Thursday, June 6, 2013

The Berry Modulus

In many fields of engineering, dimensionless numbers are used to compare the relative contribution of two simultaneously-occuring processes or phenomena, irrespective of scale or units (which allows for an easy comparison of experiments done at different times, in different labs, etc.).  For example, the Reynolds number (Re) is used to compare the relative roles of inertial and viscous forces as a fluid flows through or around an object (which in turn are important in calculating energy losses due to friction or drag), and the Thiele modulus (Φ) is used to compare the relative rates of a chemical reaction and the diffusion of reacting molecules to the site of reaction (which are important in determining catalyst activity).

We had the idea that it would be useful on the homestead to have a similar metric to quantitatively compare the relative productivity of different berry patches, or of a certain berry patch from one week (or year) to the next.  Thus, we have adapted the concept of the Thiele modulus to a new dimensionless number: the Berry modulus (ß).  In essence, it compares the rate of picking berries in a given area to the time spent looking for them, or rather, it answers the question, "when moving through a berry patch, are you more limited by your walking pace or your picking pace?"

Starting with a generalized equation for the Thiele modulus (for a first-order reaction), we can adjust the units to something easier to measure for berries and simplify the equation:

where f is the frequency of picking events (i.e., the number of berries picked divided by the time spent picking) A is the area covered, and D0 is how long it would take you to search the area for berries but not find any.  For D0, we suggest a standard value of 0.25 acres per hour, which works out to just over three square feet per second (imagine yourself walking along a row of strawberries, brushing back bushes and looking to look for berries).

Therefore, calculation of the Berry modulus requires knowing simply the number of berries picked, the time spent picking them, and the amount of land covered in the process.  The time part is easy--just look at your watch (or sun dial) before and after.  In order to find the number of berries picked, you can either count them as you pick them or figure out afterwards how many you picked.  If you prefer the former, you should also get yourself tested for OCD.  Otherwise, it's possible to approximate the number of berries picked based on how many fit in a (small) known volume or mass, and the total volume or mass picked.  Here's how we calculate the total number of berries picked:

Place a quart jar on a kitchen scale and tare it (adjust the dial to zero).  Fill the jar with berries, counting the number added.  When the jar is full, record the weight.  Remove the jar from the scale, and add one cup milk and a tablespoon of honey, if you're so inclined.  Blend with stick blender into delicious smoothie.  All you actually need are the numbers in the first step: if you measured your total picked quantity in volume (quarts, cups, etc.), multiply that total volume (converting to quarts, if in another unit) by the number of berries in the quart jar.  If you measured your total picked quantity in mass (pounds, kilograms, etc.), multiply that total volume by the number of berries in the quart jar, divided by the mass of berries in the quart jar (again keeping units consistent).

Calculating the area searched can be a little bit tricky.  Fortunately, Google maps is pretty awesome, and there are lots of smart people out there making it even awesomer.  If you have a berry patch that you can work through completely, you can find the area of the patch using Acme Labs' Google Planimeter, and plug that area directly into the equation.  If you're out wandering through the woods, but not really covering a specific area, you can find the distance you traveled with the Map Pedometer (make sure to select 'straight line').  Assuming a continuous search field width of about three feet (left to right in front of you), and the total distance in miles, multiply by 5,280 feet per mile, multiply that by three feet wide, and divide by 43,560 square feet per acre.  There's your area covered in acres!  Ok, now we've got everything we need to calculate the Berry modulus.

We can see from the equation above that the higher the frequency of picking events for a given area, the higher the Berry modulus will be.  That makes intuitive sense.  However, we can also make it easier to see whether the outcome of the picking is determined more by searching, or more by the speed at which we can pick.  For the Thiele modulus mentioned above, a related parameter called the 'effectiveness factor' is often calculated.  Using an analogous equation for the Berry modulus, we can calculate an 'emptyness factor,' since at low values of the Berry modulus (i.e., for poor picking yields), the factor will be higher.

Here, tanh is the hyperbolic tangent function.  Ok, how about some examples?  This last weekend, we went out to a pick-your-own strawberry farm and picked about 14.5 pounds of strawberries in 45 minutes.  Our quart jar held 21 strawberries, which was equivalent to 14 ounces, or 0.875 pounds.  Thus, in total, we picked about 16.6 quarts, or 348 strawberries (not including what we ate in the field!).  Using the planimeter above, we calculated that we worked an area of about 0.05 acres.  These numbers work out to ß = 92.8 and ε = 0.011:

The Berry modulus can be extended beyond just berries, as well.  Actually, the approach is amenable to just about anything that can be hunted or gathered.  For example, we spent four hours (walking 2.6 miles or covering about 0.96 acres) in search of morels this spring and only found one little one.  That works out to ß = 0.96 and ε = 0.777.  As you can see below, that outcome was clearly determined more by the searching than by the picking.  But we still made off better than some of the National Geographic explorers looking for thought-to-be-extinct tropical amphibians like the Stubfoot Toad--they spent many months searching to find just one!

The relationship of the Berry modulus, the Emptyness factor, and the yield-controlling processes during berry-picking expeditions.
How might you use the Berry modulus in a sentence while talking to other people?  Here are a few examples:

"Our raspberry patch has been doing really well!  We're getting a Berry modulus of about eighty this week, while neighbor Joe down the road says he's only getting about fifty from his.  Heck, even the folks from the pick-your-own farm say theirs are only at about seventy-five!"

"We went out picking elderberries last weekend, and calculated our Berry modulus to be close to a hundred!  The same patch has never been that productive in the past, so this must be a good year for elderberries."

"The Berry modulus for our blueberries is only at about seventy and there are still quite a few unripe ones, so we're probably not quite at the peak yet.  Normally we're already a little past the peak by this time of year, so it seems like the effects of the late spring are still lingering."

There are a few caveats to the Berry modulus that should be mentioned.  First, it doesn't take into account differences in selectivity or speed between pickers.  On a normal day, Katie would probably generate a slightly lower Berry modulus than Jake, not due to any differences in the berries they're working, but just because she's more selective about what goes in her bowl.  Similarly, berry quality is not factored in.  Sure, it's possible to achieve high Berry moduli at a commercial farm or (heaven forbid) a grocery store, but the berries might have been sprayed with pesticides or be of a variety that ships well but has lower nutritional value.  So there are other factors to consider as well.  Also, if abbreviating the Berry modulus, please use the Greek letter beta (ß) and not 'BM.'

Still, the Berry modulus is a new and exciting way to quantitatively compare the productivity of your berry patches, both wild and domestic.  It can also be used to compare many other hunted-and-gathered foodstuffs.  Let's spread the word and bring the Berry modulus into the mainstream lexicon!

How are your berries doing?  What kind of Berry moduli have you achieved in your berry-picking expeditions?  Let us know in the comments section below!

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