The largest terrestrial animal of today is the four to seven ton African Elephant. The Woolly Mammoth was another 'modern day' large terrestrial animal since it went extinct only 4,000 years ago; it weighed around six tons. When comparing mass, the six-ton Ankylosaurus is not a problem since it would fit right in with these large modern day animals. Even at nine tons, the Triceratops is surprising large and yet by itself it might still be an explainable outliner. However, the T-Rex brings even more questions because not only was it heavier but its weight was supported on only two legs rather than four. Once we get to the largest of dinosaurs, - the sauropods - all hope of reconciling the incongruities is gone.

Within the last couple of decades, paleontologists have discovered a few super sauropods that are even larger than the Brachiosaurus. These super sauropods - the Argentinosaurus, Patagotitan, and Titanosaur - are approximately three to five times the mass of the Brachiosaurs and so they are just as massive as the largest present day whales. To create an exhibit of the Titanosaur paleontologists have made fiberglass cast of recovered fossilized bones. One of these Titanosaur exhibits is at New York's American Museum of Natural History while another Titanosaur exhibit is at Chicago's Field Museum of Natural History. Please make vacation plans to see this incredible large dinosaur!

The Relative Bone Strength and Relative Muscle Strength Problem

Relative bone strength can be defined as the strength of the bone divided by the weight being supported by the leg bones. Likewise the relative muscle strength can be defined as the strength of the animal divided by its weight.

The relative bone strength and the relative muscle strength are grouped together because they are similar scaling problems. For both, strength is function of the cross-sectional area. If we look at the longest length of a bone or muscle and then imagine cutting this length in half, the newly exposed area is the cross-sectional area. The strength of either a bone or a muscle is directly proportional to this cross-sectional area, so both bone and muscle strength are two dimensional attributes. Yet body mass is a function of volume, a three dimensional attribute. In accordance to Galileo's Square Cube Law, as we look at increasingly larger animals, the mass of each animal increases at a faster rate than the cross-sectional areas of either the bone or the muscle. Thus, larger animals have less relative muscle strength and less relative bone strength than that of smaller animals.

Horse Race

In regards to relative bone strength, the larger animals are at a much greater risk of breaking their bones than the smaller animals. The likelihood that a broken bone will cut an animal's life short is a strong possibility for the larger animals. This possibility of broken bones affecting the animal's survival thus becomes a limitation on the size of the largest animals.

For example, a race horse can easily shatter a leg just by running. These breaks usually occur at various places within the lower front leg. Yet it is possible for other parts of both the forward legs and the rear legs to be injured as well. This indicates that the breaks are not a result of a specific inherent weak spot within the leg. But rather it is the simple physics of the heavy weight of the horse producing an impact that exceeds the material strength of the bone within the leg.

Clydesdale Horses Ploughing

Another indication that these 500 kg animals are pushing the size limitation are the problems that arise when attempts are made to heal one of these magnificent animals after they have shattered a leg. Horses often sleep standing up as a successful evolutionary survival technique so that they can quickly flee from predators. But if day and night a horse is able to stand on only three good legs and it does this for an extended time, these overloaded good legs may develop a condition known as laminitis. Soon it becomes just as painful to stand on these legs as on the original broken leg. It is because of these and other associated complications that it is often more humane to put the horse down rather than have it suffer through its final days.

While it is easy to show that the largest animals have the lowest relative bone strength and the lowest relative muscle strength, it is more challenging to determine precisely the largest possible terrestrial vertebrate. One problem is that as we look at ever larger animals they change their behavior so that they can stay within the limitations.

While race horses are large they are far from being the largest terrestrial animals. Weighing in at about a ton, Clydesdales have twice the mass of the typical racehorse. Looking at even larger terrestrial animals, the typical male African elephant has a mass of five to seven tons.

Bison Roaming Yellowstone National Park, Wyoming

Here the lower muscle strength of the larger animals is actually beneficial in reducing the possibility of them carrying out potentially dangerous activities that may cause a broken bone. By running more slowly or in the case of elephants by running more slowly and not jumping, the largest terrestrial animals usually manage to avoid the higher impact forces that may break a leg.

Bones break when the stress applied to bone exceeds the bone material’s breaking point. To get an idea of the greater risk that larger animals have of breaking their bones, we can compare the stress on the leg bones of animals as they do nothing more than support their own weight.

The table below lists a representative selection of mammals ranging from the smallest to the largest. From the measured data of the front and rear leg bone circumferences the amount of cross sectional bone area is determined. The stress being applied to the bone while the animal is standing can then be calculated by dividing the weight of the animal by the bone cross sectional area. The final column on the right is the stress on the animal’s legs as it is standing.

Stress in the Leg Bones of Mammals while they are Standing

In comparing mammals while they are just standing, the bones of the larger animals are subjected to greater stress than those of smaller mammals. The larger mammals are at a much greater risk of breaking their bones than the smaller mammals.

The stress on bones can be many times greater when an animal is landing after a fall. The stress on the bone that comes at the end of a fall generally depends on how large the animal is and how far it falls. A mouse can easily survive a fall from a tall building. At the other extreme, an elephant can be contained with a one meter (about three feet) deep dry moat, because an elephant falling from this height would most likely result in one or more fractures. There is truth to the expression “the bigger they are the harder they fall”.

Just as the largest animals have the lowest relative bone strength, it is also true that the largest animals have the lowest relative muscle strength. Absolute strength can be defined as how much weight an animal can lift regardless of the animal’s own weight, and clearly the larger animals have greater absolute strength than the smaller animals. But when we look at relative strength, the lifting ability of an animal relative to its own weight, it is the smallest animals that have the greatest relative strength. For example, an ant can lift an object fifty times its own weight, a strong person can lift another person, while an Asian elephant can lift only one fourth of its own weight. The larger four to seven ton African elephant is not a working animal because its relative strength is even less.

No matter if we are comparing the muscle strength of different size animal species or if we are comparing different individuals of one animal species it still holds true that relative strength decreases with size. For human beings we can observe how this statement holds true by comparing the relative strength ability of men that are of different size.

To produce an accurate representation of how human strength varies with size we look at the world record data for weightlifting. While most physically fit human beings have the strength to lift another human being, what we really need to know is the absolute maximum amount of weight that either a large or small human being can lift. This is available to us in the form of the world wide weight lifting records.

Weightlifters compete only against others weightlifters that are the same size or more precisely the same mass as themselves. This way, regardless of size all of the best athletes have a chance to win within their class. By plotting the world records achieved within each weightlifting class we observe how the ratio of the maximum mass lifted to the mass of the weightlifter changes with the mass of the weightlifter. The world records for the snatch event shows that a 56 kg weightlifter lifted a 138 kg mass over his head demonstrating a relative strength of 2.46 while the much larger 105 kg weightlifter lifted a 200 kg mass over his head showing a relative strength of 1.90. Besides the snatch event, any one of numerous other weightlifting events could be use to demonstrate these ideas. Thus we see that while the largest weightlifters have the greatest absolute strength it is the smallest weightlifters that have the greatest relative strength.

For most physically fit human beings we have more than enough relative strength so that getting out of bed in the morning is not outside our physical capacity. But the larger animals that have lower relative strength lifting their body off the ground can be a serious issue. Large farm animals such as cattle or horses exert all the strength that they have when they pick themselves up off the ground. Likewise the large wild animals such as elephants and giraffes need all their strength to perform this task that is not challenging for the smaller animals. As a consequence of these difficulties, it is not surprising that many of these larger animals evolved the behavior of sleeping while standing up.

Yet numerous dinosaurs were much larger than these animals. Their greater size would mean that their relative strength would be substantially less than that of the large animals of today. It is not realistic to imagine that the large dinosaurs never fell or otherwise found themselves on the ground throughout their entire lives. If a Jurassic Park was actually created, any sauropod or other large dinosaur would be stuck lying on the ground much like a helpless whale stranded on a beach.

The Blood Pressure Problem

The graph shows that several tall dinosaurs held their heads approximately nine meters above their hearts. Giraffatitan, Brachiosaurus, and Sauroposeidon were giraffe-like sauropods that lived during the late Jurassic and early Cretaceous periods, while Argentinosaurus and Dreadnoughtus were even larger, elephant-like sauropods that lived later in the late Cretaceous. For all of these dinosaurs, paleontologists do not have a scientifically acceptable explanation for how they managed to pump blood up to their heads.

Many researchers have questioned how these tall dinosaurs supplied blood to their heads, leading to several highly questionable hypotheses. Some paleontologists suggest that sauropods had an enormous heart capable of generating the necessary pressure. Another theory proposes that they evolved multiple, evenly spaced hearts along their necks to act as a sequential pumping system. More recently, a popular idea suggests that sauropods never raised their heads above their shoulders but instead kept them low, moving them horizontally while feeding on vegetation.

The variety of hypotheses stems from the challenges of pumping blood to great heights. In a fluid column, pressure increases with depth according to the equation P = ρ g h, where P is pressure, ρ is blood density, g is gravitational acceleration, and h is height. As a result, a pump and its tubing must be strong enough to withstand the high pressure at the base of the column.

Taking Blood Pressure

To understand how blood pressure varies with height, consider how a person's blood pressure is measured. The cuff is placed around the bicep while the person is seated because this aligns the measurement with the heart’s elevation, providing a close approximation of the pressure as blood leaves the heart. If the arm were raised, the reading would decrease; if taken at the ankle, it would be much higher. This demonstrates how blood pressure depends on height.

Pumping blood to body parts at the same elevation as the heart is relatively easy since the heart only needs to overcome viscous drag in the arteries. In these horizontal circuits, blood pressure remains nearly constant until it reaches the capillaries. This is why a bicep measurement closely reflects the heart’s output pressure.

When we are standing, our blood pressure is much greater at our feet than at our heart or head.

When the heart pumps blood to the lower parts of the body the work is even easier since gravity is helping the blood flow downward. However, once the blood passes through the capillaries in the feet it has to travel back up to the heart. This is accomplished in part by being pushed along by the weight of the blood in the arteries. Valves in the veins also take the pressure off the lower parts of the veins during the time between the beats of the heart. In addition, the valves in these lower veins allow the leg muscles to work like the heart in squeezing the blood up to the next level whenever the leg muscles contract. The reason we feel discomfort while standing for long periods or sitting during a long plane flight is because our leg muscles are immobile and that causes the blood to accumulate in our lower veins.

The heart has to work the hardest when it is elevating the blood up to the head. This is because with every beat the heart, must lift all the blood within the vertical column that is in the arteries going up to the head. We can use the equation P = g D h to calculate how high the blood pressure P must be as it leaves the heart so that it can reach a height of brain h. For an upright adult the top of the head is about 45 cm above the heart and thus the minimum pressure the heart needs to reach this height is 35 mm Hg. Once it reaches this height there needs to be still more pressure to push the blood through the capillaries. To accomplish the complete task of lifting the blood and pushing it through the capillaries a normal person requires a blood pressure of about 120 / 80 mm Hg. The reason the heart is located closer to our head than it is to our feet is because of the challenges of pumping blood up a vertical distance.

A couple examples will give additional insight into how height affects the cardiovascular system.

Unlike humans, small mammals such as squirrels and bats feel little if any discomfort from being upside down.

The adventurous person that has attempted inverting themselves so as to stand on their head knows that this is a mildly painful position. In this unusual position blood pools in the head causing the face to turn red. Yet we need not wonder why bats and other small mammals do not care about which side is up because their bodies are too small to experience much of a pressure difference between the highest and lowest parts of their bodies. It is only the larger, taller terrestrial animals that must deal with the challenges of a large blood pressure gradient due to elevation.

Besides standing on our heads, a much more common experience people have is the dizzy feeling we sometimes get when we stand up too quickly. While resting horizontally our heart is not working nearly as hard as when we are standing or exercising. When we stand up the heart must suddenly work much harder to pump blood up to the brain. When we stand up quickly the blood momentary fails to reach the brain and the cells in the brain momentary starved for oxygen causing us to feel faint.

Giraffe reaches up to feed on leaves that other animals cannot reach.

At approximately six feet, or a little less than 2.0 meters, human beings stand tall among most terrestrial vertebrates, yet at 18 feet or 5.5 meters the giraffe is the much taller modern-day champion of height. Our occasional feeling of light headedness when standing up is hardly comparable to the 15 feet or 5.0 meters elevation change a giraffe goes through in obtaining a drink of water. If not for valves in the veins and arteries of its neck, the extreme pressure would cause the blood vessels to break when the giraffe lowers its head, and conversely the giraffe would pass out from lack of blood when it later lifts its head.

Another potential problem is the extreme pressure that exists in the giraffe's lower legs while it is standing. Anyone who has a job where they are standing most of the day is aware of how uncomfortable it can be as the blood pools in the lower legs, and yet a giraffe is three times taller, so the pressure is three times greater. Furthermore, if their legs were similar to other animals then even a small cut on the leg would bleed profusely and potentially be life threatening.

To prevent blood from pooling in its lower legs, the legs are surrounded with a tough thick skin that counteracts the blood pressure to prevent the blood from pooling. Inside the skin there is a thick inner fibrous tissue and the leg's blood vessels are far from the surface so as to avoid the potentially lethal problem of bleeding from a cut.

Yet the giraffe's greatest cardiovascular problem is having a strong enough heart to lift blood up to its brain. To produce the necessary blood pressure the giraffe's heart is a huge muscle with walls up to three inches (eight cm) thick and weighing 25 pounds (11 kg). But even more impressive is that the giraffe's resting heart rate is 65 beats per minute. This is about twice what is expected for an animal of its weight. The giraffe's massive ‘revved up’ heart produces the 300 / 180 mm Hg blood pressure needed for the blood to reach the giraffe’s head. Giraffes have a relatively short lifespan of only 20 years and are prone to heart attacks as a consequence of their cardiovascular adaptations.

Yet if the giraffe is an amazing animal in overcoming all of these cardiovascular problems to achieve its height, what should we think of the Brachiosaurus that stood at a height of 13 meters? While the giraffe's head is 2.5 to 3.0 m above its heart, the Brachiosaurs' head was about 9.0 m above its heart. As the variety of unlikely proposals show, paleontologist are baffled by this problem.

The sauropod blood pressure paradox has been debated for several years and now it is showing up in physics textbooks. Increasingly, paleontologists are coming to the belief that the Brachiosaurus could not have held its head up. Likewise Apatosaurus the other sauropods could not have reared up on their hind legs to reach the higher foliage.

Yet remounting all the Brachiosaur exhibits so as to lower the head is not the solution. This ad hoc solution does not explain why the Brachiosaurus has a posture for reaching up high. The Brachiosaurus, the ‘arm lizard’, and its cousins, are the only dinosaurs with longer forward legs than rear legs. The logical explanation for the longer forward legs is that the addition of longer legs and its long neck serve the purpose of extending the Brachiosaurus' reach up to the highest foliage. Thus we have the paradox of having an animal that is built for its head and mouth reaching the maximum height and yet at this great height its heart lacks the ability to pump blood up to its head.

The paradox of how the giant pterosaurs flew is the subject of the next chapter.

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