Dot Physics

Size of 91,000 documents

Here is a quick one. One of the big news stories recently was this regarding WikiLeaks and the release of the Afghan War Diary. There could be tons of things to discuss regarding this – but I am not going to do that. The first thing that struck my mind was “over 91,000 documents”. That seems like a lot.

If each one of these documents were printed on one page, how big would the stack of paper be?

I could just estimate this – fermi-problem style. But instead, I thought would use a stack of paper. Here is a pack of 500 sheets of paper.

i-23c3d1768b5816a5600402a87e6821b6-2010-08-09_04082010003jpg.jpg

Opening it, I can measure the thickness:

i-85dca997bd79027d7ea27bbe2e4c5a3a-2010-08-09_04082010004jpg.jpg

How thick is this stack? I am going to estimate the stack as 5.2 cm (I should use uncertainty here, but I just want a first estimate). This would put the thickness of one sheet at:

i-152a20d525d493984d403dd4554f50c7-2010-08-09_la_te_xi_t_1.jpg

So, what would be the height of 91,000 pages?

i-5f9133c0cfbee8eb108f23cf55b60020-2010-08-09_la_te_xi_t_1_1.jpg

Over 9 meters (31 feet) is one serious stack of paper. I would hope you wouldn’t have to bind this. How tall would it look? Here is a picture of me standing outside with this stack.

i-c398c06b5bf97111ea894c8bf7ea4768-2010-08-09_untitled.jpg

Ok, one more thing. What if I downloaded these things and printed them out? How long would it take?

Take a look at cnet’s top 5 printers. How fast do they print? Oddly, cnet doesn’t list this for all printers. Ok, after some digging it looks like most have a speed of around 10 pages per minute. The Samsung ML-2525W says it has a print speed of up to 24 pages per minute. It also says it has a capacity of 250 sheets – this could be important also. How long would it take to print out these 250 sheets?

i-e0cb38780d1c3912ccec7c02a4168d25-2010-08-09_la_te_xi_t_1_2.jpg

For 91,000 pages, I would need to change the paper tray 91,000/250 = 364 times. How long would it take to change the paper? I think with practice, I could get it around 15 seconds. This would give a total print time (assuming the time spent changing printer toner is small) of:

i-65723d818771fc73fc18fef7b96f9ed0-2010-08-09_la_te_xi_t_1_3.jpg

Homework

  • How much would this cost in printer toner?
  • If you used an ink-jet, how long would it take and how much would it cost (with paper)?
  • If you had to retype this, how long would it take?
  • How long would it take you to scan through these documents looking for something?

Be sure to turn in your homework on plain paper. If it has three-hole punch paper, I will take off points. If it is not stapled in the upper left corner, I will take off points.

Comments

  1. #1 Aaron
    August 9, 2010

    Wouldn’t the weight of the paper compress the stack making it less than 9.5m?
    Also, you would have to work in shifts to print it in 2.7 days because you need sleep. I also doubt that a person would be able to concentrate on such a task well, or might be in the bathroom when the paper needs to be changed, so it would be more than 2.7 days.

    91,000 pages, assuming 300 words per page, with my my typing speed of 35 wpm:
    (91000*300)/(35/60/24)=514.667 days.
    772.00 days if I worked at it 16 hrs per day (2 8-hours shifts). 308 40-hour weeks. Just shy of six years. We can talk about the overtime. When did you need this done?

    Toner for that Samsung ML-2525W is $61 for 2500 pgs. 91000/2500*61=$2220.40 without sales tax.

    A case of paper is 24.99 (5000 sheets) 91000/5000 rounds up to 19 cases. 19*24.99 = $474.81 before sales tax.

    total cost:
    474.81 (paper)+2220.40 (toner)+149.99 (printer) = $2845.20 plus my wage and overtime (which is negotiable) plus overhead (utilities, office rent, etc.). I am sure I can get free shipping.

    I read pretty quickly. I estimate I can scan a page really well in about 10 seconds. (91 000 * 10) / 3 600 = 252.777778 hours. 6.32 weeks at 40 hrs per week.

  2. #2 jeremy1701
    August 9, 2010

    Aaron, got some free time today? Lol!

  3. #3 Greg Laden
    August 9, 2010

    “If each one of these documents were printed on one page, how big would the stack of paper be?”

    About half the size of the shit piled on my desk and nearby chairs?

  4. #4 Aaron
    August 9, 2010

    Oh, I must be tired. I thought this was my online math class. Now if could just remember what blog I posted my history paper on.

  5. #5 Todd
    August 10, 2010

    The more pertinent question is, “Could God stack a pile of paper so high that Jesus couldn’t read it?”

  6. #6 Grep Agni
    August 10, 2010

    @Aaron: I doubt that the paper would compress much. Or rather, the ream of paper Dr Allain measured is pre compressed; the sheets were squeezed by several sets of rollers during production and I think the entire stack is squeezed before being wrapped. Once the paper is used it fluffs up a but as air gets between sheets, especially if there are any folds. The 9.5 meter estimate of the height of the pile is most likely an underestimate, since the top part would be looser than measured. Exactly how much looser would depend on exactly how the paper was handled.

    Also, the printer speed used in the article is for small personal printers. Larger, high volume printers are much faster. From this 3-year old press release “The new enhanced speed Oce VarioStream 9000 version can print black- only pages at 1,350 per minute — 60 percent faster than the existing version.” Printing only would take a bit more than an hour (67.4 minutes.) I don’t know how much paper it can hold, but I expect it’s quite a bit, and most likely it’s possible to add more without pausing the job.

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