Question

Consider an animal like a horse. Now scale its neck longer and longer.

How can a giraffe, or even worse a huge dinosaur, raise its neck without the tendons snapping? The dinosaur case in particular seems ridiculous. Is there a "physics trick" the animals use to make this more manageable? Or does the tendon tension not scale as badly as my intuitiion is claiming?

Answer 1

Let's scale up an animal.

If length is , and we don't change the proportions, then the mass of the head+neck will scale as . If the neck & head are being held horizontally, the lever arm scales as , so the torque at the base of the neck scales as .

The width of the neck scales as , so the force on the tendons/muscles scales as . The yield strength of a tendon/muscle scales with its cross-sectional area: .

The force is going as , but the yield strength is going as . My math agrees with your intuition: as you make an animal bigger, eventually the neck won't be able to handle the stress.

The reason why the giraffe can get away with long necks is twofold, I'd guess:

1) They have a proportionally thicker neck. Look at a picture of giraffe. Note that the neck gets extremely thick toward the base along the front-to-back axis (which is the the axis along which they lower their head), while it's slender side-to-side. Of course, this you can only change proportions so far: eventually the animal will be all neck.

2) We've got a lot of overhead with our short human necks. Ferinstance, I can support weights much heavier than my head with my arms, despite my arms being much longer AND a bit thinner than my neck.