One Rombe Wrong, and What Do You Get?

In the brand new edition of our textbook Inland and Coastal Navigation, we use throughout what we call the Small-angle Rule. It is an approximation to the tangent of 6º that says the sides of a 6º right triangle are in the relation of 1:10. This can also be scaled up to about 18º (3:10) or on down as low as you like, ie 3º (0.5:10 = 1:20). We use it to estimate DR errors (ie steering 6º off course, you get 1 mile off your intended track for every 10 you sail); to estimate current sailings; cross track corrections; and other applications. We were proud to have made up this convenient formulation that has so many applications, and is so easy to remember.

Last night, however, I got one more reminder that there is rarely anything truly original in traditional marine navigation. There have just been too many people working on it for too long. Rarely is something without precedent; it is just rediscovered or reformulated. And so is the case with our handy Small-angle Rule.

Below is a page of an early textbook with the unusual title M. Blundevile, His Exercises, published in 1594. This is in one of eight sections, called the Art of Navigation, Chapter 37.  (I am crawling through books like this looking for something very specific, and if I find it, you will be the first to know!)

He is here in a section discussing compasses and related position reckoning and wants (as we do) to offer a way to make estimates of errors. This is the time period when navigators were just learning compass use on a global scale (Columbus had no idea how his compass worked on his famous voyage), and taffrail logs to measure distance traveled through the water were first described just 15 years earlier than this book, in 1580. The reference to Mariner's Card, refers to early form of a Mercator chart.

His angle units here are Rombes, which one learns earlier in the book is what we now call compass points.  In fact, it is books like this where we learn where the concept of compass points (11.25º, 1/32 of a circle) comes from. His units are leagues, and since at this time the English were absorbing navigation from the Spanish as they developed their own, he deals with both Spanish leagues (2857 fathoms) and English Leagues (2500 fathoms), but the units do not matter at this point. (England and Spain were  more or less at war during this period, so there was much competition in navigation.)

Below is a copy of his angle rule for DR errors. It is not directly our Small-angle Rule, but the principle is the same. That is, we skip the trig, and give specific values that can be scaled.  Below this picture is the interpretation of what he means.  In short, if you make good one point wrong from what you steered, you will be 19.6 miles off course for every 100 miles you log.

 

After running 100 leagues with a course wrong by 1 Rombe, you will be off course by 19 3/5 leagues.

His Small-angle Rule would then be: Tan (11.25º/2) = [(19 3/5)/2]/100 or 

Tan 5.625º = 0.098

which is analogous to our 

Tan 6º = 0.1

See how much easier it is to navigate now than it was 419 years ago.

Notes on Loran

In updating our new text Inland and Coastal Navigation, 2nd Edition  we finally removed all reference to Loran, though it might indeed be on the uptick in Europe. Here are the notes we removed, which we archive here.

In this section we review other electronic aids that are either new or remain options to small-craft navigation. The technologies are not so far reaching as GPS, but nevertheless impressive in the convenience and precision they offer. Before covering new developments, we briefly review Loran, an electronic navigation system we thought was completely replaced by GPS, but there is now a renewed interest in it, especially in Europe. Keep an eye out for eLoran (e for enhanced).

The oldest of all electronic aids is radio direction finding (RDF), which is covered in Chapter 11 in the High Seas Navigation section. Although this is in an entirely different class of electronic navigation, it will long remain a valuable method to know about since it can be applied with an inexpensive pocket radio using commercial AM radio broadcasts. New high-tech developments in communications are covered in Section 12.16 on Marine Radios.

Loran was definitely on the way out as GPS emerged, but with increased concerns about its vulnerability, Loran is getting another look by some.  It is worth a few notes here for general knowledge. GPS is still cheaper, more accurate, and easier to use, so if you do not have interest in this historical (or maybe future) aspect of navigation, you can safely skip this short section.

Loran is a land-based navigation system operated by the Coast Guard. It has been in operation (with several upgrades) since World War II. It was intended solely for coastal waters, but it has been used extensively and successfully on inland waters for the past decade and was crucial to the fishing industry until GPS came along. The name derives from long-range navigation, which in some senses is an outdated acronym these days.

The system works by determining lines of position from the observed arrival times of radio signals broadcast simultaneously from two stations several hundred miles apart. The lines of position are hyperbolic curves that trace out across the chart the path of all points with the same arrival-time difference between the two signals. The intersection of two such curves (from one master station coordinated with two slave stations) produces the fix. Programming within the individual Loran units then converts this information to latitude and longitude. The precision of this last step varied among the models and manufacturers and from region to region for the same unit.

Regions are covered by separate groups of four or five stations each. The West Coast from Alaska to California, for example, is covered by three such groups. Positions can be determined up to 1,000 miles from the stations, but the stations themselves are often hundreds of miles inland.

Although Loran measures and computes the same things as GPS (position, COG, SOG, XTE, WCV) and uses waypoints in the same manner, there are still very important differences, and these differences are still only slowly being appreciated by new users of electronic navigation. If you know how to use GPS, as outlined above, you automatically know how to use the functions of Loran—although historically the statement should be reversed; all the convenient user interface design applied to GPS was developed with Loran.

But though the outputs are the same, the accuracy of the data and dependability of its operation are different. Loran has, indeed, a high reproducible accuracy (60 to 100 feet), but it has significantly less intrinsic accuracy. That is, if you store a present position as a waypoint and then travel away from it, the unit will guide you back to that precise point very accurately. But if you compared the latitude and longitude of that location read from the Loran with that read from a large-scale chart, you would find the instrument might be off as much as a couple tenths of a mile. This places limits on its use in confined waters and also on the accuracy and immediacy of its derived data, such as COG and SOG.

There are ways around the intrinsic accuracy problem for position navigation, either by relying on repeated routes that have been directly stored when at the site of each waypoint, or by entering fudge factors to offset the errors for specific locations. But there is no way around its influence on COG and SOG, which, again, is the primary information required for careful navigation.

It takes a Loran unit a minute or two and sometimes longer to figure your COG and SOG, because it must average over a longer period to compensate for its lower position accuracy. If you were sailing at a constant rate, in constant current and constant wind for five minutes, then the COG and SOG it shows will be as accurate as that of GPS. But the moment you turn or the current changes, you will get inaccurate readings on the Loran until things have stabilized for a few minutes. In contrast, GPS takes just a few seconds to detect new motion, although even GPS results (without differential corrections) should also be averaged over at least thirty seconds for reliable speed and course information.

Another drawback with the early Loran was its much higher vulnerability to local electromagnetic noise or static. This is not nearly the problem for small vessel use as it is for larger vessels with engines, fluorescent lights, televisions, and so forth, but it still influences operation in some areas because ambient noise levels in the environment outside of the boat depend on location and time of day. Likewise, electrical storms interfere with Loran but have little influence on GPS. There also are other factors that inhibit the use of Loran that can all be traced to the fixed geometry of the land-based transmitting stations. Many of the problems that arise from these factors can in fact be corrected for by user adjustments, but the vast majority of Loran users, on any size vessel, did not get involved in this level of its operation. GPS, on the other hand, provides what most users want—a true black box, with no required tuning or adjustments.

The 2012 Federal Radionavigation Plan does not mention eLoran, but it is much in the 2013 international navigation news and in professional journals. It is definitely something to keep an eye on.

Print-on-Demand Charts and pdf Charts

NOAA has just announced that the federal government is discontinuing printing of the traditional lithographic paper charts in April, 2014. The reasons given include echarts are becoming more popular, and (more to the point) the NOAA print on-demand (POD) paper charts have gained wide acceptance. Agents who can sell both types of charts sell some 80% more of the POD charts than the litho charts, in large part because when they get back to the ship the navigators know the charts are up to date. "Federal budget realities" was also mentioned, but this is not a predominantly economic decision, even though traditional litho charts have been heavily subsidized.

At the time of writing, this transition is still six months away, so we do not know what options will arise between now and then. But is it clearly a change in a direction that could be expected. Many books are now published in this manner, and the percentage grows steadily. As prices go down and quality goes up, even more books will be printed this way. It also has the virtue, similar to nautical chart printing, that even rarely sold books can now be printed and made available without increased costs, not to mention that each printing is the latest edition or version of the book. Only the master file has to be changed. In contrast, traditional book printing yields warehouses full of books, with or without known errors in them.

At present POD charts cost a few dollars more than litho charts (same as in book publishing), but the masters are updated weekly and the charts are readily available. Granted, there are not many authorized sales agents who have the printing capability in house, so we will not have as many places to walk in and buy them, but they can be purchased by mail order or online from authorized agents. Another trend that is not unfamiliar.

We have already taken one big hit in outlets when the printing of nautical charts was transferred to the Federal Aviation Administration in 2000. In recent years, the FAA proceeded to close all but the largest chart agents. This will be another step in that direction. But we still have need for conscientious chart agents who provide advice on selections and who might stock samples of the charts for us to view in full form–or they guide users through the excellent online chart viewers at NOS. Then after selection, they either print the chart on the spot (if they have the facilities) or they order online to be shipped either to the store or direct to the customer. Chart selection is an important part of navigation, so we look forward to keeping the agent support we have grown accustomed to.

The POD chart process has been long tested, but it can still improve, and it likely will. Up until March of 2012, there was only one NOAA-certified print-on demand provider (oceangrafix.com), but now there is also East View Geospatial (geospatial.com), which offers not only updated NOAA charts, but also nautical charts from around the world. These two companies, both based in Minneapolis, MN, have different options and also paper choices.

We will have to see how things develop. For now, one sample of an early OceanGraphix POD paper we tested is not as durable as the litho charts. It definitely tears more easily, but it responds to multiple folds in about the same way. Water runs off this POD paper more readily, but it did not respond well after being wet for a long time. Traditional litho charts, on the other hand, can be soaked in saltwater and wadded up, then dried out and ironed, and they look remarkably good. Neither type of chart likes to be rubbed when it is wet, but this sample POD chart  liked it a lot less. You can easily make smears that obscure the printing. If they get wet they should be carefully patted dry and then let dry thoroughly.

The main difference we detect is how they erase. If anything, they take pencil lines even better than the litho charts, but they do not erase well at all. Normally we recommend not erasing past routes as you might go there again and benefit from your past tracks, but we all make mistakes in plotting, and these mistakes are very difficult to remove on a POD chart. Again, I refer to the present paper in use by just one company. Once POD is the only option, we expect the technology will improve. Or maybe someone will invent a special pencil for writing and plotting on POD nautical charts. East View Geospatial has 4 paper options, and we will test these with a follow up report as soon as possible.

The UK and Canada also offer POD charts, and I understand they have also been well received, and may use a different type of paper.

If you have not used one of these charts in the past, you might find it valuable to buy your next chart in that format to see where we are headed. Maybe try a sample from each outlet. If you really want a set of the latest and last litho charts for your region, you may want to buy them now. There is a chance they have already stopped printing some charts and are relying on existing stock, knowing there is no new edition on the horizon. You can stay informed on the chart news by monitoring the excellent nauticalcharts.noaa.gov website or follow @nauticalcharts.

From a practical point of view for many mariners, paper charts are a back-up to echarts. And it won’t be long until the back-up to an electronic charting system (ECS) is second ECS. NOAA has already begun producing free tablet apps to read their echarts, as well as the GPS and display relevant Coast Pilot data at places of interest. There are numerous commercial ECS apps that do this as well. Nevertheless, mariners are rightfully conservative and do not want to be 100% dependent on electronics, so some form of printed chart will be with us for a long time, and with other new changes at NOAA we have related options.

NOAA now offers free high-res pdf files of the full nautical charts. It is a brand new system and we have to see where this goes as well. But now we have options of our own. In principle we could print our own charts, but large size color printing is very expensive (about $7.25/sq. ft.  or about $80 for a 3 ft. x 4 ft. chart). In lieu of a full chart, we can crop a pdf and just print the part we need. In some cases for local sailing you might need just one corner of the chart. Or print the chart on 11 x 17” paper in sections, and make a booklet.

If you do want the full chart in printable pieces, NOAA has had this option already for several years, though now these are updated automatically, just as the POD charts are. They are called BookletCharts. These are very nice products, and you can print them on letter size or tabloid size (11 x 17) paper and have a nice set of chartlets.

Cover of a BookletChart

Sample page from the BookletChart

On the other hand, if we are thinking of back-ups, then we could use a gray-scale print, and these are more like 75¢ per sq. ft.. A gray-scale  chart would be about $9, much less than they are now in color (about $20). This would not be a good choice for routine navigation, because so much information is in the color, but it would serve as a back-up.

Once we do print our own charts, or buy some that we do not want to replace with every new edition then we should look into the process of updating the charts ourselves. Recreational vessels have this option, but some commercial vessels are required to carry the latest edition, and needless to say we recommend using the latest editions or updating if not.

This is an easy process. The corrections are all online, and well organized by chart number–and by chart edition, if you have to go back several editions. There is also an option to print out a text list of the corrections that you can take with you if you don’t get to the updates before departure. Normally it takes just a few minutes to update a chart from one edition to the next, which is a big savings, and a worthwhile exercise. The more you get involved with the charts you use, the better off you will be when you need them.

The changes listed in the above link are all those made since the last edition. They are incorporated online weekly into the latest pdf or POD chart; they just do not appear on older editions. The changes listed are called critical changes, which relate to safe navigation. New editions, when offered, will also include the accumulated non-critical changes, such as newly surveyed shoreline boundaries in non critical areas, new structures on the land, soundings in non critical areas, or maybe slight compass rose adjustments, and so on.

Sample of chart corrections.

Checking your Compass with the Sun

We have just added this new section to our training materials, which we post here for feedback and comments.  Earlier sections of the text addressed compass checks by simply swinging ship promptly and watching that the shadow bearing does not change. Here we expand the use of the sun with a more versatile and accurate method.

The sun method just described uses several approximations and also calls for changing course to make the checks. Often we are underway and just need to be sure the compass is right on our present heading, and then we will worry about other headings when we can. This comes up, for example, in an ocean yacht race, where some doubt about the steering compass might arise because the electronic heading sensors are reporting other headings; in a race you do not want to stop and swing the ship.

But we do not have to. Here is a quick and easy solution that you can use in the ocean or in your local lake. We are relying now on celestial navigation in a sense, but we do not need any of the details if we are on land and have access to the Internet.  We just assume if you are in the ocean, you have the full tools to solve this with conventional cel nav methods.

We start with the measurement of Figure 12.9-1 where we learned that the compass bearing to the sun was 135 C when the vessel was headed 000 C. Note that this heading does not matter for this application. We just happen to have a nice picture with the compass in that direction. For this method, you measure the sun bearing on whatever heading you happen to be on.

Figure 12.9-1. Reading the sun’s bearing form the reciprocal of the shadow pin bearing. Here the shadow is at 315 C, so the sun’s bearing at the moment is 135 C, when the vessel was headed 000 C. From convenient resources on line we can determine the true bearing of the sun at this time, and from this and the known variation for our location we compute the magnetic bearing of the sun. The difference is then the deviation of the compass on our present heading.

But we do now need more information. We need to know the time accurate to within a minute or so, and we need to know our location. Both you can get from the GPS. Now we need to look up or compute what the true bearing of the sun was at this moment based on cel nav principles, or we just go online and look it up.

Go the starpath.com/usno for a quick link to the right place at the US Naval Observatory. Then type in the time of the bearing and your Lat-Lon. As example is in Figure 12.9-2, which assumes we were headed north in Chesapeake Bay on Oct 14, 2013, and we recorded the bearing at 0930 EDT, which is 1330 UTC.  The true bearing to the sun at the time was 123.5º.

Figure 12.9-2. Data from the USNO. The true bearing of the sun (Zn) is 123.5º at 0930 EDT from this location in Chesapeake Bay, VA. We also see that the height of the sun at this time (called Hc) was 24º 29.5’ above the horizon, along with other data we are not using. We can convert this true bearing to a magnetic bearing using the local magnetic variation

Next we need the local magnetic variation which we could get from a chart, but for this type of precise compass check we might want to go back online and get the most accurate and up to date value. This you find at the National Geodetic Center (ngdc.noaa.gov/geomag/geomag.shtml) for specific times and locations. For our example time and location the correct value is 11º 05.3’ W, or about 11.1º W.   

Input screen for online GeoMag. Note you can download a Windows version of GeoMag for your own computer if you like. It makes a nice backup underway. Note too, land navigators call variation "declination," but this is never done in marine navigation, because we have other meanings for that name in marine navigation.

Output screen from online GeoMag

So the proper magnetic bearing of the sun is 123.5 + 11.1 = 134.6 M. The compass showed 135 C, so the deviation on heading 000 C is -0.4º which would be called  0.4º W.

We  have learned that this compass is essentially correct at this heading, as it is difficult to be confident we have read the shadow bearing to this precision. But the main point is, this method has no other approximations in it. The result you get is as accurate as you can read the shadow bearing on the compass card.

This is a very powerful method. It would be instructive to try it once or twice whenever you see a nice shadow on your compass card, no matter where you are.  Just write down the shadow bearing, the time, and the location, and your actual compass heading at the time. Then you can check the compass for that heading when you get back home. If convenient, record the data headed roughly north or south by compass and also roughly east or west by compass, and then you will have a pretty good analysis of your compass with a few minutes of paperwork at home.