Answer: How many center-pivot irrigation systems do you see? | Hacker News Reader

Answer: How many center-pivot irrigation systems do you see?

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88 pointsrhema50 comments

I always wondered why these are laid out in a grid, and not hexagonally, which is optimal for circle packing. You could fit more in that way.

me too. i finally got to ask a professor at an agricultural college that question. all i can do is give you the non-definitive answer he gave me: "there are access roads between all those circles for planting, harvest, and, maintenance. straight roads are a helluva lot easier to build. land is cheap, gravel isn't."

This, and the related square (ish) grid survey pattern in the US explain the parceling.

The tilling of soil ruining embedded networks explains why that isn't used (probably also pests).

Circular irrigation sprayers; now those I have to wonder about versus a single over-farm arm that can run down a length.

Also, if the water is valued as it should be, why aren't 'growing season' tent structures with build in irrigation used instead?

A single large arm operating the way you describe would need synchronized drive wheels on both sides, adding cost and complexity over a single-drive anchored system. You'd also need a lot more slack in the hose that feeds it.

    > Circular irrigation sprayers; now those I have to wonder about versus
    > a single over-farm arm that can run down a length.

    > Also, if the water is valued as it should be, why aren't 'growing season'
    > tent structures with build in irrigation used instead?

I suspect that the answers to those are maintenence and materials respectively.

If you have a circular arm you essentially just need an engine, a pivot, and a wheel at the end of the arm, whereas if you have an arm that runs linearly you need a lot more moving parts (some sort of mechanism to turn the rotational motion of the engine into a linear motion, some sort of mechanism to keep the two ends of the arm in sync, some sort of mechanism to make the arm travel in the opposite direction, etc.). All that adds up to a bigger initial cost and more maintenence.

For the tent on the other hand you would really need a lot of raw materials. If we just make the tent 1 mile (which is the size of the bigger circles) in diameter and 10 feet high, then you would need over 500 acres[1] of plastic/tarp/(whatever you're gonna cover the tents in) per circle. Add on to that the metal needed for the irrigation system and building costs, and I really start to doubt whether it would be cost effective.

[1]: http://www.wolframalpha.com/input/?i=pi+*+(0.5+miles)%5E2+%2...

From what I've observed, each of the wheels on the center pivot has its own controller to keep the system in line. Some appear to have GPS controllers. The issued with having a large linear arm is re-connecting the water supply every time the arm moves.

If I'm going to build a giant greenhouse in Oklahoma, it's going to need to be weather resistant. A slack covering over a grid of 10-foot-tall supports won't work. If you consider the cost of structural supports will likely dwarf the tent covering, different architectures probably make more sense.

I would suggest a half-torus with major radius 0.25mi and minor radius 0.25 mi. The structural shell would be a tensegrity grid, with the covering affixed over it. That's 790 acres of covering over 502 acres of land. You're going to need a lot of steel cable, and a few truckloads of rigid 50' pipes. You will also need at least two types of pipe-to-cable junction.

Sprinklers under the apex ring (0.25mi above the ground) could easily irrigate the covered area from a fixed position, without rotating, and condensers above the apex ring could recycle water out of humid exhaust air and feed it right back into the sprinklers. There would be no moving parts at all, other than in the groundwater pump and sprinkler heads. You have one ring-shaped pipe (a gutter could work, if the sprinkler heads don't require pressure to operate) to supply the sprinklers that is 1.57mi long, and one pipe from ground to apex ring 0.39mi long.

But with center-pivot, you only need a well pump, 0.5mi of pipe, A-frame supports, and wheels. But then you lose water to evaporation and transpiration. So I think giant greenhouses could not appear until the aquifer dries up, and water costs skyrocket. Even then, I'm not sure it wouldn't be better to just put a bunch of mirrors and a collector tower up, and transmit the solar energy to a vertical farm that is closer to a cheaper, more reliable water source.

Because land in the US wasn't surveyed with hexagons.

In the PLSS system (used in a majority of US states), land was initially surveyed using one-mile sections as the base unit. The next division is into section quarters, a half-mile on the side.

The article has an image which I suspect illustrates differing ownership of the SW quarter:

https://4.bp.blogspot.com/-k0CA9Q64oOI/V6iHkNVv8EI/AAAAAAAA0...

Why not in Saudi Arabia? Who knows, but they certainly show more creativity in the layout.

If that is owned by a different person, that brings an interesting opportunity cost problem.

If the owner of the smaller area shared it with the owner of the bigger area. An agreement could be struck to pay for 1 quarter of the operating costs and receive one quarter of the harvest.

Both parties would save on operating costs, yet receive the same harvest.

Good question.

That would be fairly (ok, wildly) impractical.

Most of the roads are gravel, which means that maintenance would be a nightmare. Road graders aren't great at keeping the blade level on turns. So you'd get buildup/digout at every turn.

When it rained you'd get run-off and erasion. Which makes me think of drainage, wow, with the water making 120 degree turns roughly every half mile you'd get some serious washout on those occasions when we get 2" dumped on us in what feels like 10 minutes.

Zig-zagging across the country with a 24-row planter in tow would be a giant pain in the ass (you plan your route minimize the number of turns you're making). Would be a pain driving a combine fitted with a 12 row head. And at harvest the trucks taking grain to the elevator or silos would be doing the same zig-zagging.

It's not like the grain that's outside the obvious circle doesn't yield. It get irrigated via runoff as well as powerful sprinkler guns at the end of the pivot arm.

Credentials: grew up farming in central Nebraska, married into a 5th generation farming family. Thousands of acres, all centrally irrigated via pivot.

Edit: Didn't want opening tone to sound argumentative/condescending.

Edit 2: Just thought about power lines. They'd have to zig-zag too. Which means the pole on the zag would have lateral force vectors acting on it, so it would have to be reinforced/anchored. When the afore-mentioned washouts happened, down goes pole and powerline.

Your points are totally valid. But you wouldn't need to make sharp 120 turns. You could just have very slight waves with a frequency of 1 mile.

http://i.imgur.com/vJq0Q3i.png

Of course, driving on roads like these would be annoying.

But it would help you not fall asleep while driving.

If you would pack the circles slightly less densely, then you could have straight roads.

Also, if the circles are sufficiently large, I don't think it would be annoying to drive these slightly wiggly roads.

Packing the circles such that you get a straight road would negate the need to pack them hexagonally.

> Of course, driving on roads like these would be annoying.

ITYM awesome. Those roads are normally 30 mph, so at with 1 mile fields one would change course every two minutes

I wonder if it might help protect against highway hypnosis to have a course adjustment every mile or so.

Kansas, and likely other mid-Western states that I don't know about, have historically added "artificial" curves on their highways to increase safety by stimulating drivers and reducing boredom.

Living on a gravel road, I drive them every day. If ever there was a cure for highway hypnosis, it would be driving on gravel...

Maybe because the land in the US was mostly divided up by 1900? There wasn't any particular reason to divide lots that way a hundred years ago?

The farm land owners - which tend to have very large plots of land - could still choose to divide their own farms that way today if it were optimal.

I think it's as simple as the straight-line grids provide a good enough solution (the 85% scenario), with a few attributes that are superior in terms of ease of maintenance, surveying and land ownership division.

In the very near future those grids will gain another advantage: they'll be far easier to outline when it comes to robotic-heavy farming. The wavy, more tightly packed hex alignment would be far messier.

On the plus side, mightn't it help prevent erosion not to have tens-of-miles-long straight lines?

It's never felt natural to look out across the American West and see a North-South/East-West grid obliterating the natural shape of the land.

Almost bed time, so I can't do the math right now, but based on the following papers, how much additional money could be earned if they transitioned from rectangles to hexagons?

http://www.aces.edu/timelyinfo/BioSysEng/2008/October/BSEN-I...

http://www.k-state.edu/irrigate/oow/p07/OBrien.pdf

The 2nd paper quotes a land cost of $139 / acre? / time.

Prime agricultural land in Australia sells for $1500-2000/acre. Pumping costs can run to a quarter million dollars a year. Actual centre pivot installation (for a square kilometre like that) is approx 500,000 as well.

Source: my parents are farmers and we have centre pivots

I never understood why they haven't built them to overlap.

Is it just a cost/complexity thing?

Something with varying heights at the end and a little auto-shutoff to avoid the overlap is all I'm picturing.

Land in these areas is cheap. Maintaining hex roads is more expensive than straight ones, and also makes travelling slow if the hexes are small.

Or add a little one in the corners to fill out most of the star shaped remainder?

Probably farm land is cheap, and it's easier to expand by adding more of the same than optimising usage. Maybe there's alternative needs on the farm that provide more benefit than cramming in as many of these things as possible. After all, it wouldn't be the most complicated thing in the world to just have a thing that isn't fixed in the middle.

> Probably farm land is cheap

In particular, arid farm land is cheap. And that's clearly what we're working with here.

Wikipedia has some photos of hexagonally arranged fields, so apparently it is used in some places:

https://en.wikipedia.org/wiki/Center_pivot_irrigation

Adding to the previous answers:

Central pivot irrigation tends to be built in regions where agriculture is limited by water supply, not by land area. Where the farmer on humid lands ask "how do I work efficiently with my land area", his peer on arid lands asks "how do I work efficiently with my annual water volume". (Edit: and it always ends in tears when the actual question being asked is "how do I get most out of our shared water supply")

Where land is the main limitation, you'd most likely not go from square circle packing to hexagonal circle packing, you would get rid of circles altogether.

(Wikipedia does have pictures of hexagonally packed, so apparently there exists a level of intermediate land scarcity where the trade-offs work out in favor of hex-packed circles)

Discussions like this are why I love this site. I've seen these from airplanes, but never even thought about it enough to know it was called center-pivot irrigation. Now I know how big they are, their density, why we can't arrange them in a hex, etc.

Alright, so here's my question: Since we can't arrange the roads in a hex, why not make the grid a little smaller or the irrigation arm a little longer so that it can reach the corners of the grid. It would obviously run over the road at the midpoint of each side, so if the road needs to stay dry-ish, shut off the water supply automatically somehow at the ends of the arms. Then you can make the whole square green. This creates an obstacle to watch out for when using the road, but otherwise what am I thinking wrong here?

Or just make the arm retractable.

The more moving parts the more expensive, especially in maintenance. It's just like harddrives in server farms, even small changes in drive reliability have a big influence due to the number of them in operation in parallel.

The big cost in these systems is the water since they're placed in locations where land is cheap (read: otherwise worthless). So conquering the spaces between circles really isn't very important. The key is to increase yield-per-gallon of water not yield-per-acre as is typical with farms.

In yield-per-acre scenarios we already have horizontal irrigation systems that roll across a given area kind of like that giant lane-spanning Chinese bus that recently made the news. The only disadvantage to these systems is they have more moving parts (two sets of wheels) and are limited in how far they can roll (they're usually hooked up to coiling hose systems) so you need more of them.

Even we assume you solve the engineering and cost issues, I don't think it is a good idea. Irrigation systems are used where there isn't enough rain. Those corner areas that do not get irrigation absorb rain into the aquifer which can be drawn out latter. The aquifers are shrinking in areas with irrigation systems and this is a concern for farmers who are looking for ways to mitigate this issue. They know that if they don't solve the problem now in a few years they will be forced to take extreme measures. (some farmers already plant their irrigated fields one year out of 3)

>or the irrigation arm a little longer so that it can reach the corners of the grid.

You'll want to investigate "corner pivot". See also page 3 of

http://az276019.vo.msecnd.net/valmontstaging/docs/default-so...

...or...

http://www.pivotirrigation.com.au/valley-corner-73.cfm

One thing I didn't point out in my answer about why hex wouldn't work is that a single pivot does not to irrigate an entire section of land (a section is 1 square mile) [1].

Some pivots will irrigate a quarter of a section, but even this is rare. The standard pivot with a corner system [2] and will cover 152 acres out of a 160 acre field. Roughly a quarter of a one mile section.

[1] At least in Nebraska, I don't know about the rest of the country/world. My source is my brother-in-law a 5th generation farmer.

[2] Basically a swingarm that extends the effective length of the pivot for better corner coverage

Edit: hit enter too soon.

> It would obviously run over the road at the midpoint of each side

This isn't going to work for three reasons: drainage ditches, hedge rows, and power lines.

You could maybe build an irrigation system that traverses the drainage ditches on each side of a rural road but I'm skeptical it'd price out as a good buy for anyone.

You aren't gonna build one that can go through a hedge row.

I wonder what kind of interesting stats one could dig up from aerial images of the farms near La Crosse, WI. Instead of a grid of circles, the farms carve out a bunch of fascinating patterns in the fractal topography around the river. (I'm sure there are similar layouts in other regions, but that's the one that stands out in my memory.)

Example: https://www.google.com/maps/@43.6474645,-90.9363052,5382m/da...

Any suggestions for open source tools doing this, e.g. in python or R?

Here is one using open CV in python [1]. While there are many ways to find circles the Hough transform is a fairly simple and popular one, I don't know what Matlab uses internally but it would probably be an optimised version of Hough for circles. you can see some more here [2], implementing this process in raw python (with PIL or pillow) was something we did in our image processing course in undergrad so certainly not out of reach if you wanted to give it a go.

[1]: http://opencv-python-tutroals.readthedocs.io/en/latest/py_tu... [2]: https://en.wikipedia.org/wiki/Circle_Hough_Transform

I built a Machine Learning algorithm about a decade ago for doing this kind of feature extraction. It was targeted for finding samples on a tissue microarray, but it's basically the same problem (find approximately circular features on an approximate grid).

The research was never published and it was a kind of a hack (an EM-style algorithm that added a step to update grid parameters after the M-step of the centroid fitting).

It worked well enough, but would not be able to handle the heterogeneous circle sizes (1 mile + 1/2 mile) that are demonstrated in the post. Something like this is so well constrained (1 or 2 circle sizes) that running a hand-tuned mix of segmentation algorithms is a pretty good approach.

Thanks! I will give this a try on the next rainy weekend.

How to count them with less effort - no need to count over the whole map. Perhaps Google would ban you if they saw too many requests for map tiles.

So, here's how to do it: sample 100-200 locations in a country. In each location, extract a tile of the map and count the circles in there. Then you need to scale the sum by the total surface of the country divided by the total surface of the sampled tiles.

How did you arrive at the 100-200 number?

That number of samples is a good rule of thumb, to approach the normal distribution.

I have heard it on several occasions, but would be happy to see someone link to a derivation for why that is so.

The number of samples you want to take depends on the variance of the population and the precision with with you want to estimate the population mean (if both of these are greater you want to take a larger sample). 200 is normally sufficient, but its possible to calculate confidence intervals as a robustness check.

The Central Limit Theorem states that even if your underlying distribution is not normally distributed, square_root(n)* (sample_mean - population_mean) will converge to a normal distribution with mean 0 and variance = population variance. Sample variance also gives you an unbiased estimate of population variance.

This means that if n is large, you can compute confidence intervals from n and observation = [x1, x2 .. xi .. xn]

1) computing the sample mean and sample variance.

sample_mean = x_bar = 1/n sum(xi) and

sample_variance = 1/n-1 sum((xi- x_bar)^2)

2) computing x_bar +- square_root(sample_variance/n)

Eg if sample mean is 102, sample variance is 50 and n = 200, your 95% confidence interval would be:

102 +- 1.96 *square_root(50/200) =approx [101, 103]

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

https://en.wikipedia.org/wiki/Central_limit_theorem#Classica...

https://en.wikipedia.org/wiki/Confidence_interval#Definition

The problem with that is that the locations of the sites are probably very correlated, meaning that your samples will no longer be independent, and your estimate would probably be biased.

If the sampling process gives you a random subset of tiles, I don't see how the estimate could be biased. Even if you have a strange distribution of circles (heavily clustered in certain geographies), the weak law of large numbers would mean that the sample mean is an unbiased estimator for population mean if your sampling process is iid (random number generation is by definition iid).

https://en.wikipedia.org/wiki/Law_of_large_numbers

I think you're confused between which restrictions apply to the sampling process versus the underlying population.

Ugh, you are of course correct, I should not be allowed to comment on statistics before having my first coffee. I think I had some diffuse ideas about this not being a poisson processes in my head that lead me to this faulty conclusion.

One could probably improve the detection quality by using something like the NDVI to separate vegetation from the background.

And here's the Question: http://searchresearch1.blogspot.com.au/2016/08/searchresearc...

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