Feb 15, 2008

Posted by in Fermi Problems - Simple | 6 Comments

How long of a thread do you need to weave a bed sheet?

Ā TGIF and time for Friday Fermi Problem :

Fermi Problem is described as:

In physics, particularly in physics education, a Fermi problem, Fermi question, or Fermi estimate is an estimation problem designed to teach dimensional analysis, approximation, and the importance of clearly identifying one’s assumptions. Named for 20th century physicist Enrico Fermi, such problems typically involve making justified guesses about quantities that seem impossible to compute given limited available information.

This is one of the simplest Fermi problems.

Simple Fermi Problem: What is the total length of the thread in a bed sheet?
or
How long of a thread would you need to weave/make a bedsheet?

No, you may not ask “what is the size of the bedsheet?” – look around, make an educated guess about the average size of a bedsheet.

No, you may not ask “what is the thread count of the bedsheet?” – figure out the most common thread count. If you can not figure it out, you can go to the bedroom and guesstimate the length of the thread in a square inch.

threads

Answer is in the comments. Talk Like a Physicist

  1. Answer:
    About 15 miles.
    Assumptions: Queen Sized Bed sheet
    Thread count 200.

    Thread count is defined as
    The simplest definition of thread count is the number of threads, both horizontally and vertically, within one square inch of the fabric.

    So each sq. inch has 200 inches of thread.
    Queen size bedsheet is 80″ x 60″

    Total thread is 200x80x60 = 960,000 inches
    63,360 inches = 1 mile
    total length of the thread in a bed sheet : 15.3 miles.

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  3. Yes, great job. :) Interesting indeed.

  4. By my figuring Sunny is off by about a factor of two. Recall that the threads run both head to foot and left to right so you will have 80 in * 200 t/i = 16000 threads in one direction and 12000 in the other dimension. The total length of threads should be 2*80*60*200=1.90E6″ or 30.3 statute miles. Had you used gone for some really high-end 350 count sheets you would get 53 statute miles and if that were Cal King you would get as high as 67.2 miles! For a low thread count twin sheet I get 13.5 miles, still far more than I had thought about.

    We take the cotton gin and the loom for granted these days.

  5. I am pretty sure that 15 miles length for 200 thread count Queen sheet is correct. 200 thread count includes both left to right and head to foot.

    The simplest definition of thread count is the number of threads, both horizontally and vertically, within one square inch of the fabric.

    You might be double counting because colloquial 200 “thread per inch” is not really thread per inch, it is 200 threads per inch square. With your count of threads, it will be considered 400 thread count sheet.

    Thanks for your comment.

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