Dem Bones

Last December I mentioned in passing that my Sporty students spent an afternoon looking at the gross and microscopic structure of a sheep's humerus . . . or possibly a femur: a long bone anyway. My comparative anatomy is a bit rusty. The neat thing is that the shaft of such bones has been engineered by evolution in the form of a hollow cylinder so that the limited amount of available calcium phosphate can be arranged to maximise the load-bearing capacity of the limbs. This frees up the "hollow" centre for other functions and this turns out to be primarily a factory for making red and white blood cells in the bone "marrow".

This week we're in humerus-land again with a different cohort of students. There are three parts of the analysis a) function as informed by the structure of a long-bone cut in half longitudinally to reveal the inside as well as the outside b) prepared slides to show how the hollow cylinder of the bone is made up, in its microscopic structure, of hollow cylinders 0.5 mm across c) finally . . . toilet roll mechanics.  In previous years I've asserted that a toilet-roll interior [R], as a hollow cylinder, is remarkably efficient at supporting weight.  Some at least of the students have nodded along with this reasonable seeming statement.  But agreeing with assertion is not the way science goes down, so this year I snagged a bunch of ex-toilet-rolls from the recycling and brought them into class. Yesterday we measured the load-bearing capacity of  a vertical roll [A]compared to one lying on its side [B] and came up with a rather surprising number.

First task was to find a suitable set of weights to carry out the destructive stress test.  We decided to use A4 hard-cover lab books of which there is a plentiful supply.  We also decided to create a model sheep (or model elephant) by putting a t-roll at each corner and started piling lab books on top.  Turns out that one lab-book (there are several different models and styles available) weighs 488g, so we called that 500g and piled up a stack of 42 books onto the "legs".  That's 21kg.  One of the students, more enterprising than the others, then removed one of the legs, so the average weight supportable by a single toilet roll without catastrophic deformation is at least 7kg!  Which if remarkably hefty considering that the roll itself weighs a mere 7g.

For those who a) don't have a set of gymnast's graded weights and b) want to be more precise, it turns out that a ream of photocopy paper weights precisely 2.5kg.  How do I know that? You can work it out from things that any office supply company employee knows.  Xerox paper is typically marketed as 80gsm (grams per square meter). Indeed this is the DIN 6730 [Deutsches Institut für Normung] Standard for Paper definition of  a ream.  A0 paper is defined as being 1sq,m. in size in the ratio 1 : 1.414 [numberphile youtube link] for the short and long sides, so a single sheet of A0 weights 80g.  A1 is half the size of A0 in the same proportions and weighs 40g . . . A2 = 20g; A3 = 10g; A4 = 5g.  A decimal ream is 500 sheets weighing in total 2500g.  Which means that you can use paper to weigh anything from 5g to 25kg (a stack of 10 reams or two xerox-boxfuls) or more.

And don't let me catch myself calling 480 sheets (at 20 quires of 24 sheets each) a ream.  That is a 'short' ream at best or a wholly outmoded quantity that should have been put aside with the quill pens that used to write on it . . . along with a printer's ream [516 sheets]; a mill ream [472]; and a stationer's ream [504]. Life in the stationery world used to be more interesting but also more complicated.