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## Pencil me out!

To my shock and amazement a few Tuesdays ago, I realised the appalling inefficiency of the humble pencil. The typical pencil is about 15cm long, and its lead is about 2mm thick. I’ve noticed, in my own pencil usage, that when the tip is more than about 0.75mm across that I will sharpen the pencil. This means that the outer 1.25mm of the pencil lead is wasted in the sharpening process. And because it’s the cross-sectional area that matters, this amounts to 86% of the pencil lead. Coupled with the fact that the last 3cm of the pencil is unholdable, that means that about 90% of the lead in a pencil is wasted! Isn’t that shocking!?

I, for one, am outraged. Protests are being organised. Potential slogans are invited. So far, I’ve come up with:

Don’t pencil me in

Not 2B – that is the answer

Make pencils disappear

That last one is a bit dark.

### 2 Responses

1. Not sure Luke, I think this crusade may be 2H.

2. on March 7, 2012 at 7:37 pm | Reply David Crawford

James, thanks I found this very interesting.

I think this gives mechanical pencils the lead over wood covered pencils.

I am wondering if amount is even less. I get how you got to 86%, the inner usable cylinder is 14% of the whole lead. However I was wondering about the sharpening process and this inner cylinder. Don’t we loose more of the inner cylinder when we sharpen it to a point?

I am envisaging a blunt point for the inner cylinder and then turning it into a nice cone shape. This cone would be 1/3 of the volume of inner cylinder independent of the sharpening angle. So we waste another 67%. We now have a 1/3 of 14%, roughly 5%% of the lead which we can use. So if we exclude the stump the percentage of the lead use become (5% x percentage length used in your case 80%) becoming 4% of the total lead. This brings the total waste to 96%.

Or is my thinking wrong somewhere.

I can buy a wood covered pencil for 50c or a mechanical pencil (0.7mm) with leads of total length 60cm for \$10. I would need to buy 100 wood covered pencils, costing \$50 to get the same use.

Some of my year students were much provoked by this post, so thanks.

Regards

David