A question Ive been pondering *HELP*

J-SiN

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Ive often wondered this and having drawn my own conclusion forgot about it until it came up over turkey day discussion

Ive always wondered if you had a level a carpenter or mason's level that was 10,000 miles long

that at the ends of it IT would no longer be level

so after a lot of thought I came to the conclusion it would HAVE to be curved

so we were discussing this and a couple relatives disagree

now for it to be level the whole way the world would have to be flat!

didnt we establish that 300+ years ago lol!

so anyways I looked online for something to reference and cant find anything

I know you guys are a knowledgable bunch so I thought Id ask you guys not only your opinions but to see if anyone has somethign I can use as reference
 

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j-sin- only at one point will any length of level be truly level...and thats where that point on that level is perpendicular to the center of the earth. In other words also....the point that the level is tangent to the circle that whose center is the center of the earth.

Of course for all practical purposes....most buildings are not that far off....talking thousandths of an inch. But you can easily compute technically how far true vertical walls are actually out of parallel when seperated by any distance.

If you go back into my heli-hanger thread....you will see the math I did on just this subject. I showed how far out of parallel my 28 foot foot walls are...if indeed they are perfectly plumb. I forget the figure now...and dont have time right now to compute it...but its simply the ratio of my 10 ft. tall walls to the 4000 mile point at the center of the earth that they are pointing to if actually vertical. It was in the order of thousandths of an inch...but still actually measurable with feeler gauges....if.....you had truly vertical wall seperated by 28 feet.

I recall reading the towers of the Golden Gate bridge are something like 4.5 inches out of parallel as they are indeed vertical...and seperated.

Every nautical mile on the earths surface is one minute of angle...or 1/60th of a degree. Breaking that down ...every second of angle on the earths surface is rougly 100 yards apart. So...if you had a building with truely vertical walls 100 yards apart....they would be one second of angle out of parallel....and I wish I had my calculator with me...that could easily tell you what fraction of an inch that would be....but it would clearly be visible.

Stan
 
j-sin....


This is kind of a mind twister....but I would say that if you had a 10,000 mile level....and wherever it had a bubble vial....it would read level when perpendicular to the earths center. So, the answer would be yes....with the understanding that each bubble vial is tangent to the now curved surface of this level.

Stan
 
Jason, line of sight is approximately 30 miles. This is due to the curvature in the earth. This is why FM radio stations put up towers. Is to expand there range. FM is line of sight. This is why the higher the better. Most FM station will build on a hill or mountain to gain altitude for longer range. AM is amplitude. It bounces off the atmosphere and some structures.
So to answer your question. A level is a level. The curve of the earth has nothing to do with it. It would just be balanced in the middle to remain level. Kinda like a teeter-toter on a kids playground. The ends would be in the air. The longer (as in miles in length)the level, the higher the ends would be off the ground.
 
Hi J-SIN

I would agree with Stan, the term "level" is a term of reference or comparison as in level compaired to what. If you have a level 10,000 miles long and are comparing it to the earths surface, then "true level" is only going to exist at the point of the bubble or weighted marker, in reality if you are measuring a curved surface, level is not a good term, as you can only be equi-distant at all points but not truly level.

Tony
 
I was having a realy good day till you brought this up . I'm not going to be able to do anything today but think about this .
 
I understand all of what you are saying but

a curved level would absolutly work IF you kept it ALIGNED

besides that my whole point is that if a level was that long

eventually ( not sure when noticeable) the line begins to no longer be level

be sure to see the pic I attached
 

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by design a level is not curved.

Tony
 
The curved level would only be effective in the area where the bubble existed, and only between that section of the level (1/60 of a degree?)



In geometry, the tangent is the only plane on a circle that would produce an accurate 'level' reading.

If you really want to get all balled up, try grasping the concept of 'Great Circle Navigation', which is, basically, that the shortest distance between two points on the surface of the Earth is a curve (or more accurately, an arc).

This type of navigation is used on practically all inter-continental flights.

*************
 
Every nautical mile on the earths surface is one minute of angle...or 1/60th of a degree. Breaking that down ...every second of angle on the earths surface is rougly 100 yards apart. So...if you had a building with truely vertical walls 100 yards apart....they would be one second of angle out of parallel....and I wish I had my calculator with me...that could easily tell you what fraction of an inch that would be....but it would clearly be visible.

Getting picky here, so brace yourself.

Your statement about the angle-distance correspondence is true only if you make all the measurements along a great circle. We usually measure N-S distances along a meridian, which is a great circle. But we often measure E-W distances at constant latitude, and the circumference of the earth measured that way gets smaller as you approach the poles. At 35 degrees N latitude through middle America, an east-west trip around the world is about 18% smaller than a trip around the equator, because your circular path is centered part way up on the earth's axis, and not on the earth's center.

If you really, truly, try to build walls that are plumb at every point and to align your building north-south, you can make the east and west facing walls follow the meridians. Then you get two out-of-parallel problems: they will tilt outward as you go higher up the walls, and they will also have to "toe in" slightly toward the pole as the meridians converge. Your north and south facing walls, to follow the shortest path between the building's corners, should also follow great circles, and will appear to be curved slightly with a bow toward the north. Your "flat" foundation will follow the earth's curvature and straight planed lumber will rock on it ever so slightly when you set it down.

And your surveyor and contractor will shake their heads and walk off the job if you try to explain this to them.
 
When you get to the precision levels needed by many physics experiments it gets even weirder.

What I mean by that is that what we mean word "straight" is only achievable in our minds. A straight line is only a mental experiment. The current definition of "straight" per physics and measurement standards is "the path of light". The path of light is the straightest thing reproducible with current technology, but we all know light is far from straight when measured on the cosmic scale. Gravity bends and distorts light from traveling in a straight path. Even gravity as relatively miniscule (in cosmic terms) as Earths gravity still distorts light from a completely "straight" path.

So... a level is a "straight" line perpendicular to the earths center of gravity, but "straight" is curved slightly by our gravitational pull as defined by lights path.
 
My 2 cents..
I belive you are correct in saying that a 10,000 mile long streight edge would only be level at the point of the bubble.
To make a level that would read level at any point, it would need to have a radius of 3965.21 miles. This would be accurate at the equator, parallel to it.
This is using pi to the second decimal. (3.14)
24,901.55 miles around the earth at the equator
7,930.42 miles diameter at the equator.
3965.21 miles radius at the equator.
Right?
Brad
 
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