Kintail
Well-Known Member
Mathamaticians please. If we take a 100 miles span of sea, how far below the high (mid) point are the two ends?
Curvature of earth.
- Thread starter Kintail
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Ex-SolentBoy
Well-Known Member
140m roughly.
Am I right in thinking this is the same question as how high do you have to be to see 50 miles?
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sarabande
Well-Known Member
a lemon tree.
cos (dg) = CG/OC = R/(R + h)
So a height of eye calc to obtain a distance to horizon of 50 nautical miles gives you 559 metres above sea level.
That's without refraction, geoidal discrepancies, or other 'features'.
Crossing Biscay from the North and raising the Cordillero Cantabrico mountains above Santander is just about the right illustration of that.
cos (dg) = CG/OC = R/(R + h)
So a height of eye calc to obtain a distance to horizon of 50 nautical miles gives you 559 metres above sea level.
That's without refraction, geoidal discrepancies, or other 'features'.
Crossing Biscay from the North and raising the Cordillero Cantabrico mountains above Santander is just about the right illustration of that.
FWB
N/A
Approx 1800ft for horizon dist of 50nm.
http://www.gllka.com/resources/calculators/horizon.htm
http://www.gllka.com/resources/calculators/horizon.htm
DJE
Well-Known Member
Being pedantic all points on the sea surface are at the same height.
But if you take a straight line between two points 100 miles apart and the radius of curvature of the sea surface is 3800 miles which is the approximate radius of the earths surface then the mid point of the line will be about 1700 feet below the water surface.
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DJE
Well-Known Member
It is just about the same question but look again at your diagram, it has logartihmic scales!
savageseadog
Well-Known Member
Being pedantic all points on the sea surface are at the same height.
Incorrect of course because of tides, bulging at the equator and general out of shapeness of the earth.
As a point of interest how far up and down is the tide mid ocean?
GrumpyOldGit
Well-Known Member
Since the Earth is a flat disc, as proven by pictures from space ( Aways 2 dimensional ) there is no discernible difference , as proven below;
2@100xEc =¬ **67(0.889) -Pi.3.142
Seemples
2@100xEc =¬ **67(0.889) -Pi.3.142
Seemples
lustyd
Well-Known Member
sarabande
Well-Known Member
Being pedantic all points on the sea surface are at the same height.
Sorry but, No.
There are eustatic, isostatic, and steric changes in sea level, to as much as +/- 2 metres. The reasons include thermal expansion, salinity, solar/lunar cycles.
And mean sea level can vary over quite a short distance. The Pacific end of the Panama Canal is 20cm higher than the Atlantic one. (Ask TCM, who noticed the difference in Mojomo, recently)
The Poseidon satellites measure the sea level height globally.
http://sealevel.jpl.nasa.gov/
(oh, and there are hockey stick graphs there, too
)Ex-SolentBoy
Well-Known Member
Silly me. 558m it is.
AntarcticPilot
Well-Known Member
As well as the trigonometric way of calculating it, you can do it with Pythagoras as well:
h = R - sqrt(Rsquared - (d/2)squared))
This is a little bit approximate, but good enough for short distances.
If R = 6388 km, then h works out at 196 m for 100km.
h = R - sqrt(Rsquared - (d/2)squared))
This is a little bit approximate, but good enough for short distances.
If R = 6388 km, then h works out at 196 m for 100km.
onesea
Well-Known Member
sarabande
Well-Known Member
It has been worrying me, and I'm rethinking this...
When you say 'span of sea', is that point to point through the Earth, or over the surface ?
My original answer of 559m, is in any case incorrect, as that is the answer to "At what height of eye do you have a 'span' of 100 miles sight horizon to horizon ? "
We are into a bit of Euclidean geometry - literally
When you say 'span of sea', is that point to point through the Earth, or over the surface ?
My original answer of 559m, is in any case incorrect, as that is the answer to "At what height of eye do you have a 'span' of 100 miles sight horizon to horizon ? "
We are into a bit of Euclidean geometry - literally
maxi77
Well-Known Member
And also because of the air pressure
And water temperature, the Gulf Stream is aparently severa feet higher than the surounding sea
[70521]
Well-Known Member
Apart from those naughty waves.Being pedantic all points on the sea surface are at the same height.
DJE
Well-Known Member
Apart from those naughty waves.
Ok Ok all points on the geoid are at the same height. The straight line joining two points on the geoid is not horizontal as it makes and angle of more than 90 degrees with the vertical (ie the perpendicular to the geoid surface) at both ends.
So the mid point of the straight line isn't the high point it's the low point.
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bbg
Well-Known Member
Of course it would also depend how you want to measure the angles. If you took a tangent to the earth's surface and measured 50 miles in each direction, then took a right angle from that line to the earth's surface, you'll get a significantly different result than if you measured out 50 miles then drew a line that intersected with the surface of the earth at right angles.
Incidentally, pre-transat I did a similar kind of calculation on a larger scale. Anyone know if I got it right?
Incidentally, pre-transat I did a similar kind of calculation on a larger scale. Anyone know if I got it right?
AntarcticPilot
Well-Known Member
Ok Ok all points on the geoid are at the same height. The straight line joining two points on the geoid is not horizontal as it makes and angle of more than 90 degrees with the vertical (ie the perpendicular to the geoid surface) at both ends.
So the mid point of the straight line isn't the high point it's the low point.
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.
Kintail
Well-Known Member
It has been worrying me, and I'm rethinking this...
When you say 'span of sea', is that point to point through the Earth, or over the surface ?
Thanks to all who replied. To sara, " over the surface was what I had in mind" To everyone else, what prompted my question was quite simply, I know that Australia in "underneath us" approx. I just wanted to know on a smaller scale what the curvature was like. " approx).
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?
