GPS route is 2M out due to Great Circle: beware!

[alanwilson]

Recently on passage from Lizard to Beachy Head, 200M, my Garmin GPS and Nobeltec chart plotter had cross-track errors differing by 2M: enough to substantially reduce the clearance off Start Point and the Isle of Wight.

After much head-scratching I found it was due to the Garmin creating a Great Circle route, but the Nobeltec created a Rhumb line.

The difference is that when plotted on a normal Mercator chart, a rhumb line route is a straight line, but a great circle route is not: on an east-west route, it bends N (in the N hemisphere) so should be plotted as an arc. By how much? On a 200M route, the difference in the middle is 2M; on a 100M route, 0.4M; on a 50M route, 200m.

I always thought that great circle routes were only significant for ocean crossings: not so!

Garmin have confirmed that it plots a great circle route, but did not respond to my suggestion that users should have the choice of rhumb line or great circle, or at least be told that it plots great circle and what the consequence is.

The workround is to add waypoints for each danger closer than say 3M: don't rely on straight line plots on the chart, or you may end up bouncing off the Isle of Wight!

 

[Lady Campanula]

After much head-scratching I found it was due to the Garmin creating a Great Circle route, but the Nobeltec created a Rhumb line. I always thought that great circle routes were only significant for ocean crossings: not so! The workround is to add waypoints for each danger closer than say 3M:

"On a Mercator chart projection, a Great Circle is convex to the nearer pole."

"A straight line on a Mercator chart approximates to a rhumb line, or loxodrome."

The workaround is to introduce rather more waypoints - creating what is effectively a series of ~60nm Rhumb Line segments approximating to a Great Circle - or sailing north/south until on the Destination Latitude then running your Easting/Westing down ( with nothing in the way )..... and ensuring a 'safe offing' from all hazards at all times by observation and not blind faith.

This difference between the Rhumb Line and the Mercator Distances has long been known to mariners crossing oceans ( 'The Sailings' ) but it also has a measurable effect on distance to be sailed on offshore races - consider the legs from Lands End to the Fastnet Light, then back to round the Bishop Rock Light. Many discount this as irrelevant. Focussed competitors take even this into consideration, as races are won and lost often by handfuls of seconds, and 'every little helps...'

 

[Piers]

In 2000 Kim Hollamby (ex Ed MBM) and I wrote an article on just this problem for MBM. As has been said, it's something to be aware of when using Mercator charts (which we all do) when on long legs, and is worst when travelling E - W or vice versa.

If we turn to trigonometry to calculate the midway error between rhumb line and great circle tracks, the following formula is 95% accurate for east/west tracks of up to 500nm at 50ºN, increasing to 99% accuracy for shorter legs:

(rhumb line distance)2 x Tan latitudeº = the error in nautical miles
28,800

Latitude° is the mid-latitude of the two waypoints. To convert the answer to metres, multiply it by 1852.

Kim and I carried out a 100nm practical test on Calm Voyager to prove the point. Our concluding points were,

• Rhumb line tracks are more convenient for coastal navigation. If your plotter or navigator
offers you a choice of rhumb line or great circle, set it to the former.

• Great circle courses offer no advantage on the typical passages covered by most MBM
readers. Our 100nm exercise showed a reduction in distance of only 0.1nm, equivalent to a
time saving of 16 seconds and 0.4lt of diesel at our cruising speed!

• If you don’t know whether your navigator calculates great circle or rhumb line tracks between waypoints, check the manual, or contact the manufacturer’s representative if the information is not offered. Failing that, plot a long east/west leg of at least 100nm, preferably more and see if the course to steer is shown as north of the expected 090°T or 270°T. If using a plotter, draw a leg between two waypoints of several hundred miles and see if the track curves towards the north (if in the Northern Hemisphere) and back again.

• If your plotter or navigator only offers great circle courses between waypoints, you can
minimise the difference between the calculated track and a rhumb line by breaking long legs
into shorter ones of 25nm or less.

• Courses lying close to north or south have minimal differences between great circle and
rhumb line tracks.

 

[Ex-SolentBoy]

Very interesting and something i guess most cruising folk never think about.

But, why bother which method your plotter uses. Irrespective of the type of projection, when travelling east/west you will not hit the isle of wight if you have a waypoint to the south of it.

 

[Searush]

Very interesting and something i guess most cruising folk never think about.

But, why bother which method your plotter uses. Irrespective of the type of projection, when travelling east/west you will not hit the isle of wight if you have a waypoint to the south of it.

Of course not, but if your straight line on the (Mercator projection) chart shows you passing well south, why would you think it necessary to add an apparently "on track" waypoint? Hence, when following a (Great Circle) plotter route you end up 2 miles N of your pencil line on the chart & potentially in danger. THAT is what the OP is drawing to your attention to.

Very useful post for people who completely trust their plotter & travel longer distances. However, like most people, I tend not to exceed 60Nm legs as that would require a stronger crew than I normally have.

 

[bbg]

Very useful post for people who completely trust their plotter & travel longer distances.

As I understand it, that is not the problem. Anyone who completely trusted their plotter would be fine.
The problem would be for someone who used a chart and GPS (without plotter).
The problem would arise if you plotted two waypoints on the chart, drew a line between them, plugged those two waypoints into the GPS and then used the cross track error function to keep you on the line (you assume). If the pencil line on the chart is safe, you would assume you would be safe if you kept the XTE to 0. Apparently not.

Thanks to the OP. This is something that had not occurred to me, but is obvious when you think about it. As someone else has said, the answer is to create additional intermediate waypoints.

Edit - or plot the dangers as waypoints. Even if you don't include them in your route, there is usually a display mode on the GPS which shows your own location, and the nearest plotted waypoints - even if not on your route. I use this function as a very rough chart plotter.

 

[lw395]

I would regard plotting a 200M leg that runs within 10M of hazards, without plotting waypoints to clear those hazards, as very dodgy.
Obviously if you have a chart plotter, it's not an issue.
Also in any boat I've sailed, 200M takes more than one tide, so sailing the straight line would be a poor choice anyway.
In practice, I don't think you would get in much trouble if you plotted your position on the chart every hour or so.

But it's always good to be reminded of what your 'aids' are actually doing, and this kind of thing is often buried in the manual below loads of stuff about 'features' you don't need.

 

[Bosun Higgs]

Its an interesting piece of information. I suppose that someone could just use the Garmin on a simple "go to" from Lizard to Beach but I'm sure they would notice the closeness to Prawle and the Edystone as they went by.

The reality of navigating life is that none of us use the GPS alone in such a simplistic way - if we did so, there would be a long list each season of people hitting the buoyage they use as waypoint but of course this doesnt happen ( forgetting for the moment a racing pal of mine who does bounce off all sorts of things! ).

Presumably this is one reason why Garmin and every plotter maker have the legal warning screen you see before the system boots up. Protection against plonkers

 

[so37]

Use of Plotters and Charts

I read this article with interest and commend the writer for bringing this to our attention.


In this age of Chart Plotters which has replaced the the old "Chart and Compass" method of navigation,GPS has become the
primary method of finding our way round the high sea's.


My own backgound is in Aviation, having spent 25 years teaching Navigation amongst other subjects to Commercial Pilots Licence level
and the famous Great Circle /Rhumb Line area was always one to cause confusion. My sailing background stretches over 30 years.


This is a vast subject but if I might throw out some ideas which hopefully will be of interest and helpful to readers by combining
modern GPS systems and the old Chart and Compass methods.


While the Mercator projection is the norm for navigation at sea, the Lamberts Conformal Conic projection is used in Aviation.
It differs from the Mercator insofar as a straight line drawn on this chart represents an arc of a Great Circle.
So drawing a line from the Lizard to Beachy Head on the Lambert chart, the result was the same as on the Mercator - Dangerously
close to Start Point and to the Isle of Wight.

Basic properties of both Charts.


1. Firstly, it is normal to draw a straight line on any chart to represent our track.


2. The track line drawn on a Mercator has the convenience of producing a constant Track angle to steer, (Bearing).
(Track will cut all Meridians at the same angle as all meridians are parallel lines).


3. However, the track distance measured on the Mercator will not represent the shortest distance.


4. On a Lamberts Chart a straight line drawn between two points will produce a constantly changing track angle, difficult to steer.
(As the line drawn will cut all meridians at different angles, the meridians in this case are representitive of the globe all flowing
down from a common point - the North Pole - In Northern Hemisphere).


5. However the track distance will represent the shortest distance between the points (Arc of a great circle).

It must also be remembered, that a Great Circle track (drawn as a straight line) can only be represented acurately on a matching chart
typically the Lambert's Chart and a Rhumb line track (drawn as a straight line) on the Mercator chart. Mixing the units will only lead
to a dangerous situation. It is not that easy to draw a regularly curved line on a Mercator to represent the great circle track.


So in summary the Mercator gives us a constant Track angle (Bearing) and offers up the distance, so to speak.
The lamberts Chart is the opposite giving us the shortest track distance an offering up the Track angle, (constantly changing).
The Great circle therefore has whats called an "Initial Bearing" and a "Final Bearing" to accomodate the constant change.

On the trip from the Lizard to Beachy Head the Initial great circle bearing is 075 and final bearing is 079, while the rhumb line has a constant
track of 077 degrees.

The big advantage of great circle navigation is to achieve the shortest distance between waypoints. The article mentions that on East / West
tracks the differences will be greatest. This is not strictly true, It depends on the latitudes in which your working and you really need to be
travelling distances in excess of 600nm. before any noticable difference is achieved. In our latitudes (Mid latitudes) the distance
between the great circle track and rhumb line track is not that significant, so no real advantage in milage savings.


For instance in that trip from the Lizard to Beachy Head the difference in distance is less than 0.1nm.
On a larger scale still working in the Mid Latitudes the difference in distance from Shannon Airport to New York JFK is approx 80nm.
(Atlantic Crossing). Again not a huge difference where the total distance is approx 2,700 n.m.


On the other hand an example of significant savings in milage would be a trip in the lower latitudes say from Los Angeles

latitude 33:56N, Long 118.24W to Doha 25:26N, 051.56E the Rhumb line track distance is 8,882nm and Bearing is 093 degrees,

while the Great Circle distance is 7,193nm. with an initial bearing of 010 degrees and final bearing of 170 degrees.

The great circle track takes you quite close to the North Pole at 80.37N, while the rhumb line track is Easterly all the way at 093.

(travelling round the side of the earth as opposed to going over the pole).


My preferred method to navigate is a combination of the Chart Plotter and the old fashioned chart.


I recommend the following method using the trip from Lizard to Beachy Head as an example.


Always draw the track on the chart or place the rule along the track to start with. This way you can check along the track and highlight any
likely incursions with headlands, obstructions etc on the passage.


Allow a comfortable distance off each obstruction if applicable and mark it on the chart as a "waypoint".


When happy draw the track from waypoint to waypoint to form the route. In this case allow say 2nm off Start Point and same off the
Isle of Wight. Other factors such as a "Lee shore" may be relevent if too close to these headlands, again will it be at night when passing any

of these points, sea state etc.

The chart plotter can be set up in the same way, marking waypoints on the plotter and create the route, which now gives you a safe clearance. Its
equally important to check the route (track line created by the plotter on screen) just in case a "bum" waypoint is stuck in the middle !.
This normally takes me around 15 minutes to set up a passage.


Remember the chart plotter is powered by electrics and electrical failures can occur, loss of GPS signal as the fog sets in, whatever, you need
backup and the best way is to chart your progress every few hours, just simply plot your position, maybe take a few transits using a hand bearing
compass and plot as DR positions along the way. Relight those skills buried deep within us !!


This helps relieve bordom on a longish trip, keeps your basic nav skills current and gives you more security and confidence on the passage.


The weakness I see in the writers experience is it did'nt become appearant until a cross track error of approx 2nm showed up between the pair of GPS
units. I think should the chart have been consulted at the planning stage the clearances would be more evident.


An observation at this stage, should both GPS units have created a great circle track, then no cross track error would be noticed and a close encounter
with Start Point would still be on the cards..just throw in some fog for good measure..


Ger Cashman
Cork

 

[prv]

The reality of navigating life is that none of us use the GPS alone in such a simplistic way - if we did so, there would be a long list each season of people hitting the buoyage they use as waypoint but of course this doesnt happen

Not a long list, but I've been on board a boat that did it (I was below so disclaim all responsibility!). One of the great big steel ones marking the main ship channel along the Solent. Autopilot to a waypoint, the waypoint being the position of the buoy.

Fortunately Hallberg-Rassys are strongly built!

Pete

 

[AntarcticPilot]

I am a professional in the map-making and geographic information area, and it is good to see these matters given an airing. However, I am afraid there is an error in the initial post.

A straight line on the Lambert Conformal Conic Projection does NOT describe a Great Circle. It approximates it over short distances ( perhaps 100 or so km) but is NOT a Great Circle.

The only Map projection on which a Great Circle is a straight line is the "Gnomonic" projection - you can visualize it as rays from the centre of the Earth out onto a plane. While the Gnomonic Projection is one of the earliest known - the ancient Greeks knew of it - it distorts the earth so much that it is rarely used. I've only ever used it for situations where the visualization of Great Circles as straight lines was valuable to aid in interpretation of things like Plate Tectonics.

Basically, if you want to follow a Great Circle route, you must compute points along the route and "join the dots". Software to compute points is available, but is somewhat geek- level - it is works from the DOS prompt and is command line driven. Look for "geod". But it works, and works extremely accurately.

Some GPS units have internal software to allow for following a Great Circle Route, I understand - but unfortunately, few manufacturers tend to publish exactly what their box of tricks does!

 

[so37]

Circles for Courses

In response to the previous post, Yes, you are correct and I fully accept what you say regarding the Lamberts chart.

As I already stated this is a vast subject, and without getting into the nitty gritty of the charts and their pure properties, I just wanted to point out that plotting the track from Lizard to Beachy Head on the Lambert's Chart and on the Mercator which would be representative of both tracks created by the two GPS units in use, the result would still show a conflict with the headlands.

Again, on a safety feature, I think in general terms it is better to take a good look at any proposed track on a paper chart and/or on the plotter, create relevant waypoints along the route rather than just hitting the "GoTo" button to destination..

Having these discussions, the intention is to provide a wider understanding to all concerned and hopefully we will continue to learn.

 

[Twister_Ken]

The IOW is pretty big. I suspect that if you bothered to look up from the chart plotter you'd notice you were about to bump into it.