Piloting Practice with Geocaching — You Can Do It Online

The hobby of geocaching has been popular for many years now. In its simplest form, you hide a small container with a logbook in it, then post the GPS coordinates of the cache where interested parties can see them. They then go and find it using their handheld GPSs along with whatever hints or riddles you provide, sign their name in the logbook, put the cache back where they found it, and then post that they have found it. There are many nuances and variations to the process; it is a much more dynamic and engaging activity than that simple description might imply.

It turns out that the world headquarters for this activity (www.geocaching.com) is just a couple miles from Starpath HQ. Their office overlooks Lake Union in the Fremont area of Seattle. This is a  successful business;  there are over 6 million geocachers worldwide, many of whom pay $30/yr for special access and features online, and many must want their excellent $10 app to facilitate the searching and recording. There are numerous other apps from other companies to facilitate the sport. There are more than 2 million registered caches worldwide to be found and logged. The reason the business is so successful is the participants get their money's worth and more. Even those who just do it for a while and quit, do not mind the fees. They have had fun and they learned something. Most members are devoted to the hobby and get much enjoyment from it. For many it is a key part of their social life.

It is also a fine example of American entrepreneurship in that the company was started from scratch by a couple young friends with an idea, along with the skill and determination to organize, promote, and manage the operation so it could achieve the outstanding success it has. Now with such good resources, they have topnotch software and services and they have established a set of rules that can preserve their image of the process in light of many challenges.

In the Age of GPS, this seems a natural pastime. You cannot do it without learning how to optimize your GPS work. We often get to remind even seasoned navigators about the conversions shown in Tables 1 and 2. You won't get far in caching without knowing that 0.001' of Latitude is about 6 ft, and likewise that this is not true for Lon––that is, assuming you do not have an app that does all the computations for you, which is bound to hamper the will to learn the basics.

 

Table 1. Latitude Increments
Latitude Minutes	Approx. Feet
1.0'	6000 ft
0.1'	600 ft
0.01'	60 ft
0.001'	6 ft
Latitude Seconds	Approx. Feet
30”	3000 ft
20”	2000 ft
10”	1000 ft
5”	500 ft
1”	100 ft

 

Table 2. Longitude Increments
Latitude N or S	Feet per 0.1' of Longitude
0º	608 ft
10º	600 ft
20º	572 ft
30º	528 ft
40º	467 ft
50º	392 ft
60º	305 ft
70º	209 ft

Furthermore, a commonly reported GPS uncertainty is 5 m (16.4 ft), which also teaches us something: the uncertainty is not necessarily the error. More often than not, you can home in on a target well within the reported uncertainty. GPS positions will scatter about the indicated position with some standard deviation. A good way to study this is just park your GPS linked to an echart tracking program and let it sit overnight. You will get something like what is shown in Fig. 1. Modern handheld units include an option to average the position, even reporting back to you when they have a good fix. It typically takes just a few minutes.

( For those new to echart software, we have a list of free viewers to check out. You can then connect your GPS to one of them for such tests. )

Then do the exercise at home with the GPS facing a window with limited view of the sky. The pattern will be different, and larger, and take longer to home in. The significance of that observation is when you are outside you may still  have part of the sky blocked off.  Just standing next to a big tree could matter, or in a valley, or boaters in a deep fjord. There are a lot of satellites and the units are better and better every year, but this is still something to have in mind at all times.

Fig. 1. Two 30-minute GPS tracks from stationary receivers. The red track is taken with good reception (Fig. 2) with the GPS located where word “Chair” is shown. The green track taken from a desk inside the building (about 30 ft NE of the word “Chair” viewing satellites through large windows.  The yellow line is 100 ft long. In both cases the true positions did not coincide with the centroids of the track patterns.  These patterns change with time as  available satellites and the angles to them change with time. The arrowheads indicate the COG (of the random motions) at the time the tracks were interrupted. Another example is shown at the end of this article.

Figure 2. GPS status information for the tracks in Fig. 1. Top is the status at the end of the good reception (red track) run; bottom is the start of the poor reception run (green track). This display is from the XGPS150 BlueTooth GPS, which pairs with  iOS, Android, PC, or Mac devices.  The status information was read in an iPhone app; the tracks were accumulated in OpenCPN for the Mac, and then exported as gpx files and displayed in Google Earth.

In some circumstances, however, the center of the distribution is not the true location, althrough the true position is usually within range of the displayed accuracy if it is stable long enough. I will come back to such nuances of precise navigation with consumer-grade GPS units in a later article.

When tracking down caches you also very quickly learn the limitations of the compass apps in mobile devices. These are still very sensitive to horizontal alignment as there are fixed coils in them that measure the strength of the magnetic field components, and this field is not parallel to the surface because of the dip angle. But with practice we can learn how to use them. Most mobile-device compasses have self-correcting procedures to adjust for local disturbances, but this does not address the alignment issue.

True versus magnetic is not an issue, because they are sitting right next to a GPS. They know where they are so they can compute the magnetic variation very accurately. They all use a program called geomag, which you can download and put into your own computer if you like, which is a nice back-up if you get stuck with old charts at high latitudes (www.ngdc.noaa.gov/geomag).

From what I have learned of geocaching, it seems to me this is an ideal way to practice marine piloting. First to fine-tune the use of GPS, which might include learning more about what satellites you are using, and when to expect better fixes when the present ones are not so good (66-ft uncertainty vs 16-ft, for example). Are you next to a bluff in your boat, or between skyscrapers downtown? It will show the value of having a display of the satellites in view and how to interpret it (figure 2), and how to anticipate when this will change. If you are in a real bind, ie traversing a narrow fjord with just a sliver of sky, there are handy free apps that predict satellite passes for your location, with the altitude and bearing of each as they pass. These apps are also useful for predicting the next Metop-A pass for satellite wind data. Check your AppStore for a slick free one called Satellite Tracker by MacCon.

You can also get practice sending yourself gpx files. This format is the best way to transmit waypoints, routes, and tracks from one device to another, or to Google Earth. There is a neat utility online to help with this at www.gpsvisualizer.com. (We have discussed this utility earlier here and also here.)

The main geocaching goal for mariners, however, would be to go on and practice the more sophisticated piloting skills we teach in the classroom. These days, it is only the conscientious navigator––we would say prudent––that takes the time to learn the old methods of navigation, so they are not dependent on the GPS, but there is plenty of evidence that this is worthwhile.

Beyond the basics like crossed compass bearings and the use of natural ranges, we can really home in on our position using a simple plastic sextant that costs less than $50. Few navigators and geocachers realize that you can pinpoint a position on a chart much more accurately with a sextant (essentially the same as used in the 1700s) as you can with the latest handheld GPS. There is a detailed explanation of the methods in the book  

Howto Use Plastic Sextants––With Applications to Metal Sextants andA Review of Sextant Piloting. 

Your accurate position is determined by the two horizontal angles A-B and B-C between three objects (A, B, and C) on the near horizon. These two angles are essentially the differences in the bearings to the objects, but the sextant angles will be far more accurate than bearing differences. Once you have these measurements, you need a large-scale chart that shows the three objects on it, and then there are several ways to solve for your position.

The simplest is to use a three-arm protractor, which is designed to solve this problem. Inexpensive plastic ones are available. Set the two angles on the protractor and move it around the chart until the three index lines cross your three targets, and you are located at the hub of the arms. Alternatively, you can draw the two adjacent angles emanating from a single point on a piece of clear plastic (overhead projector sheets, if you remember such things). Then slide that plastic around on the chart until the three lines defining the two angles each cross one of your targets. The Plastic Sextants book also describes plotting procedures that can be used without the need for three-arm protractors or transparencies, which can enhance the accuracy.

Line of Soundings Navigation

Another advanced skill of marine navigation that you can practice on land is depth-contour navigation. In the fog with no GPS, you sail on a steady heading and record the depth at several log readings. Then on your chart highlight a few of the depth contours in your approximate region. Then plot a line on a piece of transparency and using the same distance scale as your chart, mark off the logged runs between measured contour depths, corrected for tide and draft. Then slide that sheet over the chart keeping the line oriented in the heading you were sailing until you find the place where you cross the contours at the right rate. In many cases you can get by with a roller plotter and dividers, without the transparency. If the bottom is not flat, nor water too deep, this will often locate your position.

To practice on land you can use elevation contours, replacing the depth sounder with a good digital barometer. You do need an actual barometer, however, because GPS elevations reported are not accurate enough for this. Some GPS units and some smart phones have barometers in them, which should do the job. You must always normalize the pressure reading at some known elevation to account for the atmospheric pressure.

Both of these exercises can be practiced online, without getting up from the desk! Google Earth shows both precise locations as well as digital elevations (but no contours). You can also drop a pin at locations of interest so they will show up when you print the screen to make your chart.

For the depth-contour exercises, it is best to use the USGS National Topo Viewer (viewer.nationalmap.gov/viewer), again zooming in on what you need and plotting out a chart. Check out all the tools options for measuring distances, spot elevations, and so on. It will help ID the contours and distances between them. Google Maps has a terrain view that shows some contours, but nowhere near as good as the USGS Viewer.

Practice with Horizontal Sextant Angles

(1) Just west of Newport, RI, start at 41º 33.516’ N, 71º 26.852’ W. What have you found? Are there more of these (whatever they are) to the south? (Note this is a very precise starting point.)

When you are standing at the cache, the angle between this one (#1) and the next one to the south (#2) will be 30º 36.0’, and the angle between that #2 and the next one to the south (#3) will be 24º 18.0’. Use the base of the objects for the target. Where is the cache?

(2) Now with same targets, use 1 to 2 = 22º 16.8’ and 2 to 3 = 24º 24.0’. Now where are you?

(3) Finally, use 1 to 2 = 21º 47.4’ and 2 to 3 = 25º 41.4’. Again where are you?

In these last two examples you are finding locations that are less than 10 ft apart, and these angles viewed through a sextant are huge differences. A handheld GPS would rarely be able to pin point a location to this precision.

Practice with Line of Soundings Navigation

(1) Here is an example of depth-contour navigation. You are walking (sailing) somewhere in Central Park in NYC, and you measure the following elevation (depth) records on heading 298T on a leg that is 0.436 nmi long. Where are you located when your barometer (depth sounder) reads 88 ft?

 

Log (nmi)	Run (nmi)	Run (ft)	Elevation (ft)
0.000	0.000	0	80
0.172	0.172	1045	70
0.211	0.039	237	70
0.267	0.056	340	80
0.376	0.109	663	90
0.417	0.041	248	90
0.436	0.019	115	88

As with marine navigation, step one is identify the contours. You know the answer is just downhill of 90 ft and you were at 90 ft for a distance of 248 ft. Find where there is 0.267 nmi between 80-ft contours on heading 298, or use other patterns.  

To work this online, it is important to use the nationalmap viewer referenced above. It has many layers that let you measure specific elevations and the distance between them. There is a bit of a learning curve on their site, but well worth the effort.  Or just find any detailed view of the contours and print them out and work it by hand.

If you do soundings exercise like this just once, you will forever be a better navigator. You may not have call for depth sounder navigation very often, but when you do need it can save the day and you will be prepared.

Click here for the  answers to the above exercises.

Below is another example of a GPS running overnight with positions stored. In this case the positions were from a Yellow Brick tracking GPS and the results were posted online automatically.  The unit was left on by mistake on a hotel room deck in Snug Harbor, BC at the center of the distribution.

Wind Near Clouds

A topic has come up in our weather course that deserves extra information having to do with oscillating wind shifts.  We will address this issue more specifically shortly, but for now we need to show a couple pictures and give some references.

It is a safe assumption to expect the wind to shift when a large cumulus cloud goes by, especially with relatively low base.  We do not mean squalls. We have much written in our weather book and radar book on winds near actual squalls, before and after downburst.

The point we make now is this wind behavior on a smaller scale can also be seen under fair weather cumulus. It is especially important for sailors when there is a symmetric pattern of the clouds passing over, or a sequence of them in a line... and especially important in a yacht race, in the ocean or on a large inland lake.

A general rule easy to remember is the wind will shift when one of these clouds goes by. Predicting the shift is more involved, but a related pretty good rule is if the cloud is not raining, it is pulling the wind into it. That is, biasing the ambient flow toward the cloud. But the final surface wind is a vector combination of cloud wind and ambient wind, and thus the complication.

For now let us just give a couple references, and we will add more discussion and more references as soon as possible.

See Chapter 8, Winds near Clouds, in High Performance Sailing by Frank Bethwaite. Below is a picture from that book.

Another good reference is from a similar book by C.A. Marchaj, called Sailing Theory and Practice and a couple sample images from Part IV, Wind and Water, section (3) Local Wind.

These are not books one might have turned to for weather tactics, as they are  mostly concerned with yacht design, but they are both excellent texts on many aspects of sailing, and since the authors  are engineers as well as sailors, they use real numbers, which are often missing in sailing books.

Another discussion of this effect is in another excellent book for sailors called Weather at Sea by David Houghton and Fred Sanders.  I am pleased to thank them for the acknowledgment they included for the small contribution we made to the 1988 edition.  Below is their graphic of this effect.

Again, I will return to this topic as time and student interest requires. But the above pictures are the hints, and then just imagine a row of these clouds going by that you have the option to choose a route though.  Somewhere in our notes we have such a picture made and we will look for it.

I have seen such patterns in the trade winds and it was quite remarkable how predictable the shifts were in direct correlation to what we could see over head.  I have also seen prominent effects of a single low cumulus cloud while sailing in Lake Washington, here in Seattle.

Molasses – The Eatable Artificial Horizon

A plate of molasses as an artificial horizon for sextant sights. To get an optimum height, we use a box on the stool for coarse adjustment, and fine tune with some random book. The plate only has to be level enough to keep falling off the box.

 The nice thing about using a plate of molasses for an artificial horizon is if you spill some you can just lick it up.

After a week or so it firms up a bit more than you want, so just put a teaspoon of water on the surface and put it in the microwave for a minute, and you are good as new.  We have used the same plate of molasses for several years!

Molasses is thick enough that the surface is not affected by a light wind, which would render a water surface useless.  Some use thick dirty motor oil, but we have already pointed out why molasses is better than that.

We explain the nuances of taking sextant sights with an artificial horizon in our text How to Use Plastic Sextant – With applications to Metal Sextants and a Review of Sextant Piloting. 

This book is available as an ebook for $5.99. 

The title of that book, by the way, is a bit misleading.  It covers the best ways to take sights with all sextants, metal and plastic. It is just much more important to do it all right if you use a plastic one. Following the methods of that book, you will get usable and dependable sights from plastic sextants.  Following the same techniques with a metal sextant will reduce the scatter in your data and lead to optimum results possible from cel nav.

The Celestial Sphere. May It Rest in Peace.

Our goal is to teach practical navigation in a manner that is both functional and understandable. We want students to know how to do it, and why it works. This means we do not include formalism that is not needed to understand how something works and how to apply it, and we very especially do not cover topics that do nothing but obfuscate the subject, no matter how ubiquitous the terms or concepts might be in the standard teaching of the subject.  In fact, we don't even use words like "obfuscate" and "ubiquitous" in the classes.

Celestial navigation has a couple real dillies that must be shot down and stepped on immediately if they ever come up in class. I will tell you a funny story about one of them, the celestial sphere.

Poor navigation teacher having to haul around the celestial sphere.
Break your chains. Throw it out.

This topic did indeed come up today in class, so it gets immediate attention.

In about 2005, I was invited to give a lecture to the first ever graduating class to receive a BA degree sanctioned by the state of Washington with a major in Astrology. (The state approval of this degree was one of those rather momentous events that no one hears much about in the news–like when Canada gave back Nunavut to its native owners.)  The degree granting agency was  Kepler College, who had rented space for this training at Bastyr Univesity campus. Bastyr is one of the world leaders in natural medicine, and have no relationship at all to astrology that I know of. They do have a beautiful campus;  I have attended seminars there on various subjects unrelated to natural medicine.

It was a class of about 30 students, just a course or two away from graduating with what has become an even more unique degree. The WA state sanction did not last long beyond that first crop of students.

My job was to discuss how celestial navigation works. We have a more or less standard way of explaining this, but I assumed these folks had certainly been involved on some level with positional astronomy, so I mentioned in passing what are called celestial coordinates (equivalent to latitude and longitude on the inside surface of the imaginary celestial sphere), and how we do not need to concern ourselves with them if we want to know how the stars move around the sky.

Then there were a few notable chuckles coming from the class, which made me pause, and repeat my self more emphatically....out right saying what the celestial sphere was and how useless it is, and how it will only cause confusion in your learning celestial navigation. It provides nothing you need, and makes it harder to understand what you do need.

At that point the real belly laughs got rolling, and the whole class was involved.  Which in turn was obviously also funny to me, but I had no idea what we were laughing about. Maybe I had a wardrobe malfunction?  So I asked them what was so funny?

"We just spent three full days on the celestial sphere," was the answer.  It would have been an awkward moment if it was not so funny. So I joined them in the humor of the situation, and had to confess that they must need that for something else they are doing.... but you still do not need it for celestial navigation, and carried on with the story of how it works.

It must be true then that not just astronomers but also astrologers use the celestial sphere, and sure enough most cel nav books start right out with a discussion of it. But all that time is wasted. We do not deal with navigation in the sky, we navigate on earth, and all the coordinates that might be used in the sky to describe the location of a star, have a counterpart on earth that is much easier to comprehend and thus use in our work.

Instead of referring to the position of a star as located on the inside of some imaginary glass sphere in the sky (sometimes described as having infinite radius; a nice concept to work with!),  we can think of the location of the star as its geographical position (GP) on earth directly below the star, ie the point on earth where the star is precisely over head.... for a moment. The earth is rotating (360º of Lon per 24h), so the GPs of all the stars move west along the surface of the earth at 15º of Lon per hour.

The latitude of the GP is the declination of the star; the longitude of the GP is the Greenwich Hour Angle. We do not need to think of declination and Greenwich Hour Angle as coordinates in the sky; they are perfectly good coordinates on earth.

In fact, this is even a preferred way of discussing where stars are. If you are in Washington on the phone with someone in Florida, you can still say with perfect clarity where the star Vega is located at the moment. You simply tell your friend the lat and lon on earth where the star is precisely overhead at the moment–its GP. You can't for example say the star is NE about 35º high; that will be totally different in WA and FL at the moment, but the lat and lon of GP on earth is unique for that time and star. We do not need abstract coordinates on some imaginary sphere that does not rotate to understand where stars are and how they move. We put them on earth and let them move in a perfectly logical manner. Due west at 15º/hr, locked onto their unique constant latitude track we call their declination.

In the typical cel nav text book it then just gets worse once this sphere appears. Then they start projecting various planes cut across the sphere, with the same planes on earth intersecting those, to end up with a massively confusing way to explain that the earth's axis is tilted 23.4º from the plane of its orbit. Then a few more planes and circles and arcs are added, and it becomes pure gibberish.

The motion of stars,  apparent motion of the sun,  definition of the tropics, and anything else we need to know about the motion of celestial bodies can all be explained perfectly clearly without the celestial sphere. Everyone can understand that the Big Dipper rotates around the Pole Star once a day without a celestial sphere.  Let it please rest in peace.

Here are some samples. Hard to tell what they mean.

These are random pictures found online.  When I can, I will post actual pictures from cel nav textbooks.  They make my point much better.