This is a question which I have wanted to answer for the longest time, “What is the highest theoretical height of the human species?”
The main way I wanted to answer this question was to use physics principles and try to calculate the most reasonable answer.
First, let’s review the legends and stories of cultures which talk about giants, creatures which are said to be even hundreds of feet tall. Let’s assume that those stories of bipedal creatures are exaggerations and that if the stores were based on real life humanoid creatures, then the actual height was probably less than 30 feet.
We know that the tallest recorded human is Robert Wadlow, who right before the died at 22 was nearly up to the 9 feet point. So we can say with certainty that humans can get to at least 9 feet in height. However, as most people like Wadlow are, they seemed to have suffered from problems of their pituitary gland, whether is was from hypertrophy or tumor compressions.
We know that almost Everyone who is passed the 7′ 6″ point has had a history of pituitary gland issues. There are a few people who seem to grow to that height from genetics but they are extremely rare. Plus, even if the person does reach that height from genetics, it seems that they are more prone to injuries, especially in the joints like the knees, ankles, and hips. This suggest to us that the weakest areas of the human body will be where the answer can be reached.This means that even if people do reach enormous height from genetics, they may not traditionally have lived long enough or been healthy enough to find a mate and reproduce to mass on the tallness gene.
Since the majority of humans are of a height in the middle of the distribution bell curve, the environment would be made and tailored for people in the middle, putting people who are too tall at a disadvantage.
Humans are bipedal creatures so if we look for other species which move in bipedal fashion, we can make better and more accurate guesses. We have heard stories of Bigfoot and Sasquatch who are usually reported around the 7-9 feet mark. Many anthropologist say that is is possible the Bigfoot of Cryptozoological fame is really the modern development of a very distance primate relative of the human, Gigantopithecus Blacki which is estimated to be up to 10 feet tall.
If we then take into consideration ancient Native American stories of red haired giants and the occasional giant skeleton that seems to be found, we can state with some confidence that a height of 12 feet is totally possible.
If we were to extend the definition of research further, we can look for the largest bipedal animals that have ever lived on Earth as a model. There really is almost no mammals or animals today that only stands on two legs, but four. Creatures like the Elephant and Giraffe are tall but their huge weight is distributed across four limbs. We have to look at dinosaurs and see how tall they reached.
From resource 1, we find that the tallest herbivore dinosaur was the Shantungosaurus standing approximately 25 feet tall.
From resource 2, we find that the tallest carnivore dinosaur was the Carcharodontosaurus standing at 12 feet around the hips and estimably to be maybe 20 feet tall.
If we remember that the dinosaurs went through a sort of evolutionary arms race in terms of growing larger and larger, I would guess that the herbivores and carnivores evoked along with each other until they reached was is theoretically possible for animals on earth.
The maximum possible height for any bipedal animal on earth should be around the 30 feet mark, because anything over it will have cartilage problems in the joints of the knees when it moves. As far as biologist know animals today, most large creatures on land have their body defined by bones, and the bones are not flexible or elastic so movement in all three 3 dimensions of space requires the need for joints. Joints are flexible but their flexibility come a the cost of not being as strong as the actual bone parts.
From physics, remember principle 1, As a creature increase in height in 1 dimension, their mass which is proportional to their weight which is proportional to their volume increases in 3 dimensions, which their surface areas increases by 2 dimensions. This means that as any creature gets taller, their weight will increase at a geometric rate which is a factor of the height increase multiplied by itself 2 times over as in delW=(delH)^3.
As a creature gets taller, they take on more mass in the top and bottom. Their knees and lower joints have more pounds per square inch extorted. If we remember from our studies of human femur cortical bone strength, it is just as strong as steel, with a maximum compressive strength of being over 200 Mpa. This value was found from human femur bones being tested on mechanical instruments which exerted a compressive loading force on the bones.
Assume the human body is just a geometric cylindrical shaped weight at a proportion of 1:5.5 for width: height since average human gait is about 1 feet and average human height is about 5 and a half feet tall, and put two rods to support it.
From source 1, we know the average human body density. – Average human body density. 1400 kg/m3 = 1.4 g/cm 3
since the we can first choose a value of say 4 feet width getting 22 feet in height assuming depth=width, then we can calculate the volume with 4*4*22 which we can then divide by the density to find the weight of a human that is 22 feet tall. That weight is then equated with 2 times the loading force of a leg limb which has a width assumed to be 1/4 th the torso length of 4 feet (which is 1 feet). We know that the human long bones are not solid bone but hollow so we can use the formula
R1^2*pi-R2^2*pi= Area of single femur bone. Another assumption is to assume the outer cortical thickness is possibly the same thickness as the inter medullary cavity, so about 2 inches thick. Area of bone is around 24 area units (assume 3^2*pi-1^2*i). since the maximum compressive force is around 200 MPa of each area unit, we multiple the two limb areas by the maximum compressive load, which is a force/area unit. and cam then compare the two values, the weight of the entire creature to the maximum compressive force the two hollow limbs can handle. This calculation can be easily done using any computational tool. The value which will eventually be reached from recursive convergent calculation should be far higher than the 30 feet that nature allows. However, this is only from comparing the bone loading capacity, not the joint or cartilage loading capacity, which is far less.
Another calculation with the maximum compressive strength of hyaline cartilage will be done but the overall method has already been explained.
The 2nd major calculation is to see just how hard the heart would have to do work to be able to pump the amount of blood needed to the body to make everything work. We know that atmospheric pressure s about 760 mmHg. We also know the density of human blood. since the heart is at the center of the human body, we can take half of a height, say for a 20 feet tall beast and find out how much work would be needed to pump up to the center of the body.
From wikipedia,…Blood accounts for 8% of the human body weight, with an average density of approximately 1060 kg/m3, very close to pure water’s density of 1000 kg/m3. The average adult has a blood volume of roughly 5 liters (1.3 gal)
The amount of blood from 5 liters has to be multiplied by the increase in height factor, which is a cubed function. Once the amount of total volume of blood is found in a 20 feet tall bipedal animal, we assume more than half of that amount (say 70%) must go from the legs and arms up to the heart, The femoral arteries and arm arteries are all attached to the heart, but a significant amount of the blood must go to the brain to supply it with the needed amount of oxygen. The work is defined by a heart pump is by knowing the dimeter, a constant function, and the flow velocity, Flow velocity is from taking the entire blood volume, knowing the total surface area of the blood vessels which is found from multiplying by the same increase factor, and knowing how many times in a minute (or the rate) which the heart must pump through the system .depending on how we want to assume the type of pump the heart may be, we use different factor constants to know the amount of work the heart does. For the heart to do the type of work, we must figure out whether such a speed is possible from looking at the amount of food or chemical energy goes into the body. At this point, I am not sure how to find certain value to make that calculation.
My final guess is that humans are limited by their cartilage in the joints, and and blood pumping upwards against the force of gravity which will limit them to less than 20 feet, but I would guess 15 feet in maximum height is completely reasonable.