#### Bobby Shafto

• 1390
##### How Far Away is the Horizon?
« on: May 23, 2018, 07:14:07 PM »
I've been stumbling over this, thought I'd figured it out, but now I'm back to confused.

I know how to calculate an approximate distance to a visual (and a radar) horizon on a globe earth if accounting for atmospheric effects.
What I don't know is how to interpret Rowbotham's explanation for horizon and horizon phenomenon in a way to calculate or even estimate a distance to a horizon plane.

There are diagrams in Earth Not a Globe like this:

...where the ground plane appears to slope upward to eye-level and then level off.

That point of H, where the slope changes from rising to level, parallel (coincident) with the level plane of the eye, is what EnaG claims is the horizon. I understand that. I even understand the explanation for why things further away than H can still be seen since H isn't a vanishing point. It's a line that is the edge of a plane, beyond which more distant things can still be seen (though smaller and smaller and ultimately converging with that edge (unless obscured by atmosphere or other other reasons first).

But what I can't grasp is how to figure where H is away from the observer. Tom Bishop might have misspoken when he wrote, "The horizon is one of the the furthest thing on earth that can be measured," but that has stuck with me and I've tried to work it out for myself, reading and re-reading the pertinent sections of EnaG. I'm just not getting it.

H is obviously dependent on the height of the viewer's eyes (or camera lens), as is true for a globe earth. But I can use geometry/trigonometry to calculate where the non-level eye line of the observer is tangent to the convex surface of the globe. And I can make adjustments or figure ranges of the distance to H to account for refractions. I can do all that on a globe.

What I can't resolve is how to do that given the conventional explanation for H in a flat earth model, where perspective plays such an important role.

I thought maybe Rowbotham's H might be calculated from the claimed limit of angular resolution of the human eye being 1 arcminute. But that's working out to be some crazy numbers, never witnessed or recorded. Diagrams and explanations and analogies are fine for conveying the concept, and I think I grasp the concept of what the horizon is for flat earth. But is there a way to figure how far away a horizon is in a flat earth model for a given height of the observer?

Basically, when do you know you are seeing a "true horizon" and, given that, how far away is it?
« Last Edit: May 23, 2018, 07:16:11 PM by Bobby Shafto »

#### Max_Almond

##### Re: How Far Away is the Horizon?
« Reply #1 on: May 24, 2018, 03:04:43 AM »
I guess the problem here is in trying to explain the nonsensical.

What would even cause a horizon on an enormous plane?

Horizon is a result of curvature. On a flat plane the land/sea would merely fade into the atmospheric haze at a huge distance.

How can we conceptualise that which cannot exist?

Noah's Ark makes more sense than the flat earth horizon.

#### hexagon

• 192
##### Re: How Far Away is the Horizon?
« Reply #2 on: May 24, 2018, 11:22:13 AM »
If you put the explanation in EnaG into a formula, you get d = h/tan(1°/60), where h is the eye level with respect to sea level and d is the distance to the horizon. Let's say eye level is at 2 meters, you get something like 6.9 km. On a globe you get about 5.1 km. It's roughly the same order of magnitude. That's what sounds reasonable if you have the "I'm standing at beach and watching the horizon" state of mind.

The problem is, that the EnaG formula scales linearly with height. At 20m the ratio is already 69:16, at 200m 690:50 and so on. That's the reason for the claim, that at larger height the horizon is always too hazy to be clearly visible. With this argument you are always safe. The value is too larger, no problem, there is hazy limiting you field of view.

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #3 on: May 24, 2018, 12:07:12 PM »
If you put the explanation in EnaG into a formula, you get d = h/tan(1°/60), where h is the eye level with respect to sea level and d is the distance to the horizon. Let's say eye level is at 2 meters, you get something like 6.9 km. On a globe you get about 5.1 km. It's roughly the same order of magnitude. That's what sounds reasonable if you have the "I'm standing at beach and watching the horizon" state of mind.

The problem is, that the EnaG formula scales linearly with height. At 20m the ratio is already 69:16, at 200m 690:50 and so on. That's the reason for the claim, that at larger height the horizon is always too hazy to be clearly visible. With this argument you are always safe. The value is too larger, no problem, there is hazy limiting you field of view.
That's how I interpreted it too...

...but the rapidly increasing distances at just simple low heights didn't pass scrutiny, so I thought I must be understanding it incorrectly. But you see it the same way.

For instance, some height observation values I made some sightings from yesterday were 10', 100' and 400'. For a globe, that works out to horizon distances of 4.2 miles, 13.25 miles and 25.5 miles respectively, allowing for standard refraction.

For a flat earth, with that height/tan(0.0167°) formula, the horizon distances are 6.5 miles, 65 miles and 260 miles. That just didn't seem right, hence this topic. You're saying those are right. Would appreciate a FE proponent's affirmation. (Always wary about globe earthers explaining EnaG to each other.)

#### hexagon

• 192
##### Re: How Far Away is the Horizon?
« Reply #4 on: May 24, 2018, 12:20:47 PM »
(Always wary about globe earthers explaining EnaG to each other.)

I know, and they don't like it, too. But EnaG is no rocket science, in the end it's all very simple descriptions and explanations. The old fashioned language and the non-scientific, not really precise language is sometimes a bit of a problem. Basically one could summarize the whole content in 10 pages or so.

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #5 on: June 04, 2018, 06:10:52 PM »
It'd like to reiterate my request for a FE proponent to explain how distance to the horizon is calculated.

My question was re-sparked after reading: https://wiki.tfes.org/Viewing_Distance
"When you increase your altitude on a plane you have broadened your perspective lines and have pushed your new vanishing point backwards into the distance."

If the "the perspective lines are modified and placed a finite distance away from the observer," then how can it be determined what that finite distance is, whether it's the horizon or the vanishing point pushed into the distance?

If this is not answerable, as in there is no formula or calculation method, I'd appreciate confirmation of that.

« Last Edit: June 04, 2018, 11:13:59 PM by Bobby Shafto »

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #6 on: June 04, 2018, 09:18:04 PM »
Is this correct?

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #7 on: June 04, 2018, 10:45:51 PM »
If correct, at 100' above sea level, the theoretical maximum distance to the horizon is 65 (statute) miles before perspective has brought the horizon to eye-level.

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #8 on: June 05, 2018, 06:29:43 PM »
If correct, at 100' above sea level, the theoretical maximum distance to the horizon is 65 (statute) miles before perspective has brought the horizon to eye-level.
If correct, at 20" above the water line, H would be 1.08 miles before perspective raises the horizon to eye-level and the bottom of things start to merge with the vanishing point/line.

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #9 on: June 05, 2018, 06:32:32 PM »
2 weeks.
9 posts, 6 of which are mine.

I'll chalk this question up as one that is unanswerable.

#### junker

• Planar Moderator
• 9867
##### Re: How Far Away is the Horizon?
« Reply #10 on: June 05, 2018, 06:48:29 PM »
2 weeks.
9 posts, 6 of which are mine.

I'll chalk this question up as one that is unanswerable.

Please don't bump posts just to complain that no one wants to talk to you.

#### iamcpc

• 832
##### Re: How Far Away is the Horizon?
« Reply #11 on: June 06, 2018, 11:31:48 PM »
2 weeks.
9 posts, 6 of which are mine.

I'll chalk this question up as one that is unanswerable.

well it depends on the altitude of the observer and the altitude of the horizion. The higher up I go the further I can see. From an airplane I can see into other states that I can't see on the ground.

you could use this post to determine less than 8 miles, assuming that all photographs were taken from roughly the same altitude:

https://forum.tfes.org/index.php?topic=9775.0

Here's the Wikipedia article:

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

If you want the flat earth response:

It's difficult to measure the distance to the horizon because all horizon distance calculation systems were specifically designed to support a round earth using round earth measuring devices and round earth distances.

#### Tom Bishop

• Zetetic Council Member
• 9877
• Flat Earth Believer
##### Re: How Far Away is the Horizon?
« Reply #12 on: June 08, 2018, 01:47:20 AM »
If you put the explanation in EnaG into a formula, you get d = h/tan(1°/60), where h is the eye level with respect to sea level and d is the distance to the horizon. Let's say eye level is at 2 meters, you get something like 6.9 km. On a globe you get about 5.1 km. It's roughly the same order of magnitude. That's what sounds reasonable if you have the "I'm standing at beach and watching the horizon" state of mind.

The problem is, that the EnaG formula scales linearly with height. At 20m the ratio is already 69:16, at 200m 690:50 and so on. That's the reason for the claim, that at larger height the horizon is always too hazy to be clearly visible. With this argument you are always safe. The value is too larger, no problem, there is hazy limiting you field of view.

I can affirm that this is the correct answer.

#### AllAroundTheWorld

• 5686
##### Re: How Far Away is the Horizon?
« Reply #13 on: June 08, 2018, 07:06:12 AM »
I can affirm that this is the correct answer.
What empirical observations have you done to verify this?
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

TFES Wiki Occam's Razor page, by Tom: "What's the simplest explanation; that NASA has successfully designed and invented never before seen rocket technologies from scratch which can accelerate 100 tons of matter to an escape velocity of 7 miles per second"

#### hexagon

• 192
##### Re: How Far Away is the Horizon?
« Reply #14 on: June 08, 2018, 09:09:02 AM »
I can affirm that this is the correct answer.
What empirical observations have you done to verify this?

In the light of e.g. this quote from EnaG "This is the true law of perspective as shown by nature herself; any idea to the contrary is fallacious, and will deceive whoever may hold and apply it to practice.", there is not necessity for empirical observations.

#### Max_Almond

##### Re: How Far Away is the Horizon?
« Reply #15 on: June 08, 2018, 09:49:54 AM »
I really think for people who are confused about perspective, the best thing is to make scale models. Otherwise it's very difficult for them to get their heads around - and almost impossible for the rest of us to understand where they're coming from, and therefore tell them how it really is, so alien is their understanding.

#### AllAroundTheWorld

• 5686
##### Re: How Far Away is the Horizon?
« Reply #16 on: June 08, 2018, 10:58:28 AM »
I really think for people who are confused about perspective, the best thing is to make scale models. Otherwise it's very difficult for them to get their heads around - and almost impossible for the rest of us to understand where they're coming from, and therefore tell them how it really is, so alien is their understanding.

Unfortunately that's where you get into stuff about "OK, this works over 1 meter, how do you know it works over 10 meters, or 100, or 10,000..."
The question is how do we know things still work over larger distances?
The answer of course is "geometry", scale models are useful because the world DOES work the same over different scales (within reason, let's not get all quantum theory or relativity about this).
But I believe's Tom argument is how can you prove that?
So in a scale model if a model sun is 3m above the ground and 12m away horizontally from a point then that would represent a sun 3,000 miles above a flat earth and 12,000 miles distant (which is I think the distance it is at sunset). Can you see that model from the ground at that point? Yes. Ergo, you should be able see the sun at sunset, sunset wouldn't happen.
But how do you know reality works the same when you're talking about thousands of miles rather than meters? What experiments have you done?
Obviously the answer, again, is "geometry" and "how can you do an experiment over thousands of miles?"
But to the latter Tom would then say "well, you can't prove it then".
I may be misrepresenting him but I think that is the gist of the argument against scale models.
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

TFES Wiki Occam's Razor page, by Tom: "What's the simplest explanation; that NASA has successfully designed and invented never before seen rocket technologies from scratch which can accelerate 100 tons of matter to an escape velocity of 7 miles per second"

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #17 on: June 08, 2018, 12:50:01 PM »
If you put the explanation in EnaG into a formula, you get d = h/tan(1°/60), where h is the eye level with respect to sea level and d is the distance to the horizon. Let's say eye level is at 2 meters, you get something like 6.9 km. On a globe you get about 5.1 km. It's roughly the same order of magnitude. That's what sounds reasonable if you have the "I'm standing at beach and watching the horizon" state of mind.

The problem is, that the EnaG formula scales linearly with height. At 20m the ratio is already 69:16, at 200m 690:50 and so on. That's the reason for the claim, that at larger height the horizon is always too hazy to be clearly visible. With this argument you are always safe. The value is too larger, no problem, there is hazy limiting you field of view.

I can affirm that this is the correct answer.

Thank you.

I can use these numbers, then:

And make some modifications to ENAG figures to better reflect this flat earth horizon understanding, as such:

« Last Edit: June 08, 2018, 12:59:36 PM by Bobby Shafto »

#### AllAroundTheWorld

• 5686
##### Re: How Far Away is the Horizon?
« Reply #18 on: June 08, 2018, 01:05:30 PM »
If you put the explanation in EnaG into a formula, you get d = h/tan(1°/60), where h is the eye level with respect to sea level and d is the distance to the horizon. Let's say eye level is at 2 meters, you get something like 6.9 km. On a globe you get about 5.1 km. It's roughly the same order of magnitude. That's what sounds reasonable if you have the "I'm standing at beach and watching the horizon" state of mind.

The problem is, that the EnaG formula scales linearly with height. At 20m the ratio is already 69:16, at 200m 690:50 and so on. That's the reason for the claim, that at larger height the horizon is always too hazy to be clearly visible. With this argument you are always safe. The value is too larger, no problem, there is hazy limiting you field of view.

I can affirm that this is the correct answer.

Thank you.

I can use these numbers, then:

And make some modifications to ENAG figures to better reflect this flat earth horizon understanding, as such:

Hang on...
Am I missing something here?
If the horizon is only 6.5 miles away at sea level and the horizon is where perspective lines merge then why doesn't the sun set when it's only a few miles away if you're at the sea?

EDIT: Something to do with the height of the sun? Is there any calculation which shows how objects at various heights would "set"?
« Last Edit: June 08, 2018, 01:10:05 PM by AllAroundTheWorld »
Tom: "Claiming incredulity is a pretty bad argument. Calling it "insane" or "ridiculous" is not a good argument at all."

TFES Wiki Occam's Razor page, by Tom: "What's the simplest explanation; that NASA has successfully designed and invented never before seen rocket technologies from scratch which can accelerate 100 tons of matter to an escape velocity of 7 miles per second"

#### Bobby Shafto

• 1390
##### Re: How Far Away is the Horizon?
« Reply #19 on: June 08, 2018, 01:15:11 PM »
In the figure above, the horizon is at H. The sun appears to set at W, which is further away than H.  H is where the earth's surface stops appearing to rise to eye-level, but beyond that, object appear to sink into a convergence zone behind it.

BTW, that figure might be wrong about the angles for converging lines beyond H. For instance, W for a sun 3000 miles above earth using the same theta would "set" over 10 million miles away. Can't be right.
« Last Edit: June 08, 2018, 01:18:45 PM by Bobby Shafto »