2. The Paradox of Large Dinosaurs and Flying Pterosaurs

Applying Science to Understanding Large Dinosaurs

Comparing the Size of a Brachiosaurus to an Elephant

When we go back in time to the Mesozoic era, the world of dinosaurs becomes a magical place. It is as if the laws of physics no longer apply so as to allow the dinosaurs to grow to gigantic size.

The bone fossils giving evidence of the previous existence of monstrous terrestrial vertebrates has confused the science community. In all likelihood, if dinosaur fossils had never been discovered the science community would have long ago 1) included and emphasized in science education the teaching of Galileoâs Square-Cube Law showing how size matters, and 2) concluded that the largest terrestrial animals of today are pushing the limit in regards to size.

The brightest scientists strongly feel that our reality is rational, and so they become intrigued if ever the evidence does not seem to make sense. Their curiosity as to why something seems out of place often leads them to making great discoveries. One might say that the first step on the road to a Nobel Prize in science begins with the statement âthatâs oddâ.

The exceptionally large size of the terrestrial animals of the Mesozoic era is not a subtle oddity to be dismissed but rather it is a glaring paradox that must be investigated. The essence of science - our belief that we exist in a rational reality - is at stake here.

Something must have been different about the world during the Mesozoic era so as to allow terrestrial animals to grow so much larger. This line of reasoning should make us wonder if there is other evidence indicating that during the Mesozoic era that the world was a dramatically different place. While we do not want to get too far ahead of ourselves the author will address the immediate curiosity by stating that yes there are other indicators that the world during the Mesozoic era was quite different from the present. To give one example, consider the global climate of Mesozoic era. For all practical purposes, everywhere on the Earthâs surface the temperature was the same. There was no ice at the poles nor was there ice at the top of the highest mountains. From the equator to the poles, and from the lowest dry valley to the highest mountain, there was no more than a few degrees difference in temperature. There are other sets of evidence as well. The gigantic dinosaurs and pterosaurs is just one of several sets of evidence giving testimony indicating that the Earth during the Mesozoic era was a very different world.

The focus of this chapter is to explain the physical limitations restricting the size of the terrestrial animals of today, thus clarifying why the gigantic animals of the Mesozoic era presents a scientific paradox. Below is a list of specific issues this chapter will address. The first three issues give the evidence clarifying the anomaly of the dinosaurs being so large. The last listed issue regarding the flight of pterosaurs will be taken up in the next chapter since the paradox of how the pterosaurs flew only becomes clear after a discussion of the science of flight.

There are four problem areas illustrating why the largest dinosaurs and pterosaurs present a paradox to science:

Inadequate bone strength to support the largest dinosaurs Inadequate muscle strength to lift and move the largest dinosaurs Unacceptable high blood pressure and stress on the heart of the tallest dinosaurs Aerodynamics principles showing that the pterosaurs should not have flown

Before starting on the first issue listed above, there needs to be a discussion of what is the mass of various dinosaurs. It would be most helpful to have accurate mass estimates of the largest dinosaurs, the sauropods.

How much does your dinosaur weigh?

Skeleton of Brachiosaurus, Chicago Field Museum of Natural History

The most obvious observation about dinosaurs is that these were incredibly large animals. Kids want to know how the dinosaurs grew so large. Yet oddly enough, many paleontologists would rather avoid this subject. While paleontologists benefit from the publicsâ fascination with the immense size of these large dinosaurs, these same paleontologists find it extremely problematic to give a scientifically feasible explanation of how the larger dinosaurs could have supported their own weight.

Nearly a century ago paleontologists thought that they had the answer when they imagined that the large sauropods were like hippos in that they spent their day standing in the deep water of a lake or river to support their weight. However, the bone structure of the feet showed that these were truly terrestrial animals and so the paleontologists wisely threw out this hypothesis. However, this put the paleontologists back at square one, and in all the time since they have failed to come up with a reasonable explanation of how these animals grew so large.

Unable to solve the paradox, paleontologists began lowering their mass estimates for the sauropods as their new strategy for making the problem go away. While the first mass estimates for sauropods were around 100 tons or more, ever since the paleontologists brought the large dinosaurs out of the water the mass estimates for large dinosaurs have steadily dropped. Most recently, some paleontologists have made the outrageous claim that he Brachiosaurus had a mass of only 23 tons.

This is unacceptable. Since the paleontology community has taken the position that there is no paradox regarding the dinosaurs being so large, there is an obvious conflict of interest. These paleontologists have strained their credibility as scientists by asking the public to believe their low mass estimates.

It may be helpful to learn what is involved in making an estimate of a dinosaurâs mass. To determine the mass of a dinosaur we just need to know its volume and its overall density, since multiplying the volume and density together gives us the mass. Let us start with determining the volume.

The paleontologists have already completed the work of determining the volume of the various dinosaurs. Using the dinosaur skeleton displays as references, paleontologists have filled out the form of these animals. Paleontologists usually work off of computer generated images or full size replicas to determine the volume. But it is also possible to work off of authenticated scale models of the dinosaurs that have been created by the paleontologists. One of the first and most popular lines of scale dinosaur models is the Carnegie Collection. Paleontologists use the fossils dinosaur displays at the Carnegie Museum of Natural History as their reference in creating these authenticated dinosaur models.

If we know the volume of an authenticated model of the dinosaur and we know how this scales to a full size dinosaur then we know the volume of the actual dinosaur. One way of determining the volume of the model is to collect and measure the runoff water created in the process of submerging our dinosaur model in full tub of water. While this method is intuitive is showing us that the volume of the runoff water is equal to the volume of the dinosaur model, there is another method using Archimedesâ Principle that is more precise and easier to do. With this second method the weight of the dinosaur model is recorded as it hangs from a scale. Its weight is then recorded again as it hangs from a scale while it is submerged in the water. The difference between the two readings gives us the weight of the water displaced. Because we know the density of water, the weight of the water displaced gives us the volume of our dinosaur model.

Most of the Carnegie dinosaur models use a one to forty scale. This means that if the scale model is one foot long then the actual dinosaur is forty feet long. Because volume is a function of the scaling multiplier cubed (V = L 3 ), the volume scaling for the model is one to forty cubed or one to 64000. If you have an authenticated dinosaur model other than Carnegieâs and your scale model uses something other than forty as its scaling ratio, you can still determine your volume scaling ratio by cubing the linear scaling ratio.

Vertebrae from the back of a juvenile Diplodocus preserved in sandstone, Jurassic Period, Trail through Time, Rabbit Valley, 26 miles west of Grand Junction, Colorado

Now that we have the volume of our dinosaur we will now move on to determining the overall density of our dinosaur.

Our first step in estimating the density of dinosaurs is to recognize that dinosaurs were vertebrates and so they have much in common with the present day vertebrates. Present day vertebrates include mammals, reptiles, amphibians, and even fish and turtles. There are only slight differences in the amount of bones, muscle mass, blood, and internal organs of these animals and so there cannot be much difference in the density of these components. Most of these components have a density slightly greater than the density of water. This should not be surprising since the human body and bodies of these vertebrates is mostly water.

Since the body parts of vertebrates have a density greater than water, we along with the other vertebrates should sink in water; but instead of sinking, most vertebrates are neutrally buoyant. The reason we are able to float is because we have air trapped in our lungs. The low density air in our lungs provide an upward buoyant force on the body so as to counteract the higher density bones and muscle mass that is trying to pull the body down. Furthermore another nice benefit of our lungs being in the upper part of our body is that we tend to float top side up and as such it is relatively easy for us to poke out heads above the water for a breath of air. Most terrestrial vertebrates with lungs are like us in that their overall body density is just slightly less than the density of water and so most vertebrates just barely float with most of their body under the water.

However not all vertebrates have lungs to give them neutral buoyancy. For fish, being neutrally buoyant is an obvious advantage and yet they do not have lungs filled with air to lift them up. Without lungs, some fish species such as sharks must constantly swim so as to keep from sinking. The sideways pectoral fins of a shark act like wings that lift the shark as it swims through the water. While this works for the shark, most fish have evolved an air tank known as a swim bladder that gives them enough upward buoyancy to make their body neutrally buoyant. Thus fish are also like the terrestrial vertebrates in that they too have a body density very close to that of water.

In regards to body density birds are the exception. This is because birds have a unique circulating respiratory system that requires a larger interior cavity. The larger interior cavity gives birds a lower body density.

Mallard Ducks

The respiratory system of birds has a circulating system that assures that fresh high-oxygen air is continuously moving through the lungs. This is accomplished by the incoming air first filling the abdominal and posterior thoracic air sacs, then traveling through the lungs to the anterior thoracic air sacs, before being exhausted. This superior system is needed to supply a bird with the greater oxygen, higher metabolism, and likewise greater power that it needs to fly.

Waterfowl go to the extreme in having an internal cavity space that is much larger than what is actually needed to achieve a circulating respiratory system. Their large internal volume filled with air is their most important means of reducing their body density, thus enabling ducks, geese, seabirds, and other waterfowl to float high on the water.

Since birds have a lower body density than the other vertebrates and birds evolved from dinosaurs, we must wonder whether some dinosaurs could have had had a bird like respiratory system. If they did then this would give these dinosaurs a lower body density.

Of the two main classifications of dinosaurs, the Ornithischian (bird hip) and the Saurischians (lizard hip), the birds evolved from the Saurischians group (not from the bird hip dinosaurs!). The Ornithischians were herbivores (plant eaters) while the Saurischians were split between either being herbivores or carnivores (meat eaters).

Two main dinosaur classifying groups of Ornithischians and Saurischians are based on the three bones that make up the pelvis: ilium (green), ischium (red), and pubis (blue).

The birds evolved from the carnivorous Saurischians. Some of these dinosaurs may have evolved a bird-like respiratory system before taking the next evolutionary step of evolving wings. If this is true then these dinosaurs would have had a lower density than other dinosaurs, yet how much lower is difficult to determine.

While pinning down the density of the bird-like dinosaurs is problematic, we can still be fairly certain about the density of the much larger remaining group of dinosaurs. With their respiratory system being the same as present day vertebrates, the body density of these dinosaurs and present day vertebrates would also be the same. Thus like present day vertebrates these dinosaurs would have had a body density close to the density of water (1.0 g/cm 3 ).

Dinosaur Weighing Kit

We now have everything we need to calculate the masses of the various species of dinosaurs.

M = V ρ ( S.F.) 3

Where M is the unknown mass, V is the volume of the water displaced, ρ is the animalâs overall density and S.F. is the scaling factor.

The author has clarified the scientific procedure for determining the masses of the dinosaurs. Itâs not perfect. Nevertheless by bringing this procedure out into the open there is greater accountability for getting the numbers right. Scientists can and should continue to argue about the shape of the various dinosaurs. This is important since most changes in the shape ultimately determine the estimated mass of the dinosaur. Here is a link that explains the procedure of using authenticated models for determining the mass of dinosaurs.

Using the described procedure the author has calculated the masses for a few well known dinosaurs and has given the results in the table below.

The Mass of Dinosaurs

Dinosaur Authoritative Mass

Estimates (tons) Mass Determined by Authenticated

Dinosaur Models (tons) Ankylosaurus 4 - 8 6 Triceratops 6 - 12 9 T-Rex 6 - 14 10 Brachiosaurus 23 - 88 48

Results are for the dinosaur models that are shown. A model elephant is included in the experiment for the purpose of demonstrating the experimentâs ability to accurately give the mass of large animals based on models. Other authenticated dinosaur models may produce slightly different results.

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

Mammal Front Leg

Circumference

(mm) Rear Leg

Circumference

(mm) Approximate Total

Bone Area

(mm 2 ) Animal's Weight

(N) Standing Stress

(N/M 2 E5) Meadow Mouse 5 5 4 0.5 1 Guinea Pig 10 15 29 3.8 1.3 Gray Squirrel 10 13 24 3.9 1.6 Gray Fox 28 26 130 39 3.0 Raccoon 30 28 150 50 3.3 Cloud Leopard 45 41 330 140 4.2 Wolf 62 62 680 470 6.9 Lion 104 94 1700 1400 8.1 Polar Bear 158 135 3820 4390 11.5 Elephant 459 413 33700 57800 17.1

The initial raw data, the front and rear leg circumferences and the mass of each animal is from Anderson, J. F., Hall-Martin, A., and Russell, D. A. 1985. "Long-Bone Circumference and Weight in Mammals, Birds, and Dinosaurs," Journal of Zoology, London (A) 207: 53-61.

Area is calculated as (CF2 + CR2)/2PI, Bone Area = Area * 5/9 to account for hollow center of bones, Standing Stress = Weight / Bone Area

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 animalâ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

Many researchers have questioned how it would be possible for a Brachiosaurus to supply blood to its head. Several unlikely hypotheses have been suggested. Some paleontologists have suggested that Brachiosaurus had a massive heart to produce the needed pressure to lift the blood. Another proposal is that the Brachiosaurus evolved a series of several evenly spaced hearts in the neck as a pumping system that would get the job done. More recently a popular idea is that the Brachiosaurus never lifted its head up but instead just moved it back and forth horizontally.

The assortment of hypotheses comes from the problems associated with pumping blood to a greater height. In a column of a fluid the pressure increases during the descent from the top of the fluid to a lower level according to the relationship P = g D h, where P is the pressure, g is the acceleration due to gravity, D is the density, and h is the distance below the surface. Because of this, a pump and the tubing at the bottom of a column of fluid must be strong to withstand fluid pressure near the bottom of the column.

Taking Blood Pressure

To better understand how blood pressure can vary with height, consider the way a person's blood pressure is taken. The cuff is wrapped around the bicep of the arm while a person is sitting because at this point the blood is at the same height as the heart. The blood pressure taken this way is a close approximation to the pressure of the blood as it leaves the heart. If during the measurements a person were to raise their arm the reading would be much less, or if the measurement is taken at the ankle rather than at the arm the blood pressure would be much greater. This is because blood pressure is a function of height.

It is easy for the heart to pump blood to parts of the body that are at the same elevation as the heart. For these horizontal circuits, the heart only has to overcome the viscous drag of pushing the blood through the arteries. For these circuits there is almost no loss of blood pressure until the blood moves through the capillaries. For this reason the blood pressure taken at the bicep is a close approximation to the blood pressure as it leaves the heart.

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 8.0 to 9.5 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.