Comments on: Distance to the Horizon

By: Ahmet Faruk YAZICI

Ahmet Faruk YAZICI — Mon, 14 Feb 2011 15:18:13 +0000

I came across this blog while trying to figure out if there is an add-on for Google Earth to calculate how far is the horizon for desired point. In concept, it's a very simple calculation. Google Earth provides the elevation data for every square-meter of our land. When you use this data with the equation on the "Horizon" article @wikipedia, you got what you need.

By: Rob Gulley

Rob Gulley — Wed, 01 Dec 2010 06:25:53 +0000

Antonio,

I spent a few days trying to figure out your question with both sides of varying height. I think this might be the answer:

Using:
R1 = Radius of earth
P = Height of your “platform” from the surface
M = Height of the mast of the boat you are watching sail away

Theta = Arcsin ( R1 / (R1+M) ) + Arcsin ( R1 / (R1+P) ) – PI/2

Then subtract Theta from Pi/2 to get the “Theta traveled by the boat” so to speak, that is, the angle formed by you, the boat, and the center of the earth. Divide the “Theta traveled” by two-PI, a full circle, and multiply by whatever you are using for the circumference of the earth. That’s how far the boat will be once the top of its mast drops below your horizon.

Eh?

By: Antonio Burla

Antonio Burla — Sat, 18 Sep 2010 16:57:37 +0000

Hi Erik… A quick one: all those calculations assume that at least one of the sides is on a plain looking into a horizon… What happens if both sides are on varying heights? How does it affect the formula? E.g. I live on the 30th floor of a building (say 100 metres in elevation) and I want to see how far into the horizon I can see if the objects there are, say, 400m in elevation, 1,000m in elevation and etc.

By: Erik R.

Erik R. — Tue, 26 Jan 2010 21:43:03 +0000

Most excellent post, Marcos! To everyone reading this, please go check out his gorgeous graphics, whether you can read Spanish or not.

By: Marcos Molina

Marcos Molina — Tue, 26 Jan 2010 21:21:16 +0000

Hello Erik, I am writing you from Mallorca, Spain. I happened to find your website while I was making the last post in my blog. I found extremely interesting the calculator to find out the distance to the horizon. I decided to link this post to my post (today 26-1-2010), in the context of my recent article «Among the horizon: theory and practice» ( http://marcosmolina.wordpress.com/2010/01/26/mas-alla-del-horizonte-y-vii-teoria-y-practica ), about the tops of the mountains in the Iberian peninsula that can be seen from the roof of my dear island Mallorca. Interestingly, these observations allow us to see much farther than the actual horizon thanks to circumstancial atmospheric refraction. I hope it’s ok for you to link your blog. Otherwise please let me know and I’ll delete it.
Congratulations for such an amazing website.
Best regards from Palma de Mallorca.
Marcos.

By: Allan Davidson

Allan Davidson — Thu, 19 Nov 2009 07:57:22 +0000

It seems to me that the easiest way to calculate the distance of the horizon is the old sailor’s method, which is:

The Square Root of the Height of Eye (in feet) x 1.16 = the distance of the visible horizon in Nautical Miles.

The same formula would have to be applied to any object which the observer wished to see, and then added to the first distance above to obtain the theoretical maximum distance that the top of the object to be viewed would become visible.

By: Lance

Lance — Tue, 04 Aug 2009 13:15:09 +0000

Of course JT is trolling. Why else pretend to take offense at the statement that Americans are “metrically ignorant”? Of course we are. And, on a whole, we speak Spanish worse than Spaniards and Columbians. The average American also spends less time in Russia than the average Russian. And our turnout in the latest Japanese national elections was abysmal!

I would likewise challenge JT’s seriousness if he were to take offense (on behalf of, say, Spaniards) at my statement that Spaniards are relatively ignorant of US customary units.

Look, when it’s just Myanmar and Liberia who are refusing to adopt the metric system, the phrase “metrically ignorant” might sting. But when the world’s last superpower wants to use another system of measure, then it’s hardly a niche system. And one would hope that U.S. citizens would be better at the U.S. system than at others. There’s nothing offensive about saying so.

By: Josh

Josh — Tue, 04 Aug 2009 10:07:30 +0000

JT, you’re trolling, right? If you read the post carefully, you’ll see another opportunity to take “personal offense” — the assumption that the readers are trigonometrically ignorant. Obviously, most people old enough and sophisticated enough to be reading something like this blog are aware that there is no need to take personal offense when something does not allude to them personally. If, as you say, you have a “perfectly good mathematical sense of metric computing” then the “metrically ignorant” label doesn’t apply to you. See, no need to feel offended. [My guess is that Erik bothered with the polemic conversion table for the convenience of people like his mother (and in the case that his mother is actually comfortable with the metric system, than with my mother, and people like her).]

If what you really wanted to say is that you are offended that anybody would dare comment on the average American’s lack of knowledge of the metric system — a system of measurement which has been an international standard since the early 1960′s — than you might have a bone to pick more with the Secretary of Education than with Erik or any other stater of the obvious.

In short, the internet is such that you will waste far too much of your life getting offended by off-the-cuff comments which don’t even apply to you. Spend some time in NYC, or any other major urban center, and you’ll quickly harden your skin to such inconsequential offenses.

If my neither my ramble nor Erik’s more rational explication soothe your abused feelings, maybe the Bard’s words will:

“If we shadows have offended, think but this, and all is mended, that you have but slumber’d here while these visions did appear. And this weak and idle theme, no more yielding but a dream…”

By: Erik R.

Erik R. — Tue, 04 Aug 2009 09:13:01 +0000

JT, first of all, I’d like to thank you for reporting the bug in the calculator. My blog has been through some database migration lately, and the calculator was a casualty. It’s fixed now.

I strongly suspect that you are naively optimistic about our fellow countrymen’s knowledge of the metric system. If you gave the following test to random Americans on the street (not just 13-year-old science students) I’d be very surprised if more than 10% got them all correct.

1) Which is longer, a centimeter or a kilometer?

2) How many centimeters are there in a meter?

3) How much does a liter of water weigh in kilograms?

4) Which is bigger, a liter or a gallon?

Most Europeans wouldn’t get #4 of course, because they have no concept of what a US gallon is. And I suspect that only the scientifically minded might get #3. But every single European would know the more practical question of, “Is 100 kph too slow or too fast to drive on the motorway (interstate to Americans)?” Only Americans that had spent some time abroad would have any clue about that question.

Keep in mind that ignorant doesn’t mean stupid; it means lacking in knowledge.

By: JT

JT — Tue, 04 Aug 2009 03:39:04 +0000

I take personal offense to this line in your otherwise informative treatise:

“For the metrically ignorant Americans”

for I am an ‘American’ with a perfectly good mathematical sense of metric computing and can do it ‘in my head’, as I imagine most ‘Americans’ who stumble on this blog can, as well.

By The Way: Your tantalizing calculator at the bottom of the article doesn’t work for me on Firefox 3.5 or Safari 3.2

Cheers,