# circular farms

When I am flying from San Francisco to New York, I often look down to see these square farm plots, but it is only a circle within the square (and touching the sides of the square) that actually appear to be farmed. What the heck is going on with these? Are they indeed farms or something else? Why circles? Why not just use the whole square?

True story:

A friend of mine wrote Farm Modelling software for a NZ Crown Research organisation. This software required data inputs for pastures, etc. It was pretty successful, and the CRI decided to sell the software to Australian farmers, too.

My friend had to modify the software to account for fields that had center pivot irrigation, as the arable land was not the same as the pasture size.

Si

The area of a circle is approximately 78% of the area of a square that constrains it, my guess is that the extra complexity* of building an irrigation system that can evenly water a rectangular area costs more than can be recovered from the value of the crops that could have been grown on the other 22% in a reasonable time - particularly when available land may not be the limiting factor.

*(in centre-pivot irrigation, water can be supplied by a static pipe to the pivot point)

It’s more visible when you fly from New England to the west coast, but there’s a transition from tiny irregular fields to larger a more regular ones to squares with circles in them to nothing, and then to giant fields again in for example the San Joaquin (sp) valley. It vividly illustrates several historically important geographical themes in the US.

If they used the optimal arrangement of circles, they would use 90.6% of the land.

That seems like it might be worth it. Anyone ever seen that done?

SmackFu, are you referring to large, tangent circles, filledin with individual, smaller circles, tangent to the larger ones, at the “corners”?

Actually, no. Just a normal hexagonal packing:

http://mathworld.wolfram.com/CirclePacking.html

Seems like the easiest way to make gains since you would use the same sprinklers, just in different locations.

He’s referring to large circles arranged hexagonally. No smaller circles are needed. (On preview, I see SmackFu answered.)

I expect they don’t do that because the limiting resource is water not land. So, for a given amount of water, they choose the best land to use it on.

You also have to account for the fact that there have to be roads to allow access for trucks, tractors, combines, etc. The link you posted has no straight lines between ‘fields’. Also, as noted above, in places where this type of field is located, availability of land is not usually a large factor.

Very good point. I’m pretty sure some of the examples I’ve seen on Google Earth (maybe the ones in Libya or somewhere) were hexagonally packed.

Of course it wouldn’t be easy to move to that mode of packing from a situation where the land being farmed comprises many small separately-owned plots.

The thing to remember is that the farmers in these areas aren’t asking themselves, “Well, I’ve got all this land…what should I grow on it?” Rather they ask themselves “I’ve got so many acre-feet of water for irrigation…what should I grow with it?”. The water is the limiting factor, not the land.

Hexagonal packing might utilize more land, but if the land is parceled out in square chunks it’s not going to be easy to do that. I believe most of western North America is surveyed out in sections and quarter sections. It’s just not feasible to stack quarter section pivots into hexagonal packing.

Here are some in Libya where they’ve implemented hexagonal packing:

They’re not exactly pressed for space there, by the look of it.

And skeptics claim crop circles aren’t real …

They’re for crop rotation!

Ba-dump.

Thanks for all the replies.

On the point expressed above, I will point out, that in the case where smaller circles are allowed to fill in the gaps between the larger closely-packed same-size circles, the limit of the packing ratio approaches 1 as the radius of the additional circles approaches zero.

Two problems:

1. In areas where land is parceled in square chunks, those gaps between the large circles are owned by up to four different people.

2. The costs involved in setting up a pivot of any size (pipeline and power trenched in to central tower, etc) means small units aren’t going to be cost effective.