Telltale Article - by George de Witte.

This article is partly inspired by a comment in the previous Telltale (Newsletter of the Nepean Sailing Club, or NSC) that sailors cannot find their way home in the dark and also by questions that I have been asked around NSC re GPS.  The truth of course is that with a simple $200 handheld GPS receiver any boater can find their way around their local sailing area or the oceans of the world. One of the great contributions of President Clinton is that he ordered the US Department of Defence (DoD) in 2000 to turn Selective Availability (SA) off. As a result any basic GPS receiver now has an accuracy of around 15 meters, good enough to find any buoy or harbour entrance in the dark.  Prior to 2000, SA which is a form of classified scrambling of one of the GPS codes, reduced the accuracy to around 300m for civilian users, which is ok if you are crossing an ocean, but not so great if you trying to find your way into a narrow reef entrance.

You may have seen refinements to GPS like Differential GPS and WAAS, but they are really overkill for the cruising sailor. But it is interesting to know that professionals in the land survey or seismic research can get positional accuracy with the right hardware and software down to the mm range.

Principles of GPS

It is always useful to have a basic understanding of the systems you are using on your cruising adventures. So here is a short summary of how GPS works.  The system is operated by the US DoD and was initially intended for location positioning for military operations. It consists of 21 satellites which orbit the earth at 20000 Km height. The satellites are non-geostationary, which means they constantly move as observed from a fixed point on earth. The orbits of the 21 satellites are arranged such that at any point on the ground at least 4 satellites are visible at any time. Fig 1 shows how the 21 satellites orbit the earth.

Each satellite transmits 2 beacon signals: one at 1575 MHz and one 1227 MHz. These frequencies are considered as microwaves by radio engineers. The significance for you the sailor is that microwave propagation requires line of sight. In other words the GPS receiver antenna should not be blocked from “seeing” the satellites by metallic objects. You should know that radio waves quite happily propagate through fibreglass and wood, therefore there is no compelling need to have an external antenna for your below-deck GPS receiver.

On board of every satellite is a very accurate clock: a so called atomic clock. It is the same type that the National Research Council uses for their web clock and it can keep time to fractions of a second per year. The time signals of each satellite are coarse encoded on one beacon signal and precision coded on the other beacon signal. Since radio waves travel at a well known velocity (300 000 Km/s), time differentials between satellites and the GPS receiver can therefore be turned into distances. Et voila if you know the distance to four visible satellites, each with a known position in space, you can compute with a little bit of geometry the position of the GPS receiver.

The beauty of the GPS system is that it can update position information at a rate of once per second. From this “position-on-the-fly” capability, the GPS receiver can readily compute 2 important parameters: Speed over Ground (SOG) and Course over Ground (COG). Needless to say since the whole system is based on time measurements, the GPS can also be used to derive absolute time and you can synchronize your watch to the time zone of choice.

Course over Ground (COG)

If you ever took a navigation course you were told that your target compass course had to take the following corrections into account: 1) compass deviation 2) compass variation 3) tidal currents and 4) leeway for a sailboat.  Well that takes the fun out of recreational sailing. But it can be deadly serious. For instance when we crossed the Gulf Stream from Miami to the Bahamas, the Gulf Stream was assumed to have a current of 3.5 knot and our boat speed was assumed to be 5 knots. This will put you 35 deg off course. However by monitoring the COG on the GPS, we could constantly verify if we were on the intended track. So in summary COG is exactly what the English words imply and includes the offset due to all known and unknown forces on the boat. Read this again because I know at least one sailor with Atlantic crossing experience, who was still confused by this concept.

Speed over Ground (SOG)

Since speed is defined as distance divided by time, the GPS receiver can readily compute speed. This has to be Speed over Ground (SOG), since that is the only information the GPS can work with. On a boat the SOG has a couple of applications. First of all if you are on a lake with no current you can calibrate your knot-meter against the SOG. If you are on a river try to average the current by making a run with and a run against the current. In my estimation the Ottawa River has a current of app 0.2 to 0.3 Knot, which you may or may not find significant. The second application is an indirect calculation of a serious tidal current. For instance when we entered St Mary’s inlet in Northern Florida, the knot meter read 5.5 knots while SOG read 2.0 knots, in other words we had 3.5 knots tidal current against us. (A little later we also had a nuclear sub against us, but that is a different story). So the SOG is very useful in deciding to wait for the tide to turn or persist and go to sleep a little earlier.

Distance to Waypoint (DTW) and Bearing to Waypoint (BTW)

From nautical charts you can determine the Latitude and Longitude of any significant navigation target like a buoy or a harbour entrance. Even better most modern chart books and cruising guides have crosshairs on these targets and the Lat and Long are listed in the margins or somewhere. These coordinates can be entered into a GPS receiver and are commonly called waypoints. Since the publishers have checked all these waypoints with a GPS themselves, they are amazingly accurate. So you are no longer relying on 19^th century technology of Royal Navy chart makers. Once these waypoints are entered into the GPS, of course Distance-to-Waypoint (DTW) and Bearing-to-Waypoint (BTW) are readily computed by the receiver. Navigation has never been simpler.

My only caution is double-checking waypoint entry when using Government Issue charts. They don’t feature listed waypoints and you have to determine them yourself with dividers and the Lat/Long coordinates along the side of the chart. Our trip south nearly had a premature end off the New Jersey coast, when we almost hit an underwater jetty in the middle of the night. Has to do with longitude increasing going westward in that part of the world.

Anyway at this point I think I have resolved the issue of night sailing on the Ottawa River. All you really need to do is enter a few waypoints like Aylmer Island, bifurcation buoy KNB and the NSC Harbour Entrance and you can safely find your way home.

Most GPS’s also allow you to create a route in which you can programme the GPS to go from waypoint A, to waypoint B, to waypoint C etc. My buddy Dave calls this irreverently “connecting the dots”.  But you have to admit it is too easy for words. It always reminds me of Georgetown Harbour in the Exumas. (Bahamas). The entry requires a number of interesting doglegs and missing the dots means a sudden stop on one of the many reefs. Well the chart book conveniently lists all the dots and the GPS guides you home with the least bit of stress, which apparently is bad for your health.

Cross Track Error (XTE)

 XTE is defined as the distance between your target track (waypoint A to waypoint B) and you actual position. Refer to Fig 2. Why is this significant? All GPS receivers can be connected to an Autopilot via a standardized interface called NMEA. And it is the XTE parameter that the Autopilot uses in order to keep the boat on its target course. In other words the Autopilot constantly tries to keep the XTE to zero.

This is extremely convenient, because you can now (with the Autopilot in track mode) let the GPS worry about things like current offset and leeway. Read this again. You do not have to worry a thing about subtle navigational issues like offsets. The GPS works it all out for you and “guides” the Autopilot to take you from Waypoint A to Waypoint B. This concept that the XTE drives the Autopilot in Track Mode is very important. When I initially installed the system I thought naively perhaps that once the Autopilot is put in Trackmode it will take you to Waypoint B since the GPS knows the bearing to the waypoint. However this is not how it works and if the XTE is large because you have been sailing awhile in manual mode without paying attention to XTE, the Autopilot can do wild things if suddenly you put it in Trackmode. How wild depends on the sophistication of the software in the Autopilot: good software will flash a warning (Large XTE) and hold course, bad software will make an abrupt turn towards the target track.

From a memory lane point of view, we actually made the Georgetown Harbour entry with our hands in our pockets while saying kind things about Otto the Autopilot (who was using the GPS as his mentor).  On our local waters of course you can find your way from Constance Bay to the NSC Harbour entrance with your hands in your pockets assuming you have stored the right collection of waypoints.

Velocity Made Good (VMG)

Racing types on their way to the windward mark are of course always trading off pinching and off-the-wind speed. In order to tune their boat for optimum windward performance, racers can use the Velocity Made Good (VMG) parameter that the GPS can display.  The concept of VMG is best understood from Fig3. A boat is beating upwind from the Leeward Mark to the Windward Mark. The component of the actual SOG that results in progress towards the Windward Mark is defined as the VMG. Since the GPS knows in real time the SOG, COG and BTW, it can determine VMG in real time.

Thus the serious racer can calibrate the windward performance of his/her boat by recording the VMG for a range of close-hauled angles, say in the range of 30-45 degrees depending on the boat class. Of course, this needs to be done when the wind velocity is essentially constant.

Summary

With the right equipment you can finish your evening dinner in your favourite anchorage at your own leisurely pace and still make it home to the harbour safely in the dark.

I know that Gene the club manager will write me immediately that all the above is balderdash, because he put navigational lights on the bifurcation buoy KNB and the harbour buoys. Well Gene there is an old expression: “You can tell the men from the boys by the price of their toys”