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Ligaments join bone to bone and have no muscle, just elastin. Elastin is rubbery with a modulus of about 1MPa. The ligamentum nuchae extends from the front end of the thoracic spine to the back of the skull. It counterbalances the head and neck. Animals living on open plains have long legs for running away from lions (for example) but need to reach down to graze; they don’t want to use muscular energy lifting their head to see the lions coming. My plan was to calculate from measurements of lengths and weights, made on skeletons of species ranging from pigs to giraffes, what the elastic requirement would be for such a ligament and to see how closely this matched the published loading curves for elastin.
Curve calculation
The giraffe was first. It is the extreme example and seems to keep its neck moderately straight. I measured skeletons in the Natural History Museum in London and calculated the lever arm and the extension of the ligament when the head was raised and lowered. Neill Alexander from Leeds provided the cross-sectional area of the ligament – he was driving around the Serengeti National Park in Tanzania, noticed a dead giraffe, and kindly did a quick dissection for the data. Back at the computer I calculated the required force-deflection curve. It matched the experimental data for elastin! More complex morphologies need a better model and so are slightly less good.
Buoyed by this success, I looked for another simple system. It struck me that few had studied Euler buckling in animals. I decided to look at the spines of hedgehogs as elastic structures. A fresh hedgehog could be scraped up from the road outside my house.
Local buckling resisted
The spines covering the back of the hedgehog are about 20mm long and 1mm in diameter. They are hollow tubes with walls about 0.05mm thick and slenderness ratio of about 50. Inside they are stabilised by 22 longitudinal stringers and plates crossing the lumen. These dimensions are remarkably constant over the entire animal. I removed the plates with a syringe needle and found that they resist the tube going oval when the spine is loaded on end as a strut. Bamboo culms have similar structures that resist local buckling in the same way. The longitudinal stringers do a similar job in loaded tubes such as aircraft structures and the legs of marine oil rigs. Thus the spines are stabilised against local buckling.
The slenderness ratio is on the (theoretical) upper limit for a strut to behave as a column and fail in compression rather than bending. That the spines are curved suggests that global buckling is encouraged! The overall design suggests a strut that must buckle elastically when loaded on end, but will resist and deflect a long way before failing, so absorbing the maximum strain energy. It’s a shock absorber! A hedgehog will climb an apple tree for the fruit, roll into a ball, drop out of the tree and bounce. A non-rubbery, non-leaky shocker?
The BBC Natural History Unit got hold of this story and filmed a hedgehog falling down a cliff. I phoned them, excited, and asked if I could make measurements from the film. “You won’t learn much” was the reply. “We found a dead hedgehog, peeled the skin off and filled it with crumpled newspaper”.
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