GPS

For Christmas 2008, my family gave me a Garmin nüvi® 260W GPS (Global Positioning System) device. Although I had known about the existence of the satellites which make GPS possible, had seen a couple of GPS devices in the flesh (one on a lobster boat), and had rather cursorily followed discussion and reviews of them in various Mac-oriented mailing lists, this gift was my first real exposure to GPS. Rather a bit skeptical at first, the device, which I have named Griselda, has become much more useful to me than I would have ever believed, though not without some serious quirks.

I am not competent to discuss the technology underlying GPS devices: see the “Basic concept of GPS” section in the Wikipedia article for a basic introduction to GPS intended for non-technical readers, which is followed by a much more complete presentation, still surprisingly accessible to a non-mathematician like myself.

But regardless of how it actually works, a GPS device delivers the coördinates of its current location as a latitude (distance north or south of the equator measured in degrees) and a longitude (distance west or east of the Greenwich (England) meridian (“prime meridian”), also measured in degrees). In consumer GPS devices, such as the nüvi®, that location is typically shown by a symbol (car, arrow) superimposed on a map of the current location; as the device moves across the surface of the earth, the map beneath the symbol moves in real time, keeping the symbol centred on the map. In this way, the device allows one to visually ascertain where one is at any given moment in time (usually, of course, one knows, but occasionally, in a strange city, for example, the visualization can be very useful). Most such devices can compute a route from one location to another and provide detailed turn directions as one follows that route. Most also allow one to record locations (“waypoints”) as one moves about and nearly all are capable of recording a trip log over a period of time; in the past year, I have begun to explore the tools that allow such a trip log to be plotted onto a map, very useful, for example, for showing the route of a hike, as here. The latest version of Google Earth is capable of importing a trip log and showing it on the Google Earth surface, a much larger and more detailed map than is usually available on the GPS device itself.

The nüvi® can also be made to display the actual coördinates of a location on request. Three notations are commonly used for GPS coördinates: decimal degrees (40.1915667°), degrees/minutes (40°11.494'), and degrees/minutes/seconds (40°11'29.64")—these three values all specify the same latitude. My nuvi® will deliver coördinates in any of the three notations. The degrees/minutes/seconds form does not seem to be commonly used on the web for GPS coördinates; the decimal degrees notation is widely used, but I have chosen the degrees/minutes notation because I find it is much less error prone to record manually as well as being much more useful with maps, where degrees and minutes are commonly given and decimal degrees are not (although The Nova Scotia Atlas does show both decimal degrees and degrees/minutes, the Natural Resources Canada Topographic Maps I have do not show decimal degrees). In any case, the arithmetic for converting between these notations is straightforward and, for those who prefer to not do the calculations by hand, this web site will produce the other two notations given any one of them.

For identifying where a given photo was taken, GPS coördinates are extremely useful, as they pinpoint a location much more precisely than verbal indications such as “on the Southwest Ridge Road 3.8 km (2.3 mi) south of its junction with Route 19”. How precisely? The main Wikipedia article says that “civilian GPS fixes under a clear view of the sky are on average accurate to about 5 meters (16 ft) horizontally”. That agrees pretty well with my actual experience, where, on various hikes, I observed that if I sat on the same end of the same bench, I got slightly different GPS readings each time; using the degrees/minutes notation (40°11.494' N 74°18.540' W), the readings varied by as much as .003' in both latitude and longitude. At 40° N, 1 minute of latitude is 1.15 miles = 6072 feet, so a difference of 0.003' works out to a difference of 18 feet. At 74° W, 1 minute of longitude is 0.884 miles = 4667.52 feet; so, a difference of 0.003' works out to a difference of 14 feet.[1] On occasion, usually during two different trips to the same place, I have seen a larger variation—as much as .010' (59 feet of latitude, 46 feet of longitude); still, even such a larger imprecision will serve very well for specifying the location from which a photo was shot!

Inaccuracies in the GPS coördinates I report on this web site occur, of course, for reasons other than the inherent imprecision of the GPS device itself. Consider a junction on a busy road; traffic often precludes obtaining an exact reading at the junction—I typically turn onto the side road and use the reading at the shoulder; obviously, such a reading is not precisely correct to begin with. A cloverleaf intersection is even worse: which lane and which direction and which of the intersecting roads and ramps does one pick? Obviously, the ones where one finds oneself at the time! Or consider even a relatively small parking lot: the location at one end of the lot will differ from the location in the middle of the lot and that from the other end of the lot; the location I record is that where I parked the car, which could be anywhere in the lot. Likewise, when I stop the car for photos, the location I record for the photo is where I stopped the car, but I may at times wander up and down or off the road by as much as 300 m/yards. Until affordable cameras come with built-in GPS devices, that will have to suffice.

So, take the GPS coördinates you find attached to photos on this web site with a grain or two of salt; they may not always be pin-point accurate, but they should place you very precisely within the area from which you should be able to see what I saw. I will continue to give imprecise verbal location identifications for those without GPS devices, as I was until 2009, but the provision of GPS coördinates should considerably improve matters for those who do have them.

Occasionally, I forget to record the coördinates of the location where I took a photo. When this happens, I show a question mark for one or more of the digits, interpolating from a map or, if I have recorded coördinates for landmarks or for photos taken near that point, the recorded coördinates. Thus, a location shown with question marks, such as 46°52.???' N 60°25.???' W, indicates that I lack precise recorded coördinates for the photo and have approximated them from another source. I use this same convention for photos before I gained access to Griselda.

In 2010, I traded in my 1998 Camry for a new Prius, which I ordered with a built-in GPS device (soon named Prissy). It has substantial user interface advantages over the nüvi® and considerably better maps, but it has other disadvantages, three of them crippling:

For these reasons, I rarely record its readings and do not use them on this web site.

[1] I got the value for 1 minute using this web site by typing in 40°11.000'/74°18.000' and 40°12.000'/74.18.000' for the latitude and 40°11.000'/74°18.000' and 40°11.000'/74.19.000' for the longitude. While a degree of latitude is roughly the same surface distance everywhere (varying only from 110.574 km (68.7 mi) at the equator to 111.694 km (69.4 mi) at the North Pole), a degree of longitude varies greatly, from 111.320 km (69.2 mi) at the equator to 55.800 km (34.7 mi) at 60° to 0.0 km (0.0 mi) at the North Pole), so the values for 1 minute at 40° N and 74° W given above do not hold at other locations.↩