Geldpakhuis

From McDrake Wiki

... ==How much is 3 cubic acres?== Derived from a discussion on the Disney Comics Mailing List, 21 August 1997 - 8 September 1997 Date: Thu, 21 Aug 1997 13:24:13 -0700 From: rob gibson To: [DCML] Subject: sequel [...] WRT how I derived the weight of three cubic acres of money: The American Heritage Dictionary (Second College Edition) defines an acre as 43,560 square feet (for those of the metric persuasion, one foot = 12 inches = 30.48 centimeters). The root is roughly 208.71. Hence a square with sides of length 208.71 ft. contains an acre. It seems reasonable to assume that a cubic acre would be a cube with an acre on a side, or with edges of length 208.71 ft. The volume of such a cube would be 208.71 to the third power, or slightly more than 9 million cubic feet. 3 cubic acres would be three times this, or about 27,274,265 cubic feet. The Machinery's Handbook (Twenty-first Edition) tells us (on page 2404) that one cubic foot of water, at 39.1 degrees fahrenheit (4 degrees celsius), weighs 62.4245 pounds. Therefore (at 39.1 degrees fahrenheit) 27,302,972.4 cubic feet (or three cubic acres) of water will weigh 1,702,582,378 pounds, or 851,291 tons. With the aid of some very unscientific evidence I conclude the average weight of the contents of Scrooge's money bin is of an order of magnitude not less than water (a coin sinks in water; a jar of pennies is VERY HEAVY; panels showing the insides of the money bin seem to show that it is predominantly coins, with paper currency mixed in; the "Only A Poor Old Man" scene where the Beagle Boys crack their heads trying to dive into Scrooge's fortune implies a significant ratio of coins to paper currency). Therefore, assuming I have not committed some mathematical or logical faux pas, it follows that Scrooge's three cubic acres of money weighs on the order of half a million tons. And it will take many toy train trips to make a dent in that. Perhaps Gyro Gearloose (who soon after appears for the first time) solves the problem somehow. Rob Gibson ------------------------------------------ Date: Fri, 22 Aug 1997 18:58:24 Europe/Athens From: Kriton Kyrimis To: [DCML] Subject: Re: Disney comics Digest V97 #176 [...] ROB: ''It seems reasonable to assume that a cubic acre would be a cube with an acre on a side, or with edges of length 208.71 ft.'' It might seem more reasonable to assume that a cubic acre is an acre cubed, i.e., 1 acre X 1 acre X 1 acre. This would make it a "cube", each "edge" of which is an acre "long". This would be a six-dimensional object, that would be extremely hard to visualize. Barks, probably having little knowledge of the concept of dimension in units of measurement, probably made up "cubic acre" as a combination of various large units of measurement, like acre and cubic meter, to indicate that Scrooge's money bin was big. Thus, I would tend to interpret "three cubic acres of money" as "a lot of money", and not try to figure out how much that would be. (On the other hand, having a six-dimensional money bin might explain how in some stories Scrooge appears to have lost all of his money, and in the next story his money bin is full again: What he lost could have been only a three-dimensional part of his money, and what we see in the next story is merely another such part--sort of like skimming off a thin, two-dimensional sheet of money off the top of a garden-variety, three-dimensional money bin!) Now if one really wants to put a number to the volume of Scrooge's money, consider that it is shaped like a cube, and that the money level is (usually) at the 100 foot mark. This would make the volume of Scrooge's money equal to 100 X 100 X 100 = a million cubic feet, which is a bit less than Rob's 27,274,265 cubic feet. (Surprisingly, though, both numbers are in the order of millions of cubic feet!) -- Kriton ----- ------------------------------------------ Date: Fri, 22 Aug 1997 22:44:21 +-200 From: Harry Fluks To: "[DCML]" Subject: Cubic feet (Kriton) KRITON: ''Now if one really wants to put a number to the volume of Scrooge's money, consider that it is shaped like a cube, and that the money level is (usually) at the 100 foot mark. This would make the volume of Scrooge's money equal to 100 X 100 X 100 = a million cubic feet'' To be a bit more precise: the money usually is at the 99 feet mark, but there is a considerable amount of space above the marker. Let's say the height of the bin is 120 feet, so his money is 99 x 120 x 120 cubic feet = 1.4 million cubic feet. (120 feet seems so little for such a big building. In Holland, the marker says 100 METER. That sounds more logical to me!) --Harry. ------------------------------------------ Date: Fri, 22 Aug 1997 11:58:38 +0300 (EET DST) From: Mikko Pohjola To: [DCML] Subject: Re: Disney comics Digest V97 #176 [...] ROB: ''It seems reasonable to assume that a cubic acre would be a cube with an acre on a side, or with edges of length 208.71 ft.'' But that's not what it is. A cubic acre is basically a cube which has an EDGE of an ACRE. Impossible? Yes, in three-dimendional space. It's volume would be 208.71 feet to the SIXTH power. Three cubic acres would be three times this, or about 247'960'000'000'000 ft^6. I'm only just going to university, but my guess is that it would weigh something like billions of square tons (don't ask me how much a square ton is). Hmm... The key to the money being back in the Bin in the next story could very well lie in it's six-dimensional quality. That might also explain how Scrooge can swim in it, him being only three-dimensional creature (time not counting here). Mike - The Finnish Trekkie ------------------------------------------ Date: Fri, 22 Aug 1997 20:15:44 -0500 From: Merlin Haas To: [DCML] Subject: Re: Acre ''This is a good time to ask: What is an acre? In metric units if possible?'' ''# Cristian Lucas'' ''# From Buenos Aires, Argentina'' An acre is a unit of area used to measure land in the USA and England. It is equal to 43,650 square feet or 4047 square meters or 0.405 hectare. One square mile (often referred to in the Midwest United States as a "section") contains 640 acres. This would be 2.590 square kilometers. best -- Merlin Haas ------------------------------------------ Date: Sat, 23 Aug 1997 17:50:09 -0700 From: rob gibson To: [DCML] Subject: tons and acres [...] A six demensional money bin? I completely overlooked the two dimensional nature of an acre when calculating the cubic value. Yet the way I calculated it seemed the only way it could make sense. It seemed the logical way to proceed. I just pulled USA #13 (reprinting US 13 with censored panels restored) out of my reading pile, and lo and behold, on page 2, panel 5, Scrooge says "...And with my MILLION TONS of money at stake..." (italics mine). So the answer was right there in the Canon all the time. I'd like to see an index into the canon organized by subject, as I've seen done with the Bible. Then I could find this stuff and not have to have the luck of Gladstone Gander to stumble upon it when I need it. RG ------------------------------------------ Date: Sun, 24 Aug 1997 10:01:26 -0700 From: Dwight Decker To: [DCML] Subject: Re: tons and acres On Aug 23, 5:50pm, rob gibson wrote: ''Subject: tons and acres'' ''A six demensional money bin? I completely overlooked the two dimensional nature of an acre when calculating the cubic value. Yet the way I calculated it seemed the only way it could make sense. It seemed the logical way to proceed.'' Years 'n' years ago, I wrote a piece for The Comics Journal trying to calculate how much money Scrooge had in his bin. I don't have a copy now, but as I recall... Well, the term "cubic acre" is of course Barks's deliberate humorous absurdity, since an acre is a measurement of area and not volume, but I figured out a cubic acre by figuring the dimensions of an acre if it were a perfect square, then figuring the volume of a cube whose faces each measured an acre in area (and multiplying by three, since the money bin was three cubic acres). I then filled it with a completely arbitrary assumption. That is, I assumed the bin was filled uniformly with stacks of quarters (the US 25c piece). I assumed the pennies, nickels, and dimes compensated for the half-dollars, silver dollars, and sheaves of bills, and it all averaged out to quarters. This was to make it easier on me to do the calculating, because I could weigh a quarter and measure its width. (And there were comments in response that took issue with my assumption). Even allowing for an open area of twenty feet between the top layer of money and the ceiling, I came up with some pretty colossal numbers. The sheer weight of that mass of money per square foot was well beyond reason for most structural materials, and the face value of the money itself was more than all the money in circulation in the US. We won't even get into the fact that the coins minted before 1965 would have significant silver content making them even more valuable than their face amount. And it wasn't just the floor that was in trouble from the weight: in the comics, Scrooge's money isn't arranged in the nice even columns I postulated for my thought experiment: it's a free-flowing mass contained by the walls of the bin, so there's a lot of sideways pressure on the walls as well. I'm getting a headache... --Dwight Decker ------------------------------------------ Date: Mon, 25 Aug 1997 16:37:20 +0200 (MET DST) From: Jacob Sparre Andersen Subject: Re: tons and acres To: Dwight Decker Cc: [DCML] Dwight: Your piece about $crooge's Money Bin is one of these things every $crooge fan ought to know. I mentioned the part about the load on the floor and the walls to one of my colleagues (who studies granular materials) his first comment was: ''But there is no load on the floor!'' After a moment I could deduce that the load on the floor not really was zero, but that it was much much smaller than the pressure on the walls, because after the bin has been filled to a certain height, the friction between the coins and the walls will be sufficient to withstand the weight of the extra coins placed in the bin. I am not sure that the Money Bin is sufficiently deep to have reached the state where added coins can not be detected at the bottom, but it is probably close to it. There is much more to write about this subject. See for example "Physics of the Granular State", H. M. Jaeger and S. R. Nagel, Science, vol. 255, page 1523-, March 1992. Back to <u>fluid</u> dynamics. Jacob ------------------------------------------ Date: Mon, 25 Aug 1997 16:43:01 -0700 From: Dwight Decker To: [DCML] Subject: Re: tons and acres On Aug 25, 4:37pm, Jacob Sparre Andersen wrote: ''Your piece about $crooge's Money Bin is one of these things every $crooge fan ought to know.'' It's all howling absurdities for humorous effect, of course, but... An acre is a measurement of area equaling 46,560 square feet. Three acres, then, would be 139,680 square feet. The square root of that is about 374 feet (meaning that three acres in the form of a square would be 374 feet on a side). Since Scrooge's money bin is three cubic acres, the bin would have to be a cube 374 feet wide and 374 feet tall. That's over thirty stories! ''I mentioned the part about the load on the floor and the walls to one of my colleagues (who studies granular materials) his first comment was:'' ''"But there is no load on the floor!"'' ''After a moment I could deduce that the load on the floor not really was zero, but that it was much much smaller than the pressure on the walls, because after the bin has been filled to a certain height, the friction between the coins and the walls will be sufficient to withstand the weight of the extra coins placed in the bin.'' ''I am not sure that the Money Bin is sufficiently deep to have reached the state where added coins can not be detected at the bottom, but it is probably close to it.'' Granular physics is a little over my head, I'm afraid. In the "perfect" version of my thought experiment, in which the money was assumed to be stacks of quarters, the entire weight of the mass was on the floor, and there was no sideways pressure on the walls. I forget what the weight was per square foot, but it didn't bode well for the idea that there might be a basement underneath the bin floor. Assuming that the money was a free-flowing mass (as Barks actually drew it), I didn't have the math or the physics to come up with any numbers, but it was easy to see that the mass would have a sideways thrust, and would be contained only by the walls. My guess was that there would be significant structural engineering problems in building walls strong enough to hold a free-flowing mass of metal of that amount. It's interesting to think that above a certain point, the sideways pressure would be so much that it would take most of the weight off the floor. But wait-- the walls would be in effect suspending much of the mass, so the load would be on the walls, and thus on their relatively narrow foundations, right? --Dwight (quickly getting a headache) Decker ------------------------------------------ Date: Tue, 26 Aug 1997 10:32:17 +0300 (EET DST) From: Fredrik Sandstrom To: [DCML] Subject: Re: Disney comics Digest V97 #179 DWIGHT: ''Well, the term "cubic acre" is of course Barks's deliberate humorous absurdity, since an acre is a measurement of area and not volume,'' Hmmm... If acre was a measurement of volume, "cubic acre" would imply a NINE-dimensional unit of measurement! Anyway, I agree that Barks came up with "cubic acre" as a deliberately non-existent unit; I don't beleive Barks was simply ignorant as someone else suggested. [...] Fredrik Sandstrom ------------------------------------------ Date: Thu, 28 Aug 1997 07:12:34 -0700 From: rob gibson To: [DCML] Subject: cubic acre A dictionary is a wonderful reference document for useful information, in some ways not unlike the Junior Woodchucks' Guidebook. ''"Cubic: 1.a.having the shape of a cube. b.having a shape approximating a cube. 2.a. having three dimensions. b. having a volume equal to a cube whose edge is of a stated length: a cubic foot 3.math. of the third order, power or degree 4.Isometric -noun. math. a cubic expression, curve or equation. ..." -American Heritage Dictionary'' Applying these definitions to the phrase "cubic acre", we have... 1.a. An acre having the shape of a cube. example: a cube shaped asteroid (possibly inhabited by savages) having a surface area of one acre. 1.b. See 1.a. 2.a. An acre in three dimensions. Example: a cube whose sides each contain one acre. 2.b. An acre as a unit of length/edge of a cube. 3. An acre to the third power. 4. An acre as an isometric equation. Imnsho, if Uncle Carl used the term "cubic acre" to refer to a unit of measure in three dimensions then he was within the bounds of correct english usage (by definition 2a above). ------------------------------------------ Date: Thu, 28 Aug 1997 13:55:22 -0700 From: Dwight Decker To: [DCML] Subject: Re: cubic acre On Aug 28, 7:12am, rob gibson wrote: ''Imnsho, if Uncle Carl used the term "cubic acre" to refer to a unit of measure in three dimensions then he was within the bounds of correct english usage (by definition 2a above).'' Yes, but is "cubic acre" in any kind of general use as a measure of volume? According to Webster's Ninth New Collegiate Dictionary (Merriam-Webster), an acre is "any of various units of area, esp. a unit in the U.S. and England equal to 160 square rods," and derives from an older form meaning "field" (our German friends will recognize the word "Acker" as a related term). In every way, shape, and form, "acre" is a measurement of surface area, not volume. "Cubic acre" is a humorous Barksian absurdity. There is, however, a measurement called the "acre-foot": "the volume (as of irrigation water) that would cover one acre to a depth of one foot." It doesn't seem to apply to the present case. Anyway, an acre does not have a fixed shape. I assumed a square that would have a surface area of three acres, then derived the measurements by figuring the square root of the area (over three hundred feet per side, if I remember right). Three cubic acres would be a cube with each of those squares as a face, which would be a building over thirty stories high and just as long, filled nearly to the top with money. The structural engineering problems are left as an exercise for the student. --Dwight Decker ------------------------------------------ Date: Sat, 30 Aug 1997 00:44:29 Europe/Athens From: Kriton Kyrimis To: [DCML] Subject: Re: Disney comics Digest V97 #183 DWIGHT: ''There is, however, a measurement called the "acre-foot": "the volume (as of irrigation water) that would cover one acre to a depth of one foot." It doesn't seem to apply to the present case.'' The above may sound strange, but it is consistent: it is the product of one acre (a unit of surface) multiplied by one foot (a unit of length), which is a volume (i.e., that of a box with a base having an area of one acre and having a height of one foot). This is very similar to the more familiar kilowatt-hour: the energy produced by a 1 kilowatt (power) engine in 1 hour (time) [power X time equals energy]. All this discussion about cubic acres reminded me of something I'd written in my high school days, where, without yet having read any references to Barks' "cubic acres", I had come up with the term "cubic kilo". I wonder if someone could explain to me what '''that''' is!!! (A cube with edges 1 kilo "long"?!?) [...] -- Kriton ----- ------------------------------------------ Date: Tue, 2 Sep 1997 09:37:12 +0000 From: Soeren Schridde To: [DCML] Subject: Re: Disney comics Digest V97 #184 Kriton: ''All this discussion about cubic acres reminded me of something I'd written in my high school days, where, without yet having read any references to Barks' "cubic acres", I had come up with the term "cubic kilo". I wonder if someone could explain to me what *that* is!!! (A cube with edges 1 kilo "long"?!?)'' I MIGHT BE WRONG as physics lessons are a lot of time behind me, but I think you're wrong, especially with cubic: I think "to the third power" doesn't necessarily mean cubic... so a kilo to the third power - I'd think of it as follows: kilo is defined as the gravitation by the earth on a certain mass at a special height (on Mount Everest, things weigh less...) so kilo to the third power would be this gravitation (on earth on the same mass at the same height) to the third power ... If this is "what lawyers think of physics", then correct me! ;-) [...] Soeren Schridde Germany ------------------------------------------ Date: Wed, 3 Sep 1997 17:49:20 +0300 (EET DST) From: Kriton Kyrimis Subject: Re: Disney comics Digest V97 #187 To: [DCML] SOEREN: ''I MIGHT BE WRONG as physics lessons are a lot of time behind me, but I think you're wrong, especially with cubic:'' ''I think "to the third power" doesn't necessarily mean cubic...'' ''so a kilo to the third power - I'd think of it as follows: kilo is defined as the gravitation by the earth on a certain mass at a special height (on Mount Everest, things weigh less...) so kilo to the third power would be this gravitation (on earth on the same mass at the same height) to the third power ...'' First of all, a "kilo" is short for "kilogram", which is a unit of mass, not weight. By coincidence, at sea level, at a certain latitude (and for most intents and purposes almost everywhere on Earth), a kilogram of mass has a weight of one kilopond (a unit of weight), so in everyday life one usually does not distinguish between the two: groceries can be measured either using a balance (measures mass) or scales with a spring mechanism (measures weight). However, if you ever go to Mars, I'd recommend that you insist that the grocer weighs your groceries with a balance!!! I think it is time to explain what is "dimension" in units of measurement is, to which I had referred in previous postings. This is from what little I remember from my high school physics, so if there are any physicists in the lists, please don't hit me too hard if there any inaccuracies below. In physics, it is common practice to measure things in a consistent system. This has the advantage that whenever you apply a formula to derive a quantity (e.g., speed) from other quantities (e.g., distance traveled and time required), the result is guaranteed to be a unit in that system, and not require a conversion. To do this, a few "fundamental" quantities are selected, their units are defined, and the units for all other quantities are derived from the above by applying the various laws of physics. The most common system currently in use is SI (Systeme Internationale), but since I am not familiar with it, I'll talk about its predecessor, MKSA (= Meter, Kilogram, Second, Ampere). In this system, the fundamental quantities are length, mass, time, and electrical current, and the units are those mentioned above. All other units are expressed in terms of the above. Now, the "dimension" of a unit of measurement (or, indeed, the quantity measured) is the ordered set of exponents to which each of the fundamental units must be raised to obtain the unit in question. A few examples: Quantity Unit Dimension length m (1, 0, 0, 0) speed m/s (1, 0, -1, 0) acceleration m/(s^2) (1, 0, -2, 0) force kg*m/(s^2) (1, 1, -2, 0) (This is called a "Newton") electric charge A*s (0, 0, 1, 1) (This is called a "Coulomb") In this system, there is no place for a "cubic acre", as the unit of measurement for areas is the square meter. On the other hand, an acre is equivalent to a square meter times a constant, so a cubic acre is a square meter cubed (just like a cubic meter is a meter cubed), times another constant. Thus, the dimension of the quantity a cubic acre measures is (6, 0, 0, 0). Therefore, in terms of linear dimensions, a cubic acre is a six-dimensional object! The fundamental quantities need not be the four mentioned above, nor need they be four. E.g., I understand that SI has a few more, and another old system, CGS (Centimeter, gram, second) had only three, with electrical quantities having bizarre, often fractional, dimensions (if I am not mistaken, electric charge, e.g., would have a dimension of (3/2, 1/2, -1) in this system!) As for my cubic kilo, depending on whether I meant cubic kilogram or cubic kilopond, its dimension would be either (0, 3, 0, 0) or (3, 3, -6, 0) in MKSA; a nonsense quantity, as I had meant it to be. [...] -- Kriton ----- ------------------------------------------ Date: Mon, 8 Sep 1997 12:48:30 +0000 From: Soeren Schridde To: [DCML] Subject: cubic acre Kriton: (having read your explanations on dimensions) OK, we lawyers ("in spe", of course) should leave physics to the physicians ;-) Soeren Schridde ------------------------------------------ Source of information: Disney Comics Mailing List. Edited by Daniël van Eijmeren, 8 June 2006 [http://info.mcdrake.nl/mc_dpersonages.html#mc_dp20060608 Oorspronkelijk artikel] door Daniël van Eijmeren (8 juni 2006).

Return to Geldpakhuis.