View Full Version : Tangential area of the Earth

sundaju

2006-Aug-22, 02:15 PM

I am wondering what would be the area of the portion of the Earth that would be in touch with an imaginary Tangential line that passes along the surface of the earth..

Along the same lines ( what a coincidence of word :-) ), I am trying to guess what will be the length of a single straightest object ( I am excluding fabricated steel rods extending for metres/kilo metres, because I want to know the most basic unit of a straightest object ) ever made by the humans? ( At the moment, I can only think of rails, but then they too are joint structures.. )

ToSeek

2006-Aug-22, 02:36 PM

If you're assuming an ideal Earth (i.e., a sphere the size of Earth), the area is zero. For the real Earth, it depends on the terrain where you're touching.

For the longest straight object, it might be best to look at buildings or antennas or other such vertical structures (though I suppose they tend to be in pieces, too).

sundaju

2006-Aug-22, 02:52 PM

Are you saying that the practical Earth is not a perfect sphere, because of the surface aberrations or because of the little bulge in the middle portion of the sphere?

I am rephrasing my question, I assume that when we look out towards the sea, we see a curved horizon before us. What is the supposed length of an assumed imaginary line leading towards this horizon from the place where I am standing? is this length the same on all directions? am i not right in thinking that this imaginary horizon line is straight ?

gwiz

2006-Aug-22, 03:17 PM

I am rephrasing my question, I assume that when we look out towards the sea, we see a curved horizon before us. What is the supposed length of an assumed imaginary line leading towards this horizon from the place where I am standing? is this length the same on all directions? am i not right in thinking that this imaginary horizon line is straight ?

Given your height, h, and the radius of the earth, R (=6380 km) and assuming the earth is a smooth sphere, the horizon distance is square root of (h*h+2*R*h). In practice, you can ignore the h*h term.

sundaju

2006-Aug-22, 03:26 PM

I made a calculation as below... I assumed I will have to convert my height to kms, as i am considering earth's radius in kms...

it works out to sqrt((1.5/1000)*6380) which roughly works out to 3 ( i assume the calculated number should also be in kms..

am i looking towards a point before me which is just 3 kms away from me as the horizon? correct me, if any of my above assumptions are invalid

pghnative

2006-Aug-22, 03:53 PM

It looks like you forgot the factor of "2" in gwiz's equation. including that gives 4.4 km.

gwiz

2006-Aug-22, 04:37 PM

That sounds about right. You can check the horizon distance if you stand on the beach at a point where you can look along the coast for some way. For the nearer bits of coast you can see the beach/waves at the foot of the land, below the level of the sea horizon, but farther along the beaches are lost beyond the horizon and you can only see the higher bits of land that are above the sea horizon. Work out how far you can see and then find the distance from a map.

Here's an example, note the sea horizon extends in front of the rightmost bit of land:

http://www.westcountryviews.co.uk/towns/dawlish/dawlish03.htm

antoniseb

2006-Aug-22, 04:54 PM

Going a bit further, you could build a straight line 8.8 kilometers long that exits the Earth at each end, and is 1.5 meters below the surface of the Earth in the middle. This is useful is you are building a LIGO like apparatus or a giant linear accelerator in which the paths must be straight, and not simply parallel sea-level.

neilzero

2006-Aug-22, 05:10 PM

Small portions of Earth's surface are approximately flat if you live in a very old crater or dried up lake bed; and small portions of the horizon can appear approximately straight. In solid geometry the apparent horizon is approximately a circle. Neil

For the longest single object, we have smoke stack here in Utah, near the Kennecott Coper Mine right by the lake that is about 1100 feet tall and was made in one continuous pour. That's according to my dad, so a verification may be needed.

Jeff Root

2006-Aug-22, 08:42 PM

For the longest single object, we have a smoke stack here in Utah,

near the Kennecott Copper Mine right by the lake that is about

1100 feet tall and was made in one continuous pour.

1) Wow!

2) When was it built?

3) Wouldn't it have been nicer and no more expensive to put in

a system for precipitating the ash rather than dispersing it

via the upper atmosphere to neighboring states?

-- Jeff, in Minneapolis

Peter Wilson

2006-Aug-22, 10:33 PM

Short smoke stacks are used for dispersing particulates to neighboring states. The 1100 ft stack was needed to get the smoke to Minnesota ;)

Lord Jubjub

2006-Aug-22, 11:55 PM

That Kennecott smokestack is actually 1215 feet. It is the tallest structure west of the Mississippi and was built in from 1974-1978. I have not been able to find any reference to how it was constructed but there is a power station in Kazachstan that has a chimney that is 1362 feet tall constructed in 1987. It was made in a similar manner to the Kennecott one, so it may well also be a continuous pour.

http://en.wikipedia.org/wiki/CN_Tower

The CN Tower in Toronto is 1815 feet with a continuously poured central support that is 1465 feet tall.

rudolpho

2006-Aug-23, 08:11 AM

The distance to the horizon: Asuming height (h) of 2 meters and earth radius R=6380 km:

D^2=(R+h)^2 - R^2

D=SQR((6380.000+0.002)^2 - 6380^2) =25.52 km

As any sailor knows

rudolpho

2006-Aug-23, 08:18 AM

Sorry SQR(25)=5 km

hhEb09'1

2006-Aug-23, 09:24 AM

That's the formula gwiz gave above, but he simplified it

astromark

2006-Aug-23, 12:19 PM

while at sea. A fishing boat is not visible beyond 7 km. but at night its lights may be seen for 9 km. As for the longest straight line,? I could sagest you will not find one. Maybe a laser beam. Absolute straight. is a rare thing.

V-GER

2006-Aug-23, 12:54 PM

A comprehensive list of the tallest structures:

http://en.wikipedia.org/wiki/Tall_structures#Tallest_structure_by_category

Kaptain K

2006-Aug-23, 06:50 PM

The longest absolutely straight material construct is a diatomic molecule (two points define a straight line), since all molecules (above absolute zero) vibrate and any larger molecule would only be absolutely straight for an infinitessimal portion of any vibratory cycle!

publiusr

2006-Aug-25, 07:23 PM

Two of my favorite structures

http://en.wikipedia.org/wiki/Troll_gas_platform

http://en.wikipedia.org/wiki/Warsaw_Radio_Mast

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