Latitude by Polaris

Sum the Q correction with the corrected sextant altitude (Ho) of Polaris to quickly determine north latitude.

Classic Trig Log Sight Reduction by Ageton

Classic trig log sight reduction can be done using the Ageton Pub 211 table in lieu of trig log sin cos functions. This facilitates the log summing process, shortens reduction time, and lowers the chances of arithimetic errors. Calculating the prime vertical and amplitude can also be done by Ageton table.

http://fer3.com/arc/m2.aspx/Ageton-Classic-SR-Table-PDF-Rudzinski-oct-2015-g33280

Modern Haversine Sight Reduction

The cosine haversine Doniol sight reduction formula can be written as an all haversines formula to create the Modern Haversine Method of sight reduction. Only a single natural haversine table is needed and there are no special case rules.

http://fer3.com/arc/m2.aspx/Natural-Haversine-5-Place-Table-PDF-Rudzinski-jan-2017-g37790


Formula:

hvZD = n+[1-(n+m)](a)

Same Name
n = hv (L-d)
m = hv (L+d)

Contrary Name
n = hv (L+d)
m = hv (L-d)

L = Latitude
d = Declination
t = Meridian Angle
a = hv(t)
hv = Haversine
ZD = Zenith Distance
Hc = (90 - ZD) Calculated Altitude




Precision is 1' when done longhand to 4 places using natural haversines (see attached example). Azimuth is quickly done using the Ix graph (attached). A water resistant calculator watch such as the Casio CA 53W will make for ultra compact quick 5 place 0.1' precision as well as precise timing of observation. An Otis King slide rule will serve for quick non electronic 4 place precision.

Pocket Slide Rule

The pocket K&E Doric offers serious faster than a trig calculator navigation calculating power for time, speed, distance, eta, prime vertical, amplitude, and the radius of a horizontal sextant angle circle of position.

Circle of Position Radius Formula:

.5 (A to B)/Sin horizonal sextant angle = the radius of the circle of position. A, B, and radius are in nautical miles.

Marine Log Book Pen

The Zebra F-701 can be refilled with a Fisher cartridge to create the perfect all weather log book pen for on the water use. Completing the cartridge swap requires removing the plastic tip insert with a paper clip which allows the Fisher cartridge to drop in without any further modifications. The barrel knurling can be coated or taped to prevent pocket chafe.

https://www.youtube.com/watch?v=zlgbRxZaAqY

Square Pocket Protractor

A grid map tool that is modified with 1/16" drilled holes makes for the perfect pocket chart plotting protractor. Drill the holes by hand using a 1/16" bit spun with the index finger and thumb. Make a pilot hole at the spot to be drilled using the point of a divider leg.

Longhand Sight Reduction

An obscure sight reduction formula derived by a Frenchman named Doniol is the only reduction method that can be quickly done longhand without logarithms. Needed are four place cosine, sine, and haversine tables which can be found in the 1958, 1962, 1966, 1975 vol 2, and 1981 vol 2 Bowditch editions.


http://fer3.com/arc/m2.aspx/Haversine-how-derive-it-Bernecky-jun-2015-g31663


Doniol Formula

Sin h = n - ( n+m )a

Same name:
n = Cos ( Lat-Dec )
m = Cos ( Lat+Dec )
a = Haversine LHA

Contrary name:
n = Cos ( Lat+Dec )
m = Cos ( Lat-Dec )
a = Haversine LHA

rule:
Lat + Dec > 90 use (-)Cos of Complement

When haversine tables are not available then substitute
a = ( 1-Cos LHA )/2