Google Earth, Great Circle?

Fascadale

Fascadale

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When you use the "ruler" tool to draw a line on Google Earth you get a distance and a heading, for instance from the southern tip of New Zealand to Southern Chile is about 4000nms.

Is this a rhumb line or great circle ?

If you rotate the globe the line looks very like the arc of a circle.

Thanks
 
Probably neither. It will be the distance according to the projection used by GE, which will be fine for short distances but completely inaccurate for long distances. No map projection (the mechanism for drawing a spherical earth on a flat piece of paper) can preserve distance, so any measurement done on a map (even a clever one like GE) will be inaccurate.

You can check for Great Circle distances using web-sites like this. Rhumb line distances are here.
 
It appears google is using a non-spherical (i.e. accurate) model: http://quezi.com/11698

One can play with Google Earth to see that the great circle route between the English Channel and New York (the shortest distance on a sphere) passes over Newfoundland and Nova Scotia. Click on “Tools” and “Linear” and draw a line from the Channel to New York. This line goes north and then south over the 50th latitude, curving north of the straight line between the two on the Mercator projection image.

So you could see if you're actually using shortest distance by comparing the line to the longitude lines..
 
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I thought that one of the things about great circle courses was that you could not sail on a constant bearing (except along the equator), so what is the 149 degs? (Couldn't get the link to work to check.)
 
Neither ... it's all down to a school globe, bluetack and a piece of string .....

Fascadale said:
When you use the "ruler" tool to draw a line on Google Earth you get a distance and a heading, for instance from the southern tip of New Zealand to Southern Chile is about 4000nms.

Is this a rhumb line or great circle ?

If you rotate the globe the line looks very like the arc of a circle.

Thanks
Click to expand...




There was a program yonks ago on the TV and DHL. It was about how they (DHL) calculated their fuel load for flying from (say) gamma to delta ....

.... a non-DHL engineer stood up and said "If you have a school-size globe, some string, some bluetack and a pair of scissors a) you will find the distance to the nearest 100km and b) from the previous you will already have on you a cellphone with a calculator that will have already calculated the amount of fuel that you need for this flight .....


.... and the answer is "Great Circle" .... and if you want to get to the root of the 3D trig then you have to know about haversines :) :) :)

N
 
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alan_d said:
I thought that one of the things about great circle courses was that you could not sail on a constant bearing (except along the equator), so what is the 149 degs? (Couldn't get the link to work to check.)
Click to expand...

Here is the link again

I was'nt sure about the constant bearing either.

Perhaps somebody who understands great circle navigation may care to enlighten us.
 
alan_d said:
I thought that one of the things about great circle courses was that you could not sail on a constant bearing (except along the equator), so what is the 149 degs? (Couldn't get the link to work to check.)
Click to expand...

That is correct - the bearing continually changes. The bearings given will be initial bearings, I imagine.

You don't need haversines; the cosine rule of spherical trigonometry is the fundamental equation. Haversines were introduced to make the computation simpler and more reliable, but which foul up the maths horribly!

Software to handle these computations very accurately is "geod"; not the friendliest bit of software ever, but very accurate once you've learnt to handle it!
 
Fascadale said:
Perhaps somebody who understands great circle navigation may care to enlighten us.
Click to expand...

I use spherical geometry for distance and course calculations in my software and , as you say, the bearing changes continually along the route (otherwise it would be a rhumbline!) although over short distances a more immediate consideration, if using a magnetic compass, is changes in variation.

Although spherical geometry works well for small sections of the globe I guess the oblateness of the planet would need to be taken into account when doing accurate measurements over very large distances. I wonder if this is the reason for the difference noted in the earlier post by Fascadale.
 
Danny said:
Although spherical geometry works well for small sections of the globe I guess the oblateness of the planet would need to be taken into account when doing accurate measurements over very large distances. I wonder if this is the reason for the difference noted in the earlier post by Fascadale.
Click to expand...

Yes, it does. But the error is small, and will produce errors much less than 1% of the distance. A geodesic calculation program like geod will produce results that are good to millimetres, and has to use ellipsoidal calculations to do so. But results good to better than a nautical mile will be obtained from spherical calculations. I do geographic calculations as part of the day job; for nearly all purposes the Cosine Rule is plenty good enough!

Oh, and technically it is a geodesic on an ellipsoid, not a Great Circle.

I produced an illustration like this a while ago.

The earth is actually a rather irregular figure called the geoid (which is the surface of gravitational equipotential, for the geeks among us). The Geoid can be modelled by a sphere with residual differences of about 11 km between the "best fit" sphere and the geoid at the poles and the equator. If you model it by an oblate spheroid, the maximum errors drop to +90 and -110 m. So, the oblate spheroid is a very good model. However, the 11 km is on a sphere of radius approximately 6350 km, so in fact the sphere accounts for the vast majority of the shape of the earth, and can be used as an approximation good enough for most purposes.

I believe that only spherical trigonometry is used in navigation; the sphere is a good enough approximation until the error drops to less than 100m.
 
alan_d said:
I thought that one of the things about great circle courses was that you could not sail on a constant bearing (except along the equator), so what is the 149 degs? (Couldn't get the link to work to check.)
Click to expand...

As per AtlanticPilot, it will be the initial bearing. You cant sail an exact GC Course, so you sail a series of rhumb lines.

In the Southern Hemisphere, (NZ to Chile), the initial course will always be South of East/West, and the final course will be North of East/West. (I guess there will be some GCs where the final course could be East or West, and there may be some where the initial course is South, (in the Southern Hemisphere).

In general, you need to be travelling long distances, (like crossing oceans), to make a GC route worthwhile in terms of distance savings. You also need to be aware that they take you into colder climes, and potentially bad weather.
 
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Richard10002 said:
... You cant sail an exact GC Course, so you sail a series of rhumb lines...
Click to expand...

A GC course would therefore comprise an infinite number of infinitely short rhumb lines and would take an infinite time to complete ...

(I think I should lie down, I feel Zeno's paradox coming on ...)
 
alan_d said:
A GC course would therefore comprise an infinite number of infinitely short rhumb lines and would take an infinite time to complete ...

(I think I should lie down, I feel Zeno's paradox coming on ...)
Click to expand...

Here it is:

If the infinite number of rhumb lines are each infinitely short, they would each take no time to sail, so you would arrive the moment you set off :(
 
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