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.

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.

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.

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.