
Mulch Madness  The Winner!Q: Why is a straw hat like a kiss on the
telephone? On 03 July I wrote a blogitem as the lead up to the the declaration of the winner of the Mulch Madness Contest. Yesterday, The Fourth of July, in addition to holding my annual BBQ party for friends (food) and their small human children (a pool with a deep end if necessary), I measured, to the best of my ability, the remanent heap'o'mulch so that a winner might be declared. Today I reduce the measurement to cubic furlongs, compare this official datum with the entries, and declare a winner. The PrizeAfter much reflection, I selected a suitable prize. The criteria were:
The Mulch Pile ItselfVolumetric measurement of an uncontained mulch heap does not lend itself to great precision. I have no large container of standard volume, and even if I did, I would have no easy way of packing it with mulch. Attempting to weigh the mulch would be futile even if I had the apparatus, as it varies strongly by water absorption. Accordingly, I unlimbered a tape measure and assessed the heap's dimensions as best I could. I had help and witnesses, lest the losers accuse me of manipulating the results. I managed to destroy the tape measure in the process of determining the circumference of the pile. This was not pique caused by my inability to find a tape measure calibrated in furlongs. As I reached its end it was done in by a simple twist of tape.
For an initial approximation, I calculated the volume (V) assuming it was the frustum of an axisymmetric cone (V = 0.2618*h*(D^^{2}+D*d+d^^{2})) V = .2618 * 44 * (23716 + 11858 + 5929) = 478,000 cubic inches or 9.62*10^{7} cubic furlongs. The Entries Considered1/4 heap: I left this one in because it was valid, but it's clear by inspection that the 1.3 cubic Prii response is closer, so this loses by comparison. 3.6 billion thimblefuls: Here we have a dilemma. How many cubic furlongs is a thimble? Metric thimble or English? The entrant didn't specify. Equally problematic, mulch is a granular, largely scalefree material, and if one actually tried to measure its volume by thimble, he would find that a large proportion would not fit in the "instrument." We investigate further and find in the first line of the very first Googled item states "There are no standard thimble sizes." In addition to the common thimble used for sewing, "thimble" is a term of art in scientific fields and I've found references of 1.5ml to 120ml, a volume ratio of almost 100 to one. I contacted the entrant requesting disambiguation but received only silence. In good conscience, then, I must discount this entry since the 1/4heap entry is by definition off by no more than 4 to 1, and actually somewhat less. 75.7 cubic cubits: Finally one for which I don't have to think. Google says "75.7 (cubic cubits) = 8.88664538 × 107 cubic furlongs", which differs from my own fairly imprecise measurement by less than 10%. 1.3 cubic Prii: This entry would be a potential winner since the heap'o'mulch and the car are at least similar in scale. The official Prius dimensions are (Height/Width/Length) 58.1"*67.9"*175.0", or 1.389*10^^{6} cubic furlongs if it were truly rectangular. Multiply this by 1.3 as the entry specifies to get 1.806*10^^{6 }cubic furlongs, which is roughly twice the actual mulch measurement. This forces one to answer the question of whether there is enough nonrectangularity to a Prius to account for about half the volume of the space it would occupy were it rectangular. Carl Zeiss Inc. manufactures coordinate tracing machines that, along with some complicated mathematics and a computer, can determine the volume of irregular objects. I don't own one. I could have carefully sealed all the Prius openings, placed it in the pool, and measured its displacement. Unfortunately I ran out of silicone sealant before I could even finish all the doors, much less the trunk and engine compartment, so I decided to eschew this option. I could possibly call Toyota on the telephone and find their design department and ask them, but I don't speak Japanese and hate the telephone. Even worse, this would be research. I finally decided to look at the Prius and at the mulch pile and at the Prius and at the mulch pile and... When I was done, I concluded that the 1.3 Prii estimate, albeit a very reasonable one, is probably about 50% high, while the 765.7 cubic cubits answer is only 10% low. Given the disparity between the other answers and the closest one, I thankfully decided that I didn't need to refine my measurement to account for the lack of symmetry. The Winner
The EntryI have printed this verbatim, with no editing other than font and linelength changes. THIS is how you enter a mulchpileestimation contest. Good work, Rick!
The pictured mulch pile is described as having the footprint of a car.
Given
the shovel in the picture, it appears to be a small car. Going to the
Internet (you can find pretty much anything on the Internet) we find the
dimensions of a VW Beetle as 4.08m by 1.72m by 1.50 m. Moving to more
familiar measurements, we get 8.93 cubits by 3.77 cubits by 3.28 cubits.
With some correction to account for the fact that neither the mulch pile
nor
the VW Beetle are true rectangular parallelepipeds, we get an initial
estimated mulch volume of 82.81861 cubic cubits (use of Excel permits
extreme
precision if not extreme accuracy).
The pile will settle over time. While measures of mulch density are
available
on the Internet (unfortunately they range from "near 0" kg/m^{3}
[see
this article]
to 33kg/m^{3} so
they are of minimal practical use), values for mulch's resistance
to
compression forces were not immediately available. Since the mulch pile
is
new and thus loosely packed, we assume compression of about NP: "Runaway"  Marillion 

