# Measuring the Curvature of the Horizon with a Level

#### Trailblazer

##### Moderator
Staff member
Assuming you were standing in the middle of the disk. Which you always (kind of) are on a sphere (the "disk" being in the plane formed by the horizon)
Yes, I meant for staying in the same place horizontally and gaining altitude.

But that's also a good point - on the flat Earth, the horizon would be closer to you in one direction, depending where you were in relation to the edge.

#### Mick West

Staff member
On the Flat Earth model you would never see the horizon, as it's too far away. The existence of a horizon like we see here requires either some strange bendy light and/or a gross misunderstanding of perspective.

In fact the simply observations of the sharp horizon seen in this thread, together with the observation that the horizon recedes as you get higher, should be sufficient to demonstrate the curvature of the ocean.

#### Holy Irony

##### Member
On the Flat Earth model you would never see the horizon, as it's too far away.
What would we see, then ? I always wondered. Would the distant land be blurry or something ?

#### Trailblazer

##### Moderator
Staff member
What would we see, then ? I always wondered. Would the distant land be blurry or something ?

From an airliner at 35,000ft the horizon is about 230 miles away, and it's pretty hard to see where it is, due to the atmosphere.

On a flat Earth, the horizon would be wherever the Earth stopped, ie the edge of the disk, which would be thousands of miles away from most places, certainly most inhabited places (the Flat Earth Society says the flat Earth is 25,000 miles in diameter). If 200-odd miles of atmosphere can blur the horizon to that extent, then it's fair to assume you wouldn't be able to see a sharp horizon from thousands of miles away.

Of course, that is complicated by the fact that on a flat Earth you wouldn't be looking "over" nearby hills etc, so in practice your horizon would be limited by the visual high points of land in any given direction. Without any curvature, these would probably be reasonably close to you: you couldn't say, for example, that you ought to be able to see all the way to Mount Everest because nothing is higher, as a modest nearby hill (or even building) would present a visually higher angle.

But on a flat Earth you would never be able to look out at the open ocean and see a sharp horizon: the atmosphere would basically blur the division between land and sky into invisibility.

#### Holy Irony

##### Member
Ah, I see. Thanks for the detailed explanation.

#### Mack

##### New Member
So I just found a quick and easy way to debunk all the "Horizon is Flat, where is the curve" images using your method of compression on MS Paint.

Take the image, and resize it horizontally by 1-5%

Zoom in and witness the curve. The red line is a pixel perfect straight line as a reference.

#### Trailblazer

##### Moderator
Staff member
So I just found a quick and easy way to debunk all the "Horizon is Flat, where is the curve" images using your method of compression on MS Paint.
You have to be careful to isolate any distortion due to the camera lens, though, which can often be greater than the actual visual curvature of the horizon.

#### Mack

##### New Member
You have to be careful to isolate any distortion due to the camera lens, though, which can often be greater than the actual visual curvature of the horizon.

I understand, im new to the debunking scene and my knowledge of photography is very limited.

#### Mick West

Staff member
Take the image, and resize it horizontally by 1-5%

I prefer to crop it first, then resize vertically to 1000% (10x). That way you don't lose any pixels. Take your image from here:

Use the Crop tool:

Images size, Turn off the constraint (the chain link icon), height to 1000 Percent

Gives you this:

Small but noticeable curve.

If the image is sufficiently large, and the horizon is sufficiently sharp (generally from a low altitude, like this seems to be) you can use a large percentage, or just repeat the process. This is 100x. I also boosted the contrast:

While it does not prove anything without a straight edge parallel to the horizon (to correct for lens distortion), it DOES debunk:
all the "Horizon is Flat, where is the curve" images

And if you can get someone to understand what they are seeing, then it's a good illustration of how slight the horizon curve actually is.

#### Clouds Givemethewillies

##### Senior Member
I have a tiny fisheye lense for my webcam. That should produce an interesting curve if it will focus well enough on the horizon, and an infinitely long level.

#### Mick West

Staff member
A few weeks ago I was trying to discuss using a level with someone on twitter:

However he went in a different direction, and then went viral, becoming the subject of much mockery.
http://www.iflscience.com/environme...ent-goes-viral-just-not-in-the-way-hed-hoped/

Unfortunate, but it will be interesting if it has any effect on anything, either making people think about what "level" actually means, or some kind of backfire effect.

#### Attachments

• 20170521-100631-81og9.jpg
175.7 KB · Views: 279

#### deirdre

##### Senior Member.
and then went viral, becoming the subject of much mockery
except iflscience doesnt explain it.
so... its like .o14 degrees per mile right?

#### Rory

##### Senior Member.
Of course, the horizon is curved on a disk earth too.
To get the same curvature as in photos from 360 feet, it would be 23 miles radius.
Do we have the maths for this somewhere?

#### Mick West

Staff member
Do we have the maths for this somewhere?

I just used the distance to the horizon on a regular globe from 360 feet. But actually I guess that's not correct as you'd have to add the drop, so you'd be 360+352 feet above a similar flat disk.

#### Rory

##### Senior Member.
So I was walking in the hills and came across a bunch of junk that included some long things with straight edges:

I had a revisit with those photos I'd taken to try and show the curve and realised where I'd gone wrong: I wasn't directly 'straight on' with my level. My compression image, therefore, shows pronounced effects of perspective on the straight edge:

Just in case anyone else wants to do the same: a mistake I made to be avoided.

#### Enricks

##### Member
The astronomical horizon would be the same as the true horizon on a very large or infinite disk earth. But here on the sphere earth they are not the same. The difference is the dip of the horizon, and the dip increases with observer altitude.

Would the 25.000 miles disk FEs propose be large enough? (I'd assume yes, since the horizon - ie the edge of the disk - would be far far away from most points of the disk)

#### Trailblazer

##### Moderator
Staff member
Would the 25.000 miles disk FEs propose be large enough? (I'd assume yes, since the horizon - ie the edge of the disk - would be far far away from most points of the disk)
Rough calculations...

Assuming the radius is 12,500 miles (diameter 25,000 miles), then about 85% of the area of the Earth would be at least 1,000 miles from the rim (ratio of 11,5002​/12,5002​ = 84.6%).

From a decent sized mountain, say 10,000 feet (about 2 miles), located 1,000 miles from the rim, the dip would only be about arctan(2/1000) = 0.11 degrees. For comparison, on the globe Earth, the dip of the horizon from a 10,000ft mountain is 1.77 degrees.

#### ZigguratianA

##### New Member
Many people who are aware that we live on a globe still confuse this as they think that there is no curve at all at low altitudes. These images confirm that the curve is present always except one special case of optical distortion in a 360 degree simultaneous image.

I have posted the following to non-flat earth believers and they still seem to think it is not true :

This one seems to confuse many people horizon is always flat 360 degrees around you No, the horizon is not flat at any height or at any angle of view other than 360 degrees. A 360 degree simultaneous view or image will show the edge (horizon) of every sphere of every size distorted to be totally flat no matter how high up or low it is viewed when the 360 degree image axis is in alignment with the spheres' center, as would be the case on a hypothetical earth horizon image. There is no other geometric possibility. At any distance or height relative to any size sphere, the entire horizon or entire visible edge of that sphere is equidistant to the observer.

The earth sphere is so incredibly large that the curve is incredibly small and thus is not perceptible at low altitude and especially for human perception with the eye having a 55 degree angle of view, but it is there. This is geometric fact. If we increase the angle of view with a rectified optical lens device, then the curve will be more pronounced even at low altitude. Higher altitudes will be easier to see a curve even with a narrow angle of view, obviously.

One can photo the horizon of the ocean and detect the curve even at low heights and see the curve by a high resolution image squeezed horizontally or by drawing a straight line across the horizon. Of course the image must be sharp, on a clear day at best focus on the ocean horizon and of an adequately high resolution But if done right, it can be detected. It has been done(on this page here)

If one were to make a 360 degree view lens it would be convex vertically and the glass would curve 360 degrees with the light recorded inside that enclosed lens. The shutter would be 360 also. One could more easily use a chemical film wrapped cylinder instead of a curved CCD or CMOS image sensor. That 360 degree image taken of ANY spherical object no matter how large or small or at any height would be distorted to an absolute flat line in that image as long as the image axis is in alignment with the spheres' center, as the edge of any sphere 360 degrees from any position relative to that sphere is by geometrical definition equidistant and thus would appear absolutely flat. So the short answer is THE HORIZON OF ANY SPHERE OF ANY SIZE AT ANY HEIGHT VIEWED 360 DEGREES SIMULTANEOUSLY IS ABSOLUTELY FLAT. Again this is geometrical, optical fact as in no other possibility exists.​

Last edited by a moderator:

#### Mick West

Staff member
These images confirm that the curve is present always except one special case of optical distortion in a 360 degree simultaneous image.

While it's technically always present, it's very difficult to detect at very low altitudes - like at the beach. The problem is that a lot of Flat Earther's still try at the beach.

So telling them "the curve is always present", is probably not helpful, as they will go look for it at the beach, not find it, and declare the world is flat.

They need to be higher up. Like 500 feet up.

[EDIT] and of course the curve over the horizon is still there, and very detectable from the beach. Just not the visible curve of the horizon, which is a very different type of curve.

Last edited:

#### ZigguratianA

##### New Member
Unfortunately many people arguing FOR the globe have this idea that the horizon is literally flat

While it's technically always present, it's very difficult to detect at very low altitudes - like at the beach. The problem is that a lot of Flat Earther's still try at the beach.

So telling them "the curve is always present", is probably not helpful, as they will go look for it at the beach, not find it, and declare the world is flat.

They need to be higher up. Like 500 feet up.

[EDIT] and of course the curve over the horizon is still there, and very detectable from the beach. Just not the visible curve of the horizon, which is a very different type of curve.

Thanks. I hear you about fine details in discussion with flat earth believers. I am finding, however, many people arguing for the globe are saying that it is flat until a certain altitude. I thought this to be in geometrical error but could not find it specifically addressed in searches. after working it out in a 3d modeling program it became apparent that it is always curved, but this hypothetical special case of somehow capturing a 360 degree simultaneous image came to mind. I still was not sure. Thanks for the verification and help in this debunking...or at least straightening out this detail for those assuming this errant notion that there is no curve at low altitudes.

Last edited by a moderator:

#### Mick West

Staff member
many people arguing for the globe are saying that it is flat until a certain altitude
I think they are arguing the horizon LOOKS flat to the naked eye until you get to a certain level. Unfortunately this seems to be based more on mathematic than experience. As you get higher the horizon is less and less distinct because of the atmosphere. There's a huge section (depending on weather), from maybe 2,000 to 30,000 feet where you generally can't see the horizon well enough to tell if it's curving. Even as you get higher you are not generally seeing the ocean horizon, but the curve of the tops of clouds, and then of the atmosphere itself.

#### Rory

##### Senior Member.
Have I posted a link to this paper before?

http://thulescientific.com/Lynch Curvature 2008.pdf

They conclude that:

#### Mick West

Staff member
Have I posted a link to this paper before?

http://thulescientific.com/Lynch Curvature 2008.pdf

They conclude that:

All true, but it's worth pointing out that these are observations/detections of the curve of the horizon with the naked eye and no aids.

At low altitudes (under 1000 feet) you can detect the curve of the horizon in at least two ways:
1. With the naked eye and a sufficiently long straight level line - such as a taut string, or a long carpenters level. You can then observe the horizon being lower at the edges than at the middle (when viewed from a point opposite the middle)
2. By taking a wide angle photograph with a rectilinear lens and stretching it vertically (as above). Preferably this would also include a straight level line such as in #1

#### Rory

##### Senior Member.
All true, but it's worth pointing out that these are observations/detections of the curve of the horizon with the naked eye and no aids.
Agree with that.
You can [...] observe the horizon being lower at the edges than at the middle (when viewed from a point opposite the middle.
I'm still not 100% clear on this. First, that when we talk about "the curvature of the horizon", there seem to be two different curves: the curve that one would see when sufficiently distant/elevated (like the outline of a ball, which is what that paper seems to be talking about); and the curve formed by looking down on the arc of the horizon (the "edge of the coin", the measuring of which is what this thread is about). And second, that the curve, in the latter case, isn't formed by the middle being 'higher', but because we're looking at the edge of a circle (I imagine the middle as being 'further away' rather than higher - further away from shore, not the observer - though it will appear 'apparently higher' in a photograph).

Hope that makes sense. It's hard to be clear about something I'm not clear about.

Last edited:

#### Clouds Givemethewillies

##### Senior Member
Agree with that.

I'm still not 100% clear on this. First, that when we talk about "the curvature of the horizon", there seem to be two different curves: the curve that one would see when sufficiently distant/elevated (like the outline of a ball, which is what that paper seems to be talking about); and the curve formed by looking down on the arc of the horizon (the "edge of the coin", the measuring of which is what this thread is about). And second, that the curve, in the latter case, isn't formed by the middle being 'higher', but because we're looking at the edge of a circle (I imagine the middle as being 'further away' rather than higher - further away from shore, not the observer - though it will appear 'apparently higher' in a photograph).

Hope that makes sense. It's hard to be clear about something I'm not clear about.

Think about the horizon as the base of a cone. or a part of it, with the apex at the centre of the lense of an ideal camera. Think of a pinhole camera.. On the inside of the camera you get an image of the cone which intersects the plane of the sensor. The curve you get is a conic section which can be a circle if you are out in space and pointing at the centre of the earth. For part of a very shallow cone, that the horizon would form with a camera at the top of a small hill, the curve on the image would be a hyperbola, assuming an 'ideal' camera with a flat focal plane.

Last edited:

#### Trailblazer

##### Moderator
Staff member
I'm still not 100% clear on this. First, that when we talk about "the curvature of the horizon", there seem to be two different curves: the curve that one would see when sufficiently distant/elevated (like the outline of a ball, which is what that paper seems to be talking about); and the curve formed by looking down on the arc of the horizon (the "edge of the coin", the measuring of which is what this thread is about).
No, they are the same thing. The horizon is always a "flat circle", in as much as it is the same distance from your eye and the same elevation below it all the way round. So the curvature you see is always the "edge of the coin" curve caused by looking down on this flat circle.

It's simply that as you get higher and higher, the size of this circle gets bigger and bigger, and further and further below you, until at the extreme case when you are way out in space, the circle of the horizon is almost the same as the circumference of the Earth. (It will never quite be the same until you are at infinite distance away.)

The shift between the two is a perceptual one, really. If you play around with Google Earth slowly increasing your altitude, there's a point where your brain suddenly flips from "I'm looking at the edge of a circle" to "I'm looking at a ball", but nothing has really changed, it's just to do with how much of the horizon fits in your field of view, and whether you feel as if you're looking "out" or "down". (On GE this is artificially limited by the screen size, of course.)

Last edited:

#### Clouds Givemethewillies

##### Senior Member
Think about the horizon as the base of a cone. or a part of it, with the apex at the centre of the lense of an ideal camera. Think of a pinhole camera.. On the inside of the camera you get an image of the cone which intersects the plane of the sensor. The curve you get is a conic section which can be a circle if you are out in space and pointing at the centre of the earth. For part of a very shallow cone, that the horizon would form with a camera at the top of a small hill, the curve on the image would be a hyperbola, assuming an 'ideal' camera with a flat focal plane.

ps. The title of this thread should probably be changed to 'observing' rather than 'measuring' since the curve seen/photographed is not readily convertible to the radius of a sphere.

#### Mick West

Staff member
ps. The title of this thread should probably be changed to 'observing' rather than 'measuring' since the curve seen/photographed is not readily convertible to the radius of a sphere.

i'd thought of it as measuring how much the horizon appears to curve in the image, rather than the radius of a sphere.

#### cloudspotter

##### Senior Member.
No, they are the same thing. The horizon is always a "flat circle", in as much as it is the same distance from your eye and the same elevation below it all the way round. So the curvature you see is always the "edge of the coin" curve caused by looking down on this flat circle.

It's simply that as you get higher and higher, the size of this circle gets bigger and bigger, and further and further below you, until at the extreme case when you are way out in space, the circle of the horizon is almost the same as the circumference of the Earth. (It will never quite be the same until you are at infinite distance away.)

The shift between the two is a perceptual one, really. If you play around with Google Earth slowly increasing your altitude, there's a point where your brain suddenly flips from "I'm looking at the edge of a circle" to "I'm looking at a ball", but nothing has really changed, it's just to do with how much of the horizon fits in your field of view, and whether you feel as if you're looking "out" or "down". (On GE this is artificially limited by the screen size, of course.)

I think a good visual demonstration would be to take a ball, draw a circle on it to represent the horizon and then use that line as a guide to cut a slice off. Then put that slice down on a flat surface. I'm not really set up to do a decent job of it but I had thought a polystyrene ball with a hot wire to cut it would do it

#### Clouds Givemethewillies

##### Senior Member
i'd thought of it as measuring how much the horizon appears to curve in the image, rather than the radius of a sphere.
I don't know what came over me. Semantics is not really my thing..

#### Rory

##### Senior Member.
No, they are the same thing. The horizon is always a "flat circle", in as much as it is the same distance from your eye and the same elevation below it all the way round. So the curvature you see is always the "edge of the coin" curve caused by looking down on this flat circle.

It's simply that as you get higher and higher, the size of this circle gets bigger and bigger, and further and further below you, until at the extreme case when you are way out in space, the circle of the horizon is almost the same as the circumference of the Earth. (It will never quite be the same until you are at infinite distance away.)

The shift between the two is a perceptual one, really. If you play around with Google Earth slowly increasing your altitude, there's a point where your brain suddenly flips from "I'm looking at the edge of a circle" to "I'm looking at a ball", but nothing has really changed, it's just to do with how much of the horizon fits in your field of view, and whether you feel as if you're looking "out" or "down". (On GE this is artificially limited by the screen size, of course.)
Yes, I was going to say something about how, actually, they do seem like the same thing, just the different scale of each makes them appear different.

Moreso, though, what about the curve not being as a result of the middle of the horizon being "higher" than the edges?

Last edited:

#### StarGazer

##### Member
I've been looking into the graphic representation of Earth's Curve Horizon, Bulge, Drop, and Hidden Calculator and I've noticed that for a viewer the horizon is actually higher and closer than the Earth's bulge or at least that is what the graphic indicates.

If that is the case:

What is the formula to calculate the height of the horizon?
And could you please update the calculator if the horizon is indeed higher and there is a formula?

#### Clouds Givemethewillies

##### Senior Member
Delete the thin red line and it is fine.

#### Mick West

Staff member
I've been looking into the graphic representation of Earth's Curve Horizon, Bulge, Drop, and Hidden Calculator and I've noticed that for a viewer the horizon is actually higher and closer than the Earth's bulge or at least that is what the graphic indicates.

It simply depends on how high the viewer is.

The "bulge" point is just the midpoint between the viewer and the target object.
The horizon can be anywhere between the viewer (like if you have your eyes at sea level, like actually laying down with the water up to your eyeballs), to (or beyond) the target object.

Here's an interactive version. You can click on the "Camera" and the "Target" and see how things move.
https://www.geogebra.org/material/iframe/id/1153831

Notice that the "bulge" does not change with view height, but the horizon does.

And both points are at the same height: sea level.

#### StarGazer

##### Member
Here is a good example of a side view of Earth's curvature from sea level.

Image without zoom:

With slight zoom:

You can clearly see that from left to right the horizon is rising:

A bit more to the right I panned the camera at a lighthouse which is 11.4 miles away obscured by Earth's curvature.
The bottom of the image is where the beach ends and the sea begins:

And we still see that the horizon continues to rise from left to right:

Last edited:

#### Trailblazer

##### Moderator
Staff member
And we still see that the horizon continues to rise from left to right:
What are you basing the horizontal (yellow) line on? It looks more to me as if the camera is just a bit tilted.

#### StarGazer

##### Member
What are you basing the horizontal (yellow) line on? It looks more to me as if the camera is just a bit tilted.

Here is the Raw footage, please analyse it:

#### Mick West

Staff member
The camera is tilted.

Replies
8
Views
13K
Thread starter Related Articles Forum Replies Date
Measuring the radius of Earth using Long Range Observations (LROs) Flat Earth 0
Measuring Smart Meter RF Emissions 5G and Other EMF Health Concerns 1
Measuring 5G EMF and using ICNIRP Guidelines 5G and Other EMF Health Concerns 14
Flat Earth debunked by measuring angles to the sun Flat Earth 36
Measuring Horizon Drop And Earth's Equatorial Bulge From Rocket Launches Flat Earth 2
Method of measuring the distance to horizon Flat Earth 1
A DIY Theodolite for Measuring the Dip of the Horizon Flat Earth 148
Measuring the distance to the moon with laser reflections and the speed of light Flat Earth 5
Proposed experiment measuring Doppler shift of the sun on a flat earth model Flat Earth 9
Help: Panorama Maker and the Curvature of the Earth Flat Earth 19
Beautiful Photographs that show the Earth's Curvature Flat Earth 8
Dodgy 'Earth curvature calculators' Flat Earth 4
Illusions of Curvature - RC Boat Hidden on Small Pond Flat Earth 10
The German WWII "Knickebein" Navigation System and the Curvature of the Earth Flat Earth 11
A real-life 2D curvature analogy and a few thoughts regarding scale Flat Earth 2
Using railways to view curvature Flat Earth 3
Proving curvature: a distant island, viewed from different heights Flat Earth 0
Observations of a Wind Farm Over the Curve of The Earth Flat Earth 0
Can You Validate Earth's Curvature with a Drone? Flat Earth 14
Debunked: Isle of Man from Blackpool at water level proves flat earth [refraction] Flat Earth 19
Claim: zooming in on setting sun proves flat earth Flat Earth 23
Using a very long water level to measure Earth's curvature Flat Earth 16
Using pin hole lenses to debunk CGI Rebuttals of Photos of Earth Curvature Flat Earth 7
A Side View of the Curvature of the Earth at Lake Pontchartrain Flat Earth 55
Can 3 towers placed equidistant at the same latitude demonstrate curvature? Flat Earth 2
Water Level Showing Mountain and Horizon Dip Due to Curvature Flat Earth 32
Claim: First Image of Space Taken from V-2 Rocket Proves the Earth is Flat Flat Earth 17
Observations of Mallorca Island and the Earth's Curvature Flat Earth 28
Earth Curvature Simulation by Walter Bislins Flat Earth 9
Soundly Proving the Curvature of the Earth at Lake Pontchartrain Flat Earth 91
FE balloon video curvature analysis using Blender Flat Earth 4
Curvature and Refraction in Surveying and Leveling Through History. Old Books, etc. Flat Earth 14
Explained: Why a Spirit Level on a Plane Does Not Show Curvature "Corrections" Flat Earth 98
Problem with earth curvature calculator - Hope for revised version ? Flat Earth 5
Explained: Observations of Canigou, Curvature of the Earth & Atmospheric Refraction Flat Earth 158
San Mateo Bridge to Bay Bridge 17 mile curvature test Flat Earth 36
Help with a debate about curvature and distance calculations Flat Earth 30
Demonstrating the curvature of the Earth by Flying in a "Straight Line" Near the Poles Flat Earth 33
Curvature of earth - the definition Flat Earth 11
Views of Toronto from Hamilton and Fort Niagara Illustrate Earth's Curvature Flat Earth 44
Can you detect the curvature of the Earth with a taut line 3 miles long? [No] Flat Earth 55
Earth curvature: Differences with Sphere/Ellipsoid/Geoid models for Visibility etc Flat Earth 8
Ships beyond the horizon - Earth curvature demonstration Flat Earth 7
Video of New Orleans Superdome Illustrating Curvature and Refraction Flat Earth 5
Greenwich Meridian Laser - Can it Demonstrate Curvature? Flat Earth 20
Stephen Hawking's "Genius" Helicopter Demonstration of Lake Curvature Flat Earth 27
Curvature Experiment showing relation between x-axis and z-axis Flat Earth 15
Atmospheric sunlight refraction arguments on the Eratosthenes triangulation method Flat Earth 37
Seemingly Conflicting Curvature Observations in the Scottish Islands [Misidentified Islands] Flat Earth 6
Folsom Lake Photographs Demonstrating the Curvature of the Earth Flat Earth 36
Related Articles