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4-Legged Speed
Index:
|> Introduction
|> Speed and Endurance
|> Mechanical Disadvantage
|> Foot + Leg Design
|> Robots
|> Summary

<| Introduction
[Antilocapra americana]

Pronghorns are the true american speedsters. They are the fastest land animal in america, can hit tops speeds around 60 mph (100 kph), and can cruise for miles at 30 to 40 mph over rough terrain. The only faster land animal is the african cheetah - see (factbase). Upwards to 700,000 Pronghorn live in the high plains of the american west, where they have few natural predators, and none that can even come close to running them down. The major plains predator, the coyote, is maybe 2 times slower. Adult pronghorn tend to be about 3 feet (120 cm) high at the shoulders, and weigh upwards to 130 pounds (60 kg).

So, how is it there comes to be an animal which is so much advanced over any local natural predator? Does natural selection not apply here? In fact, in ancient times there were many large and fast predators in the american west, but for some reason, about 10,000 years ago, there was a large die off when many species became extinct. Today, on the plains, we still have bison, deer, pronghorns, and coyotes as the largest animals. Prior to the extinction, there were also various species of antelope, as well as horses, tapirs, elephants, mammoths, camels, deer, lions, saber-toothed cats, hyenas, cheetahs, wolves, giant beaver, giant sloth, and long-legged bears. The ancient north american lions and cheetahs were actually larger, by about half, than their african counterparts today. So, the pronghorn evolved in the evolutionary context of these predators, but survived them in the end. For more info on Pleistocene extinctions, see here: [1] [2] [3] [4] [5] [6]

Pronghorns are ungulates (hoofed animals), and the only members of the family Antilocapridae. About half of the people use the term "Pronghorn antelope", while the other half say they are not true antelopes, but closer to being a goat. For more info on ungulates, see here: [1] [2] [3] [4] [5]. For more on Pronghorns, see: [1] [2] [3] [4] [5] [6] [7] [8]

Brain Maffley [Maffley04] has written an article about the impact of human development in western Wyoming on the Pronghorn. Pronghorn have ancient and narrow migration routes between winter and summer ranges, and continuing development - especially fenches on ranches and gas wells on BLM land, as well as a "fenced-in" Interstate 80 corridor stretching completely across southern Wyoming - is severely impacting their ability to move over these ancient routes. In 1983, a rancher put up 28 miles of fences across one such migration path, and thousands of Pronghorn perished at the fences over the following 2 winters. Pronghorn apparently will not jump over fences, which deer will easily clear, but instead will crawl under as long as enough space is available. As stated below, Pronghorn apparently are ill adapted for jumping, despite their ability to run over broken ground at 60 mph.

<| Speed and Endurance
While most animals are built for speed or endurance, Pronghorns are built for both. Not only are they among the very fastest land animals, but they can keep their speed well above that of most other animals for long periods of time. In comparison, the cheetah is faster but not good over distance. During running, Pronghorn will hit rates of about 3 strides/sec, with stride lengths upwards to 30 feet each, topping out at speeds around 60 mph. For more on cheetahs, see: [1] [2] [3] [4] [5]

[muscles]
Pronghorn speed has to do with their unique body design. J.A. Byers [Byer03] studied Pronghorns for over 20 years, and euphemistically calls this a "four-chopsticks-in-a-bratwurst" body type. They have very long legs with extremely low mass, with most muscle located close to the torso. The lower leg segments are highly-elongated, and extremely thin. This body design is evident in the picture top-right. This design is similar to that of other ungulates, such as the horse, but here the extremities have much less mass and muscle - so the torque required for quick leg movement is that much less. At 3 feet high at the shoulders and 130 pounds tops, Pronghorns are much smaller, relatively-speaking, than other common american ungulates, such as horses, deer, elk, and moose. One imagines a flying inertia mass, propelled along by legs clipping the ground at high rates.

The pictures above and left also show that the rear-end is more heavily muscled than the front, which relates to ability to spring off the rear legs during running. Note the very noticeable rear superficial flexor tendon (corresponding to the Achilles tendon in man), which connects the "point of the hock" [tuber calcis, bone extension behind the hock] to the top of the lower thigh bone [tibia]. The tuber calcis is relatively long (cf, dog, point 26), which lengthens the torque arm pulling on the lower leg segment [cannon bone and hoof]. Many ungulates have a similar structure, which allows production of a lot of torque in the lower legs, from muscles located high up near the main body mass. The dynamics page shows the muscle-tendon arrangement of the legs of a horse.

The picture at left shows how Pronghorn attain a long stride during running. The extreme "pushed-back" position of the front legs, and criss-crossing between front and rear legs, of the animal on the right indicates the airborne phase of the stride is quite long.
[speed]
Note how the cannon bones of the front legs of both animals are held horizontally (apparently to aid ground clearance), how straight the backs are, and how the heads are carried upright - looking straight ahead.
[Borzoi]
Clearly, good frontal binocular vision is required for an animal going at high speed over broken ground - especially one with skinny legs. Judging from the positions of the legs of the animal on the left, a rotary gallop is being employed - the next 4 footfalls in order will apparently be RR, LR, LF, and finally RF.

Compare to the dog in double-suspension gallop (as shown at right). The dog's legs are held very similar to the Pronghorn's at this point in the gait, called the "collected" phase, but its back is greatly arched, and will straighten and stretch during the subsequent "extended" phase, which is one way in which dogs increase stride length, and therefore speed. Similar to the Pronghorn, the speedster Borzoi also has long and light-weight legs.

Besides that mentioned above, the following are some of the features which contribute to Pronghorn speed, as described in Byer's book:

  • the upper limb segments of Pronghorn [humerus and femur, cf dog, points 15, 23] tend to be relatively short, compared to the rest of the leg length, so that small movements of the bones above translate into much larger movements of the bones and feet below. Apparently, the humerus barely moves during walking, and moves only a couple of inches back and forth when the Pronghorn is striding at 30 mph. It moves more freely at full gallop.
  • during full gallop, Pronghorns do not flex their backs nearly so much as cheetahs, which are the "fastest" land animals at 80 mph (130 kph). See picture to right, and also notice similarity to the straight back of the running horse.
  • besides being very thin, the leg bones are a lightweight yet strong honey-combed structure. With little muscle and low mass in the legs, the torque required to move the legs is reduced, and the speed of movement is increased.
  • Pronghorns apparently do not like to jump, related apparently to the leg bones being so thin. They will crawl under fences or walk until they find an opening, rather than jump over, like deer. When they do jump, they land on their back legs in a peculiar fashion, rather than front legs like other quadrupeds.
  • Pronghorns and other animal running specialists have scapula and humerus, but lack clavicle and coracoid bones. The scapula is the "shoulder blade" in back on humans, and the clavicle is the "collar bone" in front. Absence of clavicles in ungulates apparently increases range of leg movements.
  • [ref, Mckean74] compared to domestic goats, and corrected for body size, Proghorn's hearts are twice as large, they have 50% more blood, 60% more hemoglobin, and 33% more red blood cells. The windpipe is large, and airway resistance is half.
  • maximum rate of oxygen consumption is far above that of most other land mammals.
  • Pronghorns have 4 different high-speed gaits [????]. When Pronghorns run in a pack, there is 97% synchrony of gait and 92% synchrony of lead foot.
  • the brain is prevented from overheating by 4 "heat-exchangers" located on the face near the eyes. In these exchangers, venous blood, which is cooled in the nose and ears, is routed through fine capillary networks which run adjacent to similar capillary networks carrying arterial blood from the heart+lungs to the brain. The heat is drawn off from the arterial blood and passes with the cooler veinous blood back to the heart and away from the brain.
  • with human runners, there tend to be "optimal" body types specialized for particular races - ie, sprinters tend to be very muscular especially in the lower body, while distance runners are usually thinner with much muscle mass. Pronghorns have found a way to combine speed and endurance, but doubtless few people would wish to have such a body type - robots, on the other hand ....

    Additional info about Pronghorns is given on this page Hunting101:

  • windpipes are 2" in diameter, compared to 3/4" in humans of similar size - the animals will hang out their tonques to allow more air to pass. Lungs are 3X larger than in similar sized goats.
  • a large liver provides a quick glycogen boost.
  • Pronghorn leg bones are significantly stronger than the much thicker ones of cows.
  • researchers have measured 13 different gaits, from "very slow diagonal walk" to "lateral gallop" (the fastest) - the gallop shows little rocking motion, which apparently helps maximize speed.
  • antelopes have eyes measuring about 2" diameter, which rank as some of the largest in the animal world. They also have very wide peripheral vision.

    The following page provides more details about speed runners - Animal Diversity page:

  • ways to increase stride length - (a) run on the tips of the toes, (b) lengthen limb elements (eg, cannon bone), (c) allow the scapula to swing back + forth (improved by reduction of the clavicle), (d) add spine flexing during bounding and galloping (cats and dogs do this, ungulates not as much), (e) use gaits which lengthen stride and distance traveled when feet are off the ground (eg, double suspension gallop), (f) place muscle insertions close to joints (ie, shorten the torque arm on the powered side).
  • ways to increase stride rate - (g) place muscle insertions closer to joints (ie, bones on which they insert move faster), (h) have multiple joints moving (eg, scapula + humerus + radius/ulna + cannon + digits), so individual effects are cumulative - notice the large amount of accumulated bending in the joints of the cheetah, (i) fuse the bones in the limbs for strength (eg, single cannon versus 5 metacarpals) and decrease the mass, to reduce the swing weight, (j) decrease number of digits and foot mass, (k) reduce muscle mass in limbs (tradeoff via increased tendon use for pulling bones and stabilizing joints), (l) simplify limb joint design to have maximum movement front-to-back, with less range of sideways and twisting movements (requires less bone structure and muscle-tendon complexity).

    For more info on antelope speed, see: [1] [2] [3] [4]. Some videos available on-line: [1] [2] [3]

  • <| Mechanical Disadvantage
    ['extended' dog hock]

    Here's an interesting idea. Related to items (f) and (g) in the previous section, some animals use 2 sets of muscle insertions on the bones, one further away from the joint (with longer slower-moving muscles, and better torque) to start the limbs moving, and another closer on (with shorter faster-moving muscles) to move the limbs fast. McKean mentions that this works in a similar fashion to a gearshift on a car. This idea might be usefully adapted to robots.

    Lyon50 discusses muscle attachments, joint torque, and mechanical advantage regards the rear leg of the dog. The diagram at right illustrates this situation. Here, the os calcis (bone extension above the hock, dog point 26) is shown 3X normal length, for illustrative purposes. The paw on the ground acts as a fulcrum point F, and the muscle+tendon (connected to the femur, dog point 23) apply power at P to move the weight of the dog acting through the hock joint at W. That is, the weight is pushing down through the leg, and attempting to bend the hock joint backwards, and P is resisting this movement to hold the leg straight.

    Clearly, the longer the bone extension P-W, the easier time the muscle will have. However, at the same time, the longer is length P-W, the more the muscle will have to contract to move point W the same distance. However, muscles can only contract so far and so fast, so there is a tradeoff here in mechanical advantage of long torque arm versus distance and rate the joint W can be moved. In the real dog, the os calcis is shorter than shown here, so nature took the course of less mechanical advantage and less distance moved, in exchange for higher speed of movement.

    Lyon mentions that: "... all applications of levers in nature, our dogs included, work to a mechanical disadvantage because it is more important to get speed and action than to preserve energy ... it is because of action and not because nature thought [an overly long os calcis looked bad], that mechanical advantage was sacrificed for speed ... you will find this same sacrifice in every bone and muscle placement in the dog ..."

    Putting Lyons' ideas together with those of McKean's above, we can see how a combination arrangement of some muscles with insertions farther from joints and some with insertions closer to joints can work together to improve both speed and power.

    <| Foot + Leg Design
    [hooves]

    The diagram at left shows how the antelope leg compares to that of other ungulates, such as the elk and horse. In all 3 cases, the cannon bone beneath the knee is a single bone which is essentially a "fused" homologous form of the 5 metatarsal and metacarpal bones of the lower dog leg (points 20 and 28), and the bones on the back of the human hand and foot. Given its long length, this fusing into a single bone no doubt gives the cannon bone a strength lacking in the 5 separate bones of the other animals. In Pronghorn, the cannon is about 9" long, but only as thick as a human index finger.

    To get a feel for what it would be like to have such a cannon bone leg extension, imagine running on your fingertips at 60 mph .... except imagine that each hand has only "1" finger instead of 5, and that it's 3X longer than normal.

    The 2 phalanges [toes] of elk and antelope correspond to fingers 3 and 4 of the human hand (counting from the thumb), and apparently represent an "adaptation" where the other 3 toes of earlier vertebrates were reduced during evolution. The toes have somewhat independent movement, which is apparently advantageous when running over broken ground, as compared to the horse which has only a single toe [hoof]. The foot has lost the dew-claws present in other ungulates like deer, elk, and moose - one suspects they would catch on the brush during running.
    [proghorn hooves]

    The sole pads of the Pronghorn are shown at right [front foot on left]. The entire foot bottom is one big pad, no doubt for heavy cushioning over hard ground. Why the toe has evolved to such a sharply-pointed shape is an open question - but this is similar to related species, such as deer, sheep, and goats. From the looks of it, the pads of the Pronghorn present a lesser amount of hard toe rim directly to the ground compared to the others, which seems reasonable for a foot that runs at high speeds over broken terrain.

    <| Robots
    [MIT quad]
    Will a robot ever run as fast as a Pronghorn, or climb as well as a Mountain Goat as discussed on the 4-Legger Climbing page?

    Several years ago at MIT, Marc Raibert was already experimenting with both bipedal and 4-legged robot designs that had some resemblance to running in Pronghorns. His robots had rather lightweight bodies with long thin legs, and were powered and controlled by long tethers, since a major deficiency exists in regards to good power sources for walking robots. Raibert's robots used pneumatics for leg power, and his robots had a large degree of "springiness" in their steps - cf, Robert Full's work regarding energy storage and recovery in elastic elements in muscle and tendon.

    <| Summary
    [big eyes, and wide set]
  • Pronghorns are the second fastest land animals, behind cheetahs.
  • while most animals have bodies specialized for either speed or endurance, Pronghorns are designed for both.
  • Pronghorn speed is related to their having long, thin, and very low-weight legs, which move at high stride rates and with long stride lengths. Main muscle mass is located close to the torso and long tendons, with minimal muscle mass, control limb movements.
  • Pronghorn endurance is related to the animal's large cardiovascular capacity, including a large heart, high hemoglobin blood, and large lung capacity with low air resistance. Oxygen consumption is almost 3X that of animals of similar size. They also have special heat exchangers to cool the blood flowing to the brain.
  • the lower limb of Pronghorn is long and thin, and terminates in 2 well-padded toes which have somewhat separate suspension action. This design is apparently well suited to fast running over broken terrain.
  • Pronghorns have large eyes and excellent vision. They have wide-field peripheral vision - we suspect they also have excellent "binocularity" of vision, since this would be critical for any animal which runs at such high speeds.

  • References:
  • [Byer03] - Built for Speed, A Year in the Life of Pronghorn, by John A Byers, Harvard Univ Press (2003).
  • [Lyon50] - The Dog in Action, by McDowell Lyon, Howell Book House (1950).
  • [Mckean74] - "Comparison of selected cardiopulmonary parameters between the pronghorn and the goat", by T.M. McKean and B. Walker, Respiratory Physiol, 21:365 (1974).
  • "Running energetics in pronghorn antelope", by S.L. Lindstet et al, Nature, 353:748 (1991).
  • "An analysis of locomotor movements in pronghorn antelopes", by R.E. Bullock, Canad. J. of Zool, 60:1871 (1982).
  • P. Myers, Animal Diversity Web - this site is an excellent online resource regards Pronghorns.
  • [Maffley04] - "Putting the Squeeze on Pronghorn", by Brian Maffley, Nat'l Wildlife mag, Apr/May 2004.

    Books about antelopes:

  • Racing the Antelope by Bernd Heinrich (who also has a classic book about the intelligence of Ravens).
  • American Pronghorn by John A. Byers.
  • Antelope Country by Valerius Geist, Michael H. Francis.

  • Misc: [1] [2] [3]

    <| TOP


    © Oricom Technologies, May 2004