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alterhorse
Jun. 7, 2012, 05:56 PM
We're planning on expanding an existing pasture and I'm hoping that someone here may have some knowledge about land surveying to answer a question I'm not completely certain about.

We have all the previous survey maps, and we have found all of the existing corner monuments of the property.

We have the zoning approval and we can basically put our new fence line anywhere we want on our property.

So here's the issue....

We want to figure out exactly where our fence will be located relative to our property lines, and want to know if using common math, trigonometry, and geometry calculations, are suitable for surveying our pasture layout?

I've done some research into metes and and bounds, and I now understand how to read the bearing coordinates on our survey maps and Convert Degrees Minutes Seconds into Decimal Degrees.

I understand that elevation needs to be taken account when making ground measurements with a 300 foot tape.

I understand that survey maps can basically be thought of as a horizontal plane floating above the surface of the land, and the depending on the grade of the land, the actual surface measurements may vary from those on the survey map due to differences of measuring on a straight line, vs. over rolling terrain.

But say I have two existing monuments that I know the distance between, I know the exact bearings of all the lines involved, and I want to determine a new point that is unmarked, can I simply draw straight lines on a piece of paper and use "regular" trigonometry to find that new point that I want to mark for the pasture fence?

Or, does land surveying use a "different" kind of trigonometry that I am as of yet not aware of?

I think plain old trigonometry is correct but I can't find any verification of that as a fact in all the web searching that I've done.

Hope someone knows the answer to this... :yes:

ReSomething
Jun. 7, 2012, 06:27 PM
No, I think it's regular trig.. Dad was a land surveyor and civil engineer and although I held the rod enough I always managed to miss the math part - but the calculators I borrowed from him used standard trig.

One thing I dimly recall is that the instrument had to be set to magnetic north and then the deviation needs to be compensated for in your area since the bearings are off of true north. We had the instrument mounted on a tripod, in the center of the tripod was a plumb bob hanging with the point dead center over the pin. The tripod legs were adjustable so the platform to mount the instrument was level - had little bubbles to check with. I am afraid I know nothing about the more modern instruments that use GPS and laser sighting etc.

Sometimes the old man would advocate just eyeballing a good line - I thnk this came about in the evenings after he'd had a couple and was bent about having had to come in and adjudicate a property line dispute between two neighbors quibbling about a couple of inches deviation or the location of a tree, but if you are going across a slope you will find that the line that looks straight to your eye is often curved - if you can't sight down the line of fenceposts and have them disappear behind one another you haven't got a straight line. Also if you have any kind of terrain you really need those stakes (you need to stake it out first) to keep your line straight from visual point to visual point - we have an encroachment from the neighbor where they went up the hill thinking they were going to the next stake and then discovered they were about two feet off once they got within sight of it with the fence posts - since it was family they just curved it rather than pull out the posts :sigh:. We intend to replace that section and it'll get straightened out at that time - or if they decide to sell I guess we'll have to move that project up fast!

alterhorse
Jun. 7, 2012, 07:36 PM
Thanks ReSomething :)

The line of sight is exactly the issue we have to work around.

We have a clear line of sight between two monuments that we have already staked out.

The new area consists of "pockets" of meadows with wooded areas that project towards the existing pasture. The idea is to put fence around the wooded areas, but the fence at the back of each wooded "pocket" needs to be on the same exact straight line as viewed from above (and clearing the trees is not an option).

The line between the monuments is not parallel to the fence line we need to create in the back of the "pocket meadows", but we do know the exact angle the new fence line must be relative to the line between the monuments.

So what we are thinking of doing, is to use trigonometry, and triangulate off of the stakes we placed on measured intervals on the straight line that we have between the monuments, and measure into the corner of each "pocket meadow" to find that straight line.

We did get an estimate from a surveyor to do this for us, but for the cost of the survey we can buy 300 feet of fence.

We just want to be sure that "regular Trig" will work for this.

ReSomething
Jun. 7, 2012, 08:57 PM
I think that would work, although I'm sure my dad would be asking "why bother" if your line through the woods is an arbitrary line and not a legal boundary. I have fence through woods and unless you clear trees you'll have to settle for close to straight, and if the meadows are bottom land and the wooded areas are the declining parts of hills you may find your fence taking way more woods than you had originally intended in order to stay straight. It's hard to explain but your straight fence tends to march uphill in order to be truly straight.

And the other issue is that if you plan to measure over the ground to get the distances you measured on paper you have to be prepared to measure in stadia, that is you will measure in level planes which is what the rod was for. The instrument measured to a point on the rod and then the instrument came to where the rod had been, and the rod moved on. It got more complicated on steep slopes. The instrument did some correction and I imagine the newest ones do all the calculations on the spot, but if you are measuring out to the ends of the meadows and starting to go uphill you will be adding the distance of the c squared side rather than the b squared side. For calculating the fencing materials of course you'll want the c squared measurements but for making that dead straight line from the air it's going to be seeing the b line.

I'm sure that's as clear as mud, sorry, as I said I did my darndest to skip the math part. And it is standard trig, it's just used in multiple dimensions because you are into the realm of topographical work unless your property is dead flat.

alterhorse
Jun. 7, 2012, 11:13 PM
It's good to know that common trig will work. Thanks for the verification. The slopes around here are gentle so they won't factor into the distances that much... but they will be factored in.

Thanks again for your help. :)

draftdriver
Jun. 8, 2012, 10:02 AM
Several years ago, the property next to me was being sliced up and sold. The boundary line runs through a treed area. The surveyor phoned me and asked if, rather than cutting a line through the trees, could they survey through my pasture? I was all for it. No sense cutting down perfectly good trees.

What they did was find the corner pin, measure perpendicular to the boundary in question into my property x feet for a clear line of sight to the back of the pasture, set a temporary pin at the back of the pasture, and measure x feet back to the fence line, then drive in the the new corner pin for the new lot. In essence, they measured 3 sides of a rectangle to avoid cutting trees on the fourth side.

As a side note, I asked how accurate the old stone and rail fence line was (the stone part has likely been there for 150 years) -- they said it was off about 1" . I have a lot of respect for what surveyors can accomplish with lenses, bubbles and math.

alterhorse
Jun. 8, 2012, 12:06 PM
Several years ago, the property next to me was being sliced up and sold. The boundary line runs through a treed area. The surveyor phoned me and asked if, rather than cutting a line through the trees, could they survey through my pasture? I was all for it. No sense cutting down perfectly good trees.

What they did was find the corner pin, measure perpendicular to the boundary in question into my property x feet for a clear line of sight to the back of the pasture, set a temporary pin at the back of the pasture, and measure x feet back to the fence line, then drive in the the new corner pin for the new lot. In essence, they measured 3 sides of a rectangle to avoid cutting trees on the fourth side.

As a side note, I asked how accurate the old stone and rail fence line was (the stone part has likely been there for 150 years) -- they said it was off about 1" . I have a lot of respect for what surveyors can accomplish with lenses, bubbles and math.

That sounds very close to what we are doing. Good to hear that this is how a professional surveyor would handle this type of situation, it's reassuring to know we are choosing the correct method.

The thing that got confusing when doing the research for this was the concept of "datums", true north, grid north, and magnetic north, and if they might somehow interact with the math used to calculate the angles and distances in some way where compensation would be required.

I think that over very long distances these factors actually do need to be taken into consideration, but we're only dealing with about a 1000' by 400' area with gentle slopes, and we have a survey map with topographical markings to give us elevations that we can use to cross check our field measurements against.

The most looming question though, was that we need to find a new line using the known line. The survey map gives us the bearings of all the lines involved, but it only gives us the measurements for two. The area is like a big quadrilateral which has no parallel sides, but we know the distance between the two monuments on one side of the quadrilateral, and then we know the distance from one of the monuments outwards along a bearing to a point for the corner of the new fence.

The reason for this thread was to get some validation that trig could be used to find the location of that unknown forth corner. We do have bearings for the lines that intersect it, but no recorded distances of the lengths of those two other lines.

To simplify the idea, say you were working on a completely level pasture. and you had two monuments that were exactly 1000 feet apart, and you knew the bearing of the line between the two monuments. Then two keep it simple say you wanted to make a triangle using that known line as one of the sides.

From the survey map you can find the bearings for all of the lines of your triangle.

By calculating the difference between the bearings you can derive all of the angles at all of the corner of that triangle, but you still only know one distance. But these angles when calculated into decimal values are numbers with three decimal places, or 1/1000th or a degree.

A simple Angle/Side/Angle Trig calculation can then provide you with the lengths of those unknown sides. Triangulation can find all of those points with percussion, as long as the slopes can be accounted for accurately.

We were already pretty sure that common trig was apropriate for making our measurements, I just wanted to roll the idea past the wise cothers for validation. :)