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Calculating Area from a Scale Plan


Gardian
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This isn't really House Renovations, but the closest thing to it.

I've got a scale plan (1:250) of an adjoining plot of land. It's square-ish, but not perfectly so. I'm being told what the square metreage is, but want to verify it (as near as possible, say to +/- 1%).

I've been trying to think how I could do this, by for example scanning the document and plugging it in to some software that'll do it for me, but I just don't have the knowledge / background to get any further. Surveyors must have some means or other to do this, I'd have thought.

Can anybody help with some bright ideas (that don't involve buying expensive professional software)?  Thanks in anticipation.

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Don't know whether this is of any use....

If it is land in France go to http://www.cadastre.gouv.fr/scpc/accueil.do;jsessionid=50EDFF63E7D59032BB5485FA64D6BEAC.scppup01worker1

Enter the address you require, then you may find the plot you want (your plot number may be on your scale plan ). Select this, then on the left you will see "Advanced tools" click this and you will find "measure"

Cheers

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One of those Magellan (or similar) GPS receivers cyclists and walkers use would do the trick.  I know it wouldn't be cheap, but it's not strictly "professional" kit, either.  I've got one, and was able to walk around the perimeter of my property and it measured the perimeter and gave me total area as well.  Very useful.  Failing that, you'll just have to divide the area up into geometrical shapes, and calculate the total area by adding the area values for each individual shape, then convert up from the scale

Chris

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1:250 means 250 metres actual for every 1 metre on the plan.

To break it down further every 1 cm on the plan equals 25 metres actual.

To break it down further still, every 1 mm on the plan is equal to 2.5 metres actual.

You say it's squarish so this method should give you the approximate area but it probably wont give you the +/- 1% you are looking for but at least it's an indicator.

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I think the plan cadstre either on line or at the Mairie will show the surface area in hectares and decimals thereof.

To check it do as suggested above by measuring the lengths of the sides of the rectangle/quadrangle/rhombus with either a scale rule if you have one or ruler and calculator then calculate the area, I assume that you know how to do this although am a bit confused why you want to scan it and use a computer program unless the area is nothing like a square.

Its best to use the most original map copy that you can find (probably at the Mairie) to take your measurements from, you could later use an enlarged photcopy but keep to the original measurements taken, if the shape is irregular you could divide the enlarged version into small squares and triangles to calculate the area.

Its taken longer to write this post than it would to do!

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You would never be able to achieve your desired error from a small scale plan of 1/250th, as the arithmetical error would be far too high.

The only way to achieve any degree of real accuracy would be to carry out a decent survey.

If you do not wish to employ the services of a Géomètre (Surveyor), then, realistically, there is just one option.

Using a long surveyor's tape (Sometimes a workable solution is sold in such as Aldi and Lidl for less than £10), measure and mark off with poles the square section. Pole off the remaining regular piece/pieces: by regular I mean triangles, squares or oblongs.

Calculate the areas accordingly (Area of a Square: triangle etc); add the results together.With irregular bits you can only reduce these to regular portions: laborious, but think of the fresh air and exercise!

The alternative is as already mentioned GPS.

Here is a useful bit of software for GPS surveying of area.

http://www.wildsoft.org/SurveyArea3/surveyarea3.htm

One caveat on cadastral plans, areas and boundaries.: Quote: "Even if the boundaries of the property are clearly shown, the plan cadastral grants no guarantee on the size of the land surface.Even if the boundaries of the property are clearly shown, the plan cadastral grants no guarantee on the size of the land surface."

In rural France, boundaries are known to "Wander"!

May be worth a survey after all as the decision of a Géomètre is usually considered binding.

 

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[quote user="Gluestick"]

In rural France, boundaries are known to "Wander"!

[/quote]

Or as our Notaire remarked on the date of completion with reference to our 9 parcels of land.

"You must understand that in france you may have a little bit more, or a little bit less, but its not important really"

Wonderful words that sum it up perfectly.

.

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Nell - thanks, but the plan cadastral is (to say the least) flakey. It's a group of dwellings, erected in the early 70's and nothing was done properly in terms of land registration. That's the whole point of the thing - disputed boundaries, one large plot that was subsequently split as part of a 'fire sale' (bankruptcy), no proper delineation.

I really like the GPS suggestion & know someone who might be able to help with that one. Failing that, it's the 'scale-up-from-the-plan-and-count' option.

Thanks very much indeed to all for the input - much appreciated. If I get anywhere, I'll let you know.

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If your land is bounded by straight sides you can compute the area as follow without any error. i.e. it is a rigorous solution.

Find the coordinates of each borne defining your land.

For example, you have a plot of land with five vertices (x1,y1),

(x2,y2),(x3,y3),(x4,y4) and (x5,y5),

The area A would be calculated thus:-

A = (1/2) X ( (x1*y2
+ x2*y3+x3y4+ x4*y5+ x5*y1)-(x2*y1+x3*y2 + x4y3+x5*y4+x1*y5) )

This works with any number of sides.

The error occurs in the accuracy of the coordinates and the straightness of the sides.

Remember an error of 2 metres in your side measurement will give you an error of 4 sqr metres in your area calculation.

The coordinates may be measured a number of ways.

The cadastral office may give them to you if you ask for them.

They do have a record of them as they are used to produce the cadastral plans.

They will be in a system called Lamberts Conical Orthomorphic and seem very large.

Don't worry about any of this. Just drop the significant digits.

You can measure the coordinates by GPS. This is the easiest and most reliable way.

You can scale the coordinates from a plan. This is the most error prone way.

You say you have a 1:250 plan. This is very large scale and not a normal cadastral size.

Where did it come from?

If you find this difficult you can email me the coordinates and I will do the calculation for you.

I used to do lots of these calculations when I were a lad http://www.youtube.com/watch?v=I2AcJSkUw6M

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I didn't like to chip in earlier in case anyone (OLDER and wiser) else has a better idea.

What you could do is this:

Draw yourself a grid with each square representing, say 10 x 10 sq metres (or whatever size best suits your purpose) on tracing paper.

Then overlay it on your plan of the plot.

You count the squares and estimate the part squares and there you go...........

Any good?

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[quote user="Mik from LA"]
If your land is bounded by straight sides you can compute the area as follow without any error. i.e. it is a rigorous solution.

Find the coordinates of each borne defining your land.

For example, you have a plot of land with five vertices (x1,y1),
(x2,y2),(x3,y3),(x4,y4) and (x5,y5),

The area A would be calculated thus:-
A = (1/2) X ( (x1*y2
+ x2*y3+x3y4+ x4*y5+ x5*y1)-(x2*y1+x3*y2 + x4y3+x5*y4+x1*y5) )

This works with any number of sides.

The error occurs in the accuracy of the coordinates and the straightness of the sides.

Remember an error of 2 metres in your side measurement will give you an error of 4 sqr metres in your area calculation.

The coordinates may be measured a number of ways.

The cadastral office may give them to you if you ask for them.
They do have a record of them as they are used to produce the cadastral plans.
They will be in a system called Lamberts Conical Orthomorphic and seem very large.
Don't worry about any of this. Just drop the significant digits.

You can measure the coordinates by GPS. This is the easiest and most reliable way.

You can scale the coordinates from a plan. This is the most error prone way.
You say you have a 1:250 plan. This is very large scale and not a normal cadastral size.
Where did it come from?

If you find this difficult you can email me the coordinates and I will do the calculation for you.

I used to do lots of these calculations when I were a lad http://www.youtube.com/watch?v=I2AcJSkUw6M




[/quote]

Blimey Mik!

What I need to do is get a fix on the coordinates (which are presumably synonymous with vertices?). I don't have GPS myself, but should be able to get hold of one in a few days. Taking it on from there, the formula shouldn't be a problem because I can just plug it in to Excel.

The plan has been provided by a geometre expert, who has given a bornage ruling and enclosed the plan as one of the appendices. Since he hasn't been on site with a theodolite, we want to verify the area that he claims the drawing represents (it's crucial to where the disputed boundary falls).

The plan cadastral is a waste of time and has been done on the back of a fag packet - therein lies the problem over the boundary. (see another thread!)

Thanks very much for the above. 

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Mik ...............

Derrrr.  I think that the penny has dropped as to how to apply your terrifying formula!

If I've got a scale plan, then I simply lay a piece of scaled & marked out transparent paper over the plan that I've got & read off the coordinates.  Those are my x & y values. Yes? 

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First, sorry for the formatting in the earlier post. I was in a hurry to go down the dechetterie for some free compost and had transport waiting.

[quote user="Gardian"]

Mik ...............

Derrrr.  I think that the penny has dropped as to how to apply your terrifying formula!

If I've got a scale plan, then I simply lay a piece of scaled & marked out transparent paper over the plan that I've got & read off the coordinates.  Those are my x & y values. Yes? 

[/quote]

Yes that's all there is to it, but the accuracy of the coords will depend on the plan. The formulae is not really as daunting as that. But I can calculate it for you if you prefer. It would be best to ask the geometre for the coordinates.

If your plot has four simple corners you could simply measure the length. of each side and one diagonal and calculate the area from simple trigonometry.(two triangles)

I do not remember the earlier post you refer to but the inference seems to be that you need the area to resolve a boundary dispute. This is not the normal way to do it unless a sub-division has been created transferring a specific number of sqr metres of land. The area is normally calculated after the boundary has been defined.

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[quote user="Mik from LA"]This is not the normal way to do it unless a sub-division has been created transferring a specific number of sqr metres of land. The area is normally calculated after the boundary has been defined.
[/quote]

It's the former, so not normal![:'(]

I'm enjoying this now: problem is that things like appointments tomorrow (neither anything to do with me) + going to bed at some point in time, are going to interfere.

Thanks again for your help: I'll let you know how I get on.

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Yes, if you are trying to work out where a boundary is by calculating the area of adjacent plots then you are probably barking up the wrong tree. Originally the boundary is defined by banging in bornes at each corner. These will be agreed on the ground by the landowners. Then the geometre surveys them to establish their coordinates. These then become the record of the property in case the original bornes are lost and need to be restablished at a later date and when the ownership may have changed. The area is calculated from these coordinates but is for information only. If the coordinates of the bornes and the area disagree, the borne coordinates will always settle the argument if there is no other evidence. Good luck with your dispute.

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Mik ................

First of all, the formula works![:)]  That'll be no surprise to you, because you knew that anyway, but I pressed on last night & it didn't take that long. There were actually nine datum points, so it took some careful checking of the Excel equation, but I came out with an answer that's 3% off of the alleged area. That could be explained by errors in the scale plan and / or measurement errors of the vertices by me (most likely) or the opposition 'trying to pull a fast one' (which is what I was trying to test).

Just by way of background, there was originally a roughly rectangular plot of about 3000 m2. The owner sold half to the sitting tenant (our neighbour, whose side we're on) and the other half to another party (no building on it). There was never any proper bornage done - just a notional area split of roughly 1650 / 1350 m2.

The owner of this gash bit of land wants to build on it, but we maintain that he has no access. Precisely where the boundary sits on the 4th side is crucial as to whether we have a case. There are other complications, but I won't go in to all that.

Anyway, thanks so much again for your help. The formula was precisely what I was looking for.  

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