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Author Topic: Where is the geographic centre of South Africa?  (Read 11490 times)

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Offline Fudmucker

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Re: Where is the geographic centre of South Africa?
« Reply #60 on: September 15, 2011, 06:01:23 pm »
That's why I suggested that the midway between W+E and N+S appears to be the simplest method.
But we need the TRUE Longitude and latitude values for the W, E, N + S points.
I have tried using Mapsource and Google Earth, but I arrive at a midpoint NE of Barkly West,
near the farm homestead Kilmoray.
 ???
« Last Edit: September 15, 2011, 06:09:07 pm by Fudmucker »
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Offline JourneyMan

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Re: Where is the geographic centre of South Africa?
« Reply #61 on: September 15, 2011, 08:24:41 pm »
Dibs on organising the first "Bash" there... >:D

Deal! Job is your's for 2012 National Bash. :deal: :biggrin:
Er... :peepwall:....was thinking slightly smaller.....like a dozen guys.... ;D
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You are of the hook it seems.

Might take another year before consensus is reached. :biggrin:
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Offline White Rhino

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Re: Where is the geographic centre of South Africa?
« Reply #62 on: September 16, 2011, 06:49:12 am »
just to throw a cat among the pigeons:

* Has anybody considered the earth's curvature as part of determining the centre of SA? Could well be a few meters underground...

* How much will the "centre" shift by if using different map projections? (http://en.wikipedia.org/wiki/Map_projection for more info)

* Is this centre to be determined by area calculation alone, or should it include mean elevation as a weighting?

Far too many variables for one distinct anwer - Mr Adams might well be technically correct, but for places to seek, visit or explore, this dilemma is a traveller's manna! :)

Pigeon pie comes to mind  ;D

You are spot on in that the projections of maps may be distorted from a representation perspective. That would depend on the projection method used.

If one looks for the shortest distance between two spherical points, then the elevation would become evident (i.e. below the surface).

One should therefore use a spherical surface formulae (ref: http://en.wikipedia.org/wiki/Geographical_distance}

As a result of the Earth not being a sphere and having a bulge around the equator, makes the Earth an ellipsoid. So more accurately one needs to use an Elipsoidal-surface formulae to get the approximated distance over great distances. There are several documented methods - Vincenty's Bowring's and Lambert's formulae.

For interest's sake take a look at Vincenty's formulae - http://en.wikipedia.org/wiki/Vincenty%27s_formulae

Wikipedia then goes further to say ...

Quote
The systems are needed because the earth is not a perfect sphere. Neither is the earth an ellipsoid. This can be verified by differentiating the equation for an ellipsoid and solving for dy/dx. It is a constant multiplied by x/y. Then derive the force equation from the centrifugal force acting on an object on the earth's surface and the gravitational force. Switch the x and y components and multiply one of them by negative one. This is the differential equation which when solved will yield the equation for the earth's surface. This is not a constant multiplied by x/y. Note that the earth's surface is also not an equal-potential surface, as can be verified by calculating the potential at the equator and the potential at a pole. The earth is an equal force surface. A one kilogram frictionless object on the ideal earth's surface does not have any force acting upon it to cause it to move either north or south. There is no simple analytical solution to this differential equation. A power series solution using three terms when substituted into this differential equation bogs down a TI-89 calculator and yields about three hundred terms after about five minutes.

This is enough to make a monkey fuck a pineapple.  ::)

But when one uses Lat and Long coordinates and GPS coordinates, then presentation is irrelevant.

So for the sake of DS motorcycle enjoyment, the simplest method should be applied: (E.point - W.point) /2 + W.point = Mid Horizontal .point
and; (N.point - S.point) /2 + S.point = Mid Vertical .point

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Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #63 on: September 16, 2011, 07:51:15 am »
just to throw a cat among the pigeons:

* Has anybody considered the earth's curvature as part of determining the centre of SA? Could well be a few meters underground...

* How much will the "centre" shift by if using different map projections? (http://en.wikipedia.org/wiki/Map_projection for more info)

* Is this centre to be determined by area calculation alone, or should it include mean elevation as a weighting?

Far too many variables for one distinct anwer - Mr Adams might well be technically correct, but for places to seek, visit or explore, this dilemma is a traveller's manna! :)
ergo my suggestion that all methods be used and all centres be visited. :mwink: :thumleft:
I like keeping things simple and will start planning a visit to my calculated point in Barkly West as well as the Koppie mentioned. :mwink:
 

Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #64 on: September 16, 2011, 07:53:10 am »
Might take another year before consensus is reached. :biggrin:
this is like the "What oil to use", "What is the best DS bike" and a plethora of other debates it seems... but doing them all will be fun. :mwink:
 

Offline The Rock

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Re: Where is the geographic centre of South Africa?
« Reply #65 on: September 16, 2011, 07:53:29 am »
jislaaik, this is getting way too complicated! Rob, draw a box and get the center!  :mwink:
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Offline Pistonpete

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Re: Where is the geographic centre of South Africa?
« Reply #66 on: September 16, 2011, 08:12:06 am »
We don't one day want to rock up in Kimberly to have a local yokel laugh his his head off while pointing out that the Koppie is in actual fact NOT the centre of RSA....

Now to find a map i can draw lines all over... :mwink:
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Offline ClimbingTurtle

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Re: Where is the geographic centre of South Africa?
« Reply #67 on: September 16, 2011, 08:20:00 am »
How would one find the geographic centre of South Africa? The crossing point between the most Northern/Southern & Eastern/Western points in SA?

That would be S27.89008 E25.62496


I like this one best - mainly because my next multi-day ride is going to pass within about 15-20km of the noted centre point. Based purely on that, I am going to try and visit it, just in case it makes the list of one-of-many-centre-points of SA.....!
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Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #68 on: September 16, 2011, 08:20:24 am »
jislaaik, this is getting way too complicated! Rob, draw a box and get the center!  :mwink:
I did! :deal: and got the co-ordinates and even a Google picture of the location of the point (located near the graveyard in the location).  :deal:
Now to set the date... :mwink:
 

Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #69 on: September 16, 2011, 08:24:16 am »
How would one find the geographic centre of South Africa? The crossing point between the most Northern/Southern & Eastern/Western points in SA?

That would be S27.89008 E25.62496


I like this one best - mainly because my next multi-day ride is going to pass within about 15-20km of the noted centre point. Based purely on that, I am going to try and visit it, just in case it makes the list of one-of-many-centre-points of SA.....!
I beg to differ... I calculated mine from the exact NS/EW demarcators and it is S28.59/E24.49. :deal: :mwink:
But I will add this to the list! :imaposer:
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Offline tok-tokkie

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Re: Where is the geographic centre of South Africa?
« Reply #70 on: September 16, 2011, 09:03:32 am »
This is the method I prefer (from my earlier post):
Quote
2. Center of Gravity method, which I prefer.  Get a map of SA & stick it to thick cardboard.  Cut around the edge of SA with an Exacto knife & cut out Lesotho so just the SA landmass remains.  Stick a pin through near Messina & pin to a vertical board, must be free to swing.  Hang a piece of cotton with small weight from pin.  Draw line where cotton thread lies.  Repeat near Richards Bay & Alexander Bay.  3 lines should cross at a point = CofG of the cardboard.

If you stuck a pin through that point & pinned it to a vertical board, gave it a spin there would be no heavy point so it would stop with any point at the bottom.  The thing is balanced so, to me, that is the best center.  Theoretically could also balance it on a pin stuck through there.

My method 1 was the NS & EW mid point idea but the thing would be out of balance on the pin test.
 

Offline The Rock

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Re: Where is the geographic centre of South Africa?
« Reply #71 on: September 16, 2011, 09:16:37 am »
This is the method I prefer (from my earlier post):
Quote
2. Center of Gravity method, which I prefer.  Get a map of SA & stick it to thick cardboard.  Cut around the edge of SA with an Exacto knife & cut out Lesotho so just the SA landmass remains.  Stick a pin through near Messina & pin to a vertical board, must be free to swing.  Hang a piece of cotton with small weight from pin.  Draw line where cotton thread lies.  Repeat near Richards Bay & Alexander Bay.  3 lines should cross at a point = CofG of the cardboard.

If you stuck a pin through that point & pinned it to a vertical board, gave it a spin there would be no heavy point so it would stop with any point at the bottom.  The thing is balanced so, to me, that is the best center.  Theoretically could also balance it on a pin stuck through there.

My method 1 was the NS & EW mid point idea but the thing would be out of balance on the pin test.
yes! :thumleft:

cut out my green RSA in post #29 and stick a pin through the pink dot - it will (should) be balanced!
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Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #72 on: September 16, 2011, 09:21:50 am »
The thing is there is no "standard" it seems. So what I propose is a "Pin the donkey" trip to visit all the proposals and find any donkeys along the way... :mwink:
 

Offline Bie

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Re: Where is the geographic centre of South Africa?
« Reply #73 on: September 16, 2011, 09:28:34 am »
Quote
cut out my green RSA in post #29 and stick a pin through the pink dot - it will (should) be balanced!

Please post the map you used to get your green RSA map as the projection differs from the overlay I have, meaning the point will not be exact on my overlay map.
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Offline RobC

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Re: Where is the geographic centre of South Africa?
« Reply #74 on: September 16, 2011, 09:32:10 am »
Quote
cut out my green RSA in post #29 and stick a pin through the pink dot - it will (should) be balanced!

Please post the map you used to get your green RSA map as the projection differs from the overlay I have, meaning the point will not be exact on my overlay map.
Yikes... so there is not even a "standard" RSA!  :deal: :mwink: :imaposer:
 

Offline Groenie

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Re: Where is the geographic centre of South Africa?
« Reply #75 on: September 16, 2011, 09:33:52 am »
You need one of these.



Last time I saw one was at varsity, many moons ago. It's a mechanical integrator and you trace the 'pin' around the edge of an object to find all sorts of wonderful (useless) info about it.

Here's more

http://infolab.stanford.edu/pub/voy/museum/pictures/display/4-4-Integrator.htm
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Re: Where is the geographic centre of South Africa?
« Reply #76 on: September 16, 2011, 09:35:33 am »
As long as Eskom is doing their part we are way beyond those nowadays. Only for blackout days.  :imaposer:
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Offline Groenie

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Re: Where is the geographic centre of South Africa?
« Reply #77 on: September 16, 2011, 09:36:05 am »
Don't look back, that's not where you're going.
 

Offline The Rock

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Re: Where is the geographic centre of South Africa?
« Reply #78 on: September 16, 2011, 09:37:04 am »
i found an Autocad dwg file of the outlines of african countries and used the RSA bit from that. its probably not a very accurate outline, but i didnt use an actual map - dont have the software for that.
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Offline Heimer

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Re: Where is the geographic centre of South Africa?
« Reply #79 on: September 16, 2011, 09:38:45 am »
If there is more than 1 centre point, we could plot those (which will be only a few) and then get to the centre of the centre  :biggrin:

« Last Edit: September 16, 2011, 09:40:55 am by Heimer »

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