Floating 1st Surface Mirror Project for Davis Artificial Horizon

1. Cut 3/4" Styrofoam to 5 3/4'  x  3 1/2"
2. Cut 3" x 3" rubber nonskid and center on top of styrofoam.
3. Pin 1/8" ball pins on all sides of each corner to fend float away from reservoir sides.
4. Place a 3" x 3" 1st surface laser bounce mirror mirrored side up and centered  on rubber nonskid.
5. Install in reservoir filled with 10mm of water then cover with clear glass wind shield.
6. Set assembled artificial horizon onto an 8" Lazy Susan for easy 180 degree rotation.

https://www.ebay.com/itm/Plastic-Spinner-Lazy-Susan-Turntable-Organizer-Spice-Table-Cake-Pantry-Display/273939076319?hash=item3fc80a94df:m:mSgqai9PcGqJIxkOz0KBmDw

https://www.ebay.com/itm/First-Surface-Mirror-3-Square-3x3-aluminized-1-8-glass-FS-FSM-front/184261133642?hash=item2ae6d1c54a:g:s5AAAOSwN81WDBDR

A precise observation requires averaging a sight both ways across floated mirror. It is recommended to split the time difference and observed altitudes of the sight pair then perform a single sight reduction. Expect intercepts no worse than 1 minute of arc.

Longhand Ex-Meridian

An ex-meridian is a sight reduction method for determining latitude when the bodies local hour angle (t) is near the meridian. A tabular correction can be added to the observed Ho so as to enable a reduction as if observed exactly on the meridian (LHA zero). There are quite a few tables out there that perform this task but most are multiple pages with multiple look-ups. To expedite the ex-meridian reduction process it is possible to use a one page custom table for a longhand solution by formula:

 +XM' = .5235 (t)(t)cos Lat cos Dec / cos Ho.

t = meridian angle degrees and tenths
Lat = assumed latitude
Dec = declination
Ho = observed altitude

Only two place precision is needed so a one page 10' natural cos sin trig table will work when combined with a custom factor (a) table.

Reworking the ex-meridian formula:

a = .5235 (t)(t)

+XM' corr. =  a(cos Lat)(cos Dec) / cos Ho

The (a) value is extracted from a very compact custom table (see attached). Cosine values are extracted from a one page 10' trig table (see attached). Round to two places for quick longhand reduction (see attached example).

Recovering Time From Known Position

An accurate correction to the chronometer time piece can be made using the time sight formula from a known position or confident DR position. A Casio pocket trig calculator will do a great job of time sight calculating. The Martelli Tables can be used to recover time also for navigators preferring to go old school.

https://www.amazon.com/gp/offer-listing/B006BRJZG6/ref=tmm_pap_new_olp_sr?ie=UTF8&condition=new&qid=1583076778&sr=1-1

Sight Reduction With A Casio fx-300ES Pol function Formula

The following Pol formula works well with the Casio fx-300ES pocket calculator:

Pol(Tan DEC Cos Lat - Sin Lat Cos LHA ,  -Sin LHA ) = r and Theta (see image)
North(+)  South(-)

r is stored in answer key and the x variable
Theta is stored in the y variable

Arc Cos ANS Cos Dec = Hc  (calculated altitude)

360 + theta = azimuth

See this link for a good explanation.
http://fer3.com/arc/m2.aspx/Sight-reduction-using-calculators-POL-arctan2-key-Bernecky-apr-2018-g41742


Alternate Pol formula using the Casio variables:  A (assumed latitude), D (declination), and M (meridian angle LHA)

Pol(Tan D Cos A - Sin A Cos M , - Sin M) = r  theta   

Arc Cos Ans Cos D = Hc

360 + theta = azimuth

note- to store in variables: angle entered: degree (DMS) minutes tenths (DMS) Shift STO A,D,M

Recommended Free Nautical Apps for Android Smart Phones

The following nautical apps look and work good on the Samsung Galaxy J3 Luna Pro smart phone:

1. My GPS Location
2. Anchor Lite
3. Tide Chart Free
4. GPS Anti Spoof
5. Nautical Almanac
6. Navigation Calculator
7. HiPER Scientific Calculator

https://play.google.com/store?hl=en_US

note - the free version of GPS Anti Spoof provides accurate UTC time, GPS position, and real time altitudes for the Sun, Venus, Polaris, and Acrux.

Davis Artificial Horizon Modification

Tape hinging filters and windshield glass into place allows for both sun shading or clear viewing of celestial bodies. Taping as shown keeps all the components together assembled for immediate use.

Velcro Strap for Casio Watch

The Hadley Roma velcro strap is the ideal custom upgrade for Casio digital watches.

https://www.ebay.com/itm/Hadley-Roma-MSNYLVEL-19mm-Black-Nylon-Slip-Thru-Mens-Watch-Strap/192147869000?epid=2255387500&hash=item2cbce7cd48:g:PS0AAOSwofFblsFM:sc:USPSFirstClass!10701!US!-1:rk:8:pf:0