DUBAI | Burj Khalifah (Burj Dubai) | 828 M / 2,716.5 FT - Pinnacle | 162 FLOORS

[Nicko999]

How far can you see from the top of Burj Dubai assuming the top is 850 meters above sea level?

Assuming flat earth or ocean, the maximum line of sight (distance to the horizon) is calculated by:

d = SQRT((2*R*h)+h*EXP(2))

d = farthest distance you can see to the horizon

R = Earth's radius in km

h = your height above sea level in km

d = SQRT((2*6356.75km*0.850km)+0.850km*EXP(2)) = 104 kilometers

So even with the curvature of the Earth if your boat is out on the ocean and you're 104 km out you will still see the top of Burj Dubai !

Nice, you are probably very good in math! 104 km is alot. I have been at the top of the CN Tower but I can't imagine a tower that would allow you to see more than 100km.

[aaron38]

Speaking from experience with Sears Tower in Chicago, you need exceptionally clear weather to see Sears from 50km out. Most of the time it's invisible.
Atmospheric haze won't let you see the tower from 100km.

[gsgeorge]

Speaking from experience with Sears Tower in Chicago, you need exceptionally clear weather to see Sears from 50km out. Most of the time it's invisible.
Atmospheric haze won't let you see the tower from 100km.

I distinctly remember being able to see the CN Tower and most of the Toronto skyline from 55km across Lake Ontario from the docks at Saint Catharines. In fact, here's a photo to prove it.

http://img73.photobucket.com/albums/v221/pitchaudio/toronto.jpg

It should be no problem to see the Burj from several dozen more kilometers away on a clear day.

[graham]

I distinctly remember being able to see the CN Tower and most of the Toronto skyline from 55km across Lake Ontario from the docks at Saint Catharines. In fact, here's a photo to prove it.

http://img73.photobucket.com/albums/v221/pitchaudio/toronto.jpg

It should be no problem to see the Burj from several dozen more kilometers away on a clear day.

This looks to be a shot from the island with a slightly wide lens.
distance - 3 kilometers maybe.

See next post for real world examples, not pie in sky math thats not relevant for earth curvature at these short distances.

[graham]

Burj dubai at 2600 feet will be seen from great distance given clear atmospheric conditions and of course binoculars or telescope will help.
Since above 2000 feet the tip will be of a small diameter, one may need binoculars to see anything at all, but there will be line of sight for almost the entire building available from well over 100kms. Earth curvature won't apply here.

image 1 - this is a crop ( magnified section ) of CN tower
http://home.cogeco.ca/~gm9159/cnt1.jpg


made from this image below which shows a natural/realistic view as if you were standing there (how your eyes would see it).
http://home.cogeco.ca/~gm9159/cnt2.jpg


shot from exactly 50.8 kilometers
http://home.cogeco.ca/~gm9159/map3.jpg

and from an altitude of 725ft above sea level.
http://home.cogeco.ca/~gm9159/map2.jpg

The CN tower base is at 250 feet above sea level.
So the camera was positioned at 50 kms from and at 475 feet above the base.

This image shows the distance from St. Catherines docks as 48.8 Kms
http://home.cogeco.ca/~gm9159/map1.jpg

So gsgeorge's shot does not represent realistically what the tower looks like from St. Catherines Docks.
I'm pretty sure that shot is with a wide angle lens from the island only 3 kms away.

Sine the Burj will have an extra 800 feet on the CN tower, The Burj could be seen from 100+ kms given very clear conditions. Binoculars may be needed to magnify the thin upper spire sections. The earths curvature will barely cut into the base of the building. Given telescopes and unrealisticly clear atmosphere one could see the tower from much further than 100 kms, maybe 150kms, especially if slightly elevated ( for example a 50 story rooftop ). In the end it is haze that will limit the viewing distance, not earth curvature.

What I'm trying to say is that empirical evidence will squash math theory most of the time and then some.

[malec]

^^ I don't know what you mean empirical evidence will squash math theory. It'll only squash it when the theory is not correct.

Assuming the Earth is spherical (in reality it's not exactly but doesn't matter here), its radius 6373km and the burj being 808m high then if your eye is at ground level you'll see the tip appearing over the horizon 101.486km away from it. If you assume your eye is 1.8m above the ground then you'll see it 106.276km away (see how much difference 1.8m can make?). Then if you stand on a 200m tall hill you'll see it at 151.976km.

So the conclusion is you're right, and the math proves you right also! When standing on a 50 storey rooftop you'll see it when you're 150km away (if there's no haze).


Now here's a picture by Tom Green on SSC taken from 130km away in a plane (as he claims)

http://img152.imageshack.us/img152/6839/burjxq4.jpg

[Nowhereman1280]

^^^ Sometimes atmospheric conditions actually extend the distance at which you can see a skyline. There is an effect called lensing that happens on Lake Michigan sometimes that allows you to see the Milwaukee Skyline (tallest building is like 200m) from clear across the lake which is like 80 miles or 150km or something like that.

What happens is that cold, dense air, gets on top of the relatively warm non-dense air generated by the relatively warm lake water and acts as a lens bending the light coming from Milwaukee back down by a few degrees allowing you to see it from great distances.

PS: When the Chicago Spire is complete there will be an easy line of sight between the top of CS and the top of the tallest building in Milwaukee. I have a feeling that you will often be able to see Milwaukee from the top of CS whenever there is a slight lensing effect from the lake. That would be sweet, seeing another city from nearly 100 miles away.

[graham]

[QUOTE=malec;3345226]^^ I don't know what you mean empirical evidence will squash math theory. It'll only squash it when the theory is not correct.

My point exactly! It is almost always not correct for one reason or another.

[Nicko999]

Now here's a picture by Tom Green on SSC taken from 130km away in a plane (as he claims)

http://img152.imageshack.us/img152/6839/burjxq4.jpg

This picture is taken from 100km maximum! I really don't think that the Burj Dubai is 130km away in this picture.

[towerguy3]

When h << the Radius of the Earth (as it is with buildings) a rough approximation is d = SQRT (13h) where h is in meters. If you prefer using feet it's d = SQRT (1.5r) where h is in feet and d is in miles.

My understanding is when you factor in the lensing effect of the atmosphere you can add about 20 % to the derived d value. This lensing effect is also the reason why when you see a sunrise or sunset the Sun is actually below the horizon at the moment you "see" the Sun on the horizon. The atmosphere bends the light upwards to your eyes.

White mountaintops covered in snow and glistening in sunshine are easier to see from distance. Here in Vancouver you can stand atop Grouse Mountain 4000 feet and easily glimpse snow covered Mt. Baker 60 miles away which is 10,800 feet high.

When you're 4000 feet up looking at another mountain 60 miles away that's almost 11,000 feet high, you're above most of the haze anyways. I would think the air around Dubai is quite clear being a dry arid climate...

[towerguy3]

sorry, it's d = SQRT (1.5h) where h is in feet and d in miles

from the top of Mt. Everest the line of sight distance to the horizon is an unbelievable 335 kilometers

[towerguy3]

In the first image below taken from 55 km (St. Catherines) you can clearly see the effect of the curvature of the Earth as the bottom halves of the other towers such as the TD towers are cut off by the water. The Earth's curvature is very apparent in this photo. If the Earth were truly flat you'd see those towers right down to their bottoms!

This is a great visual example of the curvature of the Earth! :

http://farm3.static.flickr.com/2065/2256494527_fd2c1c6bfe.jpg

In the second one below the observer is elevated so the curvature is not noticable and you can see the Toronto towers down to their bottoms:

http://farm3.static.flickr.com/2311/2256494531_2c354b66bd.jpg

Keep in mind that a typical person 5.6 feet high can only see a horizon distance of 2.9 miles. That distance increases rapidly as your elevation increases. At an elevation of 100 feet you can see 12.2 miles.

Mathematically d varies as the square root of 13 times the height h in meters or the square root of 1.5 times the height h in feet.

[graham]

In the first image below taken from 55 km (St. Catherines) you can clearly see the effect of the curvature of the Earth as the bottom halves of the other towers such as the TD towers are cut off by the water. The Earth's curvature is very apparent in this photo. If the Earth were truly flat you'd see those towers right down to their bottoms!

This is a great visual example of the curvature of the Earth! :

http://farm3.static.flickr.com/2065/2256494527_fd2c1c6bfe.jpg

In the second one below the observer is elevated so the curvature is not noticable and you can see the Toronto towers down to their bottoms:

http://farm3.static.flickr.com/2311/2256494531_2c354b66bd.jpg

Keep in mind that a typical person 5.6 feet high can only see a horizon distance of 2.9 miles. That distance increases rapidly as your elevation increases. At an elevation of 100 feet you can see 12.2 miles.

Mathematically d varies as the square root of 13 times the height h in meters or the square root of 1.5 times the height h in feet.

All this reliance on math to make assumptions that are actually quite complicated when pure empirical evidence is staring us right in the face to refute it, is amazing to me.

Let's take the two photos above.

1) shot from 50km at lake level elevation ( about same level as base of tower) in St. Catherines supposedly. I don't think so, but never the less the above poster assumes this. He says you can see the curvature cutting stuff off.

2) Here the view is from an elevation of 475 above tower base.
According to his math there should be a big difference.
As you can clearly see in both photos - there is the same amount of section below the restuarant level can be seen as referenced from the relative size of the section above the restaurant. Restaurant at 1100 feet - top observation at 1500 - tip at 1800. Its all there in both photos.
But as I said, I think the St. Catherines view is really from only 3 kms away with a short lens.

Anybody have images showing curvature blocking an object at 100km??
Why not just use the empirical evidence to make a deduction?
Using math just introduces all sorts of innacuracies, assumptions, half truths etc and the end result it bogus. When you have empirical evidence all theory is usually bogus or half bogus.

The initial assertion is - no matter 50 , 100 or 150 km, earth curvature is not the limiting factor by a longshot. Haze is.

Also - it's interesting - I've never seen the same equation quoted twice.
The stories about tall ships dissapearing below the curvature of the earth and leading to theory about a round earth i think is bogus. It was huge 50 to 60 foot swells, the ship and observer in swell troughs.

According to one equation with some apparent credibility, the Burj would have the bottom 140 feet cutoff when viewed from 150Kms. Since the Burj Dubai is 2650' tall, this cutoff would be barley noticable. And you would only need to view from the 15th story of a building to see it all.

Anybody watching car racing when Al Unser was an announcer might remember this........
The other announcer was going to great lengths to communicate the gap between the cars in seconds and fractions of seconds and calculating gain per lap etc all very complicating and distracting, when Al pointed out that the gap was small enuff that you can now see the gap between the cars, for crying out loud. So stop calculating. hehe LMAO

[towerguy3]

I've been to Toronto and that view in photo 1. is definitely not from 3 km away.

Are you suggesting the Earth is not round?

[Spocket]

This looks to be a shot from the island with a slightly wide lens.
distance - 3 kilometers maybe.

See next post for real world examples, not pie in sky math thats not relevant for earth curvature at these short distances.

Nope, that looks about right for 50 klicks away.

The tallest buildings in my city are about 120-130 meters high. You can see them from fifty kilometers away while driving into the city during the day. Keep in mind that the city in question is Winnipeg and it's located on a flood plain. It is flat as a pancake here and visitors are always amazed at just how flat the terrain is when they see it from the air or drive out of the city.

The suggestion that the shot in question was taken from 'maybe three kilometers away' is downright laughable. It suggests that you're either not very familiar with the metric system (unlikely) or that you aren't used to being able to see buildings from very away.

[maxon22s]

I know from personal experience that you can see Torontos skyline from Niagra Falls. Not sure of the distance but clearly visable across the lake.

[dougtheengineer]

I live across Lake Ontario from Toronto, in Niagara, and you can definitely see the Toronto skyline and it looks exactly like that picture. I can't see how that picture could possibly be from the islands.

[Sky Tower]

Why are you both asking and answering the same question?
Do you just like showing people what you know and being smug about it?
For your information those results have been posted many times for interest sake over the last 3 years, it has also been deduced that due to its proximity to the sea, the sand particles in the air and the extreme ambient heat haze pretty much year round, the maximum visible distance achievable in Dubai on the clearest of days will be no more than 60kms.

Also, as the coastline goes East to West, any vista would continue in a path with the equatorial radius of 6378.135 kms not the polar radius of 6356.75 kms as you have provided.

Also, in maths do not use the letter Q as it omitted for the more popular and correct usage of the Greek θ (theta)....and capital letters are never used in algebraic formulae.

[towerguy3]

Here are views of downtown from Toronto Islands, a distance of 3 km. You judge for yourself

http://farm3.static.flickr.com/2233/2259123295_68b8c829f0.jpg

http://farm3.static.flickr.com/2100/2259930714_b0603e747b.jpg

[Sky Tower]

This is off topic, get back to the Burj Dubai please.

[towerguy3]

quote: "The stories about tall ships dissapearing below the curvature of the earth and leading to theory about a round earth i think is bogus. It was huge 50 to 60 foot swells, the ship and observer in swell troughs."

Graham, by saying this are you claiming the world is not round?

Provide the formula showing the bottom part of Burj Dubai would be cut off by the Earth's curvature from a distance of 150 km (it would indeed) and relate your equation to my formula SQRT (2Rh + h EXP 2)

[verbl]

I have a quick question with huge amount ( and use huge lightly 'cuz it's more like gargantuan lol ) of construction and skyscrapers in Dubai who is occupying all of these places? The population is about 1,679,272 and a small middle class who is in these places they cannot be all filled if anything I think most of them are empty shells and it seems like these guys are building just to build and making a status symbol out of them. I am just speculating but if anyone has any answer for me that would be nice, and in no way am I trying to be an a$%hole with this comment I just am so amazed by this city "popping" out of nowhere and it is about the same size as Phoenix and they have all of this.

[gsgeorge]

Sorry to get back to this again but I'm coming to this late. I gotta defend myself and my photograph of the Toronto skyline.

GRAHAM ---

http://img.photobucket.com/albums/v221/pitchaudio/toronto.jpg
I took the above photograph from the pier at Port Dalhousie, immediately outside of St Catharines on Lake Ontario, April 6, 2004. Here is another shot of the whole scene. The Toronto skyline is easily visible with the naked eye.

http://farm3.static.flickr.com/2055/2259227025_23e6d75a2d_b.jpg

Also, you can view an original size here (http://farm3.static.flickr.com/2055/2259227025_64a545602b_o.jpg)

Also, a map of the exact spot with other people's photos as well (http://flickr.com/photos/gsgeorge/2259227025/map/?view=everyones). In fact, this image by Jeff Epp (http://www.flickr.com/photos/eppstein/465067833/sizes/o/) is the best I could find that also shows the skyline. He doesn't have the largest size posted, but if you look close enough you can see the skyline.

http://img.photobucket.com/albums/v221/pitchaudio/torontoskylinecloseup.jpg

I don't know what else I need to do to prove it but you're welcome to call my friends and family who were there with me. Many thanks to towerguy3 and his MATH, as well--the numbers don't lie, and neither do the photographs. Thanks for all the hard work you put into it though---

So to get back to the BURJ DUBAI-- YES, you would be able to see it from ~50km away, and probably some of the "smaller" skyscrapers along Sheikh Zayed Road as well.

PS -- yes, the Earth is round. Roundish, actually. It's not a perfect sphere, but it's pretty damn close.

[graham]

I've been to Toronto and that view in photo 1. is definitely not from 3 km away.

Are you suggesting the Earth is not round?

Of course not - let's not visit the bizzare here - lol.
If a wide angle lens was used it very well could be from 3 kms.
I should know since I make my living doing architectural photography.

Now that we see the natural angle of view shot from the St Catherines dock we can see the real effect.
The first shot was cropped hard making it look much closer.
If we compare this with my shot from 50 kms, the tower itself is about the same size on comp screen, as they should be, so we are in agreement.
There is no curvature affect noticable in either shot.

Let's all remember that using a tele lens or a wide lens or cropping the image will always decieve the image viewer about distance from object.

Anyways - back to The Burj Dubai. Yes, as suggested, about the haze - 60 kms sounds right. But IF it was a perfectly clear day AND you had good binoculars from 150 kms , you would see the Burj with only a paltry 145 feet cut off the bottom of 2650 feet, curvature being an almost non existant effect. For every 10 miles ( 16.5 kms) the curvature drops off 16 feet, I think is correct. Not sure how that relates to your formula towerguy3. It's more of a tool designed with a formula I guess. I use it this way... 150kms/16.5kms = 9.09 x 16 feet = 145 feet.
One could say roughly "1 foot per kilometer" to keep it simple. Or 1 meter per 3 kilometers.
It sure is an interesting topic though, which is even more relevant since the advent of buildings like the Burj Dubai.
50kms across lake Ontario to the CN tower would be 48 feet missing off the bottom - not a noticable effect in a photo unless is was taken with a looong tele lens and cropped hard so you could actually see the 48 feet missing. Need a very sharp lens too.

[JDRCRASH]

It's about 160 stories tall now....sheesh.

[JDRCRASH]

:D :banana:
http://www.burjdubaiskyscraper.com/2008/02February/Burj_Dubai020904.jpg

[JDRCRASH]

edit

[gsgeorge]

If a wide angle lens was used it very well could be from 3 kms.
I should know since I make my living doing architectural photography.

....

There is no curvature affect noticable in either shot.

....

50kms across lake Ontario to the CN tower would be 48 feet missing off the bottom - not a noticable effect in a photo unless is was taken with a looong tele lens and cropped hard so you could actually see the 48 feet missing. Need a very sharp lens too.

Graham, you're wrong again, but I'm not going to go to lengths to argue with you since you disproved your own point in your response. First, you say there is no curvature effect noticeable in either shot (this is wrong, it's visible in mine but not in yours since yours was taken at a higher elevation than mine). Then a paragraph later you say there IS a curvature effect, which is hiding about 50 feet of the buildings. I notice a difference in the height of the buildings, and so does towerguy3 and a number of other people here. Anyone who has ever been 3km from a major metropolitan center can tell you that the level of detail in the skyline would be far greater than my very first shot which is very obviously taken from an extreme distance. Your stubbornness is troubling.

[gsgeorge]

:D :banana:
http://www.burjdubaiskyscraper.com/2008/02February/Burj_Dubai020904.jpg

What a shot! How accessible is the site? I'm always seeing these shots from up really close. I can never get this close to major construction sites. Do Imre and the other have some kind of special access?

Also is it still on schedule?

[graham]

Graham, you're wrong again, but I'm not going to go to lengths to argue with you since you disproved your own point in your response. First, you say there is no curvature effect noticeable in either shot (this is wrong, it's visible in mine but not in yours since yours was taken at a higher elevation than mine). Then a paragraph later you say there IS a curvature effect, which is hiding about 50 feet of the buildings. I notice a difference in the height of the buildings, and so does towerguy3 and a number of other people here. Anyone who has ever been 3km from a major metropolitan center can tell you that the level of detail in the skyline would be far greater than my very first shot which is very obviously taken from an extreme distance. Your stubbornness is troubling.


You misquote me.
I said no noticable efect - no noticable effect both times.

Quote 1 ) no curvature affect noticable.
Quote 2 ) 48 feet - not a noticable effect.

These two statements are entirely consistent.

I know better than to argue with a person who only wants to argue and obviously misses the point in the first place.

Did you see the shots from the island??? did you see how the tower reproduces at the same size as your cropped tele shot from St. Cath??

You claimed your shot is a great example of curvature when in fact there is no noticable effect at all .
So - you are wrong sir! not I.

Why can't you just acknowledge that earth curvature has no noticable effect when viewing skyscrapers from long distances.
It's the haze that limits the view.
This is the crux - if you can try to stay on point - I thank you very much.

[JDRCRASH]

Hey hey...no fighting.;)

[JDRCRASH]

What a shot! How accessible is the site? I'm always seeing these shots from up really close. I can never get this close to major construction sites. Do Imre and the other have some kind of special access?

Also is it still on schedule?

I wouldn't be suprised if Imre has special access.

Yes, it is on schedule. Steel Framing continues.

[verbl]

I have a quick question with huge amount ( and use huge lightly 'cuz it's more like gargantuan lol ) of construction and skyscrapers in Dubai who is occupying all of these places? The population is about 1,679,272 and a small middle class who is in these places they cannot be all filled if anything I think most of them are empty shells and it seems like these guys are building just to build and making a status symbol out of them. I am just speculating but if anyone has any answer for me that would be nice, and in no way am I trying to be an a$%hole with this comment I just am so amazed by this city "popping" out of nowhere and it is about the same size as Phoenix and they have all of this.



yeah I posted this earlier..... nobody wants to answer or they don't know?

[graham]

I have a quick question with huge amount ( and use huge lightly 'cuz it's more like gargantuan lol ) of construction and skyscrapers in Dubai who is occupying all of these places? The population is about 1,679,272 and a small middle class who is in these places they cannot be all filled if anything I think most of them are empty shells and it seems like these guys are building just to build and making a status symbol out of them. I am just speculating but if anyone has any answer for me that would be nice, and in no way am I trying to be an a$%hole with this comment I just am so amazed by this city "popping" out of nowhere and it is about the same size as Phoenix and they have all of this.



yeah I posted this earlier..... nobody wants to answer or they don't know?

Hi verbl........
They are investing for the future.
Some of the financing is coming from oil which will eventually run out.
They planning ahead for that day.
Not a problem if not all rented out right soon. They will be in future.

[graham]

I'll let these pics do the talking........

from 48 Kms at lake level on the left, and from 3 kms at about 200 feet on the right. Results - no NOTICABLE affect of the earth curvature as might be expected to show up on the left as a difference from the right. Case closed. :shrug:

For the huge Burj Dubai - any effect would be extremely limited from 100kms or 150kms, no matter haze or no haze or binoculars on no binocs.


http://home.cogeco.ca/~gm9159/4kms.jpg

http://home.cogeco.ca/~gm9159/48kms.jpg

[verbl]

Hi verbl........
They are investing for the future.
Some of the financing is coming from oil which will eventually run out.
They planning ahead for that day.
Not a problem if not all rented out right soon. They will be in future.

Thanks man I just really needed to know but what you said makes sense to me.

[towerguy3]

No you're right the curvature of the Earth over 50 km is not that pronounced however keep in mind that the photo on the left (the one that was taken from St. Catherines) was taken with a telephoto lens to make the buildings look closer.

[towerguy3]

The Guinness Book of Records states that on the Verazano Bridge in New York, the two main towers are 1 3/4 inches out of parallel to account for the curvature of the Earth. The distance between the spans is about 4200 feet.

[kraggman]

The Guinness Book of Records states that on the Verazano Bridge in New York, the two main towers are 1 3/4 inches out of parallel to account for the curvature of the Earth. The distance between the spans is about 4200 feet.

It's interesting that they would even bother to worry about 1.75 inches over 4200 feet. Is that just standard procedure for bridge building, or was that particular engineer just a perfectionist ??

[towerguy3]

If you were kneeling down on the beach in St. Catherines and your eye was 1 foot above the water and you looked at Toronto from 50 km you would see some more cutoff than in that photo. As it's a short distance of only 50 km, any slight elevation, even standing up, and you can't see the effect.

[towerguy3]

If your eye was only 20 cm (8 inches) above the water you'd only see 1.6 km to the horizon:

SQRT {2*6381*(0.0002 km) + 0.0002 EXP 2)}

[malec]

Anyways - back to The Burj Dubai. Yes, as suggested, about the haze - 60 kms sounds right. But IF it was a perfectly clear day AND you had good binoculars from 150 kms , you would see the Burj with only a paltry 145 feet cut off the bottom of 2650 feet, curvature being an almost non existant effect. For every 10 miles ( 16.5 kms) the curvature drops off 16 feet, I think is correct. Not sure how that relates to your formula towerguy3. It's more of a tool designed with a formula I guess. I use it this way... 150kms/16.5kms = 9.09 x 16 feet = 145 feet.
One could say roughly "1 foot per kilometer" to keep it simple. Or 1 meter per 3 kilometers.
It sure is an interesting topic though, which is even more relevant since the advent of buildings like the Burj Dubai.
50kms across lake Ontario to the CN tower would be 48 feet missing off the bottom - not a noticable effect in a photo unless is was taken with a looong tele lens and cropped hard so you could actually see the 48 feet missing. Need a very sharp lens too.
Huh? From a distance of 150km you would see only 145 feet cut off? You say for every 10 miles the curvature drops off 16 feet? Definitely not true. Why? Because the Earth is a sphere. The variation is not linear. What this means is sure, for the first 10 miles the curvature drops off 16 feet. But for the 2nd 10 miles the dropoff is different. In this case the further you go out the larger the rate of dropoff will be and this makes sense if you think about it.

Of course it's the haze that mainly determines visibility but that's not what we're talking about here since everyone knows that. We're just talking about ideal conditions. Given ideal conditions (ie, that you could see through the athmosphere for as much as you want) what is the furthest distance you could see the burj dubai from.
It's clear that if the burj's base is at sea level and your eye is at sea level then you will be able to see it from about 100km give or take about 25% to allow for various effects in the athmosphere such as refraction, etc.
The formula is very easy to calculate all you need to do is apply pythagoras and there you go. To say from 150m you get a 150 foot cutoff is ridiculous. This means you would be denying the size of the Earth!

What we know is the viewing distance varies A LOT depending on how high you are positioned. In fact all you do is find the maximum distance you can be viewed from sea level, the max distance the burj can be viewed from sea level and then add the two. :)

If you don't want to work with the formula here are some results:

An object as high as: Can be viewed from:
10m 11.3km
20m 15.9km
30m 19.6km
40m 22.6km
50m 25.2km

From the following distance: The dropoff due to the shape of the Earth is:
10km 8m
20km 31m
30km 71m
40km 126m
50km 197m

Clearly the dropoff rate is not the same.


Sorry if this is getting on people's nerves. I love this type of stuff :)

[br.reese]

well said

[DUBAI2015]

Okay, we get it, you can see the CN Tower/ Burj Dubai from 50km.

[Rise To The Top]

Okay, we get it, you can see the CN Tower/ Burj Dubai from 50km.

x2. This seems to come up once every 4-6 months.

[graham]

To say from 150m you get a 150 foot cutoff is ridiculous.


Yes, the second 10 miles would be more. your right. Not linear. And the 3rd 10 miles even more.

But your figures do not matchup with the last photos I posted above, which show only about 50 feet cut off the CN tower from 50Kms.
Your saying like 600 feet. Its obvious there is no 600 feet cutoff in the photo from 50 kms. It looks almost the same as from 3 kms.

I think you are wrong about the 50KM distance and I might be wrong about the 150km distance.

We gonna need a math professor for this one lol. Anybody?

[towerguy3]

From the following distance: The dropoff due to the shape of the Earth is:
10km 8m
20km 31m
30km 71m
40km 126m
50km 197m

how do you calculate this? formula?

[towerguy3]

Yes but Graham, in the photo from St. Catherines, the camera is not at sea level. It's elevated. That throws the calculation off. If you could tell me how high the camera is in that shot from St. Catherines, I'll tell you the cutoff.

[graham]

From the following distance: The dropoff due to the shape of the Earth is:
10km 8m
20km 31m
30km 71m
40km 126m
50km 197m

how do you calculate this? formula?

This may be true with your eyeball on the ground!
That brings us around to math theory versus empirical evidence, the latter which would be gathered from a standing position of course.
Does your math formula provide for the fact that an eyeball is about 5 and 1/2 feet above the ground?
Herein may lie the difference.

[towerguy3]

sorry I meant to address Malec. Anyhoo, how do we derive a formula for amount of cutoff or dropoff, we'll call x, measured below a straight line extending from our eyes to the horizon, from a distance d using the SQRT {2Rh + h EXP 2} formula?

[Tom_Green]

This picture is taken from 100km maximum! I really don't think that the Burj Dubai is 130km away in this picture.

Why not?
I was sitting on the wrong side of the plane so i had to wait until the seat belt sign was of before i could go to the other side of the plane. The airport of Abu Dhabi alone is 100km away from the Burj Dubai and we have been flying away from the building in the direction of Irans coast. I tried to find out with google earth how far exactly we have been from the Burj Dubai. It was not 130km but 120km.
Something else. The distance between the Burj Dubai and a part of the Dubai Waterfront (the thing that is closest to my plane in the pic is alone 45km.
I have taken the picture at 135mm with a 1.6 crop camera.
And here is the not photoshopped pic.
http://img211.imageshack.us/img211/3459/burjdubaitn5.jpg

And this is the photoshopped version
http://img152.imageshack.us/img152/6839/burjxq4.jpg

[pablosan]

I can't see anything through the haze.

[Mocholate]

More construction updates , Less physics lessons please

anyhow , The Q1 in QLD australia can be seen from 200 kms away on similar terrain and is less than half the height of Burj Dubai , make an estimate

[graham]

More construction updates , Less physics lessons please

anyhow , The Q1 in QLD australia can be seen from 200 kms away on similar terrain and is less than half the height of Burj Dubai , make an estimate

Can you find any photos of that building taken from a great distance?? Thanks.

I think the issue in question is so incredibly complicated that a mathematics professor, a meteorologist, a photographer and a geologist might be needed to come to a definite useful conclusion. It sure is interesting though.
The most interesting part would be comparing the resulting theory to actual real world tests. My guess? .... a huge discrepency.

Thanks to Tom for the very interesting shots from the plane - amazing what photoshop can do!
135mm x 1.6 crop factor = 216mm = a bit more than 4 x magnification of a normal angle of view.
Your high elevation helped to "go over" the haze for a major part of the distance. Faskinating! I guess that's why google earth is even possible - haze buildup only happens when looking close to parallel to the ground below say 5,000 feet or so.

Anywhooo - 3 levels of steel beams takes 2 months + to erect? Hold it folks - something is forked! This can not possibly be right. It's moving like molasses at the North pole and I'd sure like to know why. Anybody have any news about delays, sway probelems, design probs, labour probs, people getting sick up there, financing probs, material supply probs again, etc.?

[AltinD]

^^ Nothing of that staff. Just the conversion from concrete to steel is a very delicate and must be done right, with countless measurements and tests to verify that.

Haven't you guys seen any buildings being build from foundations up?

[graham]

Maybe somebody here is good enough at math to figure this out.
If we could get a result that can be verified by multiple sources, methinks we're halfway there to figuring it out.
My reckoning is around 50 feet - but that's most likely way wrong.

http://home.cogeco.ca/~gm9159/Q.jpg

On the other hand - if we could get an explanation for the value fields of the capital letters in the formulas posted so far, that might help too.

[graham]

^^ Nothing of that staff. Just the conversion from concrete to steel is a very delicate and must be done right, with countless measurements and tests to verify that.

Haven't you guys seen any buildings being build from foundations up?

Good point for the 1st steel floor. ok.
But the conversion is done! It's just steel on steel now. And it still seems to be taking forever.
The method and material has been perfected over many decades.
I'm sooo confused - lol.

[jason111]

omg.....what are u guys? speak english

[graham]

omg.....what are u guys? speak english

What are we?? Would you mind elucidating yourself please. Thank you.
Use a dictionary if you have to. We don't mind.

How about taking a stab at the math probelm posted above.
We're talking about earth curvature cutoff from a great distance, and how much that would be for the Burj Dubai from 150kms.

[towerguy3]

Is it only in an equilateral triangle that the angles add up to 180 degrees? So the unknown angle is 90 degrees minus 0.65 degrees? Two sides (representing the Earth's radius) have the same length, 6391 km...

[graham]

Is it only in an equilateral triangle that the angles add up to 180 degrees? So the unknown angle is 90 degrees minus 0.65 degrees? Two sides (representing the Earth's radius) have the same length, 6391 km...

The central cross section of the earth is a circle which is 360 degrees.
the circumferance is 25,000 miles.
25,000/360 = 69.4 miles per degree.
90 mi. ( 150kms [the distance in question]) is 1.3 degrees.
The 0.65 degrees is just to show that the measurement for x is taken at the center of the 1.3 degree section.

So what is the value of x? That's the part I can't get.
Where are all the math geniuses?

[MikeM]

Good point for the 1st steel floor. ok.
But the conversion is done! It's just steel on steel now. And it still seems to be taking forever.
The method and material has been perfected over many decades.
I'm sooo confused - lol.

The method may have been perfected but rarely, if ever, done at that altitude. Do you know what the winds are like up there? Even on an absolutely still day there will be significant air movement at the top. Just hoisting the members up there is a challenge. Now imagine a large steel member weighing a few tonnes swinging in the wind and you have to hand-guide it to a precise location. All this while the building itself is probably moving a significant amount. One small miss-calculation and ...

I'd be very, very careful if I was up there - I'm rather attached to my fingers.

Not to mention hands, arms and neck!

[MikeM]

Is it only in an equilateral triangle that the angles add up to 180 degrees? So the unknown angle is 90 degrees minus 0.65 degrees? Two sides (representing the Earth's radius) have the same length, 6391 km...

Any triangle on a planar surface has angles that add up to 180°

[graham]

The method may have been perfected but rarely, if ever, done at that altitude. Do you know what the winds are like up there? Even on an absolutely still day there will be significant air movement at the top. Just hoisting the members up there is a challenge. Now imagine a large steel member weighing a few tonnes swinging in the wind and you have to hand-guide it to a precise location. All this while the building itself is probably moving a significant amount. One small miss-calculation and ...

I'd be very, very careful if I was up there - I'm rather attached to my fingers.

Not to mention hands, arms and neck!

Yeah - sounds like your speaking from experience.
So - wind related safety issues due to extreme altitude - makes sense.
Thanks for your input.

[towerguy3]

We can ignore the h^2 term for small h and get only a tiny error in the process. To a very good approximation, h = (d^2)/2R.

For d = 150 km, I get h = 1.65km, which is about 2.5 times the height of the building currently (2000 feet). A mountain of that height would have its summit just reaching the horizon.

The longest distance at which you could just see a light on the top of Burj Dubai as it currently stands (2000 feet high) would be about 93 km. That is assuming no atmosphere. Actually the atmospheric refraction would extend the range a bit.

[towerguy3]

The 69.4 mile figure is equivalent to 60 Nautical Miles, each Nautical Mile being 6080 feet as opposed to 5280 feet for a Statute Mile. There are 60 Nautical miles in one degree of latitude.

The term Nautical Mile is defined as the arc length of 1/60th of a degree of Latitude, or one arc minute.

The length of a degree of Longitude varies as the Cosine of the Latitude. At the equator one degree of longitude is 69.4 miles whereas at 60 degrees North it's one half of that (Cosine of 60 deg is 0.5)

[graham]

We can ignore the h^2 term for small h and get only a tiny error in the process. To a very good approximation, h = (d^2)/2R.

For d = 150 km, I get h = 1.65km, which is about 2.5 times the height of the building currently (2000 feet). A mountain of that height would have its summit just reaching the horizon.

The longest distance at which you could just see a light on the top of Burj Dubai as it currently stands (2000 feet high) would be about 93 km. That is assuming no atmosphere. Actually the atmospheric refraction would extend the range a bit.

wow - so your saying from only 100kms the entire building ( at 2000' now) would be cutoff, atmospheric lensing notwithstanding. But is that calculated with the eyeball at 5 or 6 feet above the ground?

Can you calculate for the value of "x" in my diagram?

[graham]

The 69.4 mile figure is equivalent to 60 Nautical Miles, each Nautical Mile being 6080 feet as opposed to 5280 feet for a Statute Mile. There are 60 Nautical miles in one degree of latitude.

The term Nautical Mile is defined as the arc length of 1/60th of a degree of Latitude, or one arc minute.

The length of a degree of Longitude varies as the Cosine of the Latitude. At the equator one degree of longitude is 69.4 miles whereas at 60 degrees North it's one half of that (Cosine of 60 deg is 0.5)

Ok - but what do you get for x in my diagram?

[towerguy3]

yeah we're back to square one; all I've shown is from a height of 600 meters you can see a light on the horizon 93 km away... not the other way around... I'm stuck, help

[MeTP]

I hope nobody takes too much offense at this, but would it be asking too much to take the math conversation to a new thread? This really is only peripherally related to the topic of this thread and it's getting a bit old for those of us who aren't really interested in it.

[towerguy3]

using Quadratic formula:

h = R (+/-) sqrt (R^2+1) that's for d=1

here it is in general: h = R (+/-) sqrt {(R^2)-(d^2)}

[graham]

using Quadratic formula:

h = R (+/-) sqrt (R^2+1) that's for d=1

here it is in general: h = R (+/-) sqrt {(R^2)-(d^2)}

That's greek to me.

But I just did my best calcs I could do and now think that x = 1425 feet.
With this number in hand I think you could see the top 600 feet of the finished 2650' Burj Dubai tower. So - about 2050 feet cut off wehn viewed from 150 kms.
That seems to fit closer to yours and some other forecasts for 150kms.

Sorry if it's getting old MeTP - just that progress is almost at a standstill and at least this is something related to chat about.

You want to change the subject - go ahead.
If you do, I'll stop posting about this stuff right away.

[MeTP]

You want to change the subject - go ahead.

Again, no offense intended, but this thread already has a subject and you're way off of it. It's just a big let down to keep coming to this thread thinking there's some news about Burj Dubai construction only to find a continuation of page-after-page-after-page of this snooze fest. I'm sure it's very interesting to you but it has nothing to do with the topic of this thread. Anyway, I'm not going to say any more about it. If the moderators don't think it's worth saying something it's certainly not up to me to do anything about it. I'll just go read something else.

[towerguy3]

h = R (+/-) sqrt {(R^2)-(d^2)} Here I'm letting h represent the height above the ground of Burj Dubai visible above the horizon from a distance d.

It works both ways: from 93 km out you could see the top of a 600 meter tower (where BurjDubai is right now) or from the top of a 600 meter tower you could see to the horizon. h = 600 m or 0.6 km

so from 10 km out, the bottom 7.8 meters of BurjDubai should be cut off by the Earth's curvature

20 km out = bottom 31 meters cut off

30 km out = bottom 70 meters cut off

40 km out = bottom 125 meters cut off

50 km out = bottom 195 meters cut off

60 km out = bottom 281 meters cut off

70 km out = bottom 383 meters cut off

80 km out = bottom 500 meters cut off

as you can see it's not a linear variation

[malec]

graham, I'm more than halfway through a physics degree and that involves a shit load of math. The formula that I used to calculate those numbers is the correct one based on geometry and to deny it's right means you either deny the size of the Earth, or Pythagoras's theorem. In fact it's the same formula on wikipedia: http://en.wikipedia.org/wiki/Horizon

The question is what external factors contribute to the viewing distance (not including haze). One is if you're on a hill. If you are standing 50km away from the tower but on a hill of 10m only. Then you'd see as much of the tower as if you were standing about 40km away at ground level. This makes a HUGE difference. Also refraction of light will play a role. I have no idea how much this affects but if you want a detailed analysis it's impossible because it involves understanding the turbulence in air and turbulence is an unsolved problem.

[Rise To The Top]

Again, no offense intended, but this thread already has a subject and you're way off of it. It's just a big let down to keep coming to this thread thinking there's some news about Burj Dubai construction only to find a continuation of page-after-page-after-page of this snooze fest. I'm sure it's very interesting to you but it has nothing to do with the topic of this thread. Anyway, I'm not going to say any more about it. If the moderators don't think it's worth saying something it's certainly not up to me to do anything about it. I'll just go read something else.

x2. Lets see some updates please.

[johnandahalf]

x2. Lets see some updates please.

x3

[towerguy3]

sorry actually h represents the amount of the tower cut off by the Earth

[towerguy3]

So in the image of Toronto taken from 50 km out in St. Catherines, what we're seeing is the effect of the atmosphere bending the light (refraction). According to our calculations the bottom 600 feet or so of the CN Tower should be cutoff by Lake Ontario's water and that's clearly not the case.

So rather than saying the photo is an excellent example of the curvature of the Earth, rather it's an awesome example of the power of the atmosphere to act as an optical lens!

[graham]

graham, I'm more than halfway through a physics degree and that involves a shit load of math. The formula that I used to calculate those numbers is the correct one based on geometry and to deny it's right means you either deny the size of the Earth, or Pythagoras's theorem. In fact it's the same formula on wikipedia: http://en.wikipedia.org/wiki/Horizon

The question is what external factors contribute to the viewing distance (not including haze). One is if you're on a hill. If you are standing 50km away from the tower but on a hill of 10m only. Then you'd see as much of the tower as if you were standing about 40km away at ground level. This makes a HUGE difference. Also refraction of light will play a role. I have no idea how much this affects but if you want a detailed analysis it's impossible because it involves understanding the turbulence in air and turbulence is an unsolved problem.

yeah - it's incredibly complicated and frought with undeterminable variables.
Thanks for the Wikpedia link. Some good info there.
I figure the only way to really understand it is to do real world tests with
gps equipment and very good telephoto lenses and photoshop and using good weather reports and a whole lot of patience.
I wonder what the results would be.
I guess we'll know soon since the Burj Dubai is almost finished and there will be peeps taking shots from all over the place.
Looking forward to it.

Is it not funny that some guys seem to blame us curvature chatters because there are no construction updates recently.
Like we told the updaters to shutup while we're posting our stuff? lmao
There are no updates because there are none. It has nothing to do with our "view from distance chat". What a laugh eh?

[graham]

So in the image of Toronto taken from 50 km out in St. Catherines, what we're seeing is the effect of the atmosphere bending the light (refraction). According to our calculations the bottom 600 feet or so of the CN Tower should be cutoff by Lake Ontario's water and that's clearly not the case.

So rather than saying the photo is an excellent example of the curvature of the Earth, rather it's an awesome example of the power of the atmosphere to act as an optical lens!

By golly - I think you got it!!! congrats

[towerguy3]

The silence is deafening. I honestly think there's a major issue up and they're just not going public about it.

A building of this scope has never been tried before.

It could be financing. It could be the banks. And it could be something far worse.

How about cracking of the foundation? The problems may not be up in the sky but rather down at ground level.

[Chitown]

x3
x4. I can not believe this derail is still going.

[graham]

The silence is deafening. I honestly think there's a major issue up and they're just not going public about it.

A building of this scope has never been tried before.

It could be financing. It could be the banks. And it could be something far worse.

How about cracking of the foundation? The problems may not be up in the sky but rather down at ground level.

Yeah - something is up. This sort of delay must be very costly for them.
I hope it's not foundation problems as you suggest.
But it must be something big.

Oh - by the way - Chitown - why don't you make an effort to rerail it if your unhappy about it? As that Ghandi guy said " be the difference you want to see in the world" . Or not. It's your stuff.

[MeTP]

Maybe those of use who don't want to waste our time wading through this off-topic crap should start a new Burj Dubai construction thread and leave these two to discuss math to their hearts content. No doubt they'd feel free to hijack that thread too. I wasn't going to say anything more but I see no reason to be polite since it doesn't seem to phase these two one bit. Get a room math geeks!

[graham]

Maybe those of use who don't want to waste our time wading through this off-topic crap should start a new Burj Dubai construction thread and leave these two to discuss math to their hearts content. No doubt they'd feel free to hijack that thread too. I wasn't going to say anything more but I see no reason to be polite since it doesn't seem to phase these two one bit. Get a room math geeks!

Now he's getting hostile.
Here ya go............

February 05, 2008, 23:41

Dubai: Burj Dubai, the world's tallest building being developed by Emaar Properties PJSC, has completed 50 per cent of its cladding work, undertaken on an accelerated schedule by Arabian Aluminium Company.
More than 12,000 panels covering over 50,000 square metres have been installed on the tower, which is now the world's tallest free-standing structure.
Burj Dubai is currently 604.9 metres high. The final height and number of levels have not been revealed.
The cladding work is being undertaken in phases across various levels to match the project timelines. More than 80 storeys currently have the cladding system.
The primary materials used are reflective glazing, aluminium and textured steel spandrels, and vertical stainless steel tubular fins.
-------------------------------------------------------------------------------------------------------------------------
Happy now?
Where's your contribution but to complain what others are saying ??
Here's a recent shot of a new crane section being hauled up....

http://home.cogeco.ca/~gm9159/craneup.jpg

[MeTP]

This really is the last I'll have to say in THIS off-topic conversation, graham. If you don't get it there's nothing I can say. Several people, not just me, have asked you to stop this but evidently that doesn't matter to you. If there is no Burj Dubai news, fine, there's no news. When I see the Burj Dubai thread in the "New Posts" list, I come here because there might be news and I'm interested in it. When time after time I find nothing but another private-gone-public exchange of equations between you and your buddy, it pisses me off. It's a let down and a waste of time. This is what private messages are for. Or, if you think this topic is of interest to others, it's very easy to start a new thread.

[graham]

This really is the last I'll have to say in THIS off-topic conversation, graham. If you don't get it there's nothing I can say. Several people, not just me, have asked you to stop this but evidently that doesn't matter to you. If there is no Burj Dubai news, fine, there's no news. When I see the Burj Dubai thread in the "New Posts" list, I come here because there might be news and I'm interested in it. When time after time I find nothing but another private-gone-public exchange of equations between you and your buddy, it pisses me off. It's a let down and a waste of time. This is what private messages are for. Or, if you think this topic is of interest to others, it's very easy to start a new thread.

There were many people participating in the subject including thread regulars such as malec, Altin D, Sky Tower and 7 others.
Sorry that your "pissed off" (your words , not mine).
There are construction updates and pics in the post just above your last complaint.
Where are your contributions?
Go elsewhere if your unhappy.
Here's another great pic............

http://home.cogeco.ca/~gm9159/bd2.jpg

and another...........
http://home.cogeco.ca/~gm9159/bd3.jpg

[borgo100]

^^ Holy Cow!!!!!!!!!!!!!!!!!!

[graham]

Yeah - that shot by Josh von Staudach hints at the masterpiece about to fully unfold before our eyes. The cladding really bringing it around nicely.

Say Imre? that shot was done with a long lens from a big distance (maybe 1 km) . That's why the vertical lines are not too converged.
You can do it too.
Long lens maybe about 300mm equiv. + good tripod + 20 minutes after sunset with a clear or mostly clear sky. About 1 second @ f8 @ iso 100 You can do it too. For 1 sec or more, you might get clearer image if you turn on noise reduction, if your camera has that feature available.
Take a series of different exposures. Choose the best one later from your comp screen.
Take any and all filters off the long lens for the shot. Replace the protective filter after taking the shot.
You maybe can rent the lens if you dont have one.
Be sure to post it. Good luck.
Wish I was there.

[theWatusi]

Agreed. That Staudach photo is amazing.

[Austin55]

I have to admit the base is absoloutly awesome,but it gets "Twiggier" as it rises and doesnt look as great.

And this is a totaly stupid qestion,And I cant believe im asking,but I was reading a magazine and I saw and ad it said something like "Burj Dubia,1,Emaar". What does the one mean? #1? the best? theres not pllans for a twin is there?

[Jasonhouse]

Maybe somebody here is good enough at math to figure this out.
If we could get a result that can be verified by multiple sources, methinks we're halfway there to figuring it out.
My reckoning is around 50 feet - but that's most likely way wrong.

http://home.cogeco.ca/~gm9159/Q.jpg

I drew it in autocad, and got a result of 428 feet for the diagram depicted.

[Jarrod]

Okay... I really don't like Dubai and what they're doing (just me), but this tower is turning out better than I thought it was going to. It's very beautiful and not tacky as I thought it was going to be.

IT's a very nice tower.

[graham]

I drew it in autocad, and got a result of 428 feet for the diagram depicted.

Autocad! brilliant! Thanks.
428 ft. seems realistic.

Can you use autocad to get the final number too?

A straight line from the eyeball starting at 6 feet of elevation, that runs for 90 miles just clearing the earth's curvature (428 feet over 90 miles), will end at what elevation?

I'm guessing 800 feet.

Thanks again.
I gotta get me an autocad proggy.

[FrancoRey]

and another...........
http://home.cogeco.ca/~gm9159/bd3.jpg


Absolutely STUNNING! You could double this finished skyline into a futuristic/sci-fi movie any day of the week!

[kenratboy]

I drew it in autocad, and got a result of 428 feet for the diagram depicted.

You beat me to the punch.

I solved many nasty math problems with AutoCAD. Makes you appreciate the math in that software!

[Mocholate]

surely somewhere on the net you will find info regarding the distance that is viewable from the tower

[Imre]

I put some new Burj Dubai, Lake Hotel pics here because the internet connection is wrong here, thanks for the du :) ( will post later The Index, Emirates Towers and some Business Bay pics as well)

http://www.flickr.com/photos/imresolt/

They promised , maybe after 2-3 days will be good again:)

flickr , yahoo and some websites good but most of them I can not open.

[AltinD]

And this is a totaly stupid qestion,And I cant believe im asking,but I was reading a magazine and I saw and ad it said something like "Burj Dubia,1,Emaar". What does the one mean? #1? the best? theres not pllans for a twin is there?

The only thing that comes in mind is: "Burj Dubai Boulevard, No. 1", that would be the address of the tower.