Dinosaur bones likely carried less weight than originally thought, according to this article, because the math used to measure load on bones simplified them by visualizing them as columns. Insert the traditional joke about perfectly spherical cows.
Now, the folks who came up with the new analyses said that the curves seem to weaken the compressive strength of bones rather than strengthen them. They wondered why bones are curved, then.
Of course bones are curved. Bones aren't meant to be compressed end-to-end by weight as a stationary column, but are designed to move from one position to another while bearing weight all the while. That requires curved, often grooved. articulatory surfaces. The rest of the bone is curved to compensate for the changing surface-- counterweighting and also ensuring good compression through the axis of force. Additionally, they must serve as anchors for tendons and muscle and withstand oblique forces while functioning.
The strong effect of oblique forces are easily seen in trees. Many trees will grow in tall, reasonably straight columns with symmetrical branching to equally balance the weight of its branches all around. But where winds are strong and often uneven, as on exposed mountain slopes or deserts, or where snowpack can be high (snow can thaw and refreeze to ice, weighing branches, breaking them, or pushing them to one side), trees do not grow straight, but twisted, often extremely so.
The major differences are that bones grow according to predictable oblique forces exerted by muscles, and most animals are not columnar (humans are a rare exception due to being tailess bipeds.) Therefore, most of a bone's mechanical load is not distributed vertically.
Mammals (and dinosaurs/birds) have evolved a more efficient, elbows-in, under-the-body architecture for weightbearing limbs which has been called "columnar" as opposed to the sprawl of lizards and amphibians. Yet, simply because the limbs now bear weight vertically does not mean they function as columns, even when standing, as no animal stands perfectly straight on a level incline and the skeleton must compensate for irregularities.
Rather, if you take a skeleton in the ideal standing position, look at the limb structure carefully, then draw a plumb line from the top of the hip through the center of the foot, (or the shoulder through the foot) you will realize that most of the bone is out of that straight line altogether. This effect is especially exaggerated in smaller animals like cats or mice, which do not have as much weight to hold up.
Elephants are closer to the columnar ideal, but still show a lot of bone out of that plumb line. No joint is perfectly horizontal. In fact elephant's bones are more knobbed and twisty than cats' limb bones, showing how much oblique forces the bones must take just to move due to the greater size and weight of the elephant.
But why are those bones so crooked? Why can't limbs be straighter? After all, humans are pretty columnar and our bones are up and down, right? We're not that straight, either. Our femurs are pretty curved and hips flared to help move our limbs, and we have lowered our heels to form part of our foot, instead of a locomotive joint, increasing our stability and ability to control the forces through our legs. Our spines have a S curve to help take and then return the energy from our up and down gait-- just like springs.
THAT is the key to why legs are built crooked: they're acting as springs. Yes, even elephants' legs are springy. Tendons act as pulleys and joints as levers, allowing the bones NOT to compress and absorb the full force caused by movement or gravity, but to partly store that energy and return it in movement.
We don't recognize it because unlike our man-made springs, the components are not of equal size, and the springs are locked in two dimensions-- back and forth, suitable for forward movement, with limited rotation to the right or left through the joints. At least one mid-joint in that series is a pure hinge joint, blocked from rotating sideways at all-- the elbow, or the knee joint, increasing the stability of the entire limb. A stiffer joint needs less muscle force to keep it in place. This need for stability is why elephants have knobs around their knees and elbow joints; it's not just for muscle attachments, it's also to restrict their movement and keep them slip-proof. A stiffer spring is a more powerful spring-- if it doesn't break from all the energy in it first.
Now, on the other hand, the cat skeleton, designed for stalking, jumping and pouncing, is far more springy and flexible than it is stable; it is designed to yield major bursts of power, rather than sustained stable standing or efficient walking. The joints have so much range of movement that they need heavier muscling relative to weight to keep them stable. Stalking and pouncing take great energy. Free-ranging cats have been tracked and they don't travel more than 1-2.5 miles per day. In comparsion, a hamster may run 8 miles a night on a wheel, and a sled dog, which is well-designed for running, can travel 50 miles a day.
DINOSAURS:
In the past people assembled bipedal dinosaur skeletons and visualized them standing nearly upright, like humans-- an very inefficient configuration-- and it is only in the last fifteen years or so that people have realized that bipedal (theropod) dinosaurs must move more like birds and that means a horizontal torso. The above theropod model is an example of this new vision. We also discovered that their bones are also very bird-like, being hollow and light.
By this reframing, now we see a more agile dinosaur that can easily bob its head down or up to strike at prey, use its long neck to groom itself. The horizontal torso is balanced over the hips by a heavy tail, and powerful legs must propel the body forward. The reduced fore limbs make more sense in this configuration, but we can't be absolutely sure how flexible or stiff the limbs would be without being able to see a fully fleshed out dinosaur.
Other dinosaur genera, being less bird-like, are visualized as elephant-like but still reptilian in their limb build, like Apatosaurus, which is shown with a slight outward sprawl at the knee. This would be suitable in an animal that swam a lot, but for a heavy land animal, this seems alarming. Crocodilians are mostly water animals, and the biggest fossil tortoises top out at an estimated ton. They don't provide a reliable guide for how a large dinosaur would arrange their limbs. Reptilian muscle is actually much stronger than mammalian muscle, pound for pound, as reptiles don't waste energy making heat, but their efficiency is very reliant on temperature.
But it's strange how a tyrannosaur's bones lack knobs or other jutting surfaces which would stabilize a knee joint, similar to an elephant's. The long, keel-like pelvis is a clue, as is their bird-like anatomy. But there are major differences. Tyrannosaurus "Sue" has a very forward pointing pubic bone that almost looks like a ship's keel, with a solid ring that would have made for small eggs and hatchlings, unless her kind laid soft-shelled eggs that hardened only after expulsion.
Birds have lost a heavy, flexible tail and evolved towards a rear-facing pubic bone without a solid ring, allowing more room for solid eggs and air sacs. Instead of using the now-lost pubic keel and tail as anchors for leg muscles, birds have hip flanges that flare over the legs-- like human hips to an extent-- for running birds. The ostrich is the only bird that has any pubic symphasis (joining of the pubic bones.)
It's likely the pubic keel helped stabilize the limbs somehow, but without comparable structures in modern animals, we're going to have to guess.
Because theropods had bird-like respiration and bone structure, my suspicion is that the pubic keel helped control the back-and-forward motion of the gut (torso), preventing energetic damage to the diaphragm and air sacs from damage, as well as acting as an anchor for torso, tail, and leg muscles. Let's look at how the two connect in mammals.
In most mammals, respiration is coupled with movement; they can't breathe out of sync with their stride (humans and sea mammals excepted.) Large mammals, like horses or elephants, have stiff spines and the energy of movement is transmitted through their gut as well. Their large guts act like a bellows on the diaphragm, compressing and decompressing it. Carnivores, having smaller guts, require more flexible spines which action actually drives their gut in and out of the diaphragm for a weaker bellows effect; the real effect is caused by the ribs expanding in response to the spine curvature. It's a tidy built-in system: the faster the animal moves, the faster the animal breathes.
But there are times when this automatic system is unwanted. Humans (and great apes) have decoupled respiration from movement in part due to our bipedalism and specialized use of our arms for climbing, using tools, etc. Incidentally this adaption allows us to speak while walking. Sea mammals decouple respiration from movement precisely because they can't breathe underwater.
Birds (and probably dinosaurs) don't have their lungs expand and constrict like mammals. It's all about pressure changes in their air sacs, caused by the movement of their sternum (breastbone.) Gut movement could either help or ruin respiration by causing extreme pressure changes. This may suggest why Tyrannosaurus has such small forearms; lighter arms would impede the sternum less.
Interestingly, "Sue's" pelvic keel looks very robust, not unlike a modern bird's breastbone, which anchors strong wing muscles. Therapods like Sue had the saurischian tripartiate hip, and the pubis bone forms a joint with the ilium (which forms a joint with the femur) and the ischium (which flares towards the tail.) This is the older reptile pattern, which allows some joint motion, and therefore energy loss, from limb movement. The pelvic keel probably had strong and stiff soft-tissue connections to the spine and sternum which allowed propulsive energy to be transmitted up and forward through the whole body at once, reducing the amount of energy needed to move forward. An anchored, yet mobile gut could transmit energy back to the pubis through levering the keel, then.
Mammals and birds have more fused, stiffer designs that allows more energy to be transmitted to the limbs and spine instead of lost in the hip (but they don't have hip keels at all.) The ischium in mammals is somewhat fused with the lower part of the spine (coccyx) to more efficiently transmit energy to the spine. This fusion, and subsequent lack of shock absorption in the hip, may result in greater limb bone compression for similar gaits in birds and mammals than would occur for reptiles or dinosaurs.
Since dinosaur limbs are built like nothing alive today, it's not hard to understand the considerable confusion over just how they are supposed to be put together with the torso, never mind trying to calculate their strength and function in propulsion. Yet, the role of every bone in the body in managing stress and movement can't be overlooked, even if we don't have the soft tissue evidence to really know for certain.
I hope this kind of "spherical cow" math will never be used again to calculate an animal's probable weight from its limb bone. Instead, we should be working on a better visualization of dinosaur joint function. After all, bones are designed to move, which affects their shape and strength.
Now let's get back to eating today's dinosaur descendent: turkey.