Surveying / maths question

Hi all. :D
I am looking at sub-dividing my block into two equal parts. One block will be the front portion, ie the top of the plan.(less 4 metres on the LH Boundary)
The second block will be the rear (bottom) of the plan plus a 4 metre wide driveway down the left hand Boundary, from the road marked LANE.
My question is where does the horizontal dividing line meet the RH Boundary, assuming a 90 degree angle from the LH boundary. :?:?

It is probably a fairly simple calc for those who know how, but I'm an old bloke so give me a break :doh:
I promise I could do it if it was a rectangle:2tsup::U

Thanks,
Phill.

So, how far down the LH boundary would the dividing fence intersect? Halfway, at 115.66 (give or take)? Or from the same post as the neighbouring block's dividing fence, the one giving the 120 mark?

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Originally Posted by ptrott

Hi all. :D
I am looking at sub-dividing my block into two equal parts. One block will be the front portion, ie the top of the plan.(less 4 metres on the LH Boundary)
The second block will be the rear (bottom) of the plan plus a 4 metre wide driveway down the left hand Boundary, from the road marked LANE.
My question is where does the horizontal dividing line meet the RH Boundary, assuming a 90 degree angle from the LH boundary. :?:?

It is probably a fairly simple calc for those who know how, but I'm an old bloke so give me a break :doh:
I promise I could do it if it was a rectangle:2tsup::U

Thanks,
Phill.

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Phil
Measure 115m away from lane along the boundary
the position will be close enough +/- 1m to visualise.

Afterall, you're going to have to pay a surveyor to place the pegs in the right spots anyway.


ian

Please ignore the above, I rushed the maths and forgot to add 1 when working out the ratios

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Originally Posted by ian

Phil
Measure 115m away from lane along the boundary
the position will be close enough +/- 1m to visualise.

Afterall, you're going to have to pay a surveyor to place the pegs in the right spots anyway.


ian

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Given that it is not a rectangular block, I beg to differ on this one, the take off point will be a fair bit closer to the road than the 115m half way point. The access way is only four metres wide and that extra being taken from the front block for the rear will not compensate for the triangle on the right of the front block, my guess is there is about 1500m extra in that front section at least so I would think the take off point would be less than 100m from the road. Then again it's late and my brain isn't really switched on.

That's only true if it's the acreage that's being halved.

I guess my question should've been "just how do you want it halved?" :D

this time with the right maths, I hope

The block is near enough to being a long narrow triangle with the corner cut off — from memory the shape is called a trapizoid

Area of trapizoid = (front boundary + rear boundary)/2 x length

to divide into two equal parts the ratio of the long side of the front block to that of the rear block should be the same as the ratio of the front boundary to the rear boundary of the original block (for a first approximation I'm ignoring the 4m wide driveway)

the frontage is about 116.5m which is 2.08 times the rear boundary length, so the ratio is 1 to 2.08
to divide the block in two measure in 231.32/3.08 = 75.1m from the lane. The block is about 96m wide at this point.

BUT the driveway takes about 300sq.m from the front block, so the dividing boundary needs to move 300/96 = 3.1m towards the rear.

Again to a first approximation 75 + 3 = 78m (from the lane) is the approximate location of the LH subdivision boundary and I'm saying about 77m for the RH boundary to allow for the front boundary not being in one line


ian

Thanks for the input gents.
Based on what you have said and playing with this neat doohickey (http://www.mathopenref.com/trapezoidarea.html) I recon that if I draw a line across the block at 130 metres from the bottom (on the LH boundary), parallel to the bottom boundary, (that makes it a trapezoid) and allow 410 sqM for the driveway, I would have to be pretty bloody close to 10,000 sqM which is near as damit to half. Does anyone disagree or have a more accurate calculation? It only needs to be accurate to within a couple of metres on the side boundary.

Thanks again,
Phill.

Damn close, Phill. I haven't done today's crossword puzzle yet, so I had a shot at it in CAD. I got 101.00m along the left boundary (130.32 vs your 130), with 87.04m to the right boundary from the new corner (except perpendicular from the left vs parallel to the bottom). Area of 9977.55 vs 9977.5 "exact." I got slightly different angles in the upper right region of the intact block. But field traverses never quite close. Rules for distributing the error of closure (called "balancing the traverse") can be somewhat soft, IIRC. (Note I haven't done this since Uni about 40 years ago.) Your surveyor can take it from here.

[Oops! My "today" is your yesterday, of course.]

Joe

Joe,
thanks for your input. You have given me some hope with your mention of "Balancing the traverse". Reason is that the shire will not approve subdivision of less than 10,000 SqM
and I am 5 SqM under, so they told me to have it re-surveyed to see if it is really 10,000.
From what you have said, it sounds like there is room for movement in the final answer???
Phill.

I would divide it up using triangles B*H/2
les

I dunno Phill. I just tweaked my CAD sketch, using the angles stated on the plan, and got a gap at the upper left of only 0.06m; the calculated area of the added sliver is only 1.4sqm.

A re-survey might or might not get the original results, depending on how well the monuments are defined, and use of state-of-the-art instrumentation. The block on the right seems to have an area of 1.9something, so the original subdivision might have been deliberately planned to prevent later subdivision. See what size the other blocks in the area have, to confirm or deny this.

You'd best consult a local surveyor. You can't rely on somebody you've never even met, who isn't a real surveyor, and who lives on the other side of the world.

Joe

Thanks Joe.
I was looking at getting it surveyed again depending on how close it was to 10,000 SqM. X2
It looks close enough to warrant the outlay on the off chance.
The original sub division was done in a way that does not make much sense to me. Some blocks are well over 20,000 and others are just under.
I can't find the pegs so best to get it done.
Thanks again.
Phill.

Interesting problem. As far as I can make out, the area of your existing block is 19971sq.m. Your council requires a block to be at least 20,000sq.m. before allowing it to be subdivided. So you are short by 29sq.m. If you are hoping that your block has been incorrectly measured, the issue is how far out the initial measurements have to be to lose those 29sq.m.

Assuming the measurement error to be one of incorrect scale, then we can ask how big the scaling has to be to get the overall area up to 20,000sq.m. The answer is that a scale of 1.000725 applied to your block (29/20000/2) will bring it up to 20,000sq.m. I.e. 0.0725 percent.

This scaling equates to your longest boundary (the slope on the right of the plan) being 232.84m instead of the current 232.67m, a discrepancy of 17cm. I note that according to your plan the top boundary of 87.2m (assuming all the other angles and lengths are spot-on) should actually be 87.33m, a discrepancy of 13cm. This discrepancy would seem to constitute evidence that the measurement errors are enough to allow the possibility that block's area is 20,000sq.m.

As to how to divide the block into two equal areas using a line parallel to the southern boundary, (exercise for the reader) such a line should begin 134.82 up from the lower left corner.

(Imagine every 'mm' is a 'm' in the attached.)

like Joe it's many, many years since I've done this stuff
but if I recall correctly, your survey should be accurate to at about 1 in 5000, to pick up an extra 45sq.m to give you 2ha, you'd be looking at an error of about 1 in 440 which equates to moving your LH boundary 200mm to the left with no change to any other boundary


ian

Conversion to metric may scramble the following, but here goes anyway:

In US, measurements are usually to the nearest 0.01ft; =0.012"; abt 3mm. Say 5mm for approximately equivalent precision, or 0.005m. It appears that reporting is to two decimal places in both systems, so reported measurements include rounding. More modern electronic surveying instruments may achieve greater precision, but each reported measurement is individually rounded from its more precise value anyway, after balancing for error of closure, so the final report still might not close. (I think)

Zen, the area is reported on the plat as 19955, so the deficit is 45sqm. Note that there are no 90-degree corners on most surveys; just doesn't happen that way. Also, the proposed division must provide 4m-wide access to the back block, to be included in the back block area. Although that might be converted to an easement in the front block instead, the deficit is still 45sqm.

Ian, I calculate a perimeter of about 637m. If the deficit were distributed equally around the perimeter, we'd get an expansion of about 71mm, or 2.8in; I doubt that creative monument finding could be so egregious. We surely don't want to encourage any unpleasantness between the surveyor and the licensing board.

Phill, are there any provisions for some sort of special appeal? The whole thing seems terribly arbitrary for such a small accommodation.

Joe

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Originally Posted by ian

to divide into two equal parts the ratio of the long side of the front block to that of the rear block should be the same as the ratio of the front boundary to the rear boundary of the original block

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Ian, where did you get that from? I don't think that is right.

Wongo, it's a vague recollection from 35 years ago when I had to calculate volumes by end area. On reflection I'm not sure it's right either, but Phil has his answer so it doesn't really matter

ian

Could you re-post the image of your plan, this time showing the internal angle that has been cut off from what I presume to be your north western corner. (It is plotted in the adjoining property). It is always good to have all the information when performing these calculations. As pointed out by others, the distances have been rounded to 0.01, where the angles are quoted to an almost rediculous accuracy.

Also, do you have any additional information, such as the age of the original subdivision. This would give a good indication as to the possibility of any "error" in measurement in the original survey. Remember too, a fresh survey could find shortage, not necessarily excess, although surveyors have long known it is better to err on the positive side of the ledger. (However, they are noted for understating areas).

Also the lay of the land may have some impact. Is it relatively flat open country, undulating and heavily timbered, rocky and mountainous....?? All will have had an impact on the original survey.

I would like to see the whole plan if its available, just for interest sake.

The missing angle shouldn't be needed. The deflection angles (as shown for exteriors (assumes a straight-line continuation), 180 degrees minus the displayed value for interiors) must sum to 360 degrees.

As to the precision, from Handbook of Chemistry and Physics, 41st ed. (1960), p. 347:

RELATIONS BETWEEN DEGREE OF ACCURACY OF COMPUTED LENGTHS AND ANGLES
When solving a triangle for any of its parts the following should be observed:

Length to .............. (requires) Angle to:
2 significant digits .............. nearest 30' = 0.5 deg
3 significant digits .............. nearest 05' = 0.083 deg
4 significant digits .............. nearest 01' = 0.0167 deg
5 significant digits .............. nearest 0.1' = 0.00167 deg

0.1' is 6 seconds, and longest length is 5 significant digits, so substantially consistent.

Age of the original subdivision could be of value, especially if before metric conversion.

Shape of the terrain shouldn't matter. Surveys should be measured in a level plane, or for a large survey in a plane tangent to the reference sphere and/or including boundaries between such planes. Elevation could be significant, though, depending on the height above or below the official datum.

Joe

Joe

I'm perplexed by the angle of 160° 47' 66" It appears redundant, so I'm wondering what it represents ?



as to Phill's intent, when he says "the Shire" wont approve subdivisioons smaller than 10,000 sq.m he really needs to examine the "fine print" of the clause and planning scheme.
<O:p
If most of the blocks in his subdivision are big enough to be divided into 2, then because he's only 45 sq.m short of the council requirement there is a very good chance that the subdivision would have to be approved on the basis that nearly every other block can be so divided. <O:p
The process is called seeking approval to non-complying development.<O:p


ian

That one threw me too, Ian. I thought it might refer to the angle on the boundary on the opposite side of the LANE. But I printed the pic, and it doesn't measure at about 10 degrees difference from the 29.58 line. I measure about 160 degrees between the 87.2 line and the line beyond the angle of 85deg0'xx", though. Maybe that's it.

The "fine print" should definitely be examined. Phill's subdivision would result in two parcels, each of which would ROUND to 1ha, which should satisfy the spirit of the regulations.

Joe

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Originally Posted by joe greiner

The missing angle shouldn't be needed.

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In the real world, it would be folly to begin calculations without all the information. Never assume.

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Originally Posted by joe greiner

0.1' is 6 seconds, and longest length is 5 significant digits, so substantially consistent.

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To put it into "field" perspective, one second of arc makes 1mm over the longest distance (232) shown on the plan. It is not possible for a surveyor to measure that accurately - thus my comment. Theory is fine for textbooks, but being practical is better in the field.

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Originally Posted by joe greiner

Shape of the terrain shouldn't matter. Joe

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LOL, try telling a surveyor that. Of cause it does. Imagine the poor surveyor traversing up and down the hills, over rock and shale, through woods and gullys. One of the boundarys could be a vertical cliff for all I know.

All I am suggesting was that if the survey plan was "oldish" there are more likely to be inconsistancys if the conditions are difficult.

I'm not setting out to knock you mate, you've provided some good theory, but theory is not the be-all and end-all.:wink:

OK, as much as I hate maths, I enjoy a challenge (well, within reason).

I have prepared a sketch (hand drawn, and not to scale - sorry) using the available angles and distances. I have assigned the boundarys arbitary bearings. This should allow those tinkering in CAD programs to accurately enter the data should they desire.

Using this information I calculate a misclose in the "mystery" corner of 0.004, so the information on the plan seems sound within itself. This gives an accuracy of 1:147591 which is more than acceptable.

My only dislike about this, is that the misclose is created on the street frontage. I would much prefer use the original angle on the plan at this point, and possibly fault slightly 2 of the distances (being they are rounded to begin with), but this is just preference, and not really justified considering the size of the alotment.

I have calculated the area to be 19955.4. This would be consistant with the surveyor disclosing the area on the conservative side. (ie to the nearest sq m rounded down.).

See Sketch (1).

To divide the block into equal halves (with a line at 90 degrees to the side boundary), the distances are as shown on sketch (2). {Other information remains as sketch (1)}.

The possibility here would be to create some kind of easement for the rear block, however this may not be looked favourably upon, as the rear block would not have a legal street frontage. It would just depend on local council policies.

The other possibility is to create the "battleaxe" lot formation as mentioned previously, and I might just be too tired to calculate that tonight. If someone doesen't beat me to it, I might have a go tommorow night.

Now there's a challenge if I saw one.......:D

LOL, couldn't let it rest. Nothing much else to do ATM.

Here is a possible solution that may interest you.

You would have the best idea if these boundary lines would suit the topography. Obviously the battleaxe is suitable for vehicular traffic etc ?

Anyway, best of luck with the project.

Ph.

PS - All calculations are guaranteed error free.

If there is an error, it is free......:D

Perhaps not, Ph.

1. "Missing" angle: the angle isn't actually missing; its complement is shown on the adjoining parcel, just as the interior angle's complement is shown at the lower right corner. It just isn't viewable on this fragment.

2. Consistency: I said "substantially consistent." Office calculations likely default to the nearest second, so that's the precision depicted.

3. Shape of the terrain: These aren't the surveyor's field notes. This is the recorded plat. I doubt Oz surveyors work different from Oosa, but the recorded plat should be corrected to a level reference. If it weren't, nothing would ever close.

Your "possible solution" differs from mine by only 65mm on the vertical leg, and 105mm on the horizontal. Isn't that amazing? (And mine had an inequailty of 0.05sqm - I just bailed out at that point.)

Joe

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Originally Posted by joe greiner

Perhaps not, Ph.

1. "Missing" angle: the angle isn't actually missing; its complement is shown on the adjoining parcel, just as the interior angle's complement is shown at the lower right corner. It just isn't viewable on this fragment.

2. Consistency: I said "substantially consistent." Office calculations likely default to the nearest second, so that's the precision depicted.

3. Shape of the terrain: These aren't the surveyor's field notes. This is the recorded plat. I doubt Oz surveyors work different from Oosa, but the recorded plat should be corrected to a level reference. If it weren't, nothing would ever close.

Your "possible solution" differs from mine by only 65mm on the vertical leg, and 105mm on the horizontal. Isn't that amazing? (And mine had an inequailty of 0.05sqm - I just bailed out at that point.)

Joe

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Geez Champ,

When I said the angle is missing, that was exactly what I meant. It is missing from the plan provided.

Would you be confident if you commissioned a surveyor to mark your land and he showed up with only a thumbnail sketch dipped in tar, which was hard to read and didn't show all the information.

Sure, it is fine to do the office calculations nice and accurate. But a practical realisation of what the numbers actually mean in the field is important. That is why IMO it is not necessary in a situation such as this to show angles or bearings to the nearest second. This generally only leads to confusion.

No-body mentioned surveyors field notes, or heights above datums, or spheroids or any of that other mumbo jumbo which is all irrevelant in this situation. I simply asked the owner what the topo was like to gain more of an insite into the task at hand, and to allow me to contribute to the comversation more meaningfully.

Possibly you have mentioned them to impress others you have a basic understanding of some of the theory behind the principles of surveying. Hey....thats cool with me.

And the difference between your solution and mine is that mine is correct and yours is almost correct. :D

Possible your misclose was because you didn't interprate the information correctly because it was hard to read, and wasn't all there....

Still, I cant help feel in all the quoting from text books and other diversions the most simple answer to the problem has been overlooked.

Possibly it would be possible to purchase a small sliver of land from one of the adjoining owners so as to increase the size of your own block so it meets the minimum requirements.

Simple.

Ph, your appreciation of simplicity and the practical approach is commendable. But you've misinterpreted a few things about the original post and my suggestions.

The original post is a fragment from the officially recorded plat. Field measurements never close exactly, and the error of closure must be balanced around the traverse before submitting the plat for record. Calculations to distribute the error are done to a higher precision and then rounded to the precision depicted in the plat, as demanded by regulations.

The angles depicted in the recorded plat must have deflection angles summing to 360 degrees. If the "missing angle" prevents this, the entire plat is in error and can't be relied upon, and remaining arguments are moot.

My credentials are listed in the user profile. Yours aren't.

Let's put this thing to bed.

Joe

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Originally Posted by joe greiner

My credentials are listed in the user profile. Yours aren't.

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Exactly....a very wise old surveyor once told me.....the only people who will try to proclaim they know more about surveying than an actual surveyor are retired architects and retired engineers.

Land surveying has put the bread and butter on my table for longer than I care to remember, and land boundary definition just happens to be my specialty.

Guess I wasn't playing fair....eh.

I stand by my original comments that most of what you have said is not relivant in this case, and in a way I feel you have spoiled this thread for others by continually butting in and presuming to answer questions that were not directed to you.

But hey, its a public forum, and you are free to do as you see fit.

Not sure if it changes the numbers or not, but just on the off chance it does and no-one else spotted it..

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In US, measurements are usually to the nearest 0.01ft; =0.012"; abt 3mm.

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3mm's actually about 118 thou. 12thou's around 0.3mm. (Check these numbers again, they're off the top of my head. Don't have a calculator handy.)

Looks like jg's just slipped on a decimal point in his explanation. It's no big deal and doesn't affect the debate. PH might disagree though. :wink:
I'm sure if he was submitting a plan, all the numbers would be double checked.

Very interesting debate guys. I'm learning a bit about surveying from both of you :2tsup:

Popcorn anyone? :D

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Originally Posted by Article99

Not sure if it changes the numbers or not, but just on the off chance it does and no-one else spotted it..



3mm's actually about 118 thou. 12thou's around 0.3mm. (Check these numbers again, they're off the top of my head. Don't have a calculator handy.)

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Nah. The middle one was haywire. 0.01ft = 0.12" ~= 3mm.

Tempest in a teapot, though. The only matter of significance is the level of precision required by council for approval of the subdivision. However accomplished, "exact" halving of 1.9955ha would be 0.99775ha, which rounds to 0.9978ha, which rounds to 0.998ha, which rounds to 1.00ha. (Bingo?) Or does council require 1.0000ha?

I think Phill has enough (more than enough) information for further consideration.

Joe

Hi Joe, I just couldn't resist

Quote:

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Originally Posted by joe greiner

0.01ft = 0.12" ~= 3mm.

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Nah 0.01ft = 0.12" = 3.0mm or 3.05mm or 3.048mm as you expand the precision

However, you are quite correct, all that really matters is the number of square metres Council can be persuaded they need before they have one hectare.

AND this will depend largely on things other than the size of Phil's lot.

if the most of the lots in Phil's subdivision are larger than 2ha then it will be possible to persuade Council that a lot a bit smaller than 1ha (say 9978sq.m) is OK on the basis that it would be silly to have 2 or 3 ~2ha lots in the middle of a subdivision where all the other lots are ~1ha. One reason will be that Phill will be paying twice as much in rates compared to his neighbours.

The persuasion will be a lot more difficult, if most of the 2ha lots in the subdivision are actually less than 20,000 sq.m, because in this case Phil would be halving his rate bill compared to his neighbours.


ian