From the Telegraph:
Steffan Llewellyn of Leicester University’s Centre for Interdisciplinary Science, worked out that Pinocchio’s head weighed 4.18kg and his nose six grams with an initial length of one inch.
From that calculation, he concluded that when the nose grew to 140 metres the force exerted downwards would cause the neck to snap.
And Mr Llewellyn found that, if Pinocchio’s nose doubled with each lie, then it would reach that length after 13 fibs.
The study was published in the Journal of Interdisciplinary Science Topics, which, according to the Telegraph article, has also published papers called "Does Winnie the Pooh have a B12 deficiency?" and "The viability of throwing giant tortoises into mines".
Clearly, I need a subscription.