Gradient teaser for REs

Just for fun ...

The town of Hamilton in New Zealand and the town of Cordoba in Spain are antipodes (allegedly  ). Exact opposite sides of the earth.

http://en.wikipedia.org/wiki/Antipodes

Hamilton Airport is at an elevation of 172ft AMSL.
Cordoba is 394ft AMSL

Lets assume I built a perfectly straight road (or great circle road) between the two, what would be the gradient and hence angle between them?
For flat earth it would be ...
394-172 = 222ft
222ft = 67.6656m

Distance between the two points is 40075.16 km / 2 = 20037.58 km
67.6656 / 20037580 = 0.0000033
so the FE gradient is 0.0000033   A very shallow descent or climb depending on your direction.
So on a flat earth the angle is tan * 0.0000033 = 0.00000005759586 degrees

The gradient represents the angle between the straight line joining the points at their base (gradient  = tan*angle) and the straight line between their elevations (note straight, not curved). So for a round earth the gradient or angle should be very close to 180 degrees should it not? IE my road wraps round the earth 180 degrees and this gives an average gradient (or rate of change) and hence angle of around 180 degrees.
I would very much like to see how a RE would calculate the exact angle as it is not quite 180 degrees. The towns miss each other by a few kilometres.

Below is an article on gradient mathematics to give you plenty of ways to attempt this.
http://en.wikipedia.org/wiki/Slope

PS - The straight line distance through the earth between them is 12 874 km if you need it.

Just a tea time teaser for 5 mins or so. 
Gradients are always used to calculate on the earth distances. The gradient of the river Nile or the gradient of Eyre Highway. So how does it work? The great circle distance along the River Nile is curved with the earth. The straight line (base) underneath is far shorter.
Source elevation = 8858ft.
Base is in the med - elevation 0ft
Distance 6580km.
What is the angle between the two? What's the gradient of the river for an RE'r? Should be the same as the earth rises as much as it falls over that distance. But the base is shorter with a round earth?

Thoughts and calcs welcome 

Inverse Tan90=89.363

For example,

89.363 = 804.27/9

That's a rise of 804.27m and a run of 9m.

Same problem, the numbers don't fit. Am I doing it wrong?

You are correct. It should be 90 degrees. We are using tan. A flat earth should be close to 0 degrees. A round earth 90 degrees.

The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the grade m of a road is related to its angle of incline ? by

m = tan ?

Apologies for that. 

it sucked out my omegas. The question marks are omega s lol!

 First, I don't see the difference with the slopes and gradients in flat or round earth. You take the height from the sea level and then you calculate. In the same way in both cases.
 Second, in your case you got it wrong at the start. You don't know the distance between the town of Hamilton in New Zealand and the town of Cordoba in Spain. You took the RE distance and you can't use that. Just take a look at the supposed FE map and try to figure out the distance between these towns from there. And come back when you have measured the FE distance between these two towns.

First, I don't see the difference with the slopes and gradients in flat or round earth. You take the height from the sea level and then you calculate. In the same way in both cases.
 Second, in your case you got it wrong at the start. You don't know the distance between the town of Hamilton in New Zealand and the town of Cordoba in Spain. You took the RE distance and you can't use that. Just take a look at the supposed FE map and try to figure out the distance between these towns from there. And come back when you have measured the FE distance between these two towns.

He also failed in that the earth isn't a perfect sphere lol. It's a spheroid. And yes, he might want to actually take a look at the FE map thread. 

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth. Curvature isn't factored in so the maths doesn't work. This is usually fine for short distances, but if you wanted to work out the gradient of the River Nile (maybe to calculate its speed for example) you couldn't do so as the distance is too great. RE's use FE mathematics all the time. It was just a little food for thought.

Vindictus was able to reverse the axis to get an answer for the antipodes problem. (Which was very clever on his part). But you can't do that for the Nile example as the angle isn't close to 90 degrees. You just couldn't use standard gradient maths to get a gradient over that distance. Unless of course the earth was flat. 

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth.

No, it isn't. It is just math. And on round earth you just take the height from the sea level for one point and height from the sea level from other point and then you calculate. You don't need to use tangent for such great distances, it's only for short ones.
 EDIT: As I was rather in hurry then I take back last sentence. You can use it whatever distances. And there is no need to take account the curvature of the earth. The heights are taken from the sea level and the sea level follows the curvature of the earth. So you would get the same results on the flat and round earth.

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth. Curvature isn't factored in so the maths doesn't work. This is usually fine for short distances, but if you wanted to work out the gradient of the River Nile (maybe to calculate its speed for example) you couldn't do so as the distance is too great. RE's use FE mathematics all the time. It was just a little food for thought.

Vindictus was able to reverse the axis to get an answer for the antipodes problem. (Which was very clever on his part). But you can't do that for the Nile example as the angle isn't close to 90 degrees. You just couldn't use standard gradient maths to get a gradient over that distance. Unless of course the earth was flat. 

Fail.

you can start here:

http://www.ehow.com/how_6931489_calculate-distance-between-points-lines.html
http://www.ehow.com/facts_6907238_calculate-distance-between-two-lat_longs.html
http://www.ehow.com/how_6590446_calculate-location-within-utm-grid.html

Then you can Watch this:

http://www.ehow.com/video_4980152_use-geometric-compass.html

And when you are done, google how to get your longitude and latitude by using the sun, stars, and moon. And you might just realize how accurate and consistent the RE mapping system is, and navigation systems are.

When you can provide a working coordinate system for FE, you let us know .. Especially over long distances. And please do visit the FE map thread.

Quote from: Thork on September 19, 2010, 05:13:09 PM

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth. Curvature isn't factored in so the maths doesn't work. This is usually fine for short distances, but if you wanted to work out the gradient of the River Nile (maybe to calculate its speed for example) you couldn't do so as the distance is too great. RE's use FE mathematics all the time. It was just a little food for thought.

Vindictus was able to reverse the axis to get an answer for the antipodes problem. (Which was very clever on his part). But you can't do that for the Nile example as the angle isn't close to 90 degrees. You just couldn't use standard gradient maths to get a gradient over that distance. Unless of course the earth was flat. 

Fail.

you can start here:

http://www.ehow.com/how_6590446_calculate-location-within-utm-grid.html

And when you are done, google how to get your longitude and latitude by using the sun, stars, and moon. And you might just realize how accurate and consistent the RE mapping system is, and navigation systems are.

When you can provide a working coordinate system for FE, you let us know .. Especially over long distances. And please do visit the FE map thread.

This entire post is completely irrelevant to anything he said.

Everyone in this thread needs to go through this peer-reviewed thread:


This should clear up any delirium issues that you may have.

Everyone in this thread needs to go through this peer-reviewed thread:

http://theflatearthsociety.org/forum/index.php?topic=16948.0

This should clear up any delirium issues that you may have.

That thread is far too long and people don't even stop ranting and start understanding and answering the actual question until many pages into it.

Quote from: TheJackel on September 19, 2010, 09:54:24 PM

Quote from: Thork on September 19, 2010, 05:13:09 PM

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth. Curvature isn't factored in so the maths doesn't work. This is usually fine for short distances, but if you wanted to work out the gradient of the River Nile (maybe to calculate its speed for example) you couldn't do so as the distance is too great. RE's use FE mathematics all the time. It was just a little food for thought.

Vindictus was able to reverse the axis to get an answer for the antipodes problem. (Which was very clever on his part). But you can't do that for the Nile example as the angle isn't close to 90 degrees. You just couldn't use standard gradient maths to get a gradient over that distance. Unless of course the earth was flat. 

Fail.

you can start here:

http://www.ehow.com/how_6590446_calculate-location-within-utm-grid.html

And when you are done, google how to get your longitude and latitude by using the sun, stars, and moon. And you might just realize how accurate and consistent the RE mapping system is, and navigation systems are.

When you can provide a working coordinate system for FE, you let us know .. Especially over long distances. And please do visit the FE map thread.

This entire post is completely irrelevant to anything he said.

Wasn't supposed to be.. His fail is that circumnavigation shows Earth to be spherical. And Zork already addressed his mistake.

Quote from: EnglshGentleman on September 19, 2010, 10:26:50 PM

Quote from: TheJackel on September 19, 2010, 09:54:24 PM

Quote from: Thork on September 19, 2010, 05:13:09 PM

Zork and Jackel. You missed the point of the thread. I am not trying to prove that the earth is flat or round or an oblate spheroid. The point of it is, you will find that the mathematics for gradient calculation are based on a flat earth. Curvature isn't factored in so the maths doesn't work. This is usually fine for short distances, but if you wanted to work out the gradient of the River Nile (maybe to calculate its speed for example) you couldn't do so as the distance is too great. RE's use FE mathematics all the time. It was just a little food for thought.

Vindictus was able to reverse the axis to get an answer for the antipodes problem. (Which was very clever on his part). But you can't do that for the Nile example as the angle isn't close to 90 degrees. You just couldn't use standard gradient maths to get a gradient over that distance. Unless of course the earth was flat. 

Fail.

you can start here:

http://www.ehow.com/how_6590446_calculate-location-within-utm-grid.html

And when you are done, google how to get your longitude and latitude by using the sun, stars, and moon. And you might just realize how accurate and consistent the RE mapping system is, and navigation systems are.

When you can provide a working coordinate system for FE, you let us know .. Especially over long distances. And please do visit the FE map thread.

This entire post is completely irrelevant to anything he said.

Wasn't supposed to be.. His fail is that circumnavigation shows Earth to be spherical. And Zork already addressed his mistake.

FE maps (regardless of their accuracy) have shown that circumnavigation is possible on FE.

Everyone in this thread needs to go through this peer-reviewed thread:

http://theflatearthsociety.org/forum/index.php?topic=16948.0

This should clear up any delirium issues that you may have.

This isn't peer-reviewed thread. Its the thread which puts you in delirium.

FE maps (regardless of their accuracy) have shown that circumnavigation is possible on FE.

lol.. Let me guess, you are going to make the pontoon in a lake argument lol. And do please provide an accurate FE map and coordinate system to validate you are on a FE lol. And I can walk, take a plane, drive, and visually navigate on a RE too .

Yay for pleading for ignorance by the Englishman

Quote

FE maps (regardless of their accuracy) have shown that circumnavigation is possible on FE.

lol.. Let me guess

Lol... let me guess. You are gonna spam this thread just like every other one about coordinate systems.

Quote from: TheJackel on September 19, 2010, 11:18:38 PM

Quote

FE maps (regardless of their accuracy) have shown that circumnavigation is possible on FE.

lol.. Let me guess

Lol... let me guess. You are gonna spam this thread just like every other one about coordinate systems.

It's more of a protest than a spam. And the reason is because you can't actually claim Earth is flat without actually establishing it as such. Coordinate systems are critical to that. And I am aware that FE doesn't have one, or a Map to go along with it to which reflects the real world. The fact I can successfully navigate using spherical coordinates in accordance to the real world is all I need to collapse the entire FEC(concept). So I would like FEr's to provide me with an accurate map and coordinate system equal to the same level of accuracy I can find in RE map and coordinate system in accordance to the real world.

So until FE can establish this, they don't have a base to argue with..

However, I will tone it down for sake of not flooding the forum with it. As it does seem a bit more than necessary at this point

Quote from: EnglshGentleman on September 19, 2010, 11:23:33 PM

Quote from: TheJackel on September 19, 2010, 11:18:38 PM

Quote

FE maps (regardless of their accuracy) have shown that circumnavigation is possible on FE.

lol.. Let me guess

Lol... let me guess. You are gonna spam this thread just like every other one about coordinate systems.

It's more of a protest than a spam. And the reason is because you can't actually claim Earth is flat without actually establishing it as such. Coordinate systems are critical to that. And I am aware that FE doesn't have one, or a Map to go along with it to which reflects the real world. The fact I can successfully navigate using spherical coordinates in accordance to the real world is all I need to collapse the entire FEC(concept). So I would like FEr's to provide me with an accurate map and coordinate system equal to the same level of accuracy I can find in RE map and coordinate system in accordance to the real world.

So until FE can establish this, they don't have a base to argue with..

However, I will tone it down for sake of not flooding the forum with it. As it does seem a bit more than necessary at this point

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Done, and FE lost.

Reference: 5/6 of the way around... http://archimer.ifremer.fr/search.jsp?record=11. The other 12 chapters are available from same source. Search in the English version for "The Voyage of H.M.S. Challenger 1873-1876".

Quote from: Uberrod on September 28, 2010, 05:00:22 PM

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Done, and FE lost.

Reference: 5/6 of the way around... http://archimer.ifremer.fr/search.jsp?record=11. The other 12 chapters are available from same source. Search in the English version for "The Voyage of H.M.S. Challenger 1873-1876".

wrong.

Quote from: ClockTower on September 28, 2010, 06:07:10 PM

Quote from: Uberrod on September 28, 2010, 05:00:22 PM

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Done, and FE lost.

Reference: 5/6 of the way around... http://archimer.ifremer.fr/search.jsp?record=11. The other 12 chapters are available from same source. Search in the English version for "The Voyage of H.M.S. Challenger 1873-1876".

wrong.

Would you elaborate?

Quote from: parsec on September 28, 2010, 06:23:37 PM

Quote from: ClockTower on September 28, 2010, 06:07:10 PM

Quote from: Uberrod on September 28, 2010, 05:00:22 PM

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Done, and FE lost.

Reference: 5/6 of the way around... http://archimer.ifremer.fr/search.jsp?record=11. The other 12 chapters are available from same source. Search in the English version for "The Voyage of H.M.S. Challenger 1873-1876".

wrong.

Would you elaborate?

You must be new here.

Quote from: Uberrod on October 01, 2010, 02:22:30 PM

Quote from: parsec on September 28, 2010, 06:23:37 PM

Quote from: ClockTower on September 28, 2010, 06:07:10 PM

Quote from: Uberrod on September 28, 2010, 05:00:22 PM

Speaking of maps, couldn't you just pick a point on the "ice wall" and measure how far you go to circumnavigate it? Because looking at the FE maps the thing is freaking huge. On the RE maps it's relatively tiny. Wouldn't that settle the question?

Done, and FE lost.

Reference: 5/6 of the way around... http://archimer.ifremer.fr/search.jsp?record=11. The other 12 chapters are available from same source. Search in the English version for "The Voyage of H.M.S. Challenger 1873-1876".

wrong.

Would you elaborate?

You must be new here.

Yes I am new, but I've seen Parsec's one word answers before. Thought I'd give it a shot anyway.