How do Surveyors' instruments work?

[Matty F]

Since I've Googled and not found what I want to know, I thought there might be people here who know how surveyors' instruments work. The reason I am asking is that three different surveyors have surveyed the same boundary peg (and others) and put the peg in three different places, by up to 500mm away. They have all used the same Council survey mark in the footpath outside.

While I would have thought that a GPS unit would do the job very easily, the surveyors did not use a GPS unit, except maybe to get the position of North (an assumption by me). My cheap GPS unit locates the pegs to within a metre.

They all used a device (probably with a laser) on a tripod, and a rod with a mirror on top. I'm actually not interested in discussing any other kind of equipment. I want to know how three surveyors could get different results in the last few years using equipment that they say is accurate to within a millimeter. The Council survey mark has not moved and there have been no landslips and nobody has moved the pegs. The pegs are next to trees and structures that have not moved.

The process for a survey appears to be:

1. find a spot across the road that is visible from the section being surveyed.

1. put a peg there, put the laser above it and the mirror above the survey mark and measure the angle and distance and declination. Somehow the equipment knows where North is - I hope it's not using a compass.

2. find a spot inside the section being surveyed that is visible from where the boundary pegs are guessed to be. Put the laser there and measure to the mirror on the spot in 2 above.

1. Put the mirror above each peg position. At the laser, key in the distance and angle where the peg should be, and move the mirror up and around until the peg position is deemed to be correct by the equipment. This process takes seconds only and requires no calculations by the operator. The raising and lowering of the mirror is allowed for by the equipment by some magic unknown process (obviously that changes the distance, if the laser is a different altitude from the mirror). The mirror needs to be raised above vegetation in the vicinity. The mirror has a small bubble level on it so can be made vertical.

All around me people are putting up buildings and fences, and we need to know where the boundaries are. My neighbour's fence is reinforced concrete blocks and will never be moved again I'd say.

I can't measure most of the peg positions accurately with a tape measure because the land has a slope of up to 60 degrees and is covered in trees.

Now surveyors are highly paid professionals who in theory know what they are doing. How come they don't agree where boundary pegs should be put?

[Tim Watts]

Matty F ( [e-mail]) wibbled on Wednesday 26 January 2011 00:19:

Operator error and lack of full circle checking (see point 10) - or machine has lost calibration...

I have actually used such an instrument - I wanted to survey this property, especially with respect to the "building line" of the other properties.

My property slopes every which way and nothing is square, so using a tape would be prone to serious error and/or tedium...

Long story short - I got a very good bank holiday weekend rate on a Leica Total Station hire (that's the name for the instrument your guys were using

- it is an electronic theodolite - ie angles in two planes, plus, crucially, a very accurate laser range finder - which gives yoy the distance - the third and final variable to being able to ascertain relative positions in 3D space.)

Please note the use of "relative".

A surveyor friend had given me a theory run down and I spend the preceeding

3 weeks reading the manual which Leica kindly emailed me.

My method, which I understand, is "standard" at least for a novice surveyor was: (terminology shakey...)

1) Define a 0,0 point in the X,Y plane - that's bang a pin in the drive basically - completely arbitrary and chosen for convenience. 2) Put the instrumnet over this pin and fine adjust using the optics to sight the pin on the crosshairs vertically, levelling the instrument too. Some machines use a plumb laser for this. 3) Point the instrument along known bearing. This could be north if you have an accurate compass and correct for mag vs geo north. Not the best method. Better method would be to sight a number of distant landmarks using the best map you can get. Range is not required so you may exceed the laser's range for this.

If you like, this bearing can be arbitrary if all you want are relative measurements to other houes rather than true to map reults. I roughly guaged mine as all my work was relative.

Enter in the bearing into the machine's setup station mode screen.

4) Hopefully your base station point (0,0) was chosen wisely so you can see as much as possible from there. Now point the machine at something you wish to measure. Aim, press button, get result in a variety of formats including x,y,z cartesian or polar formats depending on machine. It just did the 3d trig calcs for you. 4a) Write down, or if the machine is fancy, enter a code name for this point. It helps to have a sketch of the whole plan and mark roughly each point and the ID code for reference later. 5) Repeat - you can use the mirror stick for boundary points (the stick must of course be perfectly plumb - I suspect this is where the error creeps in). Or you can measure to the tops of walls, gutterboards, chimneys and anything else the laser can get a reading from (quite a lot - the lasers are pretty powerful - enough to measure your immediate neighbours' houses too). 6) When you have seen all you can see, you need a new station point. Choose one you can see, and from where you can see things you can't from the zero point. Pin in ground, set up mirror stick, survey stick from zero point. 7) Move machine and set up over the new base point. Tell the machine it's new coordinates and survey back to the original point to get the bearing calibrated. My machine had a fancy mode where you pointed it back to the stick of the zero point and just gave it the station code fo rthe zero point and it looked up the reading and set itself up for the new frame of reference. 8) Survey more points of interest. The machine knows its new poistion and results are still calculated as if in the zero point's frame of reference. 9) Set up the 3rd base station point - for a detached property you will effectively be going to the four corners of the house. If not detatched, you need to either try and sight through open windows or survey through the house itself. 10) Now the cunning bit - at some point you should end up with a final station base that can see the original zero point base pin. Survey it. If it reads anything other than 0,0,0 you have an error. You will always have an error - but it should be small. Mine was about 1cm IIRC - which is pathetic by professional standards - but good enough for me. If that validates, the majority of your other readings should be trustworthy. If it does not validate, you have to assume some margin of error of similar value in *all* your other readings. 11) Dump the readinsg out of the machine and write them into a log book - not a scrap of paper. Now type them into the computer and save all over the place (some machines can dump direct via lead).

You will not believe how useful this data is - from drawing an accurate base plan of you house, including the unsquare walls, to knowing how high your chimney stack is to knowing your property in relation to other properties.

The hire rate I paid was little over 100 quid (which is a massive discount as no professional wants it for a B/H weekend) and it was very instructive.

Was scary though - having 5-6k's worth of machine with no insurance - I was fecking careful!

Does that help in any way?

Cheeers

Tim

[Owain]

...

I think there's a wiki article in that.

Owain

[Matty F]

I have phoned Land Information which is a NZ government department dealing with boundary pegs. Amazingly, their suggestion was for me to pay for yet another survey to establish the position of the pegs. So that will be four surveyors. Who is right? The last one? The surveyor with the biggest company? Clearly nobody will be interested in my measurements, no matter what quality of equipment that I hire. I have measured all of the pegs, and am quite sure that one of the pegs installed two days ago by the latest surveyor is two metres wrong. I actually found a peg two metres away. Are surveyors allowed to pull out pegs that they disagree with? I have photographed all of the pegs in case anyone shifts one. I may haveto go to a governent mnister about this. The incompetence is incredible.

[Tim Watts]

Matty F ( [e-mail]) wibbled on Wednesday 26 January 2011 05:58:

Quite frankly, I would DIY it - then see which surveyor I agree with...

Then kill the other(s).

I imagine your land is rather bigger than mine, but I bet I could do better than 2m! (unless you own land the size of a village).

You these people have a professsional body you can disput with?

[Matty F]

Yes there is a professional body. My friend who was a surveyor's assistant said that the measurements are self-checking and should end up at 0,0,0 or they've made a mistake. I have just found a peg that I have been looking for for years - it was a metre further up the hill but within 20mm of my measurement with a tape measure. I have just come back from speaking to the neighbour who contracted the latest surveyor. He's relaxed about the boundary position and we both have simliar ideas abouit how to stop the cliff falling down.

This is typical though - once again, professionals have ridiculed suggestions that they are wrong, and me with rudimentary equipment (i.e. a tape measure) can prove them wrong. WhatI know is that if three surveyors put the peg in three different places, then at least two of them are wrong.

[Tim Watts]

Matty F ( [e-mail]) wibbled on Wednesday 26 January 2011 08:03:

Yep - "professionals" are never wrong...

[Roger Chapman]

As far as I know GPS units (certainly the cheap ones) have to be moving in order to recognise direction. But that doesn't matter with a GPS, the position is the same whichever direction the unit happens to be facing.

Here in the UK cheap GPS units are by no means as accurate as quoted above. Ten figure grid references do resolve to 1 metre but the unit I now use has an accuracy at the 95% confidence level of only 15 metres. Even DGPS (addition of a base station) increases the accuracy only to 3

- 5 metres.

And while it is obviously reprehensible for a professional surveyor to be 500mm adrift over a relatively short distance such accuracy is difficult to achieve with a tape, magnetic compass and inclinometer even over a few hundred yards of uneven ground as I found to my chagrin when I tried to add unmapped field boundaries to our local map.

But do not despair. Even on a map scale as large as 1:10,000 500mm isn't really discernible on a map.

FWIW the GPS units used by Ordnance Survey surveyors are linked to mobile base stations and will not allow a position to be taken until the error is one centimetre or below.

[Jim K]

but who measures the "error" and how to decide it's less than 1cm? that suggests "all is known" before they start...

Jim K

[Roger Chapman]

You are looking at the problem from the wrong perspective. It is not a matter of measuring the error but the limits of accuracy in the calculations that underlie the reported position. We might well doubt such supposed accuracy and I have no idea how they actually arrive at the answer but it would be easy to confirm such predictions experimentally and, for all I know, that might be how they get to their basic calculations.

[Roger Chapman]

Just an afterthought really. If you survey round a series of points and get back to point one with only an infinitesimal error there is still scope for considerable error if the relationship with true North is not know with exactitude. The military often use a 'mil' instead of a degree. A mil is an angle the subtends 1 metre at 1000 metres so if the orientation is just one mil out there will be a transverse error of 1 metre at 1000 metres distance.A mil is approximately half a degree and is about as close as even a prismatic compass can be read.

[Dave Liquorice]

No all three are wrong, some are more wrong than the others. B-)

With a boundary you are probably better off putting in a series pegs, manually, along the line that you can agree on with your neighbours. You can sight a straight line very accurately and get any angles pretty damn close with careful measurement from the ends of an agreed base line.

[Jim K]

??clear as mud! gotta link?

Jim K

[Tim Watts]

Roger Chapman ( [e-mail]) wibbled on Wednesday 26 January

2011 10:16:

No - I don't believe so - *if* all you care about are relative coordinates.

Effectively you are only declaring to the machine *once* which way the north axis is pointing. The east axis is 90 degrees to this and the height axis is sorted out by levelleling the machine (they have a *very* fine electronic level built in the good ones).

It would only matter when you need to reference a map and even then the error is not cumulative as you only set a known bearing once - the rest of the station points are measured back to the last one - you may get cumulative error here (which is why it's important to check back to the first "zero" point), but this is independant of any error of the absolute bearing. Effectively the bearing can be as arbitrary as your choice of the (0,0) point. And you can always bulk transform the coordinates later if you ascertain a correction factor relative to the maps.

So if you have a super-scale town planning map, you'd probably do no worse than survey a few other property boundary coner points in a couple of directions as far as you can see to align the machine to the map well enough (ie any error in your boundaries as a result would be tiny).

If you have a more normal scale map but can sight a hill, tower or church or some other landmark, that would work too.

The machine I had has many units and coordinate systems as options - wouldn't be surprised if that was on offer - I didn't look.

Cheers

Tim

[Peter Parry]

Your cheap GPS unit may have told you a grid reference which appeared to be accurate to 1m, it almost certainly wasn't.

DGPS can achieve 1-2m accuracy in static mode, For anything better real time kinematic carrier phase differential GPS achieves centimetre accuracy but isn't the sort of thing you buy for a few hundred pounds and requires paired work using at least one accurately positioned base station nearby (within a few km).

The Great Trigonometrical Survey of India started in 1800 and surveyed the whole continent using nothing more than chains and theodolites (albeit BIG theodolites - the great theodolite weighed over half a ton). In 1852 it determined the height of Everest to be 29,002 feet. The latest measurement of the height of Everest is 29,035m so having carried the survey line from its original 7.5 mile baseline on the East Coast near Madras the error was a mere 33ft.

The Principal Triangulation of Britain was carried out from 1783 to

1850ish using chains and the Ramsden theodolite.

Accurate survey does not require any electronics.

[Jim K]

just attention to units....

Jim K

[Peter Parry]

Very simply, there is only one base instrument, the theodolite, which measures angles , both horizontal and vertical, to great accuracy. See

Distance would have been measured with a calibrated chain, or these days an Electronic Distance Measurer (EDM). For small areas Gunter's chain alone will provide surprisingly good accuracy. The reason I am asking is that three different surveyors have surveyed

Whatever process they used it wouldn't qualify as surveying if that was the repeatability achieved.

It wouldn't.

By not knowing what they were doing. I'm assuming this piece of land is quite small (less than 1 mile square). If this is the case using a Theodolite (or its modern equivalent the "total station") the survey point should have been carried around the boundary and back to the start to within a cm..

It doesn't need to know where north is.

The EDM isn't a laser used conventionally but a modulated infra red beam (or sometimes a modulated microwave source). Using modulated IR the instrument accuracy in range is in the order of 1mm at 2km. The Porro prism reflector is designed to give a range reading to the pole centre. Angular accuracy should be about 1 to 3 seconds of arc

Most people when building a house say "that's a nice level bit of ground - just right for a house. Only in New Zealand do people say "Wow - nice vertical cliff face - let's build lots of houses on it. earthquakes? What earthquakes?"

Incompetence. Or you were employing construction surveyors (who are not usually properly trained surveyors) rather than geophysical surveyors. The problem is simple and there is no reason why a high degree of accuracy and repeatability should not be achieved.

[Roger Chapman]

But relative coordinates are not a great deal of use without direction. If I understood the OP correctly Matty has three different points with a maximum divergence of 500mm. It could be that all these points are on a arc exactly the same distance from a reference point and the only error is one of direction.

How do you manage to maintain that particular version of north when the machine is moved to a new location?

I don't dispute that you can get the relative position of any three points very accurately by triangulation but I can't see how, on the information available, you can arrive at the true orientation.

If you are working from two known points on an existing map then you have established a base line that orients your survey and your triangulation should, generally speaking, be as accurate as the map from which the base line is taken.

How?

You could measure the angles in radians if you wanted to, it wouldn't make any difference to the final outcome. I mentioned the mil as it directly translates into offset regardless of unit of length as well as being about the limit as far as measuring direction with a compass is concerned. (At 1000 inches the offset is one inch).

[RobertL]

it's a thousandth of a radian.

Robert

[Skipweasel]

Don't try to fly to Mars using a mixture of metric and Imperial units?