Great Circle Sailing with the 2102-D Star Finder

The 2102-D Star Finder is used to identify stars after sighting them or to choose the optimum set of stars before sighting them. It has other uses as well, as we describe in The Star Finder Book: A Complete Guide to the Many uses of the 2102-D Star Finder.

It turns out that this title is not quite true for the 1st and 2nd editions of the book, because the 3rd ed (Sept, 2019) includes a new application—namely great circle sailing solutions; the subject at hand.

We did not invent this new application, and indeed did not think of it ourselves over the years working with this star finder. We learned of it by chance because one of the original 1921 versions  (HO 2102-A) was found by Mike Walker in a garage sale in Rowley, MA. He recognized its historical value and kindly donated it to Starpath. We are in the process of documenting the device, after which we will post it on the Institute of Navigation's  Virtual Museum, and then donate it to a real maritime museum.

The original patent for the device by Capt. Gilbert Thomas Rude (pronounced Roo dee) did not mention this new application (solving for great circle initial heading and total distance), but the instruction sheet included with the actual Navy versions did include a couple sentences outlining the procedure. It seems those instructions are not quite right, but the principle is clear, so we can work around them. The method will definitely work better on the original 2102-A (star disk diameter 14") than on the present 2102-D (disk diameter 8"), but as we show below, and in an accompanying video, the current version that thousands of mariners own does indeed still provide a useable initial heading and total distance for great circle sailing. This technique was not mentioned on the later versions 2102-C (1932) and 2102-D. Obviously, it is not as precise as we get from an app in our phones, but it is one more tool in our bag of tricks that does not require power and can be dropped into water, stepped on, and kicked around, and still work fine.

Let's consider a hypothetical—but not at all random!—case of being located at a waypoint called Deneb and we want the great circle distance and initial heading to a waypoint called Hamal, as shown below.

For comparisons in the following, accurate great circle (GC) and rhumb line (RL) solutions can be computed online at www.starpath.com/calc.

These waypoints happen to be the fixed positions of two navigational stars that are plotted on the white disk of the 2102-D star finder. The GC solution by star finder comes about because the arcs on the blue templates are great circles plotted on the same projection used for the white star baseplate. A sample is below.

We chose Deneb for this example because its declination (N 45º 21.2') nearly matches the Lat 45 N blue template of the star finder. There is a template for every 10º of Lat, up and down from 45. We chose Hamal more or less randomly.

Thus we imagine the earth not rotating and we are at the geographical position of Deneb, meaning it is directly overhead, 90º above the horizon, and we want the initial GC heading and distance to Hamal. The blue lines are all great circles, so we just find the one that goes from Deneb to Hamal, and read that true bearing on the rim of the blue template, which corresponds to the horizon as viewed from Deneb, or more generally from the center of the template, wherever it is located.

In this case, we see the bearing to Hamal is about 078 or 079 T, and the altitude (Hc) of Hamal is about halfway between 20º and 25º above the horizon. We know from cel nav that the distance between them is the zenith distance, or  90º - 22.5º = 67.5º, and each degree is 60 nmi, so the GC distance we read is 4050 nmi.

Thus in this example we get from the star finder disk an initial heading of 079 ±0.5 compared to correct value of 078.5 and a star finder distance of 4050 compared to a correct value of 4063.5.

This GC heading is a whopping 30º north of the RL route in this example,  so this could have a major impact on navigation decisions.  We don't care so much that one route is shorter than the other, even when this difference is large as in this case, because we are dominated by wind and rarely can make good such routes. But knowing that 078 is just as good or even better than 108 gives us some freedom in planning what to do in local winds.

In the real world, our initial latitude will not coincide with a template value, so we have to improvise the process.  We will work two examples.

Example 1. West Coast of US at 45N, 125W to Japan 38N, 142E. For this route the GC distance  is 3962.1 nmi, with an initial heading of 300.6º T. This heading is 36.3º north of the RL heading of 264.3.  The GC distance is 247.1 nmi shorter than the RL distance of 4209.2 nmi.

Example 2. Exit of the Strait of Juan de Fuca at 48N, 125W to HI at 21.5N, 157W.  This is a GC distance of 2210.3, which is just 14.7 nmi shorter than the RL distance of 2225.0. The initial GC heading of 235.3º T is 10.9º north of the RL heading of 224.4.

The question is, how close can we get to these GC values using the 8" disk of the 2102-D star finder?  We see the answers in the video below which works these two examples from scratch.

The procedure 

Illustrated in two videos below for Northern Lat departures

(1) On the N side of the white disk, draw a thin line to mark the departure meridian going through 0º on the rim to the center of the centerpin.  Or perhaps easier, draw in two meridians, one from the precise rim location (0º) to the left of the centerpin, and one to the right of the centerpin, and know the proper location is between those two lines.... all done carefully, with a sharp pencil.

(2) Use the red template scales to plot your departure point on the white disk on the departure meridian.  The celestial equator on the white disk is equivalent to the equator for this plotting. It is likely best to use dividers on the red template to get the right lat spacing, and then transfer that to the white disk. All of this plotting should be done as carefully as possible as the scales involved are all compressed.

(3) Figure the Lon difference (dLon) between departure and arrival, and note if arrival is west or east of departure.  If arrival is to the east, the arrival meridian is just dLon to the right of 0º on the rim. If arrival is to the west, the arrival meridian is located at 360 - dLon to the left of 0º. Again, draw in the arrival meridian carefully as noted in (1).

(4) Set dividers to arrival Lat on the red disk and then plot it on the arrival meridian.

(5) Find the blue template with the closest Lat to your departure Lat. Do not put it on the centerpin, but instead move it above or below the pin (keeping the blue arrowed line on the template coinciding with the departure meridian on the white disk) until the crosshair at the center of the blue template is precisely over your departure point.

(6) Then hold the template in place and carefully read the altitude (Hc) and bearing (Zn) to your arrival point, interpolating as best you can. The initial GC heading is Zn; the total GC distance is approximately (90 - Hc) x 60 nmi.

The answer is in Example 1 we get from the Star Finder initial heading of 302 T (correct is 300.6) and distance of 3900, whereas correct is 3962.

The answer is in Example 2 we get from the Star Finder initial heading of 235 T (correct is 235.3) and distance of 2100, whereas correct is 2225.

The two examples above worked on the star finder.

This method of solving great circle sailings basic data (range and initial heading) is not accurate enough for the USCG exam for unlimited masters. Indeed, we show in another article that the only method that works dependably for all exam questions is to compute the solution directly. See Great Circle Sailing by Sight Reduction.

* * * The above method works for distances <5,400 nmi (90º) because that is the span of the blue disks. For larger distances, this is a two-step process starting at the departure, figuring where you end up in the direction of the destination, then starting at the destination, work towards the departure, and measure the full distance.  An example NYC to Hong Kong  (7,000 nmi over the Pole) is online.

* * * Also for some real fine tuning on great circle distances see this note: Great Circle Distance: The Three Options.

Inverse Barometer Effect in Puget Sound

We did this analysis in 2008 and just rediscovered it.  We will come back shortly and analyze a few of the pictures. The effect is clear without actual numbers, but I will add some numbers in the next day or so to compare with the predictions.

There are many factors that can cause the observed tide height to differ from the predicted tide heights found in tide books. Atmospheric pressure studied here is only one, and in many circumstances or regions this is not the most important effect. Wind speed and direction creating unaccounted for wind-driven currents is another factor, as is unseasonable river runoff. 

The effect of atmospheric pressure on water level is called the inverse barometer effect (IBE). Pressure is just the weight of the air above us, so when the pressure is higher than normal, the rising tide has more air to lift and so it cannot lift it quite as high as in normal conditions.  When the pressure is lower than normal, the tide rises higher than predicted, because is has less air to raise than was anticipated.  

We show here that this effect can be observed and anticipated in at least one tide station in Puget Sound, Cherry Point, near Edmonds, WA. The theoretical magnitude of the effect is about 1 cm of tide height for each 1 mb of pressure difference from the seasonal mean. 

The effect was known in the 1800s, often stated as "Fog nips the tide" — which was almost right. It is not the fog, however, but the high pressure that usually accompanies the fog that is doing the nipping.

In the data presented we see both the rise in tide height in lower than normal pressure, as well as the lowering of tide height in higher than normal pressures. This simple theory accounts for the observations quite well, considering the large uncertainties of the model. 

The mean surface pressure in Puget Sound is about 1017 ± 1mb throughout the year. So we have looked at pressure incidents that exceed the mean by ± 13 mb. The standard deviation of the mean in Puget Sound is about 5 mb in the summer (June, July) and about 11 mb in the winter (Dec, Jan). The dates covered are Jan 1 to Oct 26, 2008. All incidents that meet these pressure criteria are included.

The IBE is discussed in The Barometer Handbook See also the long list of related articles on barometry at the support link for that book.

Below we show the data in Part I for all 2008 incidents of pressures above 1030 mb at Cherry Pt, Puget Sound, and in Part II, all 2008 incidents of pressures below 1004 mb at Cherry Pt, Puget Sound. The data are from http://tidesandcurrents.noaa.gov.

Part I High Pressures, above 1030 mb

At the peak, 1036.3 mb -1017 = 19.3 mb difference leading to a height difference of 1.2 ft = 15.6 " = 30.5 cm, so peak effect is about 58% higher than expected, based on the prediction of 1 cm/mb. 

Part 2. Low Pressures, below 1004 mb

Exciting New Barometers for Navigators

Note added March 20, 2024: We leave this article online for historic reasons, but Starpath now has a similar device for notably less cost and notably more features called the Starpath USB Baro.

Barometric pressure remains crucial data for navigation decisions based on the weather. An accurate measurement of the  absolute value of the pressure is needed to evaluate surface analyses maps and hence the associated forecasts. We also watch pressure trends for judging the timing of the forecasts. Indeed, consistent changes of just a few tenths of a millibar can be our first sign that the pressure is rising. This can mean we are getting too close to a stationary isobar, or the High is moving towards us, or the High is building. In any event we can get very early warnings from slight pressure changes that a potentially serious change in our wind is possible—providing we have a good barometer and a good way to watch it, meaning a way to store and display recent values.

Historically, we needed an expensive device to do both things: be accurate and offer a clean versatile display of past pressures, but that is all different now, thanks to Dracal Technologies in Quebec. They have just announced a new USB barometer  that puts out the pressure every second in two NMEA 0183 sentences (XDR and MDA). This data can be read by any navigation program, which in turn will do all the data storage and graphing for us.

No power and no programming required. Just plug it in a USB port and tell your navigation software where it is located. Below is a sample screenshot from OpenCPN followed by one from Expedition. Video links at the end illustrate the set ups.

A Dracal barometer input to a serial connection to OpenCPN, viewed in the Dashboard plugin (comes stock with program) and in the Plots plugin, which is a separate plugin download. The OpenCPN program and all its many plugins are free products for Mac or PC—some of the Mac plugins are not quite ready yet for the latest ver 5.0.  There is a history function in the Dashboard, but it does not have enough resolution to match the precision of this device, hence we need the Plots plugin.  Also, we need to use the outdated MDA sentence for Plots; it will not read the XDR.

A Dracal barometer being read in Expedition using a Number Box and also being displayed in the Expedition app called StripChart, which is a powerful tool for presenting any instrument data.

Calibration offsets

A beauty of the Dracal USB Barometer is its simplicity. There is no interaction with it at all; we count on any manipulation of the output to be done by third party software, in this case the navigation programs, OpenCPN and Expedition, or others.

This device uses a modern pressure sensor, and these have become very good over the years. A new one out of the box, assembled according to instructions, will generally read the correct pressure to within ± 1.5 mb.  If the maker has access to an accurate pressure standard, they can then set the device to a higher level of accuracy.  This also applies to the barometer sensors in our cell phones, which will likewise, out of the box, untouched be accurate within 1.5 mb.  Using our free Marine Barometer app you can then find an accurate reference pressure (explained in the app's help file) and then enter an offset to make the pressure accurate to within a couple tenths of a mb.

The same is true with the Dracal barometer. We can fairly expect that it can be off by a few tenths, which we can learn from watching it, and then we can make the needed corrections in the programs we use to display it.  In expedition, this is done very easily with a digital offset accessed from the main menu/calibrations/baro. In OpenCPN, the correction process takes a few steps. We use the plugin called NMEA Converter, where we modify the NMEA sentence itself, as shown in one of the video links below.

At Starpath we have a full barometer calibration station with pressure control and two NIST traceable pressure standards plumbed into the system as shown below.

We used this system to do a full range calibration of the Dracal barometer, and for the sample we have the results are shown below.

The blue circles mark the calibration points we can enter into Expedition.

This is a very good instrument, with pressure correction varying by just 0.2 mb over the full range of pressures.  Over the typical sea level pressure range of 990 to 1040 mb, the instrument correction is -0.4 mb (it reads slightly too high). Knowing that we can insert that correction into our nav program so we always have an accurate pressure value.  If the weather maps do not agree with our pressure, then the maps are wrong!

Expedition is unique in that we can add a full calibration curve and not just an offset at a single pressure.

I should mention that there is also NMEA 2000 device from another company, Yacht Devices, that works in a similar way, namely plug and play accurate baro sensor. This fine barometer has a lot of extra features accessible from a NMEA 2000 gateway and deserves an article of its own. We are doing first a review of NMEA 2000 (Jan 2020) and then we will have a new article on the YDBC-05.

A hearty thanks to Dracal Technologies and Yacht Devices!  We no longer have any excuse for not having accurate pressure at hand and in our nav programs to view at all times.

For a set of reference articles and links on use of barometers in marine navigation, see starpath.com/barobook.

Video illustrations

Display Barometer with Full Calibration Curve in Expedition

Display Barometer with an Offset in OpenCPN

Assigning O-SENC Charts to a Dongle

The dongle install option at o-charts.org is a revolutionary step in international chart distribution. This note is a text description (prescription) of the process of acquiring these charts and loading them onto your computer. There are several related videos linked at the end.

Notes and steps

(1) O-SENC charts from o-charts.org are vector (ENC type) charts that can only be viewed in OpenCPN.  To learn about this type of nautical chart, see our text Introduction to Electronic Chart Navigation, or see other references listed at the end here.

(2) You will need the latest version of OpenCPN along with latest version of the o-senc charts plugin. We recommend that you copy the program and the plugin to a thumbdrive as a backup to potential need offshore when you do not have internet. (Technically there may be exceptions to needing latest version, but we recommend using the latest version of each.)

(3) It does not matter if you install the plugin first or buy the charts first. You will need the plugin before you can install and view the charts, but you do not need the plugin to purchase the charts. So let's get the plug in first, using the link above.

(4) While you have an internet connection, go to o-charts.org and purchase the chart set you want (ie all of BC Canada for 20 €), and purchase a dongle to be mailed to you (~24 € with shipping)—I think from Spain. The charts purchase and download takes place online, but the hardware will be some days to arrive. You will need to set up an account with o-charts, so recording your login info on your thumb drive might be helpful.

Here is what your account will look like at o-charts after the purchase of one chart set (Poland in this example).

Under System Identifier we see the two allowed slots, but neither one has been used so far.

(5) After you purchased the charts and have your dongle, and have the plugin installed, then insert the dongle and open OpenCPN, then go to plugins and Enable the o-senc plugin, then click Preferences to see the window below.

On first view you will not see the System Identification file (xxx.fpr) showing as it will not have been created.

So first thing is to press the "Create USB key dongle System ID file creation"  button  and then wait patiently a few seconds to let it proceed. In a few seconds a pop up states it is done and the name appears with extension .fpr (finger print) and a copy is saved to the desktop.  Now we are done with this stage, and can close OpenCPN and go back online to o-charts.org.   Note we are not using here the other create button; that is for assigning the charts to this particular computer.

(6) Now we return to o-charts.org, log in and go to our list of o-senc charts as before. This time we will tell the program what the identifier is for our dongle.  The view below shows what we see after the process we describe.

When we first get here, the system info at the top will be blank.  Then follow these steps.

6-1)  Press Choose File, meaning the fingerprint file we created above.  We do not need a name. Navigate to that file on the desktop, till the name shows in the field, then

6-2) Press "Add new system identifier."

6-3) After that is accepted, we will see the dongle id show up below under system identifier. Then Press Assign button, and you will  see possible options, but in this case we have only the dongle so you will see and accept your dongle ID.

6-4) Once you have assigned the charts to the dongle ID, you will get a notice (green above and gray to the right) that the chart order is being processed. You can wait if you like, or close the browser.  In a few minutes you will receive an email that looks like:

This email includes a link to the charts for downloading... or you could return to o-charts.org and now there will be a download link next to your purchase that you can come back to later as needed. It is important to download the charts and save them to a thumbdrive while you have internet connection. The package is way too big for satcom download at sea.

(7) Once you have the charts copied to a computer that is running OpenCPN with the dongle plugged in, just open the charts tab in options, and assign the location of the charts. Always insert dongle before opening OpenCPN.

You should see the green chart outlines showing. If not use the bottom right menu to turn on chart outlines so you can see the boundaries of individual charts.  Then you can shut this off if not needed.  NOTE: this computer does not need to be the one we used to identify the dongle. It can be any computer (mac or pc) running OpenCPN.

Here are a few videos showing this process.

O-SENC 2 of 3. Buying an O-SENC ChartBuying an O-SENC Chart 

O-SENC 3 of 3. Assigning an O-SENC Chart Set to a Dongle

O-SENC 1 of 3. Viewing OpenCPN O-SENC Charts Using a Dongle

Related Articles
    About SENC charts
    Revolutionary nature of dongle distribution

O-Charts.org—Revolutionizing Nautical Chart Distribution

There is a revolution going on in international nautical charting, the significance of which is only slowly being recognized.  I refer to the chart distribution options at

o-charts.org, 

but we need some background to appreciate what is happening. An earlier introduction (Best International Chart Deal Ever) describes the types of charts being offered, but I want to stress now the revolutionary aspects of this program.

That introduction points out we are discussing electronic charts, not paper charts, and we are talking about international charts, not US charts of US waters—electronic charts of US waters are the best in the world, and they are free, not just to American mariners but to all mariners. So they are in a class of their own.

We are discussing charts for all the rest of the world, covering the waters most mariners sail in now and most American mariners want to sail in at some point, at which time they will face, abruptly, the fact that international charts are expensive and in many cases, it is not even clear where to buy them. Again, for background, we are discussing official Hydrographic Office charts, not third party renditions of official charts that may or may not be up to date or even correct in the first place. (One source of inexpensive global charts brags that they make 2,000 chart updates every day!  One of our instructors, after a solo voyage from Portland, OR to Glacier Bay, AK and back, during which he confronted “dangerous rocks” that were non-existent, and other truly dangerous rocks that were not marked, would suggest they are not "updating" often enough.)

So what is the revolution? 

...and what allows this revolution to take place at this time?

The first revolution, as noted in the introduction, is the price. For example, all charts, all scales of Australia for 35 euros; all charts, all scales of British Columbia, Canada for 20 euros, both being a tenth to a hundredth of the price of those from other sources.  These include updates for one year; after which the charts remain active on your computers, but you no longer receive updates until repurchased.

The second revolutionary step is the ease of purchase and installation. This can only be appreciated by those who have purchased, registered, and installed official charts (S-63 format) from other sources in the past. The O-charts procedure is well designed and easy to use, plus they have excellent instructions, including videos and support. The process takes just minutes and is even easier after the first set of charts has been installed. See the O-charts video linked in our Introduction and our new videos below on Use of O-Chart Dongles.

Third, and maybe most notable revolutionary step, is the ability to view the purchased charts on multiple computers using their new USB dongle system. Most sources of commercial charts allow for installation on two systems, where "system" is defined as the combination of computer and software. That is, use them with the same or different nav program on two computers, or two different nav programs on the same computer. After those two installations, the charts cannot be viewed on any other system.  To my knowledge, none of the sources for official charts offer anything like this, nor a way to "un-install" from one computer to free up a new install on another.

O-charts has the same limit of two installs, but they offer the unique opportunity to assign one of the installations to a USB dongle. Once that is set up, the dongle itself is an authorization to use charts registered to it. The dongle does not include the charts; they still have to be downloaded to the computer in use, but when the dongle is inserted you can view the charts. This means you could use the charts on two or more computers that you own, or you could take the dongle with you when sailing on another vessel using its computers. Or you could loan, swap, or sell the charts to someone else if you no longer need them.

If you cared to, you can use both of the allowed installations to go onto two separate dongles. The dongles cost 19 euros (~$25 with shipping to the US), but that could still be a cost effective solution. One dongle covers all charts you purchase.

Why is this revolution possible now?

First, these charts only work on OpenCPN. So, the fact that OpenCPN has matured to the point it has today, gathering support and use by thousands of mariners worldwide, is the cornerstone to the whole project.  There is now a large enough user set to justify the custom licensing, production, and support needed for this chart system. Once restricted to a specific nav program (OpenCPN) the charts can be distributed in SENC format, which simplifies the distribution.

Next, giving up the credential of "meeting carriage requirements" and not referring to these as "official charts" bypasses all the complexities of the IHO regulations on ECDIS, which in turn permits Hydrographic Offices to license the program-specific SENC versions without infringing on their sales and contracts with shipping companies.  Now recreational and smaller commercial mariners can be confident they are using charts equivalent to the official ones, and shipping companies with large budgets and staffs for handling these matters can carry on with their standard system of using "official charts."

The SENC format (called OE-SENC charts) use the same standards for content (S-57) and viewing (S-52) as the official ENC, and OpenCPN does an excellent job in adhering to the primary guidelines of S-52. ENC contain much more information than the corresponding paper charts and RNC, but there is a new approach to chart reading that is required.  Our book Introduction to Electronic Chart Navigation: With an Annotated ECDIS Chart No. 1 outlines the use of these new charts as well as providing a resource for symbols and a catalog of objects and attributes shown on the charts.

What's Next?

At this stage we can only hope that more nations join in to offer their charts in SENC format. There are quite a few which are nicely presented, interactively at the O-Charts website. Central America and the rest of the SW Pacific are notably missing. It will be interesting to learn more of why other charts are not available. If it is a matter of licensing fees, then the more we use the ones available, the more likely the system will expand.  Also, we are  trying to do out part by promoting the use of ENC charts. Our text (cited above) is one step, and we plan a series of videos on the use of ENC.

Related Articles with video illustrations.

    About SENC charts

    Assigning SENC charts to a dongle

Historic note:  For completeness I might add that several proprietary chart providers did at one point, many years ago, use a dongle to copyprotect their charts. This was then not an option; the dongle had to be installed to run them at all, and it was not a way to run them on different computers. It was more a belt and suspenders copy protection that was not at all popular, and did not last very long. The o-charts dongle usage is fundamentally different than these earlier systems.