Terrestrial locomotion includes burrowing, crawling, walking, running, hopping and jumping and all involve mechanically variations on lever-joint systems operated by muscles. Biomechanics is the application of engineering practice based on physical principles to biological problems with Newtonian mechanical components. Locomotion on land is a good example of such an application.

       Here are some terrestrial modes of locomotion (Figure 1). Consider the inch worm (A). Such caterpillars use a "two anchor" principle, first anchoring the anterior end of the animal drawing the body into a bow shape and then anchoring the posterior end and extending the body. (B) Bivalve mollusks such as the freshwater mussel Anodonta use the foot in a "one anchor" manner. To burrow, the clam extends the foot through the substrate, dilates the end of the foot to anchor the tip of the foot and then draws the body through the substrate using the contractile muscles of the foot. Peristalsis (D) is a common manner for soft bodied animals to move. Extension of the anterior segments of an earthworm (by contraction of the circular muscle around the body) advances the animal ahead of a contractile wave of shortened segments (produced by contraction of the longitudinal muscles of the body wall). As the wave of shortened segments moves down the body, the animal advances forward at the same rate (For an alternative description of this motion, click here). The "bristle-like" setae help to anchor the shortened segments so that the movement can be forceful and the animal can burrow. Serpentine crawling (E) is the bending of an elongated body form around stationary objects and pushing past these objects to advance. Snakes can move rapidly on land, pushing past stones, grass or other objecte. This mode also works well in unstable substrates like sand (for example the sidewinder snake) and in water it converts naturally to undulatory anguilliform swimming.

The locomotory strides of a salamander involve repeated undulation of the body from side to side and alternate movement of the feet. The bends in the body do not travel along the body, as in serpentine locomotion, but are stationary waves. The center of gravity (*) is kept within a triangle formed by the feet that remain on the ground. (Modified from Roos 1964.)

       Differences between walking and running in vertebrates include a shift in the mode of operation of the limbs, stride length and velocity. In bipedal walking, the body acts like an inverted pendulum. At each stride, a foot is planted and the forward momentum of the body forces the body to rise over the stiff leg and then fall while the other leg is swung forward and planted. In this way, the kinetic energy of the forward motion is stored as potential energy when the body rises and converts again to kinetic energy when the body falls. In bipedal running, the stride length is increased markedly and there are times when both feet are off the ground. As the body fall from the airborne part of the stride, the foot is planted and much of the kinetic energy becomes stored in elastic elements of the tendons and muscles (by stretching the Achilles tendon). The stretched tendon acts like a loaded spring that releases the stored energy when the muscle shortens at mid stride. The kinetic energy released by the tendon then adds to lift and forward motion and a portion is again stored when the other foot is planted at the end of the stride. This accounts for the "bounce" of the running gait and the intermittent storage of kinetic energy in elastic elements.

       Quadropedal vertebrates often have multiple gaits. Horses and dogs for instance have distinctly different gaits including walk, trot and gallop as well as minor modifications of these (lope, pace and canter). The study of locomotion was greatly forwarded by a bet made in Victorian times that in the gallop, one foot of the horse's feet must be on the ground in all parts of the stride. Resolution of this bet (yes, all feet DO leave the ground in part of the stride) advanced biomechanics and produced the first high speed cinema camera!

Hopping and jumping. Kangaroos, many birds, mice and humans use hopping either occasionally or as the standard mode of locomotion. Hopping involves simultaneous movements by both (hind) limbs simultaneously to effect an intermittent air borne gait that like running relies on the storage of kinetic energy in elastic elements. In Figure 3 is depicted the pattern of hopping in a kangaroo. In the experiment, the kangaroo was taught to land on a platform with strain guages attached so that the forces involved could be measured. For a large animal, aerodynamic drag forces can be ignored. Force (F) was measured in Newtons in the vertical (Fy) or horizontal Fx) directions. Note that Fy exceeds body weight by more than two fold during the landing. This represents the loading of the elastic elements in the pair of Achilles tendons. With the release of this energy, the recoil force exceeds the body weight, hence the animal is propelled peopened upward into the airborne portion of the jump. Active muscle contraction adds forward mommentum to the jump (note the negative dip in the Fx recording.

       Figure 4 is a log-log plot of metabolic cost vs. body size. Within a particular mode of transport there appears to be a close relationship between body size and metabolic cost of transport. Different modes have different inherent costs (eg. burrowing vs walking). For large animals however, the cost of transport per unit mass is more econimoicai than for small animals.

       The advantage of gait changes is made clear by Figure 5 where initially there is an increase in metabolic rate with increasing velocity when the animal is involved in pentapedal locomotion (forelimbs, hindlimbs and tail). At higher velocities, the kangaroo changes to a hopping gait and then the velocity can increase markedly with little increase in metabolic rate. Indeed the metabolic rate actually decreases at higher velocities. Clearly the kangaroo has adapted marvellously to high speed 15-20 kan/h) hopping. Generally speaking, gait changes take advantage of certain patterns of limb movement that are more efficient for locomotion at a given velocity. In this way, the animal minimizes the overall cost of locomotion.

       Flight. Air has a much lower density than water (1.18 kg/m3) compared to water (1000 kg/m3) so air offers much less drag than water (an advantage) but does not offer substantial buoyancy (a disadvantage). Most flyers rely on aerodynamic lift to counteract their body mass. In a glide the animal uses the wing as a simple aerofoil and the relative motion of the animal is forward and downward. The air flow over the wing thus is upward and backward. By angling the front of the wing upward relative to the air flow, the forward thrust balances the drag forces while the wing shape still provides sufficient lift to keep the animal airborne. The net glide path however is still downward unless the animal selects behaviourly updrafts that can allow this sort of flight to continue. There is no direct metabolic cost to gliding, other than the muscle contraction to keep the wing stiff. Generally, only relatively large flyers (eagles, hawks, vultures, albatross) are capable of prolonged gliding.

       In flapping flight the wing attitude relative to air flow over the wing is constantly changing, hence it cannot be analyzed as a simple airfoil. A flying animal experiences three types of drag forces: drag on the wings (prorde drag), drag on the body (parasite drag) and the drag induced by the wing generating lift (induced drag). Overall, the power requirements for flapping flight must overcome all three drag components. Streamlining of the body and wings reduces profile and parasite drag. During the downstroke of flapping flight the wing will provide lift for large and small wings much as an oar provides propulsive force when dragged through water. In the upstroke, large wings can still act as airfoils and provide some aerodynamic lift but varying amounts of forward thrust. The wings of small flapping fliers (insects) only provide forward thrust during the downstroke. However, for large flyers, for example ducks and loons, the up and down strokes of the wing are minor motions relative to the forward velocity and then the relatively immobile portions of the wing near the body act again as simple airfoils and provide forward thrust as well as aerodynamic lift. The membranous wings of bats are not good airfoils, hence bats seem more to "row" through the air rather than use the shape of the wing to provide lift. Interestingly, there exist minimum power requirements for flight in flapping fliers such that there is an optimal velocity for flight. (See the "budgie", budgerigar in Figure 6). Above and below the optimum velocity there are increases in one or more of the drag components.

Measured metabolic cost of flight for birds and a bat compared with the general shape of the curve calculated from aerodynamic theory. (From Rayner 1979; Alexander 1982.) - Power in Watts/kg; - The Arrow indicates optimum velocity for budgerigar

       The final graph summarizes the metabolic cost of the various forms of locomotion. Figure 7 shows that (as one would expect) burrowing is very "expensive" metabolically as a means of transport. Walking/running is less expensive than burrowing, but is more expensive than other modes of transport. Flying is more efficient than running for animals that have the appropriate size characteristics to allow this mode of transport. It is restricted to smaller animals, approximately 0.001g (mosquito) to 1000 g (loon). Surprisingly, swimming is less expensive metabolically than either walking or flying. Also superimposed on the graph are the fuel costs for transport by some human made devices. The most expensive of those listed being the helicopter and the least expensive being the freight train and steamship. Generally, aquatic locomotion is aided by buoyancy considerations that eliminate the need for lift in aerial flight or the effects of gravity in terrestrial locomotion, hence its relative efficiency.