How long a line could you draw with a single pencil?
Forget string 鈥� we now have a new saying, 鈥淗ow long is a pencil line?鈥� 鈥� Ed
鈥� My mind boggled at the range of variables implied by the question. As a scientist turned engineer (now retired), I decided to conduct a simple experiment in which the variables were reduced to a manageable number.
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Selecting a with a 0.9-millimetre diameter, and using the manufacturer鈥檚 H lead, I drew 100 lines each 30 centimetres long on high-quality printer paper. The pencil was tilted at 75 degrees to the plane of the paper. By measuring the reduction in the length of the refill and allowing for clutch-clamping wastage, I concluded that 541 metres of line could be drawn with a lead 60 millimetres long.
I also found by inspection that small changes in some variables had a large effect on the rate at which the lead was used up.
Peter Peters, Sherborne, Dorset, UK
鈥� Taking the simple case of a clutch pencil, I found by experiment that a 1-millimetre length of 0.5-millimetre 2B lead would draw about 9 metres of uniform line on ordinary photocopier paper. In my clutch pencil a new lead has a usable length of 50 millimetres, so that鈥檚 450 metres of line per lead. Looking at it another way, it鈥檚 easy to work out that 1 cubic millimetre of pencil lead is needed to draw 45.84 metres of line.
鈥淚 found by experiment that 1 millimetre of lead would draw about 9 metres on photocopier paper鈥�
A brand new wooden pencil from a reputable maker is 175 millimetres long with a lead diameter of 2 millimetres. Assuming it is possible to use all but the last 20 millimetres of the lead, and (crudely) that each millimetre of lead draws 9 metres of line as with the clutch pencil, that would give us 1395 metres of line for the whole pencil.
However, the volume of usable lead in the pencil, assuming again that the last 20 millimetres can鈥檛 be used and that half is lost to sharpening, is 243.5 cubic millimetres. At the same volumetric wear rate as in the clutch pencil, that should produce 11,162 metres of line. I expect the actual output will be somewhere between these two answers.
The hardness of the lead will make a difference, as will paper type, the density of the line and how careful the user is not to sharpen too often or too far.
Andrew Fogg, Sandy, Bedfordshire, UK