Chartwork - Measuring Distances

[sae140]

On the whole I tend not to question experts, and like many thousands of other students when I was taught that you measure *all* chart distances from the Latitude scale on the lefthand or righthand sides of a chart - I accepted this, as the reason being given was that the latitude scale (based on one minute of arc = one nautical mile) on Mercator Projection charts increases the further away from the equator you travel. And that's a powerful argument.

But it was while playing with MaxSea last night that I realised that this mantra is flawed. I was looking at the waters around Scapa Flow when I switched on MaxSea's grid facility, and - although I've looked at the Lat/Long Mercator grid distortion more times that I can think of - for some reason this time I became more aware of it.
So I took a screen capture and measured the grid dimensions (in pixels, using Paint), and for-all-intents-and-purposes there is a 2:1 'distortion' between displayed latitude and displayed longitude. Ok, so what ?

Well, MaxSea's blue grid displays more-or-less EQUAL real-world distances in both North-South and East-West directions. (discounting the small difference in longitudinal distance between the top and bottom of any grid square)
Thus, if you were to take an East-West distance from the chart with dividers, and measure that distance against the Latitude scale, it would appear to be only 50% of the distance as measured on the Longitude scale.

So - should the mantra not be: "Distance in a North-South direction should be measured on the latitude scale; distance in an East-West direction should be measured on both top and bottom longitude scales, and their mean value taken; and for distances in an intermediate direction:- measurements should be taken from both Lat and Long scales, and interpolated accordingly."

Or am I overlooking something ?

[idpnd]

As far as I understand, due to the orange/melon-shape of the globe, they should all be taken on the latitude scale on a mercator projection. (Please correct me if I'm wrong )

[edsailing]

All distances should be measured on the latitude scale.

[sabray]

rather then measure the overlay grid use the latitude as found with the cursor to measure the distance. I think you will find that the grid is altered.
so that each segment north south is .3 miles and east west .15 on your grid. Use latitude for measuring.

[estarzinger]

I am not sure what your question is . . . but 1 minute of latitude = 1 nautical mile (1852m) at any latitude (from the equator to the north pole). That's how you should measure distances on your chart of distances along any line. Measure the distance between any two point on the chart (with dividers or a ruler) and then see on the left or right latitude scale how many minutes that is and that's the distance in nautical miles (there's actually a .5% error in this due to the earth not being a perfect sphere, but you will not be measuring to .5% accuracy so you can ignore)

1 minute of longitude varies by the Cos on the longitude - eg is zero length at the poles and maximum at the equator (1855.3m so pretty much a nautical mile). I believe this is why you are seeing the maxsea squares squashed in longitude. At Scapa Flow (59N) 1 minute of longitude = .51nm, which is exactly your 2:1 squashing.

[Talbot]

If you are using Maxsea, you should be using the measurement tool anyway, rather than guesstimating from a print out.

[Talbot]

A navigator needs to understand what sort of display projection he is looking at and what that means in terms of bearings and distances.

The most common form of paper chart uses a transverse mercator projection because it is the easiest to draw. However this means that the world is flattened out and the globe stretched at the top and bottom so that the lines from north to south are parrallel instead of meeting each other at the poles.

The major drawback of this projection is in high lattitudes, where it becomes too distorted for use. It also makes great circle and rhumb line routes difficult to draw. You end up with a curved line, for great circle routes, whereas on a gnomonic projection which draws the lines in at the poles, you can draw a straight line for great circle courses.

A further complication is the datum being used. The datum actually describes the shape of the earth being used as the basis for the chart/position. The defining datum in use today is WGS84. This datum became the de facto standard because of GPS, and has even started to replace land based datums as well. As you can imagine, if the shape of the land described by the datum standard is not as accurate as possible, then some of the plotted points will also be incorrect. The WGS 84 standard replaced WGS 72 in order that the Oblate Spheroid shape of the earth was as close as possible to reality in order to make best use of the accuracy of GPS.

Therefore when you pick up a paper chart, it is REALLY important that you check the projection and the datum information to ensure that the position shown on your GPS is the same as the position on the chart. Naturally you also need to check that nobody has changed the datum in use in the GPS as most will enable you to output positions suitable for charts drawn for some other datum .

I hope I have not confused you!

[Pete7]

Interesting location, are you looking for HMS Hampshire, Lord Kitcheners battleship which sank around there?

Pete

[Hydra]

There are different issues here:
1) The scale on a Mercator chart:
On a Mercator chart, the scale varies with the latitude. In the North hemisphere, a minute of latitude is bigger at the top than at the bottom of the chart by a measurable quantity (larger if the chart covers a wide area). Then, it is necessary to use the latitude scale at the same mean latitude as the distance you are measuring.
On a “transverse Mercator” (aka “Gauss conformal projection”) chart, the scale doesn’t vary with the latitude but distortions appear when going away from the meridian used as the “transverse equator”. Since this projection is only used for large scale charts, these distortions aren’t visible to the naked eye.

2) The dimensions of the Earth
The Earth isn’t exactly a sphere. For precise navigation purposes, it is assumed to be an ellipsoid. Then, the precise length of a minute of latitude changes by a few meters from the equator to the pole (the formulas are a bit complex to type in a post but I should be able to send them to those interested).

There is no sensible difference when you measure a distance on a paper chart with dividers. But when you have to compute distances from accurate positions obtained from a “military” P(Y) GPS receiver, for the purpose of official speed trials, it can result in a few hundredths of a knot, just enough to exceed the contract target value.
1852 meters is the length of the international nautical mile, corresponding to the average length of a minute of latitude.

3) The chart datum
There are still many different reference ellipsoids in use.
All over the world, hydrographic offices progressively change their charts to WGS84 datum (semi major axis a = 6378137.0 meters; flattening f = 1/298.257223563) associated with GPS. Some still use WGS72 (semi major axis a=6378135 meters; flattening f = 1/ 298.26)
In European waters, many charts still are referenced to Europe 1950 datum (Hayford ellipsoid, semi major axis a=6378388 meters; flattening f = 1/297)

For a full discussion of the WGS84 datum, see for example: http://earth-info.nga.mil/GandG/publ...2/wgs84fin.pdf
For a simple explanation of the issue, see: NGA: (U) Office of GEOINT Sciences: Precise Positioning (UNCLASSIFIED)


Alain

[barnakiel]

You are overlooking quite a lot of things.

To start with - on an electronic chart you will use some sort of range and bearing functionality build into the software.

b.

[Lodesman]

Originally Posted by sae140

So - should the mantra not be: "Distance in a North-South direction should be measured on the latitude scale; distance in an East-West direction should be measured on both top and bottom longitude scales, and their mean value taken; and for distances in an intermediate direction:- measurements should be taken from both Lat and Long scales, and interpolated accordingly."

No, it should not be.

Lines of latitude are parallel; that's why they're called parallels of latitude. And the distance between parallels is constant regardless of latitude - the distance between 0 and 1 degrees N is the same as the distance between 50 and 51 degrees N. Lines of longitude are not parallel - they converge at the poles, so the distance between 0 and 1 degrees E is maximum at the equator; about a nautical mile, but at the poles that distance is zero. The mercator projection pulls the non-parallel lines apart by stretching the image in N-S and E-W directions until the lines are parallel. So a minute of lat is always a mile, but when you measure it you should take it from the part of the scale that is closest in lat to the position you are measuring. In a small scale chart this is especially important as the scale is noticeably longer at the top of the chart (N hemisphere). Your maxsea scale is likely set to the mean (ie. accurate at the centre of the screen), but is certainly accurate enough for use at most ranges.

[clearsea]

Originally Posted by sae140

if you were to take an East-West distance from the chart with dividers, and measure that distance against the Latitude scale, it would appear to be only 50% of the distance as measured on the Longitude scale. ... So - should the mantra not be: "Distance in a North-South direction should be measured on the latitude scale; distance in an East-West direction should be measured on both top and bottom longitude scales, and their mean value taken; and for distances in an intermediate direction:- measurements should be taken from both Lat and Long scales, and interpolated accordingly." Or am I overlooking something ?

Yes: The task is to measure distance over the surface of the earth in nautical miles, not in angular degrees of latitude or longitude. (This is another version of the answer estarzinger gave.)

Forget the fact that the earth is not a perfect sphere. Assume that it is. The difference is not significant for ordinary boating paper chartwork. Geodesy can come later, for interest.

Off the equator, one minute of longitude measured along a line of latitude is less than one nautical mile (as you noticed by observing that 92 east-west is less than 180 north-south at Scapa Flow's latitude) and progressively smaller than 1 NM travelling further north and south from the equator. However, one minute of latitude along a line of longitude is always about one nautical mile (close enough for chartwork) regardless of the angle at which one measures the distance (only at the same latitude on a Mercator chart).

Study a globe to get the concept visually. The lines of longitude always go around the earth through both poles (great circles), whereas lines of latitude get progressively smaller travelling away from the equator toward the poles (not great circles). That is why lines of latitude cannot be used to measure distance. On a globe, one can measure distance against the latitude scale on a line of longitude anywhere on the surface of the earth, not just at the same latitude as is required on a Mercator chart owing to the way the Mercator projection distorts distances north/south.

[The only line of latitude whose scale can be used to measure distance this way is the equator, since it circles the earth at its full circumference, like every line of longitude.]