Thread: Surveying / maths question

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
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
The process is called seeking approval to non-complying development.<O


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

Originally Posted by joe greiner

The missing angle shouldn't be needed.

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

Originally Posted by joe greiner

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

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.

Originally Posted by joe greiner

Shape of the terrain shouldn't matter. Joe

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.

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.......

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......

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

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

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.

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

Originally Posted by joe greiner

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

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..

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

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.
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

Popcorn anyone?