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    Guyou's Two Methods
    From: Dave Walden
    Date: 2011 Jun 30, 10:23 -0700


    GUYOU's two methods

    Your DR is 74-52W, 38-12N. UTC is 081707 on 7 Jun 2011. You have corrected observations of 3 stars:

    Alkaid 23-53.8
    Altair 59-55.3
    Hamal 16-8.7

    You discover that your inspection tables, short tables, calculator, laptop, even your backup flat Bygrave are all missing. Luckily you've been following NAVLIST, and have nine pages of a Spherical Meridional Parts table that you just xeroxed at hand. What to do? Fortunately, you have memorized Guyou's method for calculating a "time sight line of position" using just the MP table.


    First, Alkaid:

    Deg Min Decimal Radians

    d Dec 49 15.5 49.258 +49° 15.5' 0.8597 +North
    L Lat DR 38 12 38.200 +38° 12.' 0.6667 +North

    Ho 23 53.8 23.897 +23° 53.8' 0.4171

    Dec + Ho 73.155 +73° 9.3' Addition
    Dec - Ho 25.362 +25° 21.7' Subtraction

    MP (Lat)= 2483.5 MP table look up
    MP [ 90 - (Dec + Ho) ]= 1025.6 MP table look up
    MP [ 90 - (Dec - Ho) ]= 5127.8 MP table look up

    MP(Lat)+MP[ 90 - (Dec + Ho) ]=A 3509.1 Addition
    MP[ 90 - (Dec - Ho) ]-MP(Lat)=B 2644.3 Subtraction

    MP(x)=A; => x= 50.369 +50° 22.2' MP table look up
    MP(x)=B; => y= 40.275 +40° 16.5' MP table look up

    MP (90-x) = 2593.8 MP table look up
    MP (90-y) = 3448.8 MP table look up

    SUM C 6042.7 Addition
    DIFFERENCE D -855.0 Subtraction

    MP(90-Z)=C/2; => 90-Z= 44.899 +44° 53.9' MP table look up
    MP(90-Pe)=D/2; => 90-Pe= 7.107 +7° 6.4' MP table look up

    Azimuth, Z= 45.101 Subtraction
    Local Hour Angle, LHA, Pe= 97.107 Subtraction

    IF Dec > Hc, switch Z and Pe Pe 97.107 +97° 6.4'
    Z 45.101 +45° 6.1'
    (If star West, Zn=360-Z) Zn 314.899 +314° 53.9'

    Now use LHA and GHA to calc Long

    GHA 172 9.7 172.162 +172° 9.7'

    AP Long (=LHA-GHA) -75.055 -75° 3.3' -West
    AP Lat 38 12 38.200 +38° 12.' +North


    So, at your AP of 38-12N, 75-3.3 W, you plot your LOP perpendicular to Zn=315

    Then, Hamal.

    Luckily, just before you try and calculate a time sight LOP for Altair, a star almost due south, while looking in your drawer for a new pencil, you find your old (1911) copies of Guyou's Nouvelles Tables de Navigation, Vol 1 and 2. This will give a quicker solution for your last star, Altair.

    To get local hour angle to the nearest 20', we use AP long=74deg 59.5min. For lat, nearest 20' gives, AP lat=39deg 20min.

    Deg Min Decimal(or ') Radians

    GHA 81 19.5 81.325 +81° 19.5'
    D Dec 8 54 8.900 +8° 54.' 0.1553 +North
    L Lat AP 38 20 38.200 +38° 20.' 0.6690 +North
    calc fm GHA& AP Long Pe 6.333 +6° 20.' 0.1105 +West
    Long AP -74 59.5 -74.992 -74° 59.5' -1.3089 -West
    Ho 59 55.3 59.922 +59° 55.3' 1.0458

    H+D= 68.822 +68° 49.3' =4129.3'
    H-D= 51.022 +51° 1.3' =3061.3'

    Volume 1,Table Gauche(H'+D')/2 1100.8'
    Volume 1,Table Droite(H'-D')/2 2675.2'

    Sum=H' 3776.0 +63° 56.0'
    Diff=D' -1574.4' -26° 14.4'

    Volume 2, Ze 12.6
    Volume 2, He 3783.6'= +63° 3.6'

    Zn= 192.6

    H'-He (deg long at this lat)= -0.125 -0° 7.5' In nm, 5.9

    So, just one opening of Volume 1, and one opening of Volume 2. Pretty quick!

    (Please let me know where I can get these Volumes!)

    Attached are scans of excel versions of the tables and calculations, sample MP tables from Friocourt and Inman (My copy of Inman has a hand sewn canvas cover and notations on the fly of ships it has served. I got it cheap since the seller said it was pretty well used. I consider myself lucky to have it!), extracts from Goyou's Novelles Tables, a plot, and the ICE data used to generate the problem. Descriptions of Guyou's methods can be found through Google Books and other sources.

    Note also that Guyou was quite a fellow. He made contributions to mathematics, cartography, naval architecture, astronomy, and the French Academy, as well as navigation. I'm sure our French friends can tell us more.


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