Height above sea level question re horizon

[silverfoxcc]

Chatting to my lad about this and on checking on the great Wiki found that at eyeball level the 'distance' to horizon is about 3 miles,at 1oo asl it is c.12 miles

He then threw this one

If a plane was travelling at 40000ft directly towards to how many miles away would it be once it 'crosses the horizon line'
into view
Did a bit of CAD work and did a model of earth at a radius of 3.500mm and another at 3.507mm enlarged it to max and drew a line form point on circumference to another point of a circle 0.012mm and projected it to cross the 3,507 diameter.
It looks like on this that the plane would be about 200ish miles away in first sighting , always assuming a humingous telescope to see it!!

Is this a reasonable ballpark figure? did a quick calculator and it came out as 213!!

(3507x3507) -(3500x3500) = 49049 and square root of that is 213 or am i completely wrong?

[Upinflames]

No help whatsoever but I've always understood that standing on a ship another ship drops out of sight at 12 miles

[Tymb]

Seems about right, being lazy used this:
http://www.ringbell.co.uk/info/hdist.htm

[RustyMX5]

According to this website....

394 km / 245 miles

https://www.omnicalculator.com/physics/distance-to...

[jurbie]

Not a lot of help but I do recall flying from Inverness to Manchester one evening and being able to see the lights of Carlisle below me and the lights of Newcastle upon Tyne clearly in the distance which I think is about 70 miles. I probably could see much further than that but it was dark and I would have been looking at the North Sea so hard to get a reference point. No idea how high we were but I suspect somewhere below your figure of 40,000 feet.

[off_again]

RustyMX5 said:

According to this website....

394 km / 245 miles

https://www.omnicalculator.com/physics/distance-to...

Technically this might be correct, but there are a number of factors that are in place. At this type of distance, the human eye cannot differentiate the objects anyway, so it all somewhat blurs anyway. And good luck finding somewhere in the world where pollution and air temp / particulates in the air wont impact it.

[ATG]

silverfoxcc said:

(3507x3507) -(3500x3500) = 49049 and square root of that is 213 or am i completely wrong?

That looks right.

You've got a right angle triangle where the short sides are from the observer to the plane, and from the observer to the centre of the earth. The hypotenuse is from the centre of the earth to the plane. You want to calculate the distance from the observer to the plane, so using Pythagoras: theorem the distance is

Sqrt( (r+a)^2 -r^2 ) where r is the radius of the Earth and a is the plane's altitude, and of course you're expressing all the distances in the same units.

[Eric Mc]

Where I used to live growing up, from the coastline just outside Dublin, you could see the landing lights of airlines crossing the British coastline at Wallasey which is just over 170 miles.

One of my favourite pictures ever is this image of Snowdonia taken from the top of The Hill of Howth, which is eight miles north of Dublin city centre. Snowdonia is about 100 miles from Dublin.

[ATG]

Googling for the distances in miles, I get radius of Earth is 3598 miles, and 40000ft as 7.57 recurring miles, which gives plane appearing to be touching the horizon when it is 245 miles from you in a straight line.

[RustyMX5]

off_again said:

RustyMX5 said:

According to this website....

394 km / 245 miles

https://www.omnicalculator.com/physics/distance-to...

Technically this might be correct, but there are a number of factors that are in place. At this type of distance, the human eye cannot differentiate the objects anyway, so it all somewhat blurs anyway. And good luck finding somewhere in the world where pollution and air temp / particulates in the air wont impact it.

Mr Pedant (sir),

silverfoxcc didn't specify if the figure was actual or theoretical. Without knowing the refractive index of the medium he would be looking through (as he'd be gasping for breath at 40,000 ft and would need either a mask or a container in which he can reside - like a plane), the air quality, the time of day, the cloud base, the physical location where he is, whether he wears glasses and if they are optimised for extreme long distance etc etc etc, it's safe to assume that he's referring to theory rather than actual. Therefore, for the purposes of a discussion in The Lounge 245 miles is correct. However, if this was in the Science! sub forum then the chances are the number would be closer to around 60 miles (guess) because someone would be able to work it out accurately based on a series of well defined factors.

[dundarach]

Eric that photo is brilliant!

[phumy]

I was informed, that at the top of Table Mountain, SA, on a clear day, the sea horizon is approx 95 miles away.

[RosscoPCole]

Useless fact that is sort of related. When you see the International Space Station in the night sky. When it vanishes from sight in the east it is above Poland, over 1,000 miles away.

[Eric Mc]

dundarach said:

Eric that photo is brilliant!

Something I never saw for myself - although seeing the Mountains of Morne from Howth Head was and is quite easy. The distance there is around 90 miles.

[mcelliott]

Not sure if relevant to topic but a few years back in the summer I caught sight of a Contrail just above the horizon, the setting sun was lighting it up, barely visible to the naked eye, I checked flight radar and found out it was directly over Dublin, I live in Guernsey.

[Eric Mc]

Back in the 1950s, the RAE ran a number of experiments to see how far away contrails could be seen. They positioned on observer on Mount Ararat in Turkey and flew a Canberra over Cyprus at 60,000. It was easily observed.

I know this because I spoke to the chap who was stationed on Mount Ararat.

[Freddie Fitch]

Let's not forget that the earth is not a sphere. Its an oblate spheroid.

[gotoPzero]

Cracking photo - almost does not look real. Is there some tilt shift going on too?

[Lotobear]

jurbie said:

Not a lot of help but I do recall flying from Inverness to Manchester one evening and being able to see the lights of Carlisle below me and the lights of Newcastle upon Tyne clearly in the distance which I think is about 70 miles. I probably could see much further than that but it was dark and I would have been looking at the North Sea so hard to get a reference point. No idea how high we were but I suspect somewhere below your figure of 40,000 feet.

There's a point on Hadrian's wall where you can see that from ground level

[Master Of Puppets]

Freddie Fitch said:

Let's not forget that the earth is not a sphere. Its an oblate spheroid.

Try telling that to a flat earther.