The inefficiency of tall people.

It used to be that every year at the beginning of school I would point out how small the new students were and how young they looked. I feel like this has all changed. Now they mill about campus, hulking Adonis's and leggy Amazons. Is this just me?

Seeing them all in one spot I was struck by the inefficiency of this group of behemoths as they lurch up stairs and eat their hamburgers. The physics of how the body scales and the energy it requires is not kind to tall people. I'm pretty tall and when I sit down to eat, I eat a lot. How much more food it must take to support these giant students than an average sized population? Not only do tall people make more money and are perceived to be more attractive, but they also eat all the food. More than that, there's something fundamentally inefficient in being tall. And they can't help it.

1. Tall People Eat More

Let's assume that your body scales proportionally to your height: taller people have proportionally larger muscles and torsos and legs and so on. More precisely, if I change a person's height h, their volume changes proportional to h3. This is not the formula for the volume of someone of height h, but it is how that formula changes with h, or how it scales with h. It seems reasonable to say that the amount of energy to contract this muscle also scales as volume h3 and the amount of food to provide this energy also scales proportional to their volume h3. These are just scaling arguments and not actual formulas. If the average height of the population jumped 5% from say 5'8" to almost 6', the amount of food required to sustain that population jumps by 16%! You can get this number by plugging h=1.05 into the scaling arguments. Ironically, these students are probably tall and properly proportioned because they have proper nutrition, which then contributes to food shortages and poor nutrition. This scaling also means that if everyone gets the same portion of food, then tall people don't get enough and are skinny, and short people get too much and are fat. This may explain the the tall skinny, short fat cliché.

from the short and the tall of it.

2. Tall People Use More Energy

So these giants need to eat big hamburgers and oversized cookies just to live, but they also tend to lurch and lumber up stairs while they do it. I've been thinking about how tall bodies work less efficiently every since I wheezed my way up a hill recently while my friends bounded up it.

Never mind that they're in better condition than I am, I'm using physics to make excuses. Because I'm taller than my friends I weigh more than they do. As a result lifting my body up a hill takes more energy, but as we discussed earlier, muscles and the energy to run them scale with mass h3. I use more energy than my short friends and have to lift more, but I also have bigger muscles and eat more food. So it seems that climbing a hill should be as hard for a short person as a tall person, and that I have only my poor conditioning to blame. But this isn't entirely true. The disadvantage of being tall is that for long hikes the ability to take in oxygen affects performance. As one gets taller the ability to take in oxygen doesn't scale with how much oxygen the body needs.

3. Tall People have less efficient Lungs

A well known scaling advantage (energy-wise if not comfort-wise) of being big is that you retain heat better. There is less skin (surface area h2) to lose heat through compared to volume h3 for a large creature than a small one. A similar argument can be made for the ability for a tall body to take in oxygen. This depends on the surface area of you lungs which scales differently than the volume of blood in your body. If your lungs were smooth on the inside the ability for you to take in oxygen would scale as h2. But lungs have little branches inside and are more like fractals. I've read that a two dimensional lung has a fractial dimension of 1.74. In reality (3 dimensions) the surface area that can take in oxygen scales somewhere between h2 and h3, let's guess that it's h2.5.

The point is that as you get taller, your muscles get bigger your heart is bigger, but your ability to take in oxygen does not scale as well. Your lung surface area per mass scales as h-0.5, so a person who is 5% taller than you will take oxygen into the blood 97% as efficient as you, given your cardio is the same. In day to day life you wouldn't notice this, but it will factor in when you really try to push your body.

This is Bryn, Brian is long gone.

4. Tall People are Harder on Their Bodies

After huffing and puffing my way to the top of this hill, at a disadvantage because of the treacherous fractal scaling of my lungs, we just turned around and walked back down. As you know, faithful reader, this tortures the knees. The torque around your knee scales as h4, one factor of h for the length of your leg and 3 factors of h for your weight. In a weak attempt to keep my mind off the pain in my knees I calculated that the torque around my knee was near the torque of a midsize car engine.

If you increase you height by 5% the torque around your knee increases by about 21%, and the stress increases, but no matter you size the knee is still just bone, ligaments, and cartilage. This is probably why Basketball players, and tall people in general, always have such bad knees later in life. Having these ligaments and cartilage apply and lubricate these huge torques destroys them.

5. A Tall Runner Must Be Underweight

My last thought on this has to do with forcing the body to perform against the scaling. In distance running you want to be tall and efficient, a combination contrary to scaling. For efficiency you want to be short and have larger lungs compared to your body, but for stride length you want to be tall. You can't really have both so the alternative is to be underweight. Being light is obvious, but being underweight means you have the large lungs and stride of a tall person, but you only have to supply oxygen to small muscles.

Looking at a chart of champion runners we see that the taller people are more underweight and that the shortest man is actually not underweight at all. There is an ideal height that matches efficiency and stride, and if you are not that height you have to change your weight. Of course I'm simplifying it greatly, disregarding conditioning and the competitive spirit. But it is interesting.

6. Being Tall vs. Evolution

My wife pointed out to me that if being tall is so bad, why are we getting taller. My only answer beyond selection bias (tall people are more attractive and have more kids) is that the cultural evolution we are going through is allowing it. People are no longer evolving as a response to their natural environment. As evidence I found the graph that actually shows people getting shorter until the point in recent history where cultural evolution has taken over.

So, faithful reader, next time you envy your tall friend's greater earning power and intrinsic attractiveness take comfort in the fact that you need less food to survive, can climb stairs with ease, and late in life you will actually be able to move without pain.