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What is GPS?

The Global Positioning System is just a grid made up of intersecting latitude and longitude lines wrapped around the earth.

  

Latitude lines (also called parallels) run parallel to the equator and measure how far north or south you are of the equator. 

     

Longitude lines (also called meridians) run from pole to pole and measure how far east or west you are of the Greenwich Meridian / Prime Meridian. 

  

Your grid position is where the longitude and latitude lines cross.

Sounds simple, right? So, why do a lot of people find it confusing?

One of the main problems is that coordinates aren’t always written in the same position format.

Someone sends you a set of coordinates, you enter it into your GPS but there are too many numbers and not enough of those little thingamajis. So you enter it anyway and hope for the best, only to realise after the third turn that instead of heading to that picnic spot, you’re heading for a random spot in the veld somewhere in Mpumalanga. Hopefully understanding how coordinates are written and what each number means will prevent mistakes.

The most common way of writing coordinates, in this case for Cape Town harbour, is:

04-Coordinates.jpg

What do each of these mean?

Degrees latitude are measured from 0º to 90º, either north or south of the equator.

  

Degrees longitude are measured from 0º to 180º, either east or west of the Greenwich Meridian.

The distance between longitudinal degrees varies based on your latitude. Longitudinal lines converge the closer you get to the poles. For example traveling from E10º to E11º on the equator is further (and warmer) than traveling from E10º to E11º on the South Pole. Latitude stays constant. The distances I’ve calculated below are based on Cape Town. 

Degrees, Minutes, Seconds.

Distance of a degree over land.

Measuring your position in degrees only would leave a large margin of error. If a position is described as 33º South and 18º East, it means that that position could be anywhere in an area of 10 656 km²

Distance of a minute over land.

To describe a position more accurately we have to break the grid up into smaller blocks – there are 60 minutes in a degree. S 33° 54' E 18° 24’ describes an area of about 2,9 km². One minute latitude is always one nautical mile – 1 852 meters.

Distance of a second over land.

With 60 seconds in a minute we can refer to an area on the grid of about 806m² and with deciseconds and miliseconds we can describe an area smaller than 1m². Although at this scale GPSs aren’t that accurate.

Different formats of writing coordinates

The following are all possible ways of writing coordinates for Cape Town harbour:

  • H DDº MM’ SS” H DDº MM’ SS”                      S 33º 54' 23.23" E 18° 24' 39.27"
  • H DDº MM.MMM” H DDº MM.MMM”              S 33º 54.387’ E 18º 24.654’
  • H DD.DDDDº H DD.DDDDº                             S 33.90645º E 18.4109º
  • -/+ DD.DDDDº -/+ DD.DDDDº                           -33.90645º +18.4109º

They all refer to exactly the same location. All you have to do is enter them correctly on your GPS and you will find your way.

  

To avoid having to translate coordinates into a different position format, you can change the entry field format on your GPS device. It’s usually an easily-found option under GPS settings > Coordinate format

To convert H DDº MM’ SS” to H DDº MM.MMM” simply change the seconds to decimal minutes by dividing the seconds by 60 and adding it to the minutes.

> H DDº MM.MMM” = H DDº MM’ + (SS”/60)’
= S 33º 54' 23.23" E 18° 24' 39.27"
= S 33º 54' + (23.23"/60)’ E 18° 24' + (39.27"/60)’
= S 33º 54' + 0.387’ E 18° 24' + 0.654’
= S 33º 54.387’ E 18º 24.654’

To convert H DDº MM.MMM” to H DD.DDDDº simply change the minutes to decimal degrees by dividing it by 60 and add that to the degrees.

> H DD.DDDDº = H DDº + (MM.MMM”/60)º
= S 33º 54.387’ E 18º 24.654’
= S 33º + (54.387’/60)º E 18º + (24.654’/60)º
= S 33º + 0.90645º  E 18º + 0.4109º
= S 33.90645º E 18.4109º

To convert H DD.DDDDº to H DDº MM’ SS” convert decimal degrees into minutes by multiplying it by 60, and then convert the newly calculated decimal minutes into seconds by multiplying them by 60.

> H DDº MM’ SS” = H DDº (.DDDDº x 60)’ (.MM x 60)”
= S 33.90645º E 18.4109º
= S 33º (0.90645º x 60)’ E 18º (0.4109 x 60)’
= S 33º 54’ (0.387’ x 60)” E 18º 24’ (0.654 x 60)’
= S 33º 54' 23.22" E 18° 24' 39.24"

There are many online converters if you don't feel like doing the math. For when you’re not near your computer you can download a topo map tool with these formulas.

How GPS works?

Your GPS device (also referred to as a receiver) uses satellites and trilateration to obtain its position. Twice daily a number of satellites, 24 American (NAVSTAR) and 24 Russian (GLONASS), orbit the earth on predetermined paths. The orbital paths are designed so that at any given time at least four satellites are in line of sight of your receiver. These satellites continuously send out high frequency low power radio signals. 

Your receiver calculates how long it takes for a radio signal to reach it, and from that it calculates the distance to that specific satellite. You now know your position is somewhere on a sphere, exactly that distance away from that satellite. 

With a second signal it can narrow its position down to any point on a two dimensional circle, and with a third signal to two possible positions in space. 

The fourth sphere, earth, eliminates one of those positions in space. As the earth isn’t perfectly round, the exact shape of this fourth sphere (or ellipsoid) is where DATUM comes into play. Datum is covered in detail further on in this article.

GPSs use trilateration as opposed to triangulation. Trilateration is taking distances from objects to calculate a position. For example, you are 6km from one radio mast, 7km from another and 4km from a reservoir. All three circles that radiate from these landmarks will intersect at one point, that is your position. Triangulation, on the other hand, is using the bearings from these landmarks to calculate a position. For example the one radio mast is 189º from you, the other 24º and the reservoir 271º – these lines will intersect on your position.

13-Available-Satelites.jpg

Accuracy is hugely increased when more satellites are used – up to 10 at a time.

 

To increase accuracy even more some GPS receivers, called DGPS (Differential GPS) or WAAS (Wide Area Augmentation System) use land based radio towers to pin point locations. It increases accuracy to less than 3m. Currently it’s only available US, but is unfortunately lost on them as they don't know how far a meter is.

Set your GPS to use both NAVSTAR and GLONASS if it has that functionality. It helps to have more satellites to choose from, especially when you’re near cliffs, in a kloof, or, if you are that unfortunate, in the city near skyscrapers. 

What is Datum?

Hiking maps often refer to datum and require you to set your GPS's datum to match that of the map. What exactly is a datum?

Disclaimer: This section is quite technical – skip past it to the 'acquisition' section if technical details are not what interest you.

‘Datum’ essentially means a reference point. When we give directions we always start with a point of reference. For example: “From the intersection, continue for 100m and turn left.” Or “From the basement, go up two floors” etc. A reference point can pertain to a point on a horizontal plain or one in vertical space.

GPS devices and printed maps use a datum as a starting point or zero point.

Lateral zero point.

A shown in the images above, both your GPS device and printed maps use a datum as a starting point or zero point from where they start numbering degrees, minutes and seconds. Usually this is just an arbitrarily assigned point on a map.

Vertical zero point.

Datums also contain starting points for elevation or vertical height. Earth isn’t a perfect sphere but an ellipsoid, like a squashed tennis ball. The datum contains a mathematical model to predict the shape of earth that your receiver uses as zero elevation. From this point of reference it calculates your height above sea level.

The ellipsoid (vertical reference point of a datum) roughly follows sea level. I say roughly because due to a whole bunch of reasons the sea level isn’t level. Gravitational pulls from large landmasses, like continents, make the sea level higher in some places and lower in others. This makes it impossible to have an exact height of sea level saved on your device. The geoid model that the datum uses gets it as close as possible – one of the reasons that elevation has a larger margin of error than lat-long location.

There are hundreds of different datums – some global, and some local. It would be great if we could just use one datum on all devices and maps, but due to technological advancements and dated maps we have to switch between them. It does however allow us to select one that is better suited to our location. 

 WGS 84 is an example of a Global Datum and Elipsoid.

WGS 84 is an example of a Global Datum and Elipsoid.

 Cape Datum is an example of a Local Datum. KZN Wildlife topo maps use this Datum on all of  the Drakensberg 50k topo maps.

Cape Datum is an example of a Local Datum. KZN Wildlife topo maps use this Datum on all of  the Drakensberg 50k topo maps.

The global datums are better on average, but the local datums are more accurate for their intended areas – as pictured in the images above. Using a local datum at the wrong location however can throw your position off by hundreds of metres. Always look at the legend of a map to set your GPS receiver to the same datum as the map. 

Most smart phones, GPS receivers and programs like Google Earth use a default global datum called WGS84 (World Geodetic Standard from 1984) which is as its name indicates currently the world standard. Usually when GPS coordinates are mentioned it’s saved in this format. WGS84 is both a grid reference point and an ellipsoid.

Aside from just calculating elevation, the datum ellipsoid is also used to calculate distances from one point to another. The diagram to the left shows the difference between Rhumb (shortcut) distance and an over-the-earth distance. With the correct datum your receiver can calculate the over-the-earth distance more accurately. This only really becomes a problem over long distances. If you’re traveling that far, calculating the distance is usually the pilot’s job.

 

Acquisition

Every time a GPS is switched on it has to locate satellites. It starts looking for the satellites at the last known location and once a fix is obtained it just tracks it. If a GPS has been switched off for a while or moved more than 300km while switched, off the Time to First Fix (TTFF) will be really long.

On some devices you can circumvent this by downloading Almanac Data.  Simply put, Almanac Data is a schedule of where the satellites are expected to be on their orbital paths, at any given time. With this downloaded, your receiver knows where to look and finds satellites faster. The state or health of each satellite is also saved so your receiver knows which ones to skip. NAVSTAR and GLONASS launched a couple of spares over and above the required 48. At only $325 million a pop, why not launch some spares?

Some common mistakes to avoid

  • Universally latitude (north, south) is read first. Not everyone conforms to this standard. Pay attention to which coordinate your GPS asks you to enter first. 
  • Often people type coordinates onto websites, SMSs and emails and omit the degree (º) symbol. Without a º symbol on the keyboard it is often incorrectly replaced by a comma, full stop or an apostrophe. (Alt 0, you’re welcome). Naturally this causes confusion. If you have no choice, rather substitute the º symbol for a space in stead.
  • Elevation accuracy on GPS devices has a 150% bigger margin of error than that of the lat-long position.
  • Physical obstructions affect your GPS receiver's accuracy a lot. Take this into consideration when near cliffs or high buildings.
  • Longitude lines converge at the poles. This means that the distance between longitude lines change based on how far north or south you are. The closer to the poles you get, the closer to each other the longitude lines get.
  • Minutes and seconds can only go up to 59 and will roll over as they reach 60. Anything over 60 must be an error and will cause navigation errors.
  • Always ensure that the GPS's datum matches the map's datum.