Curvature of earth.

Kintail said:
To confuse the issue further. The curvature is so gradual that when we are sailing we are by and large on a flat surface. However the world is round so are we ever sailing " uphill or downhill" however gradual?:)
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Now with this question I can be of some help. It all depends upon the destination you are sailing to, the crew you are sailing with, the distance destination is away from you, the reason wanting to reach the destination the position of the sun, the moon and the direction of the wind to consider just the main points.

For example:
If you are on the first day of your voyage sailing towards a fine meal on a beautiful island with good company the tide and wind behind you and the sun setting as you arrive in the well sheltered harbour it is obvious your sailing down hill:p.

On the reverse side if you are on the final leg of the voyage and you are beating back against a foul tide, with disgruntelded crew, rushing to get to your berth in time to get to work on a Monday morning you are obviously sailing up hill :(.

The inclination of this hill could be reduced considerably by positive decision, to return to work and resign:). Then you could just turn the boat in a different not bother with that and of course the inclination of the hill will change immediately :D.

I am sure there will be more posters giving other (probably better) examples of the ups and downs of sailing... :p
 
AntarcticPilot said:
...... The Geoid is modeled pretty accurately, but it is not usually used as a reference level except for scientific purposes.
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Not totally correct. We don't use the height output from our GPS to avoid hitting the bottom. We use the echo sounder to measure depth of water and then make tidal calculations based on chart datum which is usually LAT. With LAT there is also HAT and somewhere between the two is MSL. The geoid is an attempt to model the MSL surface.

Onshore most heights are referenced to MSL. The geoid is therefore used as a reference for many non-scientific purposes.

My avtar is a model of the differences between the WGS84 ellipsoid and the geoid or MSL. The red bits indicate it's 70-90m above the ellipsoid and the dark blue areas, 80-90m below.
 
AntarcticPilot said:
This is a matter I had to explain VERY carefully in a course I used to teach about Geographic Information systems!

Height is meaningless UNLESS you state the datum level above which you are measuring. There are three possible kinds of datum:

1) A Spherical datum. This is what we usually assume for astro-navigational purposes; is is, as they say, good enough for government work. However, the maximum deviation of the Earth's surface from a "best fit" sphere is about plus or minus 11 km.

2) An ellipsoidal datum. This assumes that the cross section of the earth along a line of longitude is an ellipse, but along a line of latitude is a sphere. This is actually pretty good - it deviates from the Geoid (see below) by about 100m at most, and a lot less in most places. WGS84 uses this kind of vertical datum; it is the reference level used by GPS.

3) The most precise height datum is known as the Geoid. This is defined as a gravitational equipotential surface - that is, it is the level at which you will always measure the same value of gravity. It is the level at which a motionless fluid would rest. However, the sea is not motionless, and so sea-level MAY deviate from the geoid by a few meters - there are, for example, notable slopes in areas like the Agulhas Current. The Geoid is not precisely known in all parts of the world, but is fairly precisely known for oceanic areas. The Geoid is modeled pretty accurately, but it is not usually used as a reference level except for scientific purposes.
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geoid96 said:
Not totally correct. We don't use the height output from our GPS to avoid hitting the bottom. We use the echo sounder to measure depth of water and then make tidal calculations based on chart datum which is usually LAT. With LAT there is also HAT and somewhere between the two is MSL. The geoid is an attempt to model the MSL surface.

Onshore most heights are referenced to MSL. The geoid is therefore used as a reference for many non-scientific purposes.

My avtar is a model of the differences between the WGS84 ellipsoid and the geoid or MSL. The red bits indicate it's 70-90m above the ellipsoid and the dark blue areas, 80-90m below.
Click to expand...

Thanks to you both for these posts.

Great stuff, very interesting............................. my fact for the day is the plus or minus 11km discrepancy

Wots MSL?
 
DJE said:
It is just about the same question but look again at your diagram, it has logartihmic scales!
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It has been plotted with logarithmic scales so that it is a straight line. When you take the log of both sides of the function the square root changes to a simple 50% change in gradient.
I'm not sure it is valid to take the distance as high or far as they do in the graph because an assumption made in this calculation is that the viewing point (or more generally antenna height) is very much smaller than the radius of the earth.
 
geoid96 said:
Not totally correct. We don't use the height output from our GPS to avoid hitting the bottom. We use the echo sounder to measure depth of water and then make tidal calculations based on chart datum which is usually LAT. With LAT there is also HAT and somewhere between the two is MSL. The geoid is an attempt to model the MSL surface.

Onshore most heights are referenced to MSL. The geoid is therefore used as a reference for many non-scientific purposes.

My avtar is a model of the differences between the WGS84 ellipsoid and the geoid or MSL. The red bits indicate it's 70-90m above the ellipsoid and the dark blue areas, 80-90m below.
Click to expand...


Being really pedantic, MSL is NOT the geoid; ocean currents etc. mean that MSL can deviate from the geoid by a matter of metres. And tidal levels such as HAT, LAT etc. are equally not the geoid; basin resonances etc ensure that they are not (the amplitude of the tide is not everywhere the same, so you can see why not). However, round the UK it won't make much difference! But there are places where it matters; I mentioned the Agulhas Current as one such location, and I think that the Gulf Stream as it passes up the east coast of America also has a noticeable affect.

Just for interest, the Geoid is these days measured mainly by specialized satellites whose orbit is determined very precisely; the lumps and bumps in the orbital path indicate the gravitational field at the elevation of the satellite; this can then be downwards continued to give the geoid level.

Incidentally, there is a new Geoid model available since EGM96 (your avatar) was issued: EGM 2008 is available, which uses the results of satellite missions such as GRACE to improve the model.
 
AntarcticPilot said:
.
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You are correct that the geoid is not exactly the same as MSL. The geoid is a gravity equipotential surface whereas MSL is also influenced by the other local effects that you mention. That’s why I said the geoid is an attempt to model the MSL surface and also extend it underneath the land masses. The point I was making is that globally the geoid is far closer to MSL than it is to the ellipsoid and that MSL is the most common vertical datum for heights on maps.

I think my avtar was based on an even older global geoid model, OSU91a. EGM96 and EGM2008 are considerably refined, but at the scale and resolution, I think it would be difficult to see any difference. I’m currently working on a project using AUSGeoid09. This is a regional refinement of EGM2008 that also incorporates a several thousand extra gravity measurements and precise levelling. The trouble is that nothing stands still. The earth is slowly getting fatter and the tectonic plates are slowly shifting.
 
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electrosys said:
Ok - so a fair few years ago the Earth was nowt but a ball of molten metal and other minerals, which slowly began to cool and form a crust, which is more-or-less exactly where we are today.

So - where did all the water come from ?
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Comets, amazingly! (Now you are going to ask where comets got their water; it's like having a curious child, I imagine...)

Mike.
 
geoid96 said:
You are correct that the geoid is not exactly the same as MSL. The geoid is a gravity equipotential surface whereas MSL is also influenced by the other local effects that you mention. That’s why I said the geoid is an attempt to model the MSL surface and also extend it underneath the land masses. The point I was making is that globally the geoid is far closer to MSL than it is to the ellipsoid and that MSL is the most common vertical datum for heights on maps.

I think my avtar was based on an even older global geoid model, OSU91a. EGM96 and EGM2008 are considerably refined, but at the scale and resolution, I think it would be difficult to see any difference. I’m currently working on a project using AUSGeoid09. This is a regional refinement of EGM2008 that also incorporates a several thousand extra gravity measurements and precise levelling. The trouble is that nothing stands still. The earth is slowly getting fatter and the tectonic plates are slowly shifting.
Click to expand...

I think the OSU Geoid was the first one I used in anger!
 
Kintail said:
To confuse the issue further. The curvature is so gradual that when we are sailing we are by and large on a flat surface. However the world is round so are we ever sailing " uphill or downhill" however gradual?:)
Click to expand...

No, because wherever you are on the earth's surface "level" is at right angles to a line running to the centre of the earth at that point.
 
alan_d said:
No, because wherever you are on the earth's surface "level" is at right angles to a line running to the centre of the earth at that point.
Click to expand...

Level is a surface that is perpendicular to the local vertical as defined by the direction of a precise plumb bob. There are two reasons that this does not point exactly to the centre of mass of the earth. Firstly, the earth not being spherical means that it tends to point to a point perpendicular to the surface of the ellipse. Secondly the earths crust is very irregular in terms of terrain and density. This means there are significant local deviations of the vertical.

As AntarcticPilot has described earlier, other than gravity, there are other factors that can influence sea level Mean Sea Level. On that basis, and forgetting tidal variations, it could be argued that we are sometimes slightly sailing uphill or downhill. However I don't think it's worth trying to allow for it in your passage planning. ;)
 
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