Surveying / maths question

[ptrott]

Hi all.
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
I promise I could do it if it was a rectangle

Thanks,
Phill.

[Skew ChiDAMN!!]

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?

[ian]

Hi all.
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
I promise I could do it if it was a rectangle

Thanks,
Phill.

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

[Burnsy]

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

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.

[Skew ChiDAMN!!]

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?"

[ian]

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

[ptrott]

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.

[joe greiner]

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

[ptrott]

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.

[les88]

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

[joe greiner]

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

[ptrott]

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.

[zenwood]

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.)

[ian]

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

[joe greiner]

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