How is acreage measured on non-flat terrain?

August 18, 2009 11:58 AM

Surveying 101: How is acreage measured on hilly ground? Is the acre a measure of the surface area of the ground, or of the area inside an imaginary box that is superimposed over the ground?

For example: Say I have a flat piece of ground that measures 4400 yards x 11,000 yards = 48,400,000 square yards = 10,000 acres. That's simple enough. But what if I have a piece of land that measures 4400 yards x 11,000 yards, but there's a mountain sitting in the middle of it? Is it still 10,000 acres, or is it more acreage because the mountain increases the actual surface area of the land within that rectangle?

(Answers to a previous question brought up the curvature of the earth as an issue that complicates rectilinear-grid surveying systems. This question is more about whether the local terrain affects what we call an "acre.")

posted by Orinda to Grab Bag (11 answers total)

It is the land under an acre in the sky, projected onto the ground from zenith.
Your mountain is still 10,000 acres.
posted by the Real Dan at 12:07 PM on August 18, 2009

No, it has to be a flat (from the sky) imaginary box, otherwise maps of farmland with grids would be filled with different-sized "acres", rather than the perfect rectilinear boxes actually shown.
posted by rokusan at 12:25 PM on August 18, 2009

Doing it by surface area would really complicate things since the surface area of a given piece of land will vary between L x W and infinity, depending on how finely you decide to measure it.
posted by contraption at 12:54 PM on August 18, 2009 [3 favorites]

It is the land under an acre in the sky, projected onto the ground from zenith.
Your mountain is still 10,000 acres.
posted by the Real Dan at 8:07 PM

So, How is area determined on large areas given the curvature of the Earth? That is, large enough that the zenith on one end of the territory is not even close to being parallel to the zenith at the other end.

As an example the US state of Utah. Nice, clearly defined boundaries. The area must be defined taking into account the curvature of the Earth -- vs it being on a Euclidean plane right?
posted by vacapinta at 1:07 PM on August 18, 2009 [1 favorite]

The area must be defined taking into account the curvature of the Earth -- vs it being on a Euclidean plane right?

That's what maps are for.

The usual approach is to use a map with a given unambiguously specified projection (a reference grid) and then do the measurements on the map. There are plenty of reference grids for different parts of the world; I'm pretty sure the US has its own.
posted by effbot at 1:28 PM on August 18, 2009

Best answer: By convention, then, land area is measured on a two-dimensional common surface plane projected onto the ground. (from here) Smaller parcels of land are typically surveyed using plane methods for local surveys--the error factor of ignoring curvature is small enough.

An area as large as Utah, although hills, valleys, etc are not factored into total acreage, vacapinta is correct that one should account for the curvature of the earth; geodetic surveying methods are thus required.
posted by neda at 1:49 PM on August 18, 2009 [1 favorite]

Response by poster: Thanks, all. I did try to Google this question but did not hit the right combination of terms, I suppose. This statement from neda's link summarizes the situation nicely:

By convention, then, land area is measured on a two-dimensional common surface plane projected onto the ground. So even in hilly terrain, the acre is measured as if the hill were cut off at the horizontal, parallel to the horizon.

This convention makes a lot of sense for practical reasons, but the typical definition of an acre ("A unit of surface area, originally as much as a yoke of oxen could plough in a day") makes it sound as if the measure of an acre is more dependent on the topography of the land. Hence the confusion. Thanks for clearing it up.
posted by Orinda at 2:00 PM on August 18, 2009

Note the originally in there. As surveying techniques improved, the definition got more precise, more universal and less terrain-dependent.
posted by nebulawindphone at 2:52 PM on August 18, 2009

FWIW, here's how they measured hilly land in the old days with a gunter's chain.
posted by Knappster at 2:57 PM on August 18, 2009

Response by poster: Cool link, Knappster.

The fact that an acre is often defined as a measure of "surface area" threw me off as much as the plowing origin. It turns out that an acre does not really measure the surface of the land; it measures the surface of an imaginary plane imposed on the land.
posted by Orinda at 3:18 PM on August 18, 2009

So, if you're measuring a piece of land at 6,000 feet, and suddenly the plateau disappeared and the land were at roughly sea level how would the amount of space each person on that plateau change?
posted by MesoFilter at 6:54 PM on August 18, 2009