Scaling

Question 1

Hoyt et al. 1981.

Answer 1

Gait and the energetics of locomotion in horses.

• Horses change gait and select speed within that gait to minimise energy consumption.
• There is a linear relationship between rate of oxygen consumption and speed
• There is a curvilinear relationship between rate of oxygen consumption and distance travelled.

Question 2

Alexander et al. 1983

Answer 2

A dynamic similarity hypothesis for the gaits of quadrupedal mammals.

• Many cursorial quadrupeds move in a dynamically similar fashion with similar Froude numbers
• The hypothesis is valid across a wide range of cursorial mammals but is less so when comparing cursorial mammals to non-cursorial mammals.

Question 3

Bullimore et al. 2006

Answer 3

Dynamically similar locomotion in horses.
• Due to the size-independence of tendon elastic modulus, for horses to be dynamically similar there must be ‘compensatory distortions’ such as posture changes with size.
• RSL and DF were independent of body mass for different Froude numbers tested, RSL ∞Mb^0
• Prediction with linear stress-strain of tendon, RSL ∞Mb0.19 and nonlinear RSL ∞Mb0.11
• Therefore compensatory distortions must take place.

Question 4

Alexander et al. 1979

Answer 4

. Allometry of the limb bones of mammals from shrews to elephant.
• Made measurements of bone length and diameter over a large range of species to test whether the lengths and diameters scaled with geometric similarity Mb0.33 or elastic similarity (L∞ Mb0.25 , L∞ Mb0.375) to allow equal deformation under body weight
• Found that most mammals scaled geometrically except for Bovidae which scaled elastically.

Question 5

Bieweiner. 1982

Answer 5

Bone strengths in small mammals and bipedal brids: Do safety factors change with body size?

• Bones of mammals over a large range of body sizes do not vary in strength and therefore large mammals have much smaller safety factors than smaller mammals.
• Large animals can compensate for some of this by change in posture but not completely.

Question 6

Garland. 1983.

Answer 6

The relation between maximal running speed and body mass in terrestrial mammals.
• Over all mammals tested maximal running speed scales with Mb0.17, however the largest mammals are not the fastest and there is a curvilinear relationship of body mass and maximal running speed that yields an optimal Mb of 119kg.

Question 7

Bieweiner. 1989.

Answer 7

Scaling body support in mammals: limb posture and muscle mechanics.
• Larger animals are expected to have smaller safety factors than smaller animals (Bieweiner, 1982) however they actual maintain a safety factor between 2 and 4.
• Animals undertake a size dependent change in locomotor limb posture in order to reduce there relative PGF at larger sizes (larger animals have a more upright posture than smaller ones.
• There is a linear relationship between increase body mass and increasing EMA (effective mechanical advantage)

Question 8

Pollock et al. 1994.

Answer 8

Relationship between body mass and biomechanical properties of limb tendons in adult mammals.
• The biomechanical properties (ie. Tendon elastic modulus and hysteresis) are independent of animals, body mass and function.

Question 9

Bullimore et al. 2003.

Answer 9

Distorting limb design for dynamically similar locomotion.
• Animals must undertake systematic distortions in order to maintain dynamic similarity across a range of body sizes.
• Allometric measurements taken for limb moment arms show that the change in limb moment arm is a sufficient distortion to compensate for size independence of tendon elastic modulus.