Will do my best to explain the problem..........

    In Celestial navigation there comes a time when a plotting sheet is required. Briefly a plotting sheet is a piece of paper with a latitude scale up the side and a longitude scale along the bottom. The thing is the scale needs to be correct for your location. Commercial plotting sheets are available but I have a book that describes how to quickly produce your own and I am not at all sure whether the instructions are correct.

    On a piece of paper draw lines along the bottom and up the left hand side.

    From where the lines meet in the bottom left hand corner draw a line at an angle corresponding to the latitude where you think you are (will be close enough).

    Put some marks on the bottom line each one representing 10 degrees of longitude.

    From a couple of adjacent marks draw vertical lines up to meet the line drawn at an angle.

    The distance between where the 2 lines meet the line drawn at an angle becomes your latitude scale and represents 10 degrees of latitude or 10 miles (of the nautical variety).

    Just mark your latitude scale accordingly and you have your plotting sheet.

    The problem here I think is it does not take into account the curvature of the Earth with an error gradually being introduced up to 45 degrees then the error lessening towards the poles???

    Mike
     
  2. Ian H

    Ian H

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    50B6EE14-0B48-4C60-A3F2-EBDB3B6ACEA6.png

    I might try again after some coffee (y)
     
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  3. durhamplumber

    durhamplumber

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    If Picasso did that it would be worth millions!
     
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  4. Mike53

    Mike53

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    Cannot help thinking after the excellent response to yesterdays question there is an issue with this question? You maybe need something stronger than coffee.

    Mike
     
  5. EFLImpudence

    EFLImpudence

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    I don't know how your plotting sheet works.

    We have this. Then what?

    upload_2018-12-7_17-16-6.png
     
  6. motorbiking

    motorbiking

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    You have to adjust the lines accordingly, your plotting sheet should come with a scale.
     
  7. Mike53

    Mike53

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    Hi EFLImpudence,

    Thanks for your reply.

    The point here is I think the instructions how to make your own plotting sheet are incorrect in the book I am studying and am seeking confirmation of this and perhaps an alternate solution.

    I can see from your drawing you have misunderstood my explanation. Once you have drawn a couple of adjacent vertical lines, lets call where they meet the angled line A and B. What you need to do is measure distance AB and mark this distance off on your latitude scale. This means 10 degrees of latitude is greater than 10 degrees of longitude. This is certainly correct generally at 40 degrees latitude but I am wondering is it actually correctly to scale? As I said in my original post I think it disregards the curvature of the Earth.

    Mike
     
  8. Mike53

    Mike53

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    Hi motorbiking,

    You are correct commercial plotting sheets do come with a scale but here I am trying to create my own plotting sheet and try to ensure my scale is correct

    Mike
     
  9. Mike53

    Mike53

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    Thought this might help................

    A great circle drawn around the Earth passing through both poles is 21,600 miles (nautical) and is also 360 degrees.

    The Equator is also a great circle, it is 21,600 miles and is also 360 degrees

    As we move our latitude N or S away from the equator and draw a line around the Earth parallel with the equator we have drawn a parallel of latitude but it is no longer a great circle, its distance around is less than 21,600 miles but it still covers 360 degrees of longitude.

    The further away from the equator our parallels of latitude move the shorter around it is although still 360 degrees of longitude.

    This is the scale I am trying to get right.

    Maybe this does not help!

    Mike
     
  10. Ian H

    Ian H

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    I just don’t have a ruler :(
     
  11. EFLImpudence

    EFLImpudence

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    Misunderstanding acknowledged -

    There are calculators on the net for working out such things.
     
  12. Doug99

    Doug99

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    The video refers to a nautical mile as 2000 yds or 2000 mtrs........I don't think so!!(n)(n)
     
  13. Mike53

    Mike53

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    I did not realise that was a video and have just watched it myself. Cannot believe how someone could make such an error in what must be his area of expertees. Whichever way you look at it, it is incorrect. A nautical mile is 1,852 metres. Not sure about Plotting an LOP either. Should it be Plotting a LOP.

    Mike
     
    Last edited: 8 Dec 2018
  14. Mike53

    Mike53

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    Thanks EFLImpudence, Found one. It may be that the instructions in the book are correct. One minute of latitude is one nautical mile irrespective of latitude. However one minute of longitude is 1 nautical mile at the equator but zero distance at the poles. One might expect at 45 degrees latitude one minute of longitude to be 0.5 nautical mile but the calculator indicates that this does not occur until around 60 degrees of latitude. So if a line was drawn on the graph at 60 degrees AB should be double the length of the points of origin of the vertical lines. I do not have the skill to post such an example on here but will have a go with a piece of paper etc

    Mike
     
  15. Mike53

    Mike53

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    I am aware I am the only person with the slightest interest in this subject but I have just drawn my line at 60 degrees and AB does indeed measure 2x the distance between the origin of the 2 vertical lines. Evidence that the instructions in the book are correct.

    Mike
     
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