Venus-Jupiter conjunction of August 2014

As Frank Reed pointed in a recent NavList posting, Venus and Jupiter appeared close to each other in the morning sky of August 18, 2014, separated by about half a degree (30′, or by about the Moon apparent diameter). A quick use of spreadsheets venus.xls, jupiter.xls, and sailings.xls confirms this fact. The first two spreadsheets provide the planets’ ephemerides. The third one calculates the great circle distance of the bodies’ subpoints (geographical positions) in nautical miles, which is numerically very close to their angular separation in the sky in minutes of arc.

venus_jupiter_Aug2014

 

Additional details can be found on Steve Owens’s blog.

Five years of Navigation Spreadsheets

Navigation Spreadsheets logo
Navigation Spreadsheets

At the fifth anniversary of our website’s launch we review some of Navigation Spreadsheets functions.  All three examples are taken from the 2014 Nautical Almanac Commercial Edition.

1) Ephemeris (almanac data), Venus GP on 2014 May 5 at 13h 15m 18s (p. 256):

venus.xls

Input:
UT: 2014 May 5, 13:15:18

Output:
GHA = 58º 58.0’
Dec = S 0º 14.1’

venus2014

 

2) Sextant altitude corrections (Venus, p. 259)

alt_corr_xls
Input: Hs = 4º 32.6’
Output: Ho = 4º 17.6’

altcorr2014

 

3) The calculated altitude and azimuth (pp. 279-280)

intercept.xls
Input:
GP: GHA = 53º    Dec = S 15º
AP: Lat = N 32º    Long = W 16º
to which we add Ho = 30º 30.0’ in order to allow the calculation of the intercept and the plotting of the LOP.

intercept2014

 

Output:
The resulting LOP (intercept 38 NM away, azimuth 223) is plotted with the T-Plotter.

tplotter1

tplotter2

 

As it was also calculated by intercept.xls this LOP crosses:
the AP’s meridian at 52 NM north of the AP
the AP’s parallel at 56 NM east of the AP

tplotter3

 

(first published on February 15, 2014)

Example of a great-circle route

In a recent NavList thread titled “Great Circle Puzzle” it is revealed that a great-circle (i.e., straight, or, direct) sailing path exists between Pakistan and Russia.  This may seem impossible based on a quick look at the world map.  However, several NavList contributors established the end points and provided a general description of such a path.  Using these results it is possible to calculate this path in detail with sailings.xls and waypoints.xls spreadsheets:

waypoints.xlswaypoints

 

If you have a globe handy, check it out!

gc12

gc34

For additional details see this post and the entire thread.

World map credits:
http://www.mapsfordesign.com
http://www.bjdesign.com

(first published November 3, 2013)

Almanac spreadsheets in 2014

Selected comparisons with Nautical Almanac 2014 Commercial Edition indicate that almanac spreadsheets are good for the year 2014 as they are – with one small update described below.

The newest versions of aries_stars.xls and what_star.xls have the computed SHA of Rigil Kent. increased by additional 0.3′ before display (the original adjustment had been +0.6′, so now it is +0.9′, see cells W305 and W306) in order to better match with published almanac values.

A possible explanation for this oddity has been suggested by Antoine M. “Kermit” Couëtte in his recent NavList post.

Downloads of all (including updated) spreadsheets are available on our main page.

(August 31, 2013: Additional details were provided on the same NavList thread by Paul Hirose and Dave Walden.)

 

(first published on August 25, 2014)

Advancing/retarding of position lines due to vessel motion

This sample problem created by Greg Rudzinski provides a nice illustration of the importance of accounting for vessel motion in order to obtain the best attainable accuracy for the many-body fix.  The first plot shows the three LOPs computed and plotted at their respective times (i.e., ignoring vessel motion) forming a small triangle (“cocked hat”):

nomotion

 

In the second plot these LOPs were adjusted for vessel motion, i.e., the were advanced/retarded as needed to a common moment in time).  As a result, the previously plotted cocked hat tightens to a pinwheel:

motion

 

There are several methods to advance or retard LOPs in time (see, for example, running fix). In this plot the LOPs were shifted by recalculating their intercepts with the formula presented by Gary LaPook ( change ~ time × cosine( azimuth – course ) ) and implemented in spreadsheet alt_move.xls.

In the following illustrative calculation of Ho adjustment, the distance traveled is DR = 1 mile, the course and azimuth differ by 60º, therefore the Ho (and, in the end, the intercept and LOP location) changes by 0.5′ ( = 1 mile × cos 60º ).

alt_move.xls:

altmovexls

 

(first published on July 6, 2013)

Ex-meridian latitude calculation

A meridian transit observation allows the determination of latitude by simple arithmetic – spherical trig is not needed in this case.  For example, a noon altitude of 40º (i.e, zenith distance of 50º) of the sun with declination of S 20º observed due south from the northern hemisphere translates into latitude of N 30º (= -20º + 50º).

If, however, this altitude was observed not quite at the time of local apparent noon (LAN) but, say, 10 minutes before or after LAN, then this observed altitude is slightly less compared to what it otherwise would have been, had it been measured at LAN.  As a result, in our example, the LAN zenith distance is lower than 50º by a certain small amount, which means that the latitude is N 30º minus that value.  In cases like these it is still possible to avoid a more complicated calculation with the use of Bowditch Tables 24 and 25 to compute this small correction.  Alternatively, one might use the ex_meridian.xls spreadsheet to find that, in this example, the correction amounts to 3.5′, resulting in latitude of N 29º 56.5′.

 

(first published on April 14, 2013)

Many-body celestial fix for a moving vessel

In a recent NavList posting Jeremy provided a set of high-quality real-life observations that can be reduced to a celestial fix for his vessel at a specified moment in time.  The application of Navigation Spreadsheets to this data set results in a very good fix, both by direct computation as well as by plotting.

The following table shows the computed ephemeridescorrected sextant altitudes, line-of position (LOP) characteristics for two choices of an assumed position (AP), and the accounting of vessel motion through dead reckoning (where the mini-spreadsheet time.xls was used to express the time intervals in decimal hours).

sights

The fix at 19:00:00 local time (= 11:00:00 UT, since ZD = -8) is computed to be:
Latitude: N 8º 49.0′
Longitude: E 109º 45.2′

from the many_body_fix.xls spreadsheet:

manybodyfix

This location is marked by a black square on the two subsequent plots.

The first plot uses the VSOP plotting sheet (scale 20 nautical miles per inch) with AP at N 9º and E 110º.  The LOPs were drawn with a T-Plotter.  The LOPs in this plot are not shifted by DR.

vsop

 

The second plot “zooms in” with the scale of 1 NM per centimeter to get a more accurate look.  The reference AP is N 8º 50′ and E 109º 40′, which has been individually shifted for each observed celestial body along the vessel’s track (037) in order to account for the motion of the vessel.

metric

 

The results are excellent, with all LOPs running within a mile of the computed fix.

In the above procedures all LOPs were treated as equally valid.  The fact that there are pairs of LOPs that run nearly parallel to each other complicates matters somewhat.  The GPS fix given by Jeremy:

Latitude: N 8º 48.4′
Longitude: 109º 45.0′

is recovered almost exactly (both by computation and by plotting) if only Jupiter, Rigel, and Fomalhaut LOPs are used.

For comparison, Jeremy’s position is marked by the square in Google Earth at the top of this post.

 

(first published on March 8, 2013)

Celestial line of position with the T-Plotter

The recent addition of a protractor to the T-Plotter makes it a fully self-contained tool for plotting of celestial LOPs, as is shown in this demonstration video.  It is important to note, that the use of the T-Plotter is not limited to the scale of 20 nautical miles per inch printed on the instrument.  It is always possible to read off the equivalent number of tics from the latitude scale of any chart according to the picture below.

tpbasic4

 

(first published on December 20, 2012)

LOP plotting using metric graph paper

Some time ago Antoine “Kermit” Couëtte kindly responded to my question about chart scales by stating that he used 1 cm per nautical mile.  In this post I show how that can be achieved using metric graph paper.  As an illustration I pick the Antares line of position (LOP) from the “many-body fix” example (vessel motion is ignored in this post).

Here we really need to “zoom in” in order to use this scale, so I changed the latitude of the assumed position AP by half a degree to N 31º 30′.  The AP longitude stayed the same at W 15º.

intercept.xls:
antareslopxls

The spreadsheet intercept.xls calculates several characteristics of this LOP.  Besides the usual intercept and azimuth, it also gives its intersections with the AP’s parallel (cell F12) and meridian (cell F15).  This information allows the quick plotting of the LOP simply by marking and connecting these two points.  This technique will not work for LOPs that run close to the cardinal directions, but I believe that it is a good option to have available nonetheless.

antaresall

After the two points F12 and F15 were connected thus forming the LOP, several measurements were made on the chart to show internal consistency of all the other data computed by the intercept.xls spreadsheet.  The intercept is indeed AWAY (cell E6) with azimuth (cell F6) 152º and it is 3.4 nm (cell D6, allowing about 1 mm for plotting imperfections that only translate to 0.1 nm, which does not degrade the precision achievable in celestial navigation).

intercept: 3.4 nm away from the geographical position (GP) of the observed body
antaresintercept

azimuth: 152º toward the GP
antaresazimuth

LOP direction: 242º and 62º – both perpendicular to the azimuth
antareslop

This last piece of information allows for yet another way of plotting this LOP using parallel rules on a chart or a plotting sheet with a preprinted compass rose, as it is shown here.

 

(first published on November 16, 2012)