Curvature of the earth
 

I've heard it said that out on the open sea, under the right condititions, one can see the curvature of the earth when looking at the horizon. I suspect that this is bullshit. I don't believe that humans can see far enough and/or see enough of the horizon laterally, to notice the curvature.

what do you think?

anyone got a link to something definitive (as in, say, a NASA article)?

I agree with you. If a person were to stand on a perfectly level place on a globe, like the sea, they would always be on the highest spot, according to their perception. As they observed their view of the globe the edge of their view would appear straight. Their line of sight would make the horizon appear like a perfectly straight line. The only way to view the curvature of the earth is to not be on the earth.

I don't know if I'm making much sense, I can see it my mind, hopefully it translated clearly.

Well, I'm assuming you want direct evidence, i.e., that the horizon itself appears to be curved...

I'm not sure if this qualifies in your book, but I've heard that this can be "seen" at the Bonneville Salt Flats in Utah, and this wikipedia article seems to explain that it's somewhat of an optical illusion:

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

The indirect evidence is that when looking out into the ocean, you see the top of a sailboat that is coming towards you from the open ocean before you see the rest of the boat itself. This would be impossible if the world was flat.

There may be some more useful info here:

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

I don't have proof, but consider this:

From space (say a geo-stationary satellite) you could see the curvature of the earth, right?
Now at the same location but on the surface of the earth you assume it is completely impossible to view the curvature of the earth. This implies that if you would travel from your location on earth to the satellite, at some point a change occurs that allows you to suddenly see the curvature.

Can you describe at what altitude this would be? I contend that at diminishing altitudes (not considering obstacles) the curvature is less obvious, but will never actually reach zero. Therefore, given good eyesight it should be possible to see the curvature of the earth.

I like thought experiments such as this, I'm not always good at describing my thoughts though, so if I'm rambling please say so :)

yellowmac, yes I meant direct evidence, meaning that one could see the curvature of the horizon.

Silvy, you are probably right, but I contend that human eyesight is not nearly good enough to see the curvature of the horizon at ground or sea level.

i live on the coast, from the beach, i can see the earth curve.

Forgive me for doubting you, Dilbert. I believe that you think you see the curvature of the horizon, but as I've said, I don't believe humans have eyesight nearly good enough to see it. I myself have stood upon the shores of the Atlantic Ocean and gazed eastward. I did not see any curvature.

yellowmac's got it right with wikipedia

Here is a very pronounced picture from the mast of a navy ship

http://alpenmic.com/photos/caribbean_2000/c2000-07.JPG

Remember the amount of curvature is dependant on the height, so if you are at sea level, you will not see much curve, but if you are on the cliffs above the ocean, you will see a fairly pronounced curve.

as seen here taken just above the ocean:

http://www.dlund.20m.com/images/Mol0812g.JPG

This ones pretty good too:

http://science.howstuffworks.com/question65.htm

I've had a camera on my remote-controlled airplane at altitudes of about 200 feet. I've never noticed the curvature of the horizon any of those photographs.

go to any open beach in australia and see it for yourself. ive seen it thousands of times.

its obvious, the curve is there!

I for one have never noticed the curveature of the earth from the ground. However, in a week I plan to be at an elevation of 11,000ft. Perhaps I'll notice something.

I have however seen the curvature of the Earth from a plane on many occasions. Usually on transatlantic flights, for some reason it seems to be easier to see when you're closer to a pole. Also some neat indirect evidence of the curve of the Earth that I've seen from a plane is the termination line. When you're on a late afternoon/evening flight and you look out the window toward the east you can actually see the point on the earth where day ends and night begins, and from that point is a wall of darkness stretching up into the sky. And if you look a half hour later, you notice the wall of darkness is much closer to the plane.

earth curved? the earth is flat everyone knows that. If it wasnt everyone on the bottom would just fall off.

Sure you can see it but its never going to be real noticable. and you wont be able to see it looking directly ahead. you will just see the horizon like that. you have to notice it side to side.

I think it's a matter of perception, not eyesight. Most people wouldn't know a straight line by simply looking at it, and conversely, a barely curved one. For example, a machinist who is quite familiar with working with perfectly straight lines would be able to spot minute defects that would escape most eyes.

Also, consider that you can not focus in on a very large area across your vision. The focus is at the center of your vision, and the peripheral is, well, not.

As a cool experiment, may I suggest that you line yourself up with something straight and horizontal, say a deck railing or perhaps a yardstick strung up at eye level. Use this as a reference to the horizon in the background and compare. Now, I won't speculate whether or not a curve can be seen, as I've never tried it personally, but if it is detectable, the straight line in front of it will surely bring it out.

that's a damned good idea. next time I'm at the shore, I hope I remember to try that.

I've seen the curve from the top of a mountain when you could see the sea curve.

You seeing the curvature of the Earth is an optical illusion. To demonstrate, get a toothpick, a sharpee marker with its cap, and a basketball. Fix the marker so that the marking end is against the ball and the other end is fixed to the top of the toothpick. The toothpick should be sticking as straight as possible out of the ball, don't pop it.

The basketball is the Earth, the toothpick is you standing straight up and the marker is the line of sight to your eyes. Turn the marker around and you get a circle that is the edge of your vision of the world. This circle does not curve down at all, it curves around you! Your brain thinks it is curving down only because it perceives the horizon to be against a perfectly flat plane perpendicular to your line of sight.

So you get higher and higher, the line of sight can trace further towards the equator of the Earth.

The point is, if we follow your prescription, there is a point at which we are hight enought to see the full circle of the world.

At zero altitude, the horizon looks like a perfect plane.

At infinite altitude (say, for example, from the Moon) the horizon is clearly circular, as one can view the entire hemisphere.

There must be some transition zone. I have seen the curvature of the earth from airliners (very high), light aircraft (moderately high) Mount St Hellens (pretty high), and the French alps (fairly high).

I have not seen it from the hills near my house, or the beach.

This would make me think that the transition zone lies between 1,000 and 6,000 feet altitude.

http://alpenmic.com/photos/caribbean_2000/c2000-07.JPG

i don't think this mast is higher then 200 feet, and you can see a definite curve.

Dilbert:

Is it possible that this image displays an example of barrel distortion?

http://www.digitalfilmtools.com/55mm/lensdistortion.htm

I thought everyone was saying that they could see the Earth curving downward, not around, my mistake. My demonstrations just states that mathematically there is no transition, the horizon is always circular. For reference, the altitude when the world takes up your full field of vision when looking straight down at the Earth occurs roughly at 986km (613 miles), and that can be calculated with a simple formula:
{Altitude} = {radius of Earth, 6378km} * [csc({span of vision, 120 o}/2) - 1]
=6378km * (1/sin(60 o) - 1) = 986km

There are geometric formulas which are not difficult but are tedious to apply that would describe the deviation from straightness of an arc.

There was a period of time when I was able to fly corporate jets for some of my travel. They typically fly around 45,000 feet, something to do with fuel and different altitudes for different types of planes.

Anyway, one thing I remember from those days is the difference being that high up. The sky was a very different shade of blue and you could actually see the curve on the horizon. I felt like I was nearly in space on nice days. We'd be up so high the clouds below looked like the ground!