Sheep Collisions: the Good, the Bad, and the TBI

TL;DR

This paper reexamines sheep collisions, correcting misconceptions about impact duration and cushioning, and uses TBI research to better estimate sheep's acceleration tolerance and collision dynamics.

Contribution

It provides a more accurate analysis of sheep collisions by integrating traumatic brain injury data, challenging previous assumptions about impact duration and cushioning.

Findings

Impact time is approximately 2 ms.

Stopping distance is less than 1 cm.

Sheep can tolerate accelerations up to 450 g.

Abstract

The title page of Chapter 9 in Fundamentals of Physics (Halliday, Resnick, and Walker, 8th Edition, p. 201) shows a dramatic photograph of two Big Horn sheep butting heads and promises to explain how sheep survive such violent clashes without serious injury. However, the answer presented in sample problem 9-4 (p. 213) errs in presuming an interaction time of 0.27 s which results in an unrealistically long stopping distance of 0.62 m. Furthermore, the assertion that the horns provide necessary cushioning of the blow is inconsistent with the absence of concussions in domestic breeds of hornless sheep. Results from traumatic brain injury (TBI) research allow acceleration tolerance of sheep to be estimated as 450 g facilitating an analysis of sheep collisions that is more consistent with available observations (stopping distance less than 1 cm, impact time of roughly 2 ms).