From: varney@cbnewsd.cb.att.com (Al Varney)
Subject: Re: How big is an acre, Really?
Organization: AT&T Network Systems, Lisle, IL
Distribution: usa
Date: Thu, 10 Sep 1992 05:44:37 GMT

In article <HOLLEN.92Sep9152210@peg.megatek.UUCP> hollen@megatek.UUCP (Dion Hollenbeck) writes:
>I have looked up the acre to square mile conversion factor (1 acre is
>.0015625 acre) and am trying to figure out how many acres in a square
>1/4 mile on a side, but every time I do, the figure does not seem
>right.  One way of figuring it out gives me 40 acres, while another
>says that there are 640 acres in a square mile, which means that the
>1/4 x 1/4 mile would be 160 acres.

   I'm sure many will point out that a square 1/4 units x 1/4 units is
NOT 1/4 of a square unit  (it's 1/4 times 1/4 = 1/16th of a square unit).
And 1/16th of 640 acres = 40 acres, no matter how you or the ASCS folks
figure it.

> So, could someone please answer
>the following questions:
>
>1) What is the exterior dimension of an acre?

   What is the exterior dimension of 10 square feet?  Seems to me there are
LOTS of answers (1 x 10, 2 x 5, 1/2 x 20, etc.)  A SQUARE ACRE is about
208.7 x 208.7 feet.

>2) How many square feet in an acre?

   43,560.

>3) How many acres in a plot 1/4 mile x 1/4 mile?

   As above, 40 acres.


   Since my grandfather was both an assessor (county) and a farmer (detailed),
every field got measured with the old "wheel" at some time or another.  I
don't remember all the "rules of thumb" he tried to teach me for math,
but here's the background:

   Real surveyor's (in the "olden" days) used CHAINS of 100 links, with
a total length of 66 feet.  {Try dragging one any longer...}  An area
of 10 chains by 1 chain was an ACRE (also called 10 square chains, but
that doesn't mean 10 x 10, it means 10 1x1 chain squares).
Thus - 1 chain by 10 chains = 1 acre.
     - 10 chains = 1/8 mile.
     - 80 chains = 1 mile.
     - 1 chain by 10 chains = 66 foot strip 1/8 mile long = 1 acre.
     - 1 chain by 80 chains = 66 foot strip 1 mile long = 8 acres,
       (this is the typical area of a country mile, since it's easy for
        the surveyors to make the edge-to-edge length = 1 chain.)
     - 80 chains by 80 chains = 8 acres times 80 or 640 acres/sq. mile.

   The city folks weren't content with length in chains for measuring
smaller lots, etc.  And dividing all those estates in England/Ireland
into smaller and smaller plots (so each son got a share) made units of
a chain difficult.  So the ROD was invented (at least that's my granddad's
theory).  The ROD is 1/4 of a chain, (or 25 LINKS of a chain) = 16.5 feet.
Thus - 4 rods by 40 rods = 160 sq. rods = 1 acre.
     - 1 sq. rod. = 1/160 of an acre.
     - 1 acre = 1/160 of a "quarter section" (1/4 of a section or square mile).
     - 1 rod by 1/2 mile = 1 acre.
  (For many fields, the long dimension is often 1/4, 1/2 or 1 mile.
   Every rod (about 6 steps) in the other dimension is 1/2, 1 or 2 acres.)

   Common farm field sizes are:
1 mile square = 640 acres, commonly called a "section".
1/2 mile by 1/2 mile = 160 rods square = 160 acres (a "quarter section"),
   typically identified by it's position within a section (e.g., NW quarter).
1/2 mile by 80 rods = 80 acres. (1/2 of a quarter section)
1/2 mile by 40 rods = 40 acres.  (About 1 block wide by 1/2 mile)
80 rods by 80 rods = 40 acres. (NE quarter of the NW quarter of section ...)

   For non-farmers, one acre is about 7 60x100 foot house lots.  Due
to streets, etc., you can only get about 3000 houses to the square mile....

   The CHAIN was OK for the high-priced surveyors (working in pairs), but it's
too messy for an individual interested in a quick but accurate measure.
For example, an assessor or farmer interested in the size of a particular
plot of wheat or a pasture -- there's just one person, so the chain was
a pain :-).  But what about a wheel that could be rolled over the ground?
That would work real well, except that a chain-sized wheel is 20 feet high.
Even half that is too big.  But a wheel that's a rod is only about 5 feet high.
Bulky by today's standards, but not too bad if your vehicle is a pick-up.
(I believe today some "wheels" are 1/10th of a chain - about 2 feet high,
fits in the trunk.)

   The CHAIN should not be confused with the CABLE -- that's for measuring
"nauticals", or something like that.

   I know this was overkill, but it brought back some good memories.

Al Varney (ex-Kansas farmboy)