Offline edby

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Is surveying an accurate science?
« on: May 25, 2018, 10:12:20 AM »
This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.

With the help of my late father-in-law’s theodolite, which I am just beginning to understand, I can determine this. The first picture below shows the whole instrument. It was made by Clarkson and co Holborn, and the case says it was inspected 17th April 1962. Incidentally, my father-in-law worked for the British government, travelling to distant places to check the amount of land the government owned or controlled. I don’t know if he was in on the conspiracy, he never mentioned it.

You should just be able to see the bubble in the spirit level, which I set level before the photo was taken. This was done by turning the dial in the second picture. The idea is that when the bubble is in the centre, the optical tube is absolutely level, i.e. on a line perpendicular to the force of gravity, and any object appearing in the horizontal crosshair will lie on that line. It follows that if the horizon appears below the horizontal crosshair, it does not lie on that line. Rowbotham claimed that there were ‘collimation’ distortions in such instruments, but haven’t seen any evidence so far.

The instrument says that each division on the spirit level corresponds to 30''. I looked this up and this means 30 arcseconds, i.e. 0.3 of an arcminute, where an arcminute is 1/60 of a degree. If you think back to schooldays, one degree is pretty small, and 1/60 of a degree much smaller than that. I now need to work out how much difference that division would correspond to over 30 miles.

More schooldays. 30 arcseconds is 0.000145444 radians, 30 miles is 5,280 feet. Therefore to work out how much the 30 arcsecond division on the theodolite corresponds to, I use the tan function to convert the angle in radians to get the opposite/adjacent ratio. Then I multiply this ratio by the adjacent amount (30 miles in feet) to get the error in height. This works out to 23 feet. The question is whether we could live with that. Of course this is not a super high precision instrument. That said, when I levelled it, even a small pressure on the desk, even changing position in the room, caused a noticeable movement in the bubble.

Later on I plan to take the instrument to the North Kent coast where the wind farm and the Shivering Sand fort are a known distance from the coast.





Offline hexagon

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Re: Is surveying an accurate science?
« Reply #1 on: May 25, 2018, 10:48:04 AM »
The level of accuracy you need scales with the problem you have. If you want to measure the distance between to points in a city something like a meter is quite ok, if you want to make an accurate drawing of something, maybe a millimeter is sufficient, a biologist investigating some cell material needs a micrometer scale, and in the semiconductor business you go down to some angstroms.   

If you do standard optics, you don't have to solve the Schrödinger equation for the photons involved, but if you're playing with single photons it could be necessary. 

There is no universal rule for the level of accuracy.

Offline edby

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Re: Is surveying an accurate science?
« Reply #2 on: May 25, 2018, 11:18:14 AM »
The level of accuracy you need scales with the problem you have. If you want to measure the distance between to points in a city something like a meter is quite ok, if you want to make an accurate drawing of something, maybe a millimeter is sufficient, a biologist investigating some cell material needs a micrometer scale, and in the semiconductor business you go down to some angstroms.   

If you do standard optics, you don't have to solve the Schrödinger equation for the photons involved, but if you're playing with single photons it could be necessary. 

There is no universal rule for the level of accuracy.

I think the accuracy in question is that which would be required, using a simple experiment such as with a theodolite, to determine whether the level of the horizon is consistent with one of the bedrock assumptions (or axioms) of the Flat Earth theory. Working on it.

Offline edby

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Re: Is surveying an accurate science?
« Reply #3 on: May 25, 2018, 12:10:09 PM »
This https://en.wikipedia.org/wiki/Theodolite#/media/File:Theb1982.jpg shows a theodolite with 0.2 arcsecond precision, i.e. 60 times the precision of the instrument I have.


Offline hexagon

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Re: Is surveying an accurate science?
« Reply #4 on: May 25, 2018, 12:24:58 PM »
As I said, it depends on your problem. Calculate the expected angle you want to measure and if your tool is accurate within 10% of that value, it would be already good enough.

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Offline rabinoz

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Re: Is surveying an accurate science?
« Reply #5 on: May 25, 2018, 12:28:35 PM »
This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.

With the help of my late father-in-law’s theodolite, which I am just beginning to understand, I can determine this. The first picture below shows the whole instrument. It was made by Clarkson and co Holborn, and the case says it was inspected 17th April 1962. Incidentally, my father-in-law worked for the British government, travelling to distant places to check the amount of land the government owned or controlled. I don’t know if he was in on the conspiracy, he never mentioned it.

You should just be able to see the bubble in the spirit level, which I set level before the photo was taken. This was done by turning the dial in the second picture. The idea is that when the bubble is in the centre, the optical tube is absolutely level, i.e. on a line perpendicular to the force of gravity, and any object appearing in the horizontal crosshair will lie on that line. It follows that if the horizon appears below the horizontal crosshair, it does not lie on that line. Rowbotham claimed that there were ‘collimation’ distortions in such instruments, but haven’t seen any evidence so far.



They both look like levels to me, though once checked for accuracy they may be suitable to do part of what you want.


1947 Theodilite
A theodolite has vertical scale to measure vertical angles (dip angles etc) and a horizontal scale.

This https://en.wikipedia.org/wiki/Theodolite#/media/File:Theb1982.jpg shows a theodolite with 0.2 arcsecond precision, i.e. 60 times the precision of the instrument I have.
That's fine if you need it, but from only 10 ft above sea-level the horizon dip is 0.056° or over 3 arcminutes so your 30 arcseconds, or 0.5 of an arcminute would tell you a lot.

One thing a theodolite can do is to flip the telescope 180° and rotate 180° using the horizontal scale and so do a self-check on level.

Offline edby

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Re: Is surveying an accurate science?
« Reply #6 on: May 25, 2018, 12:34:07 PM »
That's fine if you need it, but from only 10 ft above sea-level the horizon dip is 0.056° or over 3 arcminutes so your 30 arcseconds, or 0.5 of an arcminute would tell you a lot.

Thanks, and as it happened, just the conclusion I came to after some laborious but elementary trig, see table below, height in feet, degrees in arcminutes. Right, even at a mere 10 feet, we have over 3 arcminutes, well within the precision of my instrument. Off to Kent we go.

ht   arcmins
1   1.06
5   2.38
10   3.36
50   7.52
100   10.63

One thing a theodolite can do is to flip the telescope 180° and rotate 180° using the horizontal scale and so do a self-check on level.
However this wouldn't correct for Rowbotham's 'collimation error' i.e. the tendency for the instrument to show the horizon lower than it truly is.
« Last Edit: May 25, 2018, 12:41:12 PM by edby »

Offline Tontogary

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Re: Is surveying an accurate science?
« Reply #7 on: May 25, 2018, 12:43:16 PM »
This was questioned in an earlier thread. ‘Accurate’ is relative, of course. There is accuracy down to the molecular level, and there is accuracy for the purpose of everyday measurement.


One thing a theodolite can do is to flip the telescope 180° and rotate 180° using the horizontal scale and so do a self-check on level.

If the theodolite can flip through 180 degrees in a vertical arc, then measuring the arc of the sky (as i did with a sextant) would be a doddle.
A nice high point on an island, or headland would be great, and measure both opposite horizons to get the arc of the sky...

Anyway, as to the original question, i believe it is, and is as accurate as need be.

For example, chart surveying for cartography does not need to be defining objects to a precision of better than a metre in the horizontal datum, as the users (ships) wont be needing them that accurate, (most GPS systems are not more accurate than that) so the methods and standards reflect that.
However i am sure the surveying methods for building bridges are a bit more accurate, as it would be a bit of a pain if the 2 ends were built to meet in the middle, and they were a few feet off! Therefore the methods and accuracy required are determined by the end result.

I would expect someone can detail some other instances where the siting of equipment etc is required to be much more precise, even closer than 1 MM tolerances.

The reason the world is not surveyed not the same accuracy is 1, cost, and 2, need, amongst other things.

Also, if you haven't heard of bronies before, that reflects poorly on your understanding of the world that surrounds you. It's practically impossible not to know about them.

Offline Theo

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Re: Is surveying an accurate science?
« Reply #8 on: May 30, 2018, 03:01:25 AM »
Every country on the planet uses surveyors for borders, property lines, roads, bridges, etc and if you have a property dispute who do you call?  Surveying is an extremely accurate science.

edby,

What you have there is commonly called a dumpy level.  Unlike transiting theodolites dumpy levels don't measure vertical angles directly, they work in conjunction with someone holding a graduated rod.  It will however serve your purpose to see IF there is a drop in the horizon.  My guess is that it was made in early 50s.  Do you have the tripod or is it a table top model.  I don't see any adjustment screws to plumb the vertical axis.

As mentioned above you can't self-check with it so it is VERY important to check if spirit level is exactly parallel to to the telescope. You can see where the instrument is calibrated above the round level.

Considering the scrutiny you'll be under I recommend a simple test for accuracy that will also give you some practice.

Set up 2 poles in a large area 75' apart.  Set up level in line with poles 75' from 1st pole.  Direct a helper to place a mark on the poles exactly on the cross-hairs. Repeat the process at the same distance in the opposite direction.  Don't worry about the height of first set of lines, you want them to be different heights.
The distance between the marks on each pole should be the same, if not you have some error.  Half of the difference between the sets of marks will be the error per 100'.  Use a sharp pencil as any difference will be small.

https://imgur.com/a/IaGH4Yt



Hope this helps and please excuse the primitive illustration.
If you have any questions about the instrument I'll be happy to assist if I can.

Theo

Edit:
I was mistaken about 2nd position, it should be in the center of the 2 poles, not the end!
Sorry about that, it's been a couple of decades since I've dealt with this stuff.
« Last Edit: May 30, 2018, 06:12:00 PM by Theo »