Treebeard's Stumper Answer

Soil Matters
We had a good soaking rain this week in central California, our first in many months! Where does all that water go when it soaks into the ground? It must seep into the pore spaces between the soil particles, but how does the makeup of the soil effect this? Does fine or coarse soil have more pore space, and which holds the most water for growing plants? I've heard it said that cultivating or breaking up the dry crust of soil actually conserves soil moisture better than a solid crust. Can that be? Doesn't breaking up the crust just make it easier for the soil moisture to evaporate?
A worm's eye view of soil? Nah, this is a photo of basalt boulders used to fill a slide area on Boundry Road along the North Umpqua River in Oregon. Those "particles" are really a foot or two across, but they show pore space just as well as a microphotograph. How does the percent pore space of these boulders compare with sand? How would a real microphotograph of soil look different? Fractals are mathematical objects that are selfsimilar when magnified. Nature seems to have a fractal quality, as shown in this classic Ansel Adams photograph of Mount Williamson: Clearing Storm. Soil particles also have this fractal quality. Do the physical properties of soil change with the particle size despite the similar appearance?
In my DMS science class, we've been using marbles and BBs to investigate pore space and soil. BBs pack together with smaller gaps than marbles but more of them, so the total pore space is (nearly) the same for both. But the smaller BBs have more surface area, so they hold more water, just like your wet hair holds more water than your skin after a swim. More water might evaporate from packed soil with smaller pores for the same reason. It's possible that cultivating the soil in your garden can actually conserve water. These are our ongoing experiments, and we still have lots to learn!
Notes:
Einstein is quoted as saying "Everything should be made as simple as possible, but not simpler." That's good advice for this stumper. Real soil is complicated, and we depend on it for life. Marbles and BBs greatly oversimplify soil, but that's OK as long as we remember it.
We measured the pore space of marbles and BBs by adding enough water to more than cover the balls in a graduated cylinder. The water within the (nonsoluable) balls gives the pore space. We also weighed the balls dry and wet (after draining) to calculate water retention. This is an easy procedure that gives surprising results. Who would guess that a bowl of marbles is almost half empty space! Here is our stepbystep procedure for marbles or BBs or anything else. The numbers refer to the spreadsheet that follows.
 Weigh a bunch of dry particles [1]
 Pour them into large graduated cylinder and record the volume [4]
 Measure a +/ equal volume of flat water in a separate cylinder [5]
 Add the water to the particles and let it settle
 Record the water level after mixing [6]
 Empty the cylinder through a strainer and shake twice
 Weigh the wet particles again to see how much water is held [2]
 Crunch the numbers and figure density and percent pore space and water held
I repeated the measurements with different quantities in each of my four morning classes with these results:
Marbles (1.6 cm diameter) Trial: 1 2 3 4 Average: 1. Dry mass of particles (grams) 525.22 404.98 452.12 545.48 2. Wet mass after shaking (grams) 531.18 407.05 456.50 549.65 3. Mass of water retained (2)  (1) (grams) 5.95 2.07 4.38 4.17 4. Volume of dry particles (cm^{3}) 400 300 350 400 5. Volume of water added (cm^{3}) 300 250 300 250 6. Level of water after mixing (cm^{3}) 515 417 485 470 7. Volume of water NOT in mix (6)  (4) (cm^{3}) 115 117 135 70 8. Volume of pore space (5)  (7) (cm^{3}) 185 133 165 180 9. Volume of solid particles (4)  (8) (cm^{3}) 215 167 185 220 12. Bulk Density (1) / (4) (g/cm^{3}) 1.31 1.35 1.29 1.36 1.33 g/cm^{3} 13. Particle Density (1) / (9) (g/cm^{3}) 2.44 2.43 2.44 2.48 2.45 g/cm^{3} 10. Percent pore space (8) / (4) x 100 46% 44% 47% 45% 46% 11. Percent water retained (3) / (8) x 100 3.2% 1.6% 2.7% 2.3% 2.4% BBs (0.45 cm diameter) Trial: 1 2 3 4 Average: 1. Dry mass of particles (grams) 914.10 271.78 222.55 305.90 2. Wet mass after shaking (grams) 927.45 274.92 224.85 309.10 3. Mass of water retained (2)  (1) (grams) 13.35 3.14 2.30 3.20 4. Volume of dry particles (cm^{3}) 200 60 50 70 5. Volume of water added (cm^{3}) 200 50 50 50 6. Level of water after mixing (cm^{3}) 320 86 79 90 7. Volume of water NOT in mix (6)  (4) (cm^{3}) 120 26 29 20 8. Volume of pore space (5)  (7) (cm^{3}) 80 24 21 30 9. Volume of solid particles (4)  (8) (cm^{3}) 120 36 29 40 12. Bulk Density (1) / (4) (g/cm^{3}) 4.57 4.53 4.45 4.37 4.48 g/cm^{3} 13. Particle Density (1) / (9) (g/cm^{3}) 7.62 7.55 7.67 7.65 7.62 g/cm^{3} 10. Percent pore space (8) / (4) x 100 40% 40% 42% 43% 41% 11. Percent water retained (3) / (8) x 100 16.7% 13.1% 11.0% 10.7% 12.8% The larger marbles had slightly more pore space than the BBs. That caught me by surprise since it's a geometry matter, so size shouldn't matter. But the larger marbles take up extra space on the sides and top of the graduated cylinder we used to measure them. I don't think that's signicant, but it is significent that the BBs held 12.8 / 2.4 = 5+ times more water (figured as percent of total pore space) after two shakes in a kitchen strainer. The smaller particles have about the same pore space, but they hold more water because of surface tension and capillary forces. It's just what I expected.
Real soil is more complicated than marbles and BBs. It contains a mix of particles, and it's alive!
Following Einstein's advice, I won't try to oversimplify. Particle size matters, but so do many other factors.
 Particle size matters. Sandy soils are welldrained, but they dry out quickly. Clay soils hold water too well so plants become waterlogged.
 Particle shape matters. Sand and silt particles are roundish, so marbles and BBs are a good model. But clay is decomposed mica, and the tiny clay particles are flat flakes.
 Real soil is composed of particles of many sizes. Small silt and clay particles can fill the gaps between larger sand particles and increase the surface area and water retention. All gardeners want Loamy soil with a good mix of particle sizes.
 It matters how well sorted a soil is. Small particles can fill the spaces between large particles, but they might not.
 It matters how aligned those flaky clay particles are. It makes a big difference whether they stack flat like a roll of pennies or expanded like a house of cards.
 It matters how connected the pore spaces are. Closedcell foams like Insulite have lots of pore space, but no way to get from one to another.
 Real soil has tilth because living plant rootlets and fungi mycelium holds it together. Worms, nematodes, and even gophers ("nature's plowperson") help keep soil loose and increase pore space beyond geometry. If you handle living soil too much, you can feel the difference as it looses it's tilth and turns to dust.
Soil cultiivation and water content is a different question. "If a footprint in cultivated soil is left undisturbed, the soil inside the footprint will become hard and dry." That's a quote from Jearl Walker's The Flying Circus of Physics (3.101), one of my trusted stumper sources. He goes on to say:
The soil must be broken up in order to retain its moisture. A packed ground has many small openings that will act as capillary tubes. As the water climbs to the surface, it is lost to evaporation. Cultivated ground has much larger openings and thus less capillary action.This sounds reasonable, though I've noticed that the loose soil in gopher mounds usually looks drier than surrounding soil, and that certainly makes sense too.
I found an interesting book on the Web on DryFarming by John A. Widtsoe, published in 1920. It's based on the author's real experiments in Utah, as dry as it gets. His Chapter 8 ends with these stirring words:
The conservation of soilmoisture depends upon the vigorous, unremitting, continuous stirring of the topsoil. Cultivation! cultivation! and more cultivation! must be the warcry of the dryfarmer who battles against the water thieves of an arid climate.Another source says just the opposite,
Consider the impact of cultivation on soil moisture loss... Under dry conditions and when a soil crust has formed, very little soil evaporation occurs, and cultivation disturbs the soil surface and increases soil moisture loss... If weeds or crusting are not a concern, producers should probably leave the cultivator in the shed, regardless of soil moisture status.Here's a real science stumper with practical consequences. We set up an experiment before Thanksgiving vacation, but we've had regular rain since then. Everything is soaked, so our experiment will have to wait.Here are some links for further research:
 Saskatchewan Interactive has an excellent tutorial about all aspects of soil. There is a section on Soil Density and Porosity that explains the Bulk Density and Particle Density in my spreadsheet. The University of Nebraska NebGuide on How Soil Holds Water is a another good tutorial on the physical characteristics that influence how soil holds water. The Soil texture triangle hydraulic properties calculator lets you enter values for percent sand and percent clay and obtain numerous soil properties.
 John A. Widtsoe's DryFarming, first published in 1920, is an interesting account of dryland farming in Utah. I'm not qualified to assess it. The title page has a picture of the real Jethro Tull and explains why he's relevant to this stumper! A different point of view on cultivation and soil moisture is presented by Iowa State University.
 This seems like a fruitful area for middle and high school science projects. Anyone can get their hands on soil, and simple lab equipment can do a lot. For example, Tim Conway's Soil Particle Size and Porosity is a well presented high school project.
 There's an interesting math stumper buried here. (:) What is the best way of packing spheres into a space, either infinite or constrained (like our graduated cylinder)? The mathematician David Hilbert made this the 18th problem in his famous list of unsolved problems at the turn of the century. Martin Gardner introduced the problem to my generation in a classic SciAm "Mathematical Games" column later collected in his New Mathematical Diversions from Scientific American. Kepler made the conjecture in 1610 that the familiar cannonball or orangesatthesupermarket stacking is optimal for infinite packings of spheres at about 74% or
pi/sqr(18) .
There's a mathematical introduction to the sphere packing problem at Eric Weisstein World of Mathematics hosted by Wolfram Research and MathLab. This great reference has been absent for a while because of copyright problems. I'm so glad it's back! There's lots more links at The Geometry Junkyard.
Ivars Peterson and Keith Devlin have pieces on a possible recent breakthrough by Thomas C. Hales of the University of Michigan. Hales' original work is available on the web at The Kepler Conjecture, with his comment:The full proof appears in a series of papers totaling well over 250 pages. The computer files containing the computer code and data files for combinatorics, interval arithmetic, and linear programs require over 3 gigabytes of space for storage.The reminds me of the 1976 solution of the classic Four Color Problem by Kenneth Appel and Wolfgang Haken.
After our school experiments measured greater pore space for marbles than BBs, I'm more interested in the different problem of packing circles or spheres into a constrained space of a definate size. There's an article about packing pennies by Ivars Peterson. There are sites here and here that have downloadable software to find optimal 2D solutions. This is fun geometry where the concept of "jiggling" is central!
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