Seeing the curvature of the earth.

johnalison said:
... whereas the only accurate camera, a pinhole camera, will show verticals converging.
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A pinhole, or any other, camera will show verticals correctly so long as the focal plane is also vertical. Simple geometry requires this. The fancy "rising front" architectural cameras allow the focal plane to remain vertical while the field of view of the camera is pointed upwards instead of showing too much ground in front of the building.

Also don't confuse converging lines with curved ones. Drawing perspective with "vanishing points" for parallel lines just requires a straight ruler.

Mike.
 
'I've also read that ancient mariners knew the earth wasn't flat because they could see it's curvature.'
They could see the masthead first, then the sails, and eventualy, the hull. Obviously the world was a ball!
 
mjcoon said:
Also don't confuse converging lines with curved ones. Drawing perspective with "vanishing points" for parallel lines just requires a straight ruler.

Mike.
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Although we were all taught how to draw receding parallel lines, such as a road or railway, and this used straight lines, in fact, when these lines are extended past where we are standing, they become parallel again, and so must be curved to make them join. An artist would portray them with straight lines as I have below, but this is a necessary artifice. In reality, a railway line would be more like my lower sketch.
persp_zpscqx1ahjs.jpg

persp%20a_zpsdytmml8h.jpg
 
Look at it, so to speak, this way.
Imagine that your height of eye is about 1.5 metres above ground level. "Ground" in this case is the level top of a sea-cliff, and that you, wishing to live a bit longer, are 1.5 metres from the edge.
If you look directly out to sea, and then cast your gaze a bit downwards, you can see the sea; the closest bit of sea you can see lies at an angle 45 degrees below horizontal. So the sea, viewed thus, subtends a vertical angle of -45 degrees from horizontal, to (approximately) horizontal. 45 degrees in total.
Now turn your gaze such that it passes over the cliff edge about 100 metres along the cliff from you. The cliff edge is seen about 1 degree below horizontal. So the vertical angle subtended by the sea has reduced from 45 degrees to 1degree. Approximately.
How the brain interprets this is up to you. You may think "this is just a natural result of viewing the sea from a cliff top - nothing odd here". Or you might think that the cliff top isn't level (but it obviously is). Or you might interpret this to a bending of the horizon.
Alternatively - you might be using varifocal spectacles. These distort angles (as noted previously) in an attempt to do the optically impossible, it's part of the price you pay for being able to focus on any distance.
Whatever.
 
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johnalison said:
A I mentioned, it's not nly horizons that cause confusion. Artists invariably draw buildings with walls straight within the picture, whereas the only accurate camera, a pinhole camera, will show verticals converging.
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It depends what you mean by "accurate". A pinhole camera projecting onto a flat surface produces a different image from one projecting onto a spherical surface, like your retina. Anyone else remember Brownie 127 cameras with the curved focal plane?

Kodak%20Brownie%20127%20Camera.jpg
 
Just to add to the melon twisting visualisations.

Lets start with where the horizon is. No hill or dips to confuse things, so take a view from a boat mid ocean.
We know that the ocean surface is curved, an approaching boat will appear top bits first then lower down.
So, we live on a sphere, the higher you are, the further the horizon will be, it will also be a circle around you.
On a sphere a line that is vertical at the surface will pass through the middle, so a set of vertical lines that touch the horizon will form a cone.

Now, heres where the curve comes in. which ever way you look, the vertical (relative to the planet) line right in front of you will appear vertical, even though it is leaning away from you (as per the towers of the Forth Road Bridge). The weird bit comes with the vertical to each side. If you put a flat sheet of perspex in front of you and draw those verticals you will see they will be straight, but the tops splay outwards, you see that (relative to you) they arent vertical.

Now, if you draw a short line at right angles to each vertical, so they join up to make a horizon, they will bend down from the centre to the edges of your picture.

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Another way of thinking of it is to imagine a line that is horizontal right in front of you and at the horizon. The line is straight and after a few thousand miles will be in space, the horizon however will always be below it, the further from right in front of you, the lower the horizon will be.
 
mjcoon said:
Is this because you cannot imagine floating around a circle such as a hoola-hoop. If you view from the centre of the circle (or anywhere within the plane) then you cannot see the curvature. As soon as you leave the plane it is obvious.

Now replace the hoop with a huge sphere (Earth) with a large hole cut out of it (where your boat is) and you will see exactly the same thing.

Mike.
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Perhaps the most helpful analogy I've read, Mike.
I'll take a ruler (and a spirit level) when I walk the dog tomorrow.
 
KellysEye said:
>it was only 5 miles if you were about 17 feet from the water up the mast.More like 3 miles.

Radar was showing ships appearing above the horizon at 5NMs.
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Ships are actually quite high above the horizon, If your eyes were about 17 feet up then the real horizon was 5 miles away. Try google, it will explain it to you :cool:.
 
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