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They easily could win 10% area usage by packing better. http://www.datagenetics.com/blog/june32014/index.html

While true in theory, this doesn't hold up in practice.

The farmers here are constrained in space by roads on all sides and by the price of each irrigation machine. Many small circular irrigation machines will be more expensive and harder to maintain than one large one.

The article you linked shows how given a square area, the packing efficiency of a non-square packing order increases past 80% only after you have around 30 circles and even then the increase is negligible. It would take well over 100 circles to hit the 10% additional area usage you're talking about.

For farmers who want to make use of those corners of their field just use an irrigation system which can handle corners and make 100% use of their land.

There are these type of linear irrigation devices that will cover square/rectangular fields more completely: https://www.valleyirrigation.com/linears . In practice I don't think super optimal land use is very critical for most farmers though, when compared to the additional cost for acquiring and maintaining more complex irrigators.

I initially thought the use of circular irrigation devices would be when land is cheap, but after some research I think the main reason to use them is when water is far more expensive than land.

I zoomed in to various areas in the Midwest US, and I didn't see a single use of the circular devices, only square fields which are likely using the linear irrigation device you described.

However, in areas where water is more expensive such as Colorado, I see the opposite: Only circular irrigation devices.

I think what's happening here is that circular devices shoot the water down which causes all of it to land on the crops. The farms in my area generally use a firehose style sprinkler which shoots the water up. This causes a large chunk of water to get lost but it hits the corners of the land. Due to the cheaper water costs in the midwest, this is acceptable.

If water cost is the key concern then surely alternate technologies such as drip-lines, inter-cropping, greenhouses/poly-tunnels, windbreaks and mulch could be explored? Also, selecting less water-intensive crop varieties. Fundamentally, spraying water through the air is a great way to lose a lot of it, both in transit and in evaporation thereafter.

Industrial farmers are a bit trapped in what they can sell and how they produce it. They generally can't change varieties much because the plants they're producing are what the factory wants, and anything outside that expectation will sell for significantly less. Secondly, industrial crop fields tend to be hyper optimized towards using harvesters, which don't easily permit intercropping or things in the field to get tangled. Windbreaks in the form of trees are already common in many areas.

All good points, but kinda tangential. To summarize, perhaps we can agree that there are opportunities for technology to make a substantial difference in the resource efficiency of agriculture, but there remain significant factors effecting inertia and lock-in to existing 20th century industrial agricultural processes which must first be overcome.

My understanding is that many farms in the midwest (as least corn farms) don't irrigate - rainfall is sufficient.

Linear and circular systems should in principle be able to achieve the same water efficiency (within their swept area). They're the same thing - an above ground wheeled mechanism to deposit water.

If you're farming in an area where you're water constrained, then you might not necessarily care about parts of your field not being used (as long as it's reasonably small), since what you care about is your input to output cost.

Some advantages of central pivot is that: a) you only need to feed water to a single fixed point - in a linear system you either need a ditch to draw out of (that's water loss right there), or drag a hose around (that's a possible point of failure) b) you don't need to figure out how to regulate the two ends of your line to keep them in line.

Exactly right on rain being the determining factor. In NE Iowa and SE Minnesota, where I am from, it is one of the most drought-resistant areas of farm land in the nation. No one would waste dollar-one on an irrigation system. (Getting 4 rainless days in a row so that you can bale hay is a bigger issue). As you go west, the influence of the Rocky Mountain rain shadow takes on increasing importance. About half way across SoDak or Nebraska, center-pivot irrigation starts to pencil out.

Lots of land in Michigan isn't irrigated at all. So that may be some of the difference you are seeing in the Midwest.

https://www.usgs.gov/mission-areas/water-resources/science/i... has a coarse map indicating a significant difference in practices.

The only irrigated fields I know of in the Midwest are for water hungry crops like melon (my background; I grew up in the Midwest, I’m the first generation on both sides of my family not to grow up on a farm, I spent most of my summers on the farm where my mom grew up)

Makes sense. Land is so cheap out there, that's the last place to be optimizing your trade offs.

This is only true if the circles are all of equal radius. With only 5 circles and 2 sizes you can get a significant increase to 87%. But the problem of practicality and cost benefit still stands.

Square packing density is pi/4 (~78.54%). The non regular packing approaches a hexagonal packing (pi*sqrt(3)/6 =~ 90.69%) for large N. For N=120 for example d=85% http://hydra.nat.uni-magdeburg.de/packing/csq/csq120.html

Does not seem practical in reality (39 or more systems instead of one). Maybe for extremely vast fields where you would have many systems anyway.

> 39 or more systems instead of one

They would need more irrigation systems if they packed the circles more tightly? Why?

The circles have to be smaller to be packed more tightly within a given square.

Hexagonal grids of round farms are found in areas such as Saudi Arabia which don't have a dense road network or rectangular land ownership.

What the circle packing does accomplish though is to collect more of the uncovered space into semi-rectangular areas at the edge of the plot, which could be used for other purposes, like buildings or specialty crops. The plumbing is more complex though. One circle is one pipe, 1/2 of the width (sqrt(2)/2 diagonal) Four circles is at least two pipes, 2 width or more and, you might have to run the irrigation sequentially due to flow rate. That could mean time in the field.

I was watching a Joel Salatin video recently and he was pressing the point of having irrigation and other systems where you don’t have to cross the property, on foot or with equipment, to do chores. It’s a huge time sink and some days you will run out of time. If you have to stay for the duration it’s even worse.

A more humble observer would draw a different conclusion about the economics of large scale agriculture.

Farms must clearly place a much higher value on having straight paths between fields than the the value of optimizing the packing of irrigation units. Packing irrigators into a grid gives two orthogonal directions where you can drive in a straight line.

One might suppose that early experiments in hexagonal farms wasted a lot of land on the turning radii at hexagon edges (for heavy machinery to make the corners) or spent a fortune on annual downtime to replace the steering bearings in the tractors.

Or they got carsick a lot.

Good thought. The practical barriers to better packing are access roads/tracks and property lines. Both of which tend to be straight.

Sure, if the only limiting factor was space. It is likely that the cost of being more efficient with space usage is not worth the extra costs.

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