Bakker (1972) showed that these trends are also seen in lizards and not only that but the energetic costs are equal to or somewhat less than their mammalian counterparts of similar size. The essential difference between the two concerns the period that the additional energy is available, the animals endurance. Lizards typically tire quickly when running at speed although this probably relates to a considerable dependence on anaerobic glycolysis for strenuous activity.
Larger animals are able to carry around bigger energy stores (in the form of fats and glycogen). This combined with the lower energetic cost of locomotion per unit mass and lower BMR, means that larger animals are able to forage for longer between meals. Smaller animals are restricted by these factors and are unable to travel long distances without a meal. This is an important factor in determining the locomotory habits of differently sized animals. Camels are able to go for long periods without food and travel great distances whereas a field mouse has to eat almost constantly in order to survive.
Structure
The structure and organisation of the skeleton and its related muscles and tendons is a direct response to the effects of gravity on the mass of the animal. Increasing the size of any object will increase the effects gravity has on it. There are two ways of increasing the mechanical strength of bone in response to such a size increase. The physical properties of the bone itself can be modified to be more rigid or have a higher tensile strength, or the skeleton itself can become more massive. The former doesn’t contribute greatly to adjustments in the skeleton to a change in the body mass. The more important factor is the changes in shape and relative mass of the skeleton.
This assumes that the skeleton is primarily adapted to withstand the static forces of gravity such as those experiences in sitting or lying down. Obviously this is not the case as the skeleton has to cope with the rapidly changing transient forces (such as compression, torsion and tension) that are generated by vigorous movements.
Damage to any of these structural elements in the wild is a serious matter for the animal as it will affect its fitness. However animals in the wild are seen to move at full speed over rough terrain or leap or fall large distances onto hard surfaces without injuring themselves. Rodents will quite happily leap off a table onto a tiled floor and antelopes gallop at full speed over difficult terrain. What determines such dangerous locomotion is closely tied in with the physical properties of their locomotory system. Each element in the system has what it referred to as a safety factor, the ratio of the force required to break the material against the maximum normal force sustained. Deriving this can be difficult, especially the factor of maximum normal force sustained as it requires data to be obtained from the wild. Also no two individuals are the same so safety factors vary within a population. Studies performed by McNeill Alexander on dog jumping found that the bones in the system usually operated with a safety factor of 3, that is the maximum normal force sustained was only a third of the force required to break the bone. Muscles and tendons operate at a much lower safety factor and when taking these reading into account the dog operated at a safety factor of 1, at the very edge of breakage in the system. Although the maximum normal forces are often only local and transitory, so the amount of breakage is much lower than expected.
Central to understanding how the animals in the previous example are able to perform such movements is the relationship between the forces encountered through locomotion (including gravity) and the safety factors of the elements involved. Smaller animals have smaller locomotory forces (including inertia) due to their lower mass, and the opposite is true for larger animals. Since the physical properties of the structural elements are pretty much the same regardless of body size, the smaller animals will have higher safety factors than the larger and be able to perform more dangerous movements as their skeletons can withstand larger additional forces before breaking.
This is best illustrated by looking at an elephant’s locomotion. An elephant’s larger mass requires its mass to always be distributed between two legs, and all four contribute equally to the propulsion and support of the animal. Like all large animals (including rhinos camels and buffalo) they move very slowly and carefully over difficult terrain as their skeletons operate with such a low safety factor that the slightest trip or fall could result in a breakage. Rats will readily hang from a cage by one toe but it takes a long time to train an elephant to stand on one leg and it does so very slowly as it is pushing the limits of its skeleton. In fact most large animals avoid situations where dangerous locomotion is required that is why you do not find elephants on mountains and why they often take a longer well worn route to a watering hole rather than travelling on unfamiliar terrain. This is why elephants can be kept in enclosures by digging a steep sided shallow moat around, an obstacle a smaller animal would have no difficulty getting over.
The posture taken by animals for locomotion is also affected by their size. There are two types of stance adopted by modern tetrapods. Parasagittal posture (erect limbs) is seen in larger and cursorial mammals. This provides correct support for the larger body mass and the ability for vertical displacement, which shall be demonstrated later as being important for cursorial movement. Smaller mammals and lizards adopt a non-parasagittal posture (sprawling limbs). Coombs (1978) showed that size has a direct effect on locomotive abilities. Small sized animals have constraints on their endurance and maximum speed and so preclude the enhancement of “cursorial ability” seen in larger animals. The correlation between size and sprawling limb posture appears to apply to both small mammals and reptiles. Jenkins’ (1971) work on the subject revealed that in small mammals, limb motions may be closely comparable to those seen in lizards i.e. propodial motion is markedly non-parasagittal. This is also extended to similarities in energy requirements, as the muscular effort required to prevent the collapse of the flexed limbs on both lizards and mammals of the same mass is likely to be comparable as they are both working against the same forces.
The concept of stability must also be taken into account when considering animal size and subsequent posture. Non-parasagittal limb posture provides a great deal more stability than parasagittal and since smaller animals are toppled by smaller forces due to their low mass and inertia a non-parasagittal posture is the most suitable.
Process of Locomotion
So far we have seen how size determines the energy available to locomotion and the structures that are required to perform it. In living systems energetically efficient movement cannot be entirely attributed alone to one particular element, energy, muscles, bone, tendons and behaviour are all intertwined to produce a form of locomotion that is the best compromise for the situation. There are few solutions to the problem posed by terrestrial locomotion, most animals’ use legs as their primary mechanism of transport, the only other method known to myself is seen in the snakes, which use their entire bodies to crawl along surfaces. Crawling has a much lower energy requirement for transport compared with other terrestrial animals. In fact the net cost of transport is only ½ that of a lizard of similar size and mass and 10 times less than that of a mammal. Although the frictional resistance between the animal and the ground is obviously quite high in locomotion, the internal resistance (i.e. that of the joints and muscles) is presumably low as this type of locomotion does not involve as much joint articulation as locomotion using legs.
Travelling in a straight line using legs entails two components which are easily affected by size and thus determines how the action is performed. Firstly there is a horizontal swinging of the legs backward and forwards, the length of the period akin to a pendulum in motion, the longer the legs the larger the stride. Secondly the weight of the body is also raised at each step working against gravity. These vertical movements are much more evident in the faster gaits, for example a jockey is seen to be bounced up and down whilst their horse is trotting or galloping.
Compared to using wheels as the primary mechanism for locomotion, legs appear to be extremely inefficient. The concept of the wheel is one of the few engineering principles that has not established itself in multicellular organisms. There are several reasons for this, there is a high associated cost of maintaining structures that rotate on a small axis, and the fact that wheels are only effective on level ground whilst legs can be used to jump and climb, something impossible for wheels to perform. This inefficiency is not as pronounced as originally thought, animals have several tactics for reducing energy expenditure during locomotion, they possess elastic energy storage systems and their movements closely resemble that of a pendulum.
A major advancement in understanding the dynamics of locomotion came in the 1970’s when it was realised that the energy involved in all these different movements alternated between kinetic and gravitational potential energy. For example the path of the hips in the vertical plain in walking is comparable to that of a pendulum swinging upside down. The exchange between the two types of energy account for 60-70% of the energy required to raise and accelerate the body, so muscle contraction only needs to provide the additional 30-40%, a much lower value than originally expected.
Walking
For long journeys over difficult, rough terrain, or through dense undergrowth quadrupeds and bipeds (except birds and some very small mammals) prefer to walk. Walking is a gait in which there is no suspended phase at each stride. The trailing legs do not leave the ground until they have pushed the body forward and its weight has rocked forward onto the other leg. The weight of the body is always suspended by half of the available limbs (2 for quadrupeds 1 for bipeds), offering stability and the ability to come to a complete stop at any point in the stride and not lose balance, particularly important in the smaller animals.
The stability provided by walking makes it the most suitable form of locomotion for animals that have to travel over rough or unfamiliar terrain and those that operate with smaller safety factors, i.e. larger animals. Elephants and rhinos walk hundreds of miles without falling or tripping over, and they only employ faster gaits for a hundred meters or so and even then only when absolutely necessary.
For most animals, the energy economy of walking is probably just as important as the stability. There are three main reasons why the cost of walking is low:
- The legs are swung rather than pulled forwards and backwards at each stride and the bending and extension of the joints is minimal.
- The forward momentum of the body swings it upwards at the end of each stride and the gravitational potential energy thus obtained is converted back into kinetic energy; which accelerates the body forwards and downwards on the next stride.
Both these mechanisms require some contraction of the limb muscles but reduce the need for active contraction of the muscles. For this mechanisms to work correctly the body’s centre of mass must be in the correct place. This will have a big effect on how the animal moves when this is not the case, i.e. over rough or sloping terrain.
- The stepping frequency is relatively low in walking, so slow contractions involving the slow phasic muscle fibres are normally sufficient to power the movements. A gait that uses only slow contractions uses much less energy than one in which muscles perform cycles of contraction and relaxation at a high frequency.
Walking speed has a maximum velocity which is not limited by the power production of the muscles or by their maximum shortening velocity but because the downward acceleration of the body’s centre of mass from its highest point in the stride (1/2 way through it, like an inverted pendulum) cannot exceed the acceleration due to gravity (9.812ms-1). Because of this restriction the size of the animal determines how fast it is possible to walk.
This gait, although slow requires little muscle energy so its energetic cost per km per kg body mass is smaller than for the faster gaits. Compared with galloping, leaping or climbing, walking involves little wear or damage to the musculoskeletal system. Although there is a maximum speed at which an animal can walk, animals tend to walk at an intermediate pace. For most animals the energetic cost of walking does not increase linearly with speed and so there is an ideal walking speed at which distance travelled per unit energy is maximised.
Larger animals tend to have longer legs which enable them to use fewer, longer strides than smaller animals to cover the same distance. Because the number of strides needed is lower the frequency of the strides can also be reduced allowing for slow phasic muscles to be used, which economises energy, and for the animal to operate within its lower safety factors. Small animals require more strides to cover the same distance and so must increase stride frequency to cover the same distance in the same time thus requiring more energy to do so but due to their smaller mass they can still operate within their safety factors.
So far we have only considered the effects of walking on a flat level surface. The second graph regarding the energetic costs of locomotion for differently sized animals travelling at different speeds gives us some hint as to the effects this may have regarding an animal’s size. In order to move up a slope additional work must be done against gravity, which requires additional energy. It is clear from the graph that in order to liberate this additional energy for the ascent the animal must slow down. Larger animals must slow down more in order to liberate enough energy compared to smaller animals. Difficult terrain also imposes another energetic cost to animals, walking on soft sand or sticky mud disrupts the swinging motion of the legs, each leg must be placed into position requiring more muscular work. The same is true for traversing boulders which also requires intense concentration. Whether a terrain is flat or difficult is all relative to the animal encountering it. A camel may find a pebble landscape smooth and flat, whilst a mouse would see it as a very difficult terrain to travel over.
Faster Gaits
Terrestrial animals use several different gaits when moving fast, the most common being:
In these fast gaits, the body is suspended during at least one phase of each stride and the amplitudes of the vertical movements are much more pronounced. At other phases the body’s weight is briefly supported by one, two or (more rarely) 3 legs in contact with the ground. Running animals move faster because their strides are both longer and more frequent, but these gaits are much less stable than walking. Instant stopping is impossible and tripping or misplacement of feet is much more likely to result in a fall. It also requires a different set of muscles and tendons to be used.
There are not many conclusions to be drawn with respect to the impact size has on these faster gaits but there are some. The changeover from walking to a faster gait always occurs at roughly the same speed in animals of the similar leg length (Taylor 1974), this is related to energetic efficiency as mentioned before. Since smaller animals tend to have shorter legs they switch to a faster gait at much lower speeds. Hopping and galloping are both undertaken by intermediately sized animals but larger animals tend to gallop because their larger mass and lower safety factors would not be supported by 2 legs or withstand the huge impact forces encountered during a hop. Smaller animals on the other hand can withstand these forces and so for most bipedal vertebrates hopping is the preferred gait. Thus galloping is the usual mode of travel in mouse sized animals but rhinos and buffalo use the gait very sparingly and elephants not at all.
Larger animals also have more flexible backs which are used in conjunction with specific muscles to bring the hind legs further forwards hence increasing the stride length. The effect of size appears to have an impact on the maximum speed possible. The fastest animals tend to be those of intermediate size as they are the best compromise between leg length and safety factors of the musculoskeletal system. Cheetahs and hares are the fastest of all animals and although they have some specific adaptations for galloping (i.e. highly mobile shoulders through a reduced clavicle) they are still in the intermediate size group of terrestrial animals.
Summary
From this essay it has been shown that size has a great impact on the patterns of walking and similar locomotion, which can be summarised as follows. The major cost of locomotion is supporting the animal’s weight, which determines the type of posture adopted. Large mammals, such as horses and elephants, stand on fairly straight legs but small animals crouch. This latter posture is efficient for fast acceleration and leaping but is not favourable for efficient swinging of the legs so smaller animals are proportionally more muscular. Small animals if they make a journey at all might as well run as travel at maximum speed only involves expending a little more energy and a slightly increased risk of injury. Larger animals generally have longer legs which enable them to use fewer, longer strides than is possible for smaller animals covering the same distance. Longer legs also allow higher speeds with lower stride frequencies. Smaller animals achieve the impression of speed through frequent and abrupt changes in direction using limbs with high safety factors. Fewer more prolonged cycles of muscle contraction use much less energy than a greater number of brief cycles of contraction and relaxation. Swinging rather than placing legs into position requires a lot less muscular power but it depends on the terrain relative to the animal. Most of the fastest animals on flat plains tend to be those of intermediate size 10-50kg with neither of the extremes being very fast.
Conclusion
It is important to remember that there is no “ideal” form of locomotion. Throughout this essay I have outlined the restrictions placed on locomotion by different body sizes but that is not to say that one body size it better than all the others. An animal is specifically adapted to the niche it exploits and its locomotion is a complement and compromise of all the physical (and genetic constraints) that the animal encounters.
Bibliography
McNeill Alexander, R.N. and Goldspink, G. (1977) Mechanics and energetics of animal locomotion 1st edition Chapman and Hall
Pond, C. (1995) Size and action (Animal physiology book three) 1st edition The Open University
Rewcastle, S.C. (1981) Stance and gait in tetrapods; An evolutionary scenario. Symp. Zool. Soc. Lond 48 239-267
McNeill Alexander, R. (1981) The gaits of tetrapods: Adaptations for stability and economy Symp. Zool. Soc. Lond. 48 269-287
Pough, F.H. Heiser, J.B. McFarland, W.N. (1989) Vertebrate life 3rd edition Macmillan
