# Illusions of Curvature - RC Boat Hidden on Small Pond

#### Hepper

##### New Member
I found an interesting video which shows an RC boat with a flashlight moving away from the camera, eventually disappearing below the horizon. This "test" however was conducted at a relatively small pond, no more than 600 feet in diameter. This is simply too small to allow for any curvature obstruction, which means that the water surface is almost perfectly flat. Yet we can clearly see the boat along with the flashlight vanish below the apparent horizon at some point (2:35 in the video onward). Is this attributable to wave height or atmospheric effects like negative refraction? Can this observation be used to explain how certain objects appear to vanish below an illusory horizon on a flat Earth?

Waves shouldn't have any significant influence, as all we see in the video are some small ripples and the light is mounted in fairly high above them. My money would be on, as you put it, "negative refraction". The listed temperature for the first clip 21 degrees, presumably Fahrenheit. Water freezes at 32 degrees, so because the pond isn't frozen, the water temperature must be greater than that of the air, and by a pretty significant amount, as corroborated by the strong inferior mirage seen at the opposing shoreline:

The red line in my insertion to mark the approximate location of where the inferior mirage starts. Later on, the second test is conducted, with the air temperature stated to be 38 degrees Fahrenheit. Note that there is very little obvious inferior mirage. It does look at time like there may be some, but I wonder if it's just from the light reflecting off the water:

Without actually knowing the water temperature, it's hard to make a definitive determination of what's going on. Based on the miraging that we see, and knowing that, generally, light deflects toward the colder medium, I would say it's just a bit of refraction in the upward direction.

As a final point, I'd juxtapose this with the following:

Source:

The fellow who took the video has done a lot of observations of the Turning Torso skyscraper in Sweden, and is very meticulous in specifying the details of his observations. For this one, he lists both the air and water temperature as being between 2-4 degrees Celsius, so in very close agreement. His observation point is also significantly above the water at nearly 4 meters, which reduces the possibility of significant thermal inversions directly over the water's surface.

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I think perhaps the simple answer might be that water dissolves into the air near the surface of the water and makes the air less dense which causes light to curve up near the surface of the water.

Water vapor, being 2/3 hydrogen gas is less dense than oxygen+nitrogen. As the water dissolves into the air it forms a less dense and lighter layer - just like the traditional mirage on a hot paved road - and just the same, this layer is not stable in that the lighter layer begins to rise and mingle because it's lighter, so the region of gradient is pretty thin comparatively.

This would cause the light path to curve up, which would literally cause the object to appear to have gone around the curve, which is also suggested by the fact that things still visible show up reflected upside down.

(This contrasts to the other kind of mirage where the air is more dense down lower causing light to curve down, causing things to appear higher: This is a stable gradient because the warmer less dense air naturally wants to remain above the colder more dense air, which can allow a gradient to cover a very large vertical distance.)

These two gradients can both exist at the same time creating a dense region a bit above the water with less dense (Warmer) air above and less dense (Wetter) air below - this forms a "duct" which can actually allow light to tunnel along great distances - although usually you do not get a clear image but the light can go a very long ways like light in a graded index fiber optic.

When I've been shooting telephoto close to water surface I always see that inverted mirage close to the water, even over relatively short distances.

In fact, one time I was sighting my theodolite across the water at 6 feet above, and the horizon was actually very slightly above instrument level. I then moved it up to bout 10 feet above the water, and then the horizon was below instrument level. When weather gets a little more conducive to being outside I would like to go back and try again from as low as I can get and work my way up to get some more exacting data.

To really have a chance at measuring curve with light, one needs to use an observation point and a target that are both far enough above the water that the target is not literally being inverted by the water-surface mirage.

Water vapor, being 2/3 hydrogen gas
I don't think the above statement is correct though that doesn't invalidate the general thrust of your argument. Water vapour is water vapour, the Hydrogen atoms do not dissociate from the Oxygen atoms to form a mixture of H2 and O2 when water evaporates, they remain bonded together as H2O molecules. The physical properties of water vapour are distinct from the physical properties of Hydrogen gas. I also think you might be conflating mass density with optical density?

Has anyone considered that the boat may just turn such that the light is no longer pointed towards the camera? The light reappears at 3:16 well over to the right from where it disappears. In any scenario for the light to reappear the boat must have at some point turned back towards the viewer.

Has anyone considered that the boat may just turn such that the light is no longer pointed towards the camera?
I looked at it frame by frame. you can see the red boat (a lot of it) even when the light is not pointing towards us. I think it must be that mirage thing hiding the boat (or a photoshop trick, but I couldn't really see a photoshop tell). but the boat doesn't disappear like big ships disappear over the horizon, ie. bottom up. I can see the whole red boat, then poof the whole thing is gone in the next frame.

edit add: the side of the boat... you see then it disappears. meaning the boat isnt sailing toward the shore when it disappears, its parallel to the shore.

I don't think the above statement is correct

Could you please clarify? I'm certainly aware that hydrogen is not a free gas in water vapor. But then again I wasn't writing a doctoral thesis either.

Are you saying that air doesn't become less dense (kg/m^3) when it has water dissolved into it?
Or are you saying that air doesn't get a lower index of refraction when it has water dissolved into it?
Or are you saying it gets neither lower mass density nor lower refractive index due to dissolved water?

Or were you just saying that I didn't word it technically correct?

Thanks!

Relative humidity does affect refractive index, but generally a lot less than density changes due to temperature. A 100% change in RH is about the same as 0.5°C change in temperature - in terms of the effect on RI.

I've been playing around with the refraction simulation. But I discovered it's not very good at fine detail under 1 foot in altitude.

The simplest answer to what's happening here is that it's hidden behind an inferior mirage because the water is warming the air just above it.

The simplest answer to what's happening here is that it's hidden behind an inferior mirage because the water is warming the air just above it.

Interesting. I'm in eastern Washington, USA, and the salt water is generally very cold and the air usually isn't that cold, especially on a sunny day. I would have never imagined that the water was warming the air here.

I'll definitely take a thermometer with me next time I go!

Here's a video I took of a boat in a bay. It was a sunny pleasant day (Not a hot day but not too cold either since the sun had been shining and it was a calm day) and there seemed to be quite a mirage when I held the camera close to the water:

VIDEO: Shows a boat several hundred feet away (maybe a couple thousand) at first with the camera held 3 inches above the water, then about 10 feet above the water, with a nice mirage effect when the camera is close to the water:

Source: https://youtu.be/HhfqRnQfcFw

[Mod: "Cloud Edge Effect" split to: https://metabunk.org/threads/the-cloud-edge-effect.11117/ ]

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Interesting. I'm in eastern Washington, USA, and the salt water is generally very cold and the air usually isn't that cold, especially on a sunny day. I would have never imagined that the water was warming the air here.

How else would the air get warm?

Sunlight can heat air, but not a lot. Air is mostly transparent, and the bulk of the heating comes from the sun heating the surface by radiation, and then the surface heating the air by conduction, and that that air circulating via wind and convection. Water heats slower than land, mostly because it's such a good heatsink.

We're talking about the few feet (or even inches, or sub-inches) above the lake surface here. At night, the air directly over the lake is cooled, in sunlight the lake warms, and warms the air it previously cooled. You can't just go by some generic air temperature, you need a precise temperature gradient inch by inch above the water surface.

This all is why observations of small things very close to the water are problematic - you get all these varied (and sometimes unintuitive) temperature gradients, and so a wide variety of images. So I always suggest rising up above refraction, and using the largest objects possible, like mountains.

Are you saying that air doesn't become less dense (kg/m^3) when it has water dissolved into it?

Me no physicist, but I would say a given volume of air with 'water dissolved into it' will be more dense than the same volume of air with no water, other things being equal.

But by taking up water vapour it seems that the air will also increase in pressure, since by Avogadro's Law the pressure depends on the number of gas molecules per unit volume, and this will increase as the water vapour is taken up. If the air is not constrained to maintain a constant volume, e.g. by a rigid container, then it will expand into its surroundings (usually also air) until the pressure throughout is uniform (apart from altitude gradients). At this point the 'parcel' of air with water vapour will apparently be less dense than the 'dry' air, since they will have the same number of molecules per unit volume (Avogadro again), but water molecules are lighter than those of oxygen and nitrogen. Of course, the water molecules will also tend to diffuse into the surrounding air, until there is no 'parcel' to be distinguished. Or convection will carry the parcel up until the water cools and condenses into liquid form.

I have assumed that by 'dissolved' water you do mean water vapour, i.e. water in a gaseous state. If it is water in the form of liquid droplets, all bets are off!

Could you please clarify? I'm certainly aware that hydrogen is not a free gas in water vapor.
OK, but it read to me like that's what you meant when you said:

Water vapor, being 2/3 hydrogen gas is less dense than oxygen+nitrogen.
It isn't true that if something is mostly hydrogen on a molecular level that it will be less dense than something that has a greater density than hydrogen gas. My apologies if I have misconstrued the point you were making.

Are you saying that air doesn't become less dense (kg/m^3) when it has water dissolved into it?
Or are you saying that air doesn't get a lower index of refraction when it has water dissolved into it?
Or are you saying it gets neither lower mass density nor lower refractive index due to dissolved water?
I didn't make any claims regarding how water vapour might effect the density or refractive index of air. It's probably true that the light close to the waters surface is refracted upwards and water vapour in the air could well be influencing that one way or another, but the underlying reason for this is not because water vapour is 2/3 hydrogen.

I don't know that getting bogged down theorising the mechanics of refraction as it relates to particular elements is really helpful. If humid air has a lower refractive index than dry air that is something that can be tested and demonstrated (and probably has been). It isn't then necessary to further explain why humidity has that effect on air to explain why the light disappears from sight.

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