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No doubt you have flown over the central US now and then, and there you have seen the characteristic circular patterns of fields watered by central pivot irrigation.

Generally, these circular patterns are arranged in rectangular arrays of squares, like eggs packed in a carton. Arranging the irrigation systems this way gets you π/4, or 78.5%, of the wet area (and presumably the crop yield) you would get if you irrigated the whole square (which presumably requires more hardware and labor out of proportion to the change in yield). On the other hand, if you were to pack the circles in a hexagonal pattern (as often seen in mosaics), you would get an improvement in yield of 15% "for free".

One assumes most farmers are neither idiots nor disinterested in profit.

Poll #1174860 Why do farmers pack circular fields in squares, not hexagons?
Open to: All, results viewable to: All

Why do American farmers pack circular fields in squares, not hexagons?

View Answers

Religious beliefs require them to leave something for the gleaners.
0 (0.0%)

Crop rotation: the corners just happen to be in a fallow period, and the pattern will shift next year.
0 (0.0%)

Malnutrition caused by previous generations of poor farming has deprived them of basic geometrical reasoning ability.
1 (5.9%)

Most farmers have small plots allocated in standard square lots and the overhead in cooperating with their neighbors to change the packing method is too high.
6 (35.3%)

The Man pays farmers to farm badly.
3 (17.6%)

Land is so cheap as to be basically free and farmers are farming as much as their labor and consumable inputs allow.
1 (5.9%)

Apathy.
3 (17.6%)

Sabotage: they are undermining the glorious corn-fed SUV revolution by underproducing. Damn kulaks.
0 (0.0%)

Aliens: you're actually seeing negative crop circles.
2 (11.8%)

You're just flying over the wrong farms. Most of them do pack efficiently, including using fractal technology to fill in the gaps with ever smaller irrigation circles.
1 (5.9%)

	From: ronebofh	Date: April 21st, 2008 07:33 pm (UTC)		(Link)

(•) Only gamer nerds use hexes to represent land.

	From: squishyent	Date: April 21st, 2008 08:30 pm (UTC)		(Link)

Do those sprinkler systems move on their own? If so, how do you prevent collisions in a hexagonal system?

	From: en_ki	Date: April 21st, 2008 09:16 pm (UTC)		(Link)

They rotate, but do not translate.

The current system is circles inscribed in close-packed squares. The system I'm referring to is circles inscribed in close-packed hexagons instead. In neither case is there a possibility of collision.

	From: merle_	Date: April 21st, 2008 10:21 pm (UTC)		(Link)

I think square lots are a big part of it. It would seem like space would be wasted in a hex pattern (if you don't do the math, or if the lot were just the right size of square for grid packing). Then again, it could be that the gaps caused by square packing are just the right size to park a trailer.

Also, when reaping the grain it is probably easier just to go back and forth rather than weaving in and out within a hex grid.

But generally, I would say many farmers do not learn enough higher mathematics to know about optimizing packing.

I have seen a couple of farms using hex packing, as well as a few with tiny circles in the gaps between the big circles in a square packing, but they are quite uncommon. If memory serves Arizona had the majority of the ones I saw.

	From: ocschwar	Date: April 22nd, 2008 02:23 am (UTC)		(Link)

Square lots is a main issue. I actually have flown over hex-packed circles.

But another issue is field runoff. The 20% left untilled can help a great deal with the environmental issues of farming this way.

	From: satarnion	Date: April 22nd, 2008 06:09 am (UTC)		(Link)

How? Do the areas act as runoff buffers/sponges?

	From: ocschwar	Date: April 22nd, 2008 11:08 pm (UTC)		(Link)

	From: friode	Date: April 22nd, 2008 02:31 am (UTC)		(Link)

If you have to irrigate like that, it is possible that water and not land area is the limiting factor.

	From: en_ki	Date: April 22nd, 2008 03:19 am (UTC)		(Link)

So are you saying the US has an overall water shortage? If not, it makes sense for me to get only the land I can water most efficiently (with hexagons, or even with some degree of overlap) and sell/rent the excess land to somebody else who can afford the additional water. (That's economics.)

	From: friode	Date: April 22nd, 2008 05:51 am (UTC)		(Link)

IIRC, at least 10 US states towards the left coast are kinda short on water. But I don't think all US states are.

And I guess there is a difference between being in a state that has a shortage of tap water (which actually would probably try to get farmers to go find some other state to farm in, except that I think they actually don't) and being in a place that doesn't have enough local natural rainfall.

But I think the other thing is that if you're in a sufficiently rural area, there's just not much demand for that land. It's quite possible that we have more acres of land usable for farming in the US than it's worth bothering to farm; IIRC we export corn etc, which may only be economically pratical because of government subsidies.

Name: Tuco Benedicto Pacifico Juan-Maria Ramirez

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