Land Surveying

“All you survey, or only a part? Or, does the crow fly or walk?”

In land surveying, how is acreage determined when land is hilly rather than flat?
That is, measuring the “lay of the land” land with tapes or chains will give different number of feet than the line-of-sight distance given by modern laser ranging.

How steep does a hill have to be before its sides can be ignored–that is, a cliff-face can’t be regarded as a hillside, surely?

It seems to me that in the old days of rod and chain surveying, if I had wanted to buy a farm I would choose acreage in hilly Missouri rather than flat Kansas.

Seems to me that topographical problems can’t be avoided: A timber cruiser working in the flat woodlands couldn’t use the same timber estimation calculations in the mountainous California forests.

Do geographers use the same land measurement techniques as cartographers?

Come to think of it, do modern laser ranging devices incorporate GPS?

Used to be, you had to do a lot of setups and take-downs of the transit along with short chaining steps. Nowadays, instruments have GPS on board and distance is measured electronically.

Well, that’s the problem. Short chaining steps was a crow walking, and GPS is the crow flying, and

in a three-dimensional world the two measurements are different.

Horizontal distance is horizontal distance, an acre is an acre. If you’re thinking about maximizing surface area, my question would be why? Crops and trees grow up not out.

Even so, most land measurements for normal purposes - cadasral description, sale, subdivision - would be treated as flat, two dimensional polygons. Hilly topography might give you a bit more here and there but your acreage is measured on the flat, and all chainages are measured as if horizontal.

Sorry I re-read that and it came off as snarky.

Everything is done in horizontal distance. An acre on 120% slope has the same growing space as acre on 12%. If you’re picturing an acre with a hill in it’s exact middle creating more surface area, you are technically correct, but it’s not usable surface.

It makes no difference , hilly or flat…the land is measured horizontally

Nope! whether a surveyor uses old tapes, or modern electronics, the distance along a line will give the same number of feet,whether hilly or flat. (There will be a small difference in inches, because of human error vs. electronic accuracy. But the number of feet will be the same.)

Here’s why: maps are flat. The earth is not.
When surveyors and cartographers make maps, they do it on a flat projection.
In the old days, surveyors using measuring tapes would measure the distance up a steep slope by breaking it up into a series of short measurements, like going up a “staircase” of flat steps.

For measuring purposes, the hillside is always ignored, just like a cliff face.

Yes, the hilly land will have a bit more surface area. But it’s harder to plow. :slight_smile:

Yes, this is true–the topography makes a difference, that doesn’t show up on a flat map. For example, think of a building a fence one mile long in a straight line. The line on the map will be exactly one mile long, no matter how steep the slope. But if the land slopes upwards at a 45 degree angle, the actual length of the fence will be about 1 and a half miles. Contractors and estimators take this into consideration. In this example, a contract will always state payment for one mile of fence. But the contractor’s price per mile will be higher for sloped land than for flat.

Depends. There’s a whole field of math called spherical geometry. If, for example, you want to launch a nuclear missile to another continent, you won’t be calculating horizontal distances the way surveyors do.

Yes. But not the kind of GPS you have in your car. Surveyors use GPS with accuracy of millimeters.

This is a good way to look at it.

I work in GIS - Spatial Analysis. Lets look at a hypothetical. Say you are below a neighbor and it is a cliff that separates you. Also say that you need 300 feet of distance for zoning purposes for a (pick your own , smelly, loud or otherwise legal but not generally welcome activity.

You can’t use the separation elevation of a cliff or series of small buttes or hills to meet your required set back distance.

I’ve been in land surveying for nearly 20 years now. As has been set out already in this thread, distances in surveying are measured horizontally. When calculating acreages, you are using those same horizontal measurements, so the relief of the land is not taken into account.

Yes, technically the distances would differ if you were to lay a cloth tape along the ground, but it generally isn’t as much as one would think. I’ve had landowners that want a “3D distance” measured for roads that they are leasing to oil companies, and generally, the amount of extra time required just to gather that data and put it together the way they want it more than ate up any extra money they might be able to squeeze from the companies.


The above appears to be equivalent to saying that property bounds are always determined by straight lines (or perhaps Great Circle arcs?) between points defined by latitude and longitude.

So, are property bounds ever actually described that way (i.e. with lat/lon)?

Lat/long can be used used on large parcels to define a point, or corner of a property. Often though, a local coordinate system is used to tie it to local high accuracy monuments.

One thing that I provide information for in my job is point information of where an address is. This usually given in decimal degrees, not degrees-minutes-seconds.

And if you want to describe a boundary of un-subdivided property, Meets/bounds or cogo geometry is used.

From such and such point then -
N35d45s08mW 123.34 feet (From this spot go North 35 degrees - 45 seconds - 08 minutes West a distance of 123.34 feet)

And then so on and so forth until you come back to the beginning if you are describing a closed polygon.

There is the technical point that (technically) latitude and longitude are shifting all the time – plate tectonics and all that, ya know.

To the dismay of both Los Angeles and San Francisco, the two are zooming closer to each other at about an inch per year. (Anyone got better better figures on that?)

Back in the day when I did some timber cruising the method was to measure slope distance first, then use a clinometer to determine average slope gradient along the measured line. We then used trigonometry to convert from slope distance to 2D map distance. In Forestry you are often dealing with steep slopes where the difference can be significant.

Modern GPS can measure elevation, but with the cheaper hand units I used the elevation data was a lot rougher than the 2D data. I believe the more expensive GPS units that surveyors use can, with a little effort, get pretty accurate elevation data.

One area where land shape is critical and is always modelled in 3 dimensions is hydrography - whether it is complex flood modelling or simple stormwater drainage design.

In all cases its the land surface slope and elevation that determines the water volume, speed and direction it will move, and in flooding it can move atypically as it backs up.

We citizens of all countries can thank Bill Clinton for his decision to unscramble the GPS satellite data for non-military use. Would such generosity and foresight be displayed by our current leaders?

Thanks everyone; I much enjoyed the breadth of the responses: hydrography, timber cruising, cadastral description/meets and bounds, set back calculation, and such.
My brain is 86, and leeks, so I spend hours a day trying to restock it; vainly. Thanks to the Vacuum Energy for sites like this.
"I don’t live in the middle of nowhere, but I was born just outside Erewhon.

“Such and such point” are usually also chained back similarly to some known reference point, usually a USGS benchmark hammered into a road or rock or something solid and permanent.

The USGS benchmarks have a lot of information about them recorded- elevation, latitude, longitude among other stuff.

That’s the info for one right next to the YMCA I exercise at.


An acre measured on a 45 degree slope yields a 42% increase in available surface area compared to a “flatland” acre… Even at a more gentile 30 degrees, there is a 16% increase in surface area. These are not trivial numbers.

Gentile… I make myself laugh sometimes.

They are trivial in timber cruising and agriculture because the required growing space is also increased by the same %.
ETA: I shouldn’t say agriculture as a whole, just as a reference to the example in the OP.