Lack of Proportionality in the Sinking Ship Effect

Hey,

FET proposes that the "sinking ship" effect occurs because as ships get smaller in the distance, they start to get obscured by waves. However, this would result in a strict proportionality between ship height and horizon distance; by simple similar triangles, a ship of double height should be able to go twice as far before "falling" off the horizon. However, this hasn't been observed -- most boats seem to "fall" off the horizon at about the same distance. Why is this?

Thanks!

Brilliant point!

Brilliant point!

Not really.

Quote from: geepun92 on January 31, 2013, 06:23:19 AM

Brilliant point!

Not really.

Why don't you explain it then? I mean, obviously you have the answer if you say that...

Quote from: geepun92 on January 31, 2013, 06:23:19 AM

Brilliant point!

Not really.

Go on..

also the height of the ship and the wave heights should all change the distance at which the sinking ship affect would become aparent. but they dont they all hapen at the same distance from the observer. why is this? 

FET proposes that the "sinking ship" effect occurs because as ships get smaller in the distance, they start to get obscured by waves.

Traditionally, that is precisely not the reason given for the "sinking ship" effect (though under some circumstances, I'm sure it may contribute some visual obscurance). I cannot answer to what any given poster is posting on the boards, but Chapter XIV of ZA:ENaG gives a thorough account of the subject along with several diagrams to help guide you along.

Hey, Ski,

So, I read the ENaG explanation and have to admit that it was rather heavy; correct me if my interpretation of it was wrong. What I took away from it was the following:

FET proposes that the "sinking ship" effect occurs because the ship simply gets too small to see (apparent angle less than one degree). The fact that the bottom of the ship "sinks" first is due to the fact that things closer to the sea tend to disappear first, experimentally (though I have tried this and my observations do not match up -- but we will pass over this point).

The proportionality argument seems to still apply here -- here's a crude attempt at drawing a diagram (I know the 1 degree angle is much too huge, but that doesn't matter):


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Thus PB/AB = PB'/A'B'. So ships twice as tall should still be able to go twice as far before vanishing completely.

As long as light travels straight, I think that this is true. Head Editor Tausami suggests that light may in fact refract, but that is up to experimental testing. So, what's going on?

Thanks!

In your diagram Ship 2 is not twice as far as Ship 1, unless I am completely missing your point 

Hey, Ski,

Well, to be honest, you sort of are... the point of the diagram was that the triangles were similar, and therefore the ship height is propotional to the distance at which its apparent angle becomes less than one degree.  That is, in general, a ship x times as tall should be able to go x times as far before it becomes invisible. In the diagram, Ship 2 is not double the height of Ship 1, either, but height1/height2 = distance1/distance2.

If you really need a "double-distance" diagram (which you shouldn't), here it is:


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I mean, this geometry is pretty trivial -- if you don't understand why this is so, I'm not sure I can help you (maybe someone else can try to illuminate Ski?).

Thanks.

actually, Rowbotham claims that a 60th of a degree, also known as an arc minute, is the minimum visible angular size, rather than a full degree.  If a full degree were our minimum, then the moon and sun would be invisible, as they are only half a degree in angular diameter.  But, dabbler the rest of your argument makes sense to me, and is still valid.  I have tried before to explain the mathematics behind calculating angular size to ski before, but he prefered to stick his fingers in his ears and repeat himself, then got fed up and left when that didn't work.

I'm pretty sure what happened is that I explained to you that perspective in practice does not work the way you think it does and instead compresses objects near the eyeline and cited real-life examples such as 29silhouette's photos which clearly show this. Following this you mindlessly repeated yourself, and I admittedly lost further interest.

Yes, sceptimatic. Larger objects that are closer to you will look larger. Unless your intention was that a person would be looking from opposite end of the "road" or the right in the second diagram, that picture is completely irrelevant to the basic premise of the post.

I'm pretty sure what happened is that I explained to you that perspective in practice does not work the way you think it does and instead compresses objects near the eyeline and cited real-life examples such as 29silhouette's photos which clearly show this. Following this you mindlessly repeated yourself, and I admittedly lost further interest.

I mathematically proved my point, but you left before I could.  It's no use getting fed up with someone who has a different understanding than you.  I'm not convinced any of 29silhouette's numbers were accurate.  He might have changed altitude, or there was an atmospheric change between photos.  I'd rather do the experiment myself.  I try not to take any personal accounts seriously whether coming from one source or another.

Also, Scepti, your diagram neither proves nor disproves anything, but is nonetheless a clear, albeit shaky example of perspective.  I can do perspective drawing too:

Hey, guys,

None of these pictures are particularly productive... I'm not talking about perspective here or what it looks like to the eye, but strictly which light rays can reach the person or not. Sure, perhaps perspective doesn't work like we think it does, and perhaps we've been drawing our landscapes wrong. But the 1/60th-degree concept should result in a proportionality between horizon distance and ship height. This has nothing to do with the "art-school" model of perspective. The only assumptions we make are that light travels in straight lines, and that we can only see an object if light from it hits our eyes. It is also completely concurrent with 29sihouette's pictures. I  agree that objects perhaps compress near the eyeline -- we're only dealing with when they become completely invisible.

So, FET must now either (a) show that light does not travel in straight lines, (b) contest the concept of "light" in vision, or (c) explain the "sinking ship" effect with a different phenomenon.

Nolekh and Ski, in the interests of resolving this concept, could we put aside your past argument? You can continue that discussion elsewhere if necessary.

Sceptimatic, I appreciate your contributions, but most of them are kind of vague. Could you add a little more text to explain what you mean by your drawings?

Could we try to keep to the concept? If at all possible, we should try to avoid argumentum ad hominum.

Thanks.

Dabbler, there is no "compression" from perspective.  The horizontal eye-line is not special in any way.  It is only one of an infinite number of eye-lines which surround our perspective.  You can have vertical and inclined eye-lines, and things don't compress around them.  For this reason, perspective must keep objects in vision proportional regardless of distance.  A compressing ship hull, or object in a photograph is not a result of perspective.  It is geometrically and mathematically impossible.  Such sights are explained only by light distortion or the earth being round.

I have a question about perspective etc

You're stood on the dock side, with your eye line say 10m above the water. You set a scope up so that it is perfectly horizontal and look at a nearby big ship you will see a point on that ship that is 10m above the sea, for ease in this example there's a bright line exactly at the height you're looking.

If the earth was flat then as the ship sails away from you shouldn't that bright line at 10m above the sea remain in the center of your scope?

I have a question about perspective etc

You're stood on the dock side, with your eye line say 10m above the water. You set a scope up so that it is perfectly horizontal and look at a nearby big ship you will see a point on that ship that is 10m above the sea, for ease in this example there's a bright line exactly at the height you're looking.

If the earth was flat then as the ship sails away from you shouldn't that bright line at 10m above the sea remain in the center of your scope?

The answer is yes.  But FET holds that the area below the eyeline diminishes faster than the area above.

Below is my version of a crude drawing of what I think should happen in this situation. I wonder if anyone has done this experiment.
I don't claim this to be correct, as I'm just putting some pointers forward and actually learning myself.

Your diagrams don't illustrate why the bottom part of the boat disappears.  Why does the bottom disappear, and not the top?

Hey, Nolekh,

On the eyeline compression -- I know, and I agree with you, but my purpose in saying that I agree that it might compress is that that compression does matter to my argument. That is, even if this compression existed, the proportionality that I explained would still hold.

This compression is not a point of contention here. We're discussing the fact that there is no proportionality between distance where the ship becomes invisible and the height of the ship.

Thanks, though.