The Kentucky State University farm has been blessed with rain, and our crops are all in the ground and looking good.

We direct-seeded corn, sweet sorghum and soybeans, and transplanted sweet potato slips. Planting and management is done entirely by hand in our 'biointensive' plots. Our 'market garden' plots use no machinery larger than a walk-behind tractor. Our 'small farm' plots are primarily managed with conventional 4-wheel tractors and attachments.

[video]

The video shows some of our planting, transplanting, and management activities at each of the three farm scales in June. We have been able to use smaller tractors in the Small Farm plots now that the primary cultivation is complete. We are weeding these plots with a Farmall 130 tractor built in the late 1950s; all other weeding is conducted with wheel hoes, conventional hoes, or by hand-pulling. The planting and management phases, in June, required much less energy than the soil preparation phase, in May.

Labor (top) and energy use at three farm scales at the Kentucky State University farm, 6 May - 23 June 2008. Bars are divided into soil preparation (black), planting (purple) and management (yellow) components. Each bar is the mean of 4 replicates. Error bars show standard errors of each mean.

Michael Bomford provides research and extension services related to organic agriculture and small-scale renewable energy production through Kentucky State University's Land Grant Program. He thanks Tony Silvernail, Brian Geier, John Rodgers, Joelle Johnson, Monique Marcus, and student volunteers from the CASS program for their help with planting and management in June.

The US Department of Energy (DOE) has a new factsheet entitled "Biofuels & Greenhouse Gas Emissions: Myths versus Facts." It's a fascinating mix of wishful thinking, careful data selection, and occasional outright lies cobbled together to promote the big biofuel agenda.

It begins with the assertion that US energy consumption will grow by 50% by 2030. That's twice the increase predicted by the US DOE's own Energy Information Administration (right). As I showed in a previous post, US energy consumption has actually been leveling off in recent decades, despite consistently incorrect forecasts of perpetual growth. If the trend were to continue, the nation's energy consumption would peak in 2015. A more likely scenario is a near-term decline in energy consumption in response to rising energy costs, as occurred in the previous two energy crises.

The first "myth" the factsheet adresses is that biofuels emit even more greenhouse gasses than gasoline. That happens to be the conclusion of two recent studies published in Science by researchers at the University of Minnesota and Princeton University. The greenhouse gas emissions don't necessarily come from producing or burning ethanol ("biofuels burn cleaner than gasoline," notes the factsheet), but from converting forests and grasslands to biofuel feedstock crops. Studies that assume no loss of forest or grassland show a slight net reduction in greenhouse gas emissions from using biofuels. In the likely event that forests and grasslands are displaced by biofuel feedstock crops, the "myth" may well turn out to be true.  

The factsheet goes on to tackle the "myth" that "Ethanol cannot be produced from corn in large enough quantities to make a real difference without disrupting food and feed supplies." Last year the US dedicated 25% of its record corn harvest to produce 6.5 billion gallons of ethanol. Burning all of that ethanol released 0.6 exajoules of energy. As the graph above shows, the US currently consumes about 105 exajoules of energy each year, so burning ethanol accounted for less than than 0.6% of our energy use. If we had dedicated 100% of our corn to ethanol we might have met 2.5% of our current energy demand. Whether 2.5% constitutes a "real difference" is a matter of opinion, but it's safe to say that using all or our corn for ethanol would have disrupted food and feed supplies. The "myth" is undeniably true.

The interesting thing is that the factsheet doesn't actually address the statement it labels a myth. Instead, it talks about the potential for cellulosic ethanol, little of which will come from corn. Citing the Billion Ton Study as its source, it claims that "we can grow adequate biomass feedstocks to displace approximately 30% of current gasoline consumption by 2030 on a sustainable basis —  with no conversion of U.S. croplands."

By the Billion Ton Study, I assume the factsheet refers to a 2005 report released by the USDA and the US DOE called Biomass as feedstock for a bioenergy and bioproducts industry: The technical feasibility of a billion-ton annual supply. The report concluded that, by 2030, "relatively modest changes in land use" could produce 1.3 billion tons of biomass annually (equivalent to a row of round hay bales circling the earth 75 times) for conversion to enough ethanol to replace 20% (not 30%) of the nation's transportation fuel plus 5% of the nation's electricity and 25% of the nation's chemicals. The necessary "modest changes in land use" include:

1. A 50% increase in all small grain yields (twice the rate of increase observed over the past 40 years, during an era celebrated as the "Green Revolution");
   
2. Conversion of all cropland to no-till (about one-third of US cropland is currently no-till after 40+ years of development and promotion of no-till systems);
3. Conversion of 55 million acres of cropland to perennial biofuel crops (contrary to the factsheet's claim that no cropland need be converted, the report calls for conversion of more than half as much cropland as currently grows corn);
4. Recovery of 75% of all crop residues (which help build healthy soils).

Needless to say, the likelihood of any of these happening is slim, and the chance that they will all happen together in the next two decades is almost nil. The final, unstated, assumption is that economical means of converting cellulose to ethanol will be developed by 2030. Whether that will happen is still anybody's guess. The claim that we can displace 30% of the nation's gasoline consumption with biofuels is not supported by the DOE's own report, which itself is based on unrealistic assumptions.

The next "myth" is that ethanol reduces fuel economy. Ethanol has about two-thirds the energy density of gasoline, so simple physics predicts that a car will go only two-thirds as far on a tank of ethanol as on a tank of gasoline. A recent industry-sponsored test of fuel economy in several cars running on a range of gasoline-ethanol blends confirmed that fuel economy tends to fall as ethanol content increases: In most cases the "myth" is true. The report has been celebrated by the ethanol industry, however, because of some interesting exceptions to the general rule: Some cars running on 20-30% ethanol blends got better mileage than would be expected from the fuel's energy density (See figure below). The report offers no explanation for these interesting outliers. 

Highway fuel economy of a 2007 Toyota Camry running on blends ranging from pure gasoline to 65% ethanol. Purple line shows expected fuel economy, based on energy density of fuel blend. Diamonds show mean fuel economy for three test runs. In this case, a 30% ethanol blend gave significantly better fuel economy than would be expected, offering a 1% improvement over pure gasoline. Figure from Optimal Ethanol Blend-Level Investigation, 2007.

The final "myth" is that more energy goes into producing ethanol than it delivers as a fuel. This probably isn't true, but it's not far off. A range of peer-reviewed studies have found that producing ethanol from corn takes 60-95% as much energy as the ethanol delivers as fuel. The factsheet claims that ethanol can be made from corn using as little as 30% as much energy as the ethanol delivers. I wish I knew where they got that figure; I've looked all over for a study that can support it. There may be a net energy advantage to ethanol production from corn, but it's not very big. 

I created this flow chart to help myself understand the variety of processes used to make ethanol from plants:

The large yellow arrow shows the pathway for "first generation" ethanol production from starches and sugars. This pathway consists of mature technologies: It has been used for centuries to make distilled spirits like vodka or whiskey, and it is used by today's ethanol refineries to make fuel from corn and sugarcane. It is compatible with both small and large-scale production systems. Its increasing use has led to concerns about competition with food supplies, energy efficiency, land-use efficiency, and sustainability. Some of those who feel first generation ethanol technology is irredemably flawed hold out hope for second generation technology...

Production of ethanol from cellulosic feedstocks, like wood or switchgrass, depends on further development of emerging technologies. People are pinning high hopes on such "second generation" ethanol production, with claims that it will allow efficient conversion of non-food feedstocks compatible with sustainable agriculture systems. Despite concerted research efforts to improve second generation technologies, and numerous claims of their superiority over first generation technologies, commercially viable examples are few.

My previous blog posting, with preliminary data from our farm scale study, brought several helpful comments from readers. I will refine our experimental methods to address some of the concerns raised. I see this as collaboration at its best. I am posting this diagram, which is very much a work in progress, in hopes that others may offer corrections, refinements, and critiques.

Michael Bomford provides research and extension services related to organic agriculture and small-scale renewable energy production through Kentucky State University's Land Grant Program.

Over the past two weeks we prepared the land in the Kentucky State University Energy Farm Study for planting. We started with a freshly-cut hay field that has grown an alfalfa and grass mixture for the past three years. It is rich in organic matter and naturally-fixed nitrogen, so we chose not to add additional fertilizer in the first year of the study. The soil preparation process differed between our three production systems:

1. Biointensive plots were cleared with a hoe, then double dug with a spade, spading fork, and broadfork. All labor was done by hand over the course of a week.
   
2. Market garden plots were prepared with two passes of a roto-tiller attached to a 13 hp BCS 852 walk-behind tractor, fueled by gasoline. The roto-tiller passes were spaced two weeks apart to allow sod to decompose after the initial cultivation.
   
3. Small farm plots were prepared with a single pass of a moldboard plow attached to an 89 hp John Deere 5520 tractor, fueled by diesel. The plow was followed, two weeks later, with two passes of a roto-tiller, pulled by the same tractor.
   

The following charts show the amount of labor and energy used to complete the soil preparation process at each of the three farm scales. Labor use is in minutes per square meter of land. Energy use is in megajoules per square meter of land (1 megajoule = 239 food calories). Error bars show the standard error, which is a measure of the variability between plots that were treated the same way.

The small farm plots cover about 40 times as much land as the biointensive plots, and 6.5 times as much as the market garden plots. (A previous blog post showed relative plot size on an aerial photograph of the site.)

We spent 20 hours clearing sod and double digging the biointensive plots, 2.5 hours using the walk-behind tractor in the market garden plots, and 3.0 hours on the 4-wheeled tractor in the small farm plots. The walk-behind tractor consumed 3.7 liters (1.0 gallon) of gasoline and the 4-wheeled tractor consumed 34.5 liters (9.1 gallons) of diesel fuel.

Michael Bomford provides research and extension services related to organic agriculture and small-scale renewable energy production through Kentucky State University's Land Grant Program. He thanks Brian Geier, John Rodgers, Hank Schweickart and Tony Silvernail for their help with preparing the land for planting.

On Tuesday I went to a field day on no-till tobacco production. Tobacco is a warm season solanaceous crop -- like tomatoes or peppers -- that is usually transplanted into freshly-tilled soil in late spring. After fall harvest the remaining stubble is usually left to decompose in the bare soil until the next spring, when the plow comes around again.

In recent decades people have started to recognize that soil suffers when it's left bare, or routinely disturbed by cultivation. Bare soil is susceptible to wind and water erosion. Cultivation destroys the soil structure, further increasing its susceptibility to erosion. Cultivation also introduces a lot of oxygen to the soil very quickly, resulting in a brief boom in the microbial population, and a rapid depletion of the soil organic matter that the microbes eat. (Organic matter is a valuable component of soil because it holds on to the nutrients and water that plants need; soil microbes help release nutrients into the soil solution, making them accessible to plants, and exude sticky material that holds soil particles together, reducing soil's susceptibility to erosion.) In the long term, cultivation reduces soil organic matter content and soil microbial populations.

No-till grain production is now fairly common, but very few farmers grow transplanted crops, like tobacco, without cultivating. It turns out that one of them happens to be a sixth-generation Kentucky farmer who took the 'Introduction to Sustainable Agriculture' course that I co-taught last semester. The field day was at his farm.

We saw a nice demonstration of how soil that hasn't been tilled holds together better than soil that is routinely cultivated. Clods of soil collected from sections of the farm that hadn't been cultivated for 10 years were suspended in water next to a clod collected from a routinely cultivated section. You can see the clod on the left disintegrating while the clod in the middle holds firm:

After harvest the land is seeded to a winter cover crop that protects the soil from winter erosion, saves nutrients that might leach out of the soil in the absence of plants, and feeds soil microbes. The farm is experimenting with different winter cover crop mixes, most of which include a nitrogen-fixing legume species.

At the Kentucky State University Research and Demonstration Farm we often use a mixture of rye, which grows quickly and out-competes weeds; and hairy vetch, which fixes nitrogen and twines its way up the rye. Here are the two plants together, towering over a yardstick:

Nitrogen-fixing crops like hairy vetch harbor bacteria in their roots that are able to convert nitrogen gas from the air around us into nitrogen that is available to plants. A winter cover crop of hairy vetch can add more than 100 pounds of nitrogen to the soil per acre (Kansas State University pdf), enough to feed a nitrogen-demanding crop like corn.

Of course organic farmers have been using nitrogen-fixing cover crops for decades; the organic standards don't allow synthetic nitrogen fertilizer. Conventional farmers have known about the advantages of cover cropping, but using nitrogen fertilizer has long been cheaper than managing cover crops. Soaring fertilizer prices have changed that. Suddenly tactics like no-till production and cover cropping aren't just better for the soil; they're cheaper, too.

Michael Bomford provides research and extension services related to organic agriculture and small-scale renewable energy production through Kentucky State University's Land Grant Program.

A startup company called EFuel100 is taking orders for its new MicroFueler, an energy-efficient fermentation, distillation and dehydration system that turns sugar and water into ethanol.

The MicroFueler is the brainchild of Floyd Butterfield, who designed the award-winning Butterfield still back in 1980. The Butterfield still was designed for farm scale, energy-efficient ethanol production from carbohydrate-rich crops. 250 acres of corn could keep it going for a year. (Most new ethanol plants need about 200,000 acres of corn to operate at capacity for a year.) Although a modern ethanol plant gets about 15% more ethanol from each bushel of corn than the Butterfield still (2.7 vs. 2.3 gallons/bushel), Butterfield's system was more compatible with small, diversified farming operations, and didn't require long-distance trucking of feedstock.

With the MicroFueler, Butterfield takes the "small is beautiful" philosophy one step further, aiming to bring ethanol production from the farm scale to the home scale.

The MicroFueler makes fuel out of sugar, which is food. Most large-scale conventional ethanol plants start with starch, which is food. The first step in their process is to break down the starch into sugar for fermentation.

The holy grail of current ethanol science is the production of ethanol from non-food, high cellulose materials, like switchgrass or corn stalks. The major barrier to most cellulosic ethanol production is the development of efficient means of breaking cellulose down into sugar for fermentation. In other words, to make ethanol from non-food crops we're trying to figure out how to turn them into food. Whether the sugar comes from starch or cellulose, all fermentation starts with sugar.

Sugar is the building block of life. Photosynthesis is the light-driven reaction that makes sugar and oxygen from carbon dioxide and water. Organisms digest sugar to get energy, turning it back into carbon dioxide in the process. Plants store energy in the form of starch, which is a long string of sugar molecules that can be broken down relatively easily. They also make strings of sugar molecules into cellulose, a structural material that doesn't break down easily, and is found in cell walls.

Even if you aren't a chemist you can probably tell from the figure on the left that starch and cellulose are made from the same stuff. The molecule in the square brackets is glucose, or sugar.

The promotional material for the MicroFueler claims it will make a gallon of ethanol from about 12 pounds of sugar. For the past decade 12 pounds of unrefined sugar on the world market has cost about 30% less than a gallon of gasoline in the US. Between 1976 and 1996 a gallon of gasoline generally cost about 15% more than 12 pounds of sugar. Today's commodity investment advice? Buy sugar.

According to the promotional material (pdf), the MicroFueler "solves the ethanol transportation issue by containing the refinery and pump delivery system within the same system – in other words, people can produce where they consume, using the MicroFueler to both create ethanol and pump their vehicle with fuel."

Since the Energy Farms Network is based on the premise of local resource cycling and local production, I was curious to estimate the land needed to produce enough sugar to use the MicroFueler to run my car. Last year our sweet sorghum crop gave us about three-quarters of a pound of sugar per square yard. Each gallon of ethanol, then, would require about 16 square yards of sweet sorghum to be harvested, juiced and fed into the MicroFueler. Ethanol has about two-thirds the energy density of gasoline, so I might expect my Toyota Corolla, which gets about 37 miles per gallon of gasoline, to get 25 miles per gallon on ethanol. To drive it 10,000 miles per year I would need about 400 gallons of ethanol, or about 1.3 acres of sweet sorghum.

That's about 8 times more land than I have in my backyard. I guess it's back to my bike...

Michael Bomford provides research and extension services related to organic agriculture and farm-scale renewable energy production through Kentucky State University's Land Grant Program.

I just spent three days talking about biofuels with other scientists who work at historically black land grant universities. These institutions exist in most southern states because of an 1890 law requiring states to either set up a land grant institution for people of color or demonstrate that race was not an admission factor at their existing institution. Kentucky State University, where I work, is one of these '1890 land grants.'

The 1890 land grants are interesting because of their mission to serve under-served constituencies, including minorities and people with limited resources. The 'get big or get out' prescription sometimes associated with land grant universities ought to be an anathema to 1890 land grant universities.

This week's meeting was called to explore ways for 1890 land grants to contribute to USDA goals, including "the development of biofuels and processes to efficiently convert renewable plant products to fuel." It came at a time when food prices are skyrocketing and people are going hungry, in part because a growing proportion of America's corn is being turned into fuel.

At one point I expressed to a USDA economist my opinion that the large scale corn to ethanol program has been a complete failure, neither reducing carbon emissions, nor contributed to energy independence. The economist surprised me with his defence that neither of these were program objectives. The real goal, he said, was to raise corn prices. By that measure the program has been a resounding success(!).

After three days of intense discussion we hammered out a list of research objectives for 1890 land grants working on biofuels. They are:

1. Identify, produce, characterize and improve alternative feedstock crops.
2. Develop and optimize small scale technologies for biofuel production.
3. Evaluate and improve biofuel and byproduct quality.
4. Educate and train students, farmers, and other professionals regarding biofuels.
5. Analyze economic, environmental and social impacts of biofuel production and use.

So those are my guiding principles as I continue to participate in the Energy Farms Network and collaborate with the Post Carbon Institute. Over the summer I'll work with researchers from Virginia State University and North Carolina A&T University to pull together a full proposal, based on these objectives, for a collaborative project involving all eighteen 1890 land grant universities.

Some of my current research is funded by Southern SARE, so I took note when the organization released a position paper on the type of biofuel research it will fund in the future. SARE identifies eight themes for future projects to "expand the focus in bioenergy beyond corn- and soybean-based ethanol and biodiesel:"

1. Energy conservation and efficiency;
2. Energy efficient production practices;
3. Non-biomass renewable energy sources;
4. Alternative biomass feedstock production systems;
5. Environmental impact of bioenergy production;
6. Community and rural development impacts of bioenergy production;
7. Local and regional economic impact of biofuel production; and
8. Whole farm integrated energy systems.

It looks like the Energy Farms Network is on the cutting edge.

-----

• The goal is to feed more people, not fewer people. There is an old adage that has already been quoted about putting all your eggs in one basket. If I were one of those fifty people who was being fed by only one farmer, I'd be more worried than if there were four or five-or ten. Suppose the one farmer dies?
• Two and a half percent of the population is feeding all the rest. That is very small. And as far as I can see, nobody is worrying about where the cutoff point is. There is always a bottom half. We are always concerned about eliminating the bottom half because we say they're inefficient. I think that our doctrine of efficiency is suspect anyway because it only applies to major quantities. We waste stuff at our place all the time because we can't sell it. It's too little to sell. You can't give it away unless you cook it for somebody.
• How small do you let the percentage of farmers get before you are in danger? We have no alternative energy source on the farm now. When one farmer's feeding fifty people he is absolutely dependent on petroleum. When the economy shifts to reflect the realities of energy, it may be too expensive to produce some of this food; certainly at current prices.
• --Wendell Berry, 1974 http://www.tilthproducers.org/berry1974.htm

The US Energy Information Administration (EIA) says that Americans consumed about 105 exajoules (EJ) in 2006, and predicts that energy consumption will exceed 120 EJ by 2025. That projection looks unrealistic. Here's my attempt to do better.

EIA records show that US energy consumption has increased almost every year for a long time. A look at the period between 1950 and 1973 shows each year's increase in energy consumption was even greater than the year before.

High energy prices caused energy use to decline between 1973 and '75 and again between 1979 and '83. When growth resumed after the second energy crisis there was a difference: Each year's increase was less than the year before.

If the trend established in 1980-2006 were to continue then US energy consumption would crest around 2015 before starting to decline. Consumption in 2025 would be about the same as in 2006. This projection is much lower than the EIA's, but I still think it unrealistically high. A more likely scenario is an immediate reduction in energy consumption in response to high energy prices, as occurred in the previous energy crises. A 1.2% annual decline in energy consumption, sustained until 2025, would bring the nation back to consumption levels of the mid-1980s.

Renewable sources currently provide just 7% of the nation's energy. The EIA predicts this will be up to 11% by 2025. Just as the EIA appears to have overestimated the availability of non-renewable energy sources in the near future, it appears to have underestimated the contribution of renewables.

A coalition of business, labor, and environmental groups is calling for plans to increase renewable energy production to meet 25% of the nation's energy consumption by 2025. The 25 by '25 vision has its opponents, particularly now that the corn ethanol push is widely recognized as an environmental, social, and financial disaster. Sooner or later, though, the nation and the planet must return to 100% renewable energy.

What might a 17 year transition to a 25% renewable energy economy look like? One scenario would involve a 30% reduction in non-renewable energy use coupled with a doubling of hydro, biomass and geothermal energy use and 12 and 24-fold increases in wind and solar energy use, respectively. That might have some pretty serious economic, environmental and social ramifications, but it would get us to 25%. The rate of decline in renewable energy use would be pretty similar to the rate of increase that got us where we stand today.

The Kentucky State University Energy Farm project is just beginning its first field season. We grew vegetables through the winter in our solar-heated high tunnel; now we are beginning to move outdoors, where a thick winter cover crop of rye and hairy vetch has been building soil organic matter and nitrogen levels. Temperatures still sometimes dip below freezing at night (we had frost on Tuesday!), but the first of our cool-season vegetables -- like peas, lettuce, and kale -- have been braving the temperature swings outside for the past month.

Our project will incorporate both food and energy crops: The energy crops -- sweet sorghum, sweet potato, corn, and soybean -- are all warm-season crops that will be planted in late May. Each of these crops is high in carbohydrates, making them either high-calorie food for humans or a source of sugars, starches, or oils that could be used for biofuel production.

We will grow our energy crops at three different scales. The smallest scale will be a biointensive system, in which only hand tools are used. Our medium scale will be a market garden system, using a combination of hand tools and a walk-behind tractor with attachments. The largest scale system will be tractor-based. We will measure the land, labor and energy use efficiency of production at each of these scales.

Plots representing "Biointensive," "Market Garden" and "Small Farm" scales are replicated four times. Each plot will grow the same mix of multi-use crops. The smallest ("Biointensive") plots will be managed with hand tools; the largest ("Small Farm") will be managed with conventional tractors and attachments. (Image prepared by Tony Silvernail).

The data collected from this experiment will allow us to analyze effects of farm scale on resource use efficiency, and to answer questions about farmer motivation to dedicate multi-use crops to food or fuel production under a range of possible future scenarios for land, labor and energy pricing.

I enjoyed Josh's planting plans for the Sebastopol Energy Garden. It's easy to imagine the mixed beds of broccoli and celery, corn and beans, cabbage and onions, Swiss chard and carrots...

A friend says that seed catalogs have inspired more fantasies than Playboy.

There are good reasons for planting crops in mixtures:

• Mixed crops often have higher yields than monocultures because different species use different resources, making more efficient use of land;
• Mixed plantings often have fewer pest problems than monocultures because pests have a harder time finding suitable hosts, or because diverse plantings provide better habitat for natural enemies;
• Diversity helps reduce risk. (Promoting biodiversity is a stated goal of the USDA's national organic standards.)

But how, exactly, do we go about planting mixtures? If the seed packet, or a planting guide, tells us to space cabbages 15" apart and onions 4" apart, how far apart do we space cabbage and onion plants in a mixture?

A couple of answers are offered by John Jeavons, in his classic manual How to Grow More Vegetables. He suggests that a mixed bed of cabbage and onion could consist of rows of cabbages interspersed with rows of onions. If cabbages and onions are mixed throughout the bed, Jeavons says the plant spacing should be the mean of the recommended spacing for the component crops.

According to this second method, the spacing between plants in a cabbage and onion bed would be 9.5" -- the mean of 15" (cabbage spacing) and 4" (onion spacing).

This approach has a few problems. I think I have a better way.

First I'll explain the problems. The Jeavons method sets cabbage and onion spacing to 9.5" whether the mixture is 90% cabbage or 10% cabbage. This doesn't make sense to me. It is intuitive that plant spacing for a cabbage and onion mixture should be somewhere between the recommended spacings for cabbage and onion, but it also seems intuitive that plant spacing should be closer to the recommended cabbage spacing in a mixture that is mostly cabbage and closer to the recommended onion spacing in a mixture that is mostly onion. Crop ratio is important.

How to Grow More Vegetables offers a planting plan for a two crop mixture with a 1:3 crop ratio. Using this plan we would plant three onions for every cabbage, in an arrangement like this:

This leads to the second problem: Using the Jeavons plan gives us room for 33 cabbages and 80 onions in the 60 square-foot bed above. To plant 33 cabbages in a pure stand, spaced 15" apart, would require 45 square feet. To plant 80 onions in a pure stand, spaced 4" apart, would require only 8 square feet. The total area required for the two pure stands would be 53 square feet -- 7 square feet less than the area required for the mixture.

Mixtures should make more efficient use of resources, not less. A mixture should not require more land than two pure stands with the same number of plants.

So what's my solution?

I have developed an equation to calculate plant spacing in mixtures from the recommended spacing for pure stands:

where

• s_A and s_B are the recommended pure stand spacings for crops A and B, respectively, and
• p is the proportion of plants in the mixture (a value between 0 and 1) accounted for by crop A.

In the example above, cabbage account for one-quarter of the plants in the mixture, so p=0.25. The recommended spacings for cabbage and onion are 15" and 4", respectively, so s_A=15 and s_B=4. The calculated mixture spacing, according to the equation, is 8.25" instead of 9.5".

Since using this equation is more difficult than calculating a mean I have developed a spreadsheet and an online plant spacing calculator with this equation at their heart. Provided you have the Analysis Toolpak installed in Excel (check the Add-Ins feature under Excel's Tools menu) the spreadsheet will create planting diagrams like these:

The first two diagrams show a square meter of cabbage (white circles) and onions (black diamonds) planted in pure stands. The next three show cabbage and onion mixtures planted at ratios of 1:3, 1:8, and 1:15.

Learn more here.