1665Scale effects on the biomechanical design of organismsdepend strongly on the properties of the biomaterials of whichthey are built, requirements for avoiding failure over a lifetimeof their use, and on physiological demands for performanceover a range of activities. For animals and plants constructedof similar materials, geometrical effects on the scaling ofbiomechanical function predominate. For structural support,design requirements depend mainly on the operating stresses(σ; or strains, ε) that structural elements experience relative totheir yield, or failure strength (Wainwright et al., 1976). Theratio of failure stress to peak functional, or operating, stress ismost commonly used to define a structure’s ‘safety factor’.However, it is likely that lower safety factors based on yieldstress more often apply to the functional integrity of a structure.Repeated loading characteristic of locomotion may also causefatigue damage and eventual failure at stresses well belowthose that cause failure in a single or few loading cycles (Carterand Caler, 1983; Wang et al., 1995). For this reason, astructure’s ‘loading history’ is important, in terms of design foran adequate safety factor, as well as for remodeling and repair(Carter, 1987). For the dynamic loading conditions oflocomotion, it is also likely that the amount of strain energyThe Journal of Experimental Biology 208, 1665-1676Published by The Company of Biologists 2005doi:10.1242/jeb.01520To function over a lifetime of use, materials andstructures must be designed to have sufficient factors ofsafety to avoid failure. Vertebrates are generally builtfrom materials having similar properties. Safety factorsare most commonly calculated based on the ratio of astructure’s failure stress to its peak operating stress.However, yield stress is a more likely limit, and workof fracture relative to energy absorption is likely themost relevant measure of a structure’s safety factor,particularly under impact loading conditionscharacteristic of locomotion. Yet, it is also the mostdifficult to obtain. For repeated loading, fatigue damageand eventual failure may be critical to the design ofbiological structures and will result in lower safety factors.Although area:volume scaling predicts that stresses willincrease with size, interspecific comparisons of mammalsand birds show that skeletal allometry is modest, withmost groups scaling (ld0.89) closer to geometric similarity(isometry: ld1.0) than to elastic similarity (ld0.67)or stress similarity (ld0.5). To maintain similar peakbone and muscle stresses, terrestrial mammals changeposture when running, with larger mammals becomingmore erect. More erect limbs increases their limbmuscle mechanical advantage (EMA) or ratio of groundimpulse to muscle impulse (r/R=G/Fm). The increase inlimb EMA with body weight (W0.25) allows largermammals to match changes in bone and muscle area(W0.72–0.80) to changes in muscle force generatingrequirements (W0.75), keeping bone and muscle stressesfairly constant across a size range 0.04–300·kg. Above thissize, extremely large mammals exhibit more pronouncedskeletal allometry and reduced locomotor ability. Patternsof ontogenetic scaling during skeletal growth need notfollow broader interspecific scaling patterns. Instead,negative allometric growth (becoming more slender) isoften observed and may relate to maturation of theskeleton’s properties or the need for younger animals tomove at faster speeds compared with adults. In contrast tobone and muscle stress patterns, selection for uniformsafety factors in tendons does not appear to occur. Inaddition to providing elastic energy savings, tendonstransmit force for control of motion of more distal limbsegments. Their role in elastic savings requires that sometendons operate at high stresses (and strains), whichcompromises their safety factor. Other ‘low stress’tendons have larger safety factors, indicating that theirprimary design is for stiffness to reduce the amount ofstretch that their muscles must overcome whencontracting to control movement.Key words: bone, muscle, tendon stress, elastic savings, safety factor.SummaryIntroductionReviewBiomechanical consequences of scalingAndrew A. BiewenerConcord Field Station, Department of Organismic and Evolutionary Biology, Harvard University, Old CausewayRoad, Bedford, MA 01730, USAe-mail: [email protected] 31 January 2005THE JOURNAL OF EXPERIMENTAL BIOLOGY1666that must be absorbed during a loading cycle relative to thework of fracture of a material (e.g. bone or tendon) is the mostcritical determinant of a structure’s safety factor. Because thedistribution and amount of strain energy absorption instructural elements are difficult to measure during locomotion,energy absorption is not often used to evaluate a structure’ssafety factor relative to its mechanical use.For skeletal support elements, such as animal limb bones,design to maintain an adequate safety factor and avoid failureover a lifetime of use is most critical. However, for elasticelements, such as tendons and ligaments, the capacity for strainenergy savings to reduce muscle work and lower the energycost of locomotion also has selective value. Consequently, atrade-off exits in the design of tendons for adequate strengthversus achieving high-energy savings, which depends on thetendons experiencing high strains (strain energy per unitvolume of material is αε2or, equivalently, σ2; Alexander,1988; Biewener, 2003). Morphological evidence suggests thatmost tendons are designed to have high safety factors, in excessof what is required for effective strain energy savings andnecessary strength (Ker et al., 1988). This indicates thatmaintaining sufficient stiffness (force/displacement) forcontrol of length and thus, position and movement of limbsegments, may be an overriding design requirement for manytendons. Such tradeoffs in functional design therefore canresult in quite distinct operating stresses and safety factors.In this article, I focus on the biomechanical consequences ofscaling in the limbs of terrestrial vertebrates, principally birdsand mammals, comparing design requirements for threelocomotor elements: bones, muscles and tendons. While otherstructural elements (e.g. cartilage) are clearly of keyimportance to the biomechanical function of these animals, lessis known about the scaling implications for the design ofcartilage in the joints of small