Moving on from Kirkpatrick (1994): estimating 'safety factors' for flying vertebrates.

The most cited work (by far) to provide safety factor estimates for the wing bones of flying vertebrates is inaccurate. Kirkpatrick (Kirkpatrick, 1994) presented extremely low measurements for the material properties of wing bones and anomalous estimates of applied loading that deflate estimated safety factors to around half those reported by subsequent workers. He also did not discuss the limitations of a calculation methodology that resulted in a huge range of estimated values with unreliable means. In engineering, a 'safety factor' is a multiplier applied to stresses calculated in the design phase to allow for uncertainties in loading, material properties, manufacturing tolerances and material degradation. The magnitude of a safety factor depends on the consequence of failure and the degree of certainty to which loads, material properties and the operational environment are known (Juvinall and Marshek, 1991; Hansson, 2009). In this context a safety factor is a 'forward-looking' design tool, used to ensure that a design will be capable of resisting the loads that it will encounter during its lifetime. In contrast, the concept of a 'safety factor' in biology is the opposite: retrospective. Biologists use these multipliers to look at existing structures and estimate how close they might come to failure when loaded. Three different methods have been applied in biological research to obtain the applied loading in structures. The first relies on direct calculation of loads and estimation of stresses from knowledge of structural section and material properties (Kirkpatrick, 1994); the second utilises indirect measurement of loads via techniques such as force platforms [e. Of the three approaches, the calculation method is likely to be the least accurate while in vivo measurements are potentially the most accurate. Kirkpatrick (Kirkpatrick, 1994) used the calculation method with 11 bird and seven bat species. He estimated applied bending moments from calculated lift forces during gliding and hovering flight and made estimates of bone stresses from which safety factors were calculated. There are two significant problems with this study. First, to obtain material properties, Kirkpatrick (Kirkpatrick, 1994) tested small samples of bone, recording a mean ultimate tensile stress of 125 MPa for bird humeri and 75 MPa for bats. We now know these results are extremely low when compared with subsequent studies: Swartz and colleagues (Swartz et al., 1992) recorded 150 MPa for bats while Currey (Currey, 2004) and Casinos and Cubo (Casinos and Cubo, 2001) recorded values >200 MPa for birds. …