Kum Automatic Longpoint Sharpener
After trying it myself, I felt that what I had previously read and heard didn’t really communicate how the Longpoint works. I doubt I’m alone, so with the help of a picture or two, I hope to clarify matters.
The sharpener is an oval prism container, with two externally accessible holes. It comes with two spare blades tucked into a corner of the container. This is a very nice touch. I’ve never seen a spare sharpener blade for sale at an art supply store or stationer, and it’s nice to see a sharpener given a longer life with this addition.
Let’s get to the sharpening method. The left hole has a exit diameter of about 2mm, which is the diameter of the pencil lead or core. Thus the blade catches and sharpens the wood of a standard pencil, but misses the core. (See photo.) The pencil is then placed in the second hole, where the lead gets sharpened to a very fine point.
V = ?r2h
and the formula for the volume of a cone is
V = 1/3?r2h
so turning a cylinder of lead into a cone of lead discards 2/3 of that lead.
For a 2mm lead, the radius is 1mm. The Longpoint produces a point of 3mm, so we have
V = ?*1mm2*3mm = 9.4mm2 will result in 6.3mm2 discarded to create a 3.1mm2 point.
A point which will be much harder to keep unbroken, by the way.
A more modest 2mm long point would produce only 4.2mm2 of waste.
The 2/3 of the lead discarded in making a point actually could be an argument in favour of mechanical pencils.
I’m sticking with regular sharpeners, but it’s nice to know about this alternative.
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