NavList:

picking up the thread of what was said in:
http://fer3.com/arc/m2.aspx/HavDoniol-checker-Andr%C3%A9sRuiz-jun-2015-g31782

Altitude

By computation (Hanno) -> test OK

ZD = Zenith Distance

Hc = (90 - ZD) Calculated Altitude

hv (ZD) = n+(1-(n+m))*a

Same Name

n = hv (|B| - |dec|)

m = hv (|B| + |dec|)

Contrary Name

n = hv (|B| + |dec|)

m = hv (|B| - |dec|)

a = hv(t)

Azimuth

By computation (Bergman) -> test OK

hv (Z) = (a-n)/(1-(n+m))

Same Name

a = hv (90º-|dec|)

Contrary Name

a = hv (90º+|dec|)

m = hv (B+Hc)

n = hv (B-Hc)

N Latitude:

If LHA> 180◦, Zn = Z

if LHA< 180◦, Zn = 360◦ − Z

S Latitude:

If LHA> 180◦, Zn = 180◦ − Z

if LHA< 180◦, Zn = 180◦ + Z

Z by Hanno azimuth diagram -> test NOOK
An ambiguity in the value of azimuth may arise: see the attached spreadsheets.
Z is E/W as the name of the meridian angle.

Sign criteria with azimuth diagram

If( LHA > 180º ) |t| = 360º-LHA

If( |t| > 90º ) |t| = 180º-|t|

enter with t in the diagram

Meridian angle

if (0 <= LHA && LHA <= 180)

t = -LHA [W]

else if (180 < LHA && LHA <= 360)

t = 360º - LHA [E]

hv(x) = hv(360º-x)

hv(x) = hv(-x)

-> hv(LHA) = hv(t)

Azimuth

sin LHA * cos dec = sin Z * cos Hc = C

Z = asin(sin(LHA) * cos(Dec) / cos(Hc))

0 <= LHA <= 360º

-180º <= t <= 180º (the diagram has values for t between 0 and 90º).

sin(t) = - sin(LHA)

cos(x) = cos(-x)

-90º <= Hc <= 90º -> sg(cos Hc) = +

-90º <= Dec <= 90º  -> sg(cos Dec) = +

sg(C) = sg(sin Z) = sg(sin LHA) = - sg(sin t)

sin(x) = -sin(-x) = sin(180º-x) = -sin(180º+x)

Z  -> Zn

0 <= Z <= 90º is E/W as the meridian angle is.

Sun: morning E, afternoon W

References

Doniol Hc http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-Rudzinski-jun-2014-g27982

http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-HannoIx-jun-2014-g27989

http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-Rudzinski-jun-2014-g27991

Hanno Hc http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-HannoIx-nov-2014-g29121

Bergman Z http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-Bergman-nov-2014-g29441

Greg Rudzinski article http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-FrankReed-jun-2015-g31625

Doniol, NavList : Hanno Ix, Lars Bergman, Greg Rudzinski

Other diagrams for Z:

Rust and Weir

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