More Thoughts on Rhumb lines..

[BobE]

Just took the good old Garmin 12 XL outside and had a little play
Made waypoints on the same meridian (W 001deg 46.023 ) at
N 00 deg 54.930
N10 deg 54.933
N20 deg 54.934
N30 deg 54.932
N40 deg 54.930
And told it to go to..
Got all at 180 degrees ( of course) and ranges as follows
2992 nm, 2395 nm, 1798 nm, 1199 nm, and 600 nm so there's a slight descrepancy in the ranges which could partly be the in the third place of decimals of the minutes but ????
Then I did the same but made waypoints all at the same Latitude 50 deg 54.934 but different Longitudes i e
W 046 deg 46.032 1682 m @ 288 deg
W 096 deg 46.032 3337 nm @ 310 deg
W 136 deg 46.031 4291 @ 332 deg
and
E 179 deg 46.031 4707 @359 deg
Then made a waypoint @ 11 deg 46.023 west i e 10 west from me
and got 379 nm @ 274 deg...
So the GPS must use great circles when we ask it to "GoTo"
The chart plotter allows one to draw a line from one place to another and gives range and bearings from & to...
Across Biscay it gave about 360 nm @214.2 deg
Maybe we should be using the GPS for all the calcs?
Next test maybe be to put the GPS in simulation mode and try across Biscay???
Cheers Bob E

 

[lw395]

Yes many gps's can do great circles, not sure that all do. It may be selectable on some?
I'd like to hope I was doing some proper research and planning before going far enough that it makes much difference!
How many passages do you think great circle is best option for, compared with even the crudest weather routing? I would guess not many. It would be good to have the circle on the chart as a reference though, is thard hard to do? I don't have much experience of plotters beyond the channel.

 

[AntarcticPilot]

There is no simple way of constructing a great circle on your chart; Mercator's projection is good for doing rhumb line navigation, but not good otherwise. However, the only projection on which great circles are straight lines in the gnomonic projection, and charts aren't available in that!

The way I would go about it would be to use a very ancient piece of free software called "geod" It comes with a software package called "proj ", and computes great circle distances and can output latitude and longitude at intervals along a great circle.

Health warning; this is a command line only piece of software, and probably requires that you RTFM VERY carefully!

 

[Danny Jo]

[ QUOTE ]
Yes many gps's can do great circles, not sure that all do.

[/ QUOTE ] Isn't it the other way around? I thought it was rather complicated for a GPS calculator to work in "plane sailing" mode. Enter a waypoint in Japan on more or less the same latitude as your location in Britain - why should it tell you to go the long way around (along the line of latitude) rather than via Siberia?

 

[Piers]

Most GPSs default to great circle nav. Some have the option to change to rhumb lines, and some offer a choice of rhumb and great circle for each leg of a route. Interesting when using Mercator charts in these lats and travelling along the Channel for a reasonably long leg. By half way along you'll be north of the line on your paper chart....wrote an article with Kim Hollamby some time ago on the subject. Might dig it out for some of the calcs and practicals we did.

 

[Mariner69]

The GPS will naturally calculate the Great Circle course to the next position because it uses the direct, line of sight route.

When using GC navigation on a mercator chart, it is necessary to produce a composite GC track consisting of rhumb lines as that way the course to be steered is constant whereas a true GC course is constantly variable. This is only really obvious in Ocean navigation, especially in the days before GPS and Transit when sextants ruled.

Gnomonic charts exist for polar navigation and large scale harbour plans are virtually the same albeit often being Transverse Mercator in practice. A straight line on the chart equates to the line of sight in the real world.

With reference to your original posting, keeping to the planned track is intended to ensure that you pass through safe water that you have considered in detail when planning the voyage. If you just try to head to the end point you can find yourself in deep (or rather shallow) do-do as happened to a Greek ferry which was just keeping the light on the bow when being blown sideways where she met the rocks to leeward of her track.

 

[LadyInBed]

Check it by taking one of those inflatable globes, a piece of prestretched string and two pins.
You can then measure the distance on the globe between the two pins . . . . . . .Just thought of a fatal flaw /forums/images/graemlins/blush.gif

/forums/images/graemlins/laugh.gif

Edit:
Sod it, just make a B line for the Rum line.

 

[Piers]

Here's an extract from the article Kim Hollamby and I wrote on Rhumb v GCs.
------------
Travelling due East / West creates the maximum error, which worsens the more you are north or south of the Equator.

An approximate formula for calculating the midway error between Rhumb Line and Great Circle (to an accuracy of one percent or so) is as follows, and uses trigonometry - remember ‘trig’?

[(Rhumb Line distance)2 x Tan mid-Latitudeº]/28,800 = the error in nautical miles

The mid-latitude is the average latitude between the relevant waypoints. To convert the answer to metres, multiply the answer by 1852.

Table 1 shows some examples using 50º latitude, typical of the English Channel,

Examples for a mid latitude of 50º north

Col 1 is Rhumb Line Distance between Waypoints
Col 2 Mid-way error when travelling E/W in metres and nm

Col 1 metres nm
25 nm 48 0.026
50 nm 192 0.1
75 nm 431 0.233
100 nm 766 0.414
150 nm 1724 0.931
200 nm 3065 1.655

Although the errors may not appear large at first, look at a 50 mile distance and then compare the 192 metres error with the much discussed 5 to 10 metre accuracy of GPS.

Then look at the 100 mile distance. For example, Calais to Poole, or Dartmouth to the Scillies.

However, if we are not travelling due East / West, we have to take the above formula and multiply the answer by the sine of the angle our track makes with the North / South Meridian.