Hello, physics friends. So I was watching the COPA

America earlier this year, and I got talking to a friend

about Leonil Messi’s height. He’s 5 foot 6, which seems

shorter than average. Maybe? Well, it turns out

that the average height of an Argentinian man

is 5 foot 8 and 1/2. So is Leonil Messi’s stature

an advantage for him? Well, the height of an average

male professional soccer player is 5 foot 11. So is height an

advantage in sports? Obviously, some sports

attract tall people. Michael Phelps is 6 foot 4,

but Gabby Douglas is 5 foot 2. Just last week, Olympic gymnast

Simone Biles and Olympic volleyball player David Lee

posted this photo on Twitter. And these heights are pretty

representative of their sports. In swimming, 5 foot 9 for

female Olympic gold medalists and 6 foot 3 for men. That’s around 7

and 9 inches taller than their respective

averages, worldwide. The average gold medal

gymnast, on the other hand, was 5 foot 1 for women and

5 foot 4 and 1/2 for men. Both an inch and a half shorter

than their respective averages. So swimmers are tall

and gymnasts are short. Volleyball players are

tall and divers are short. And then there’s

soccer players that are somewhere in the middle. This seems like an

obvious question, but is height an

advantage in sports? The answer seems

pretty simple at first. Volleyball players that are

tall can spike more easily. Short gymnasts have a

lower center of gravity so they can balance

on the balance beam. You know, like, it’s much

easier to stack two books horizontally, so their

center of gravity is low, than to stack them

up end to end. Try it. And shorter people,

on average, weigh less just because of scaling. So they have less inertia. That is, less tendency to keep

going in the same direction. And you can change direction

and flip more quickly. The same is true of diving. So divers tend to be short. It’s less obvious what–

somebody’s going to get hurt. As I was saying,

it’s less obvious why swimmers are tall, though. A swimmer’s goal is to be

as fast as possible in water while fighting friction and

drag, 1,000 times more of it than in air. So to accelerate

quickly, a swimmer needs to apply a lot of force

with her torso and limbs. So we need to figure out how

a swimmer’s height affect her maximum possible force. So the amount of

force you can apply is proportional to the

physiological cross-sectional area of your muscles,

which indicates the number of muscle fibers

contracting and releasing in that muscle. So imagine we have two people–

one 6 foot tall person we’re going to call Flow and

one 5 foot tall person we’ll call Bubbles– with

identical proportions. Every part of Flow is

6/5– or 1.2– times bigger than Bubbles. That means that if the radius of

Bubble’s bicep equals 3 inches, Flow’s bicep radius would be

3 times 1.2, or 3.6 inches. But the cross sectional

area of the bicep is proportional

to radius squared, because the area of any

shape is approximately proportional to r squared. So in this super

overgeneralized case, Flow’s bicep has 1.2 squared

or 1.44 times more area than Bubble’s. So Flow can apply 1.44

times as much force, just by being 1.2 times taller. And on top of

that, being heavier won’t really bog

you down in water because of the buoyant force. So tall people get a

disproportionately large boon in the strength department

just by being taller. But gymnasts need

to be strong, too. So shouldn’t they

be tall as well? Well, the type of strength

you need to pull yourself through water is different

than the type of strength needed for gymnastics. In gymnastics, what

matters is how your weight compares to your strength. That is, your strength

to mass ratio. It’s easier to hoist

up a smaller mass. So the ideal would be to keep

the mass small while increasing strength. Let’s go back to

Flow and Bubbles, although the names don’t

make quite as much sense now. Flow is actually

at a disadvantage, because tall people

disproportionately gain mass. That’s because mass is

proportional to volume, which is proportional

to length cubed. So with height, you’re

endowed with brute strength. But it’s not as easy to hoist

and throw your body about. That’s why sprinters

are, on average, taller than long distance

runners, because they need that power, the big

muscle strength, in order to increase their

speed really quickly. Whereas long

distance runners need to maintain a pace

for a long time, which is easier

if you’re lighter. So now in soccer, the

average female Olympic player is around 5 foot 6. And the average male

player is around 5′ 11″, closer to average height. Well, soccer requires you to

be more well-rounded– fast and agile with the

ball, which is better if you’re light and

short, but power to sprint and get those

headers and put pressure on the other team. So you need height there. So statistically, it’s better

to be somewhere in the middle. But, of course, it all depends

on what position you play. Now just because I’m tall

doesn’t automatically mean that I’m a good swimmer. And just because

my sister is short doesn’t automatically mean

that she is a good gymnast, although she actually is. But a little math

and physics can help explain how your

height might give you a statistical, but not

necessarily practical, edge in certain sports. But there’s an obvious caveat. Short people and

tall people aren’t necessarily proportional. A tall person might

have disproportionately broad shoulders or long limbs. But this process

gives a ballpark mathematical relationship

between height and physical strength. There’s actually an entire

field of study called allometry, or scaling, devoted to figuring

out how the physical abilities and characteristics

of living things change depending on

how big they are. It’s an interesting blend

of biology, statistics, and physics. There’s actually a bunch

of sports researchers in this field. One researcher actually

predicted how fast competitive rowers could go

based only on their sizes and the weights of their boats. And was accurate to within 1%. Medical researchers who

develop pharmaceutical pills use mathematical relationships

by first giving medicine to mice, then using

allometry to figure out what dosage a human,

who might be 15 times taller than a mouse

is long, might need. Kind of strange, isn’t it? That you can make

all these predictions just by knowing one thing. That is, how tall something is. That’s one of my favorite

things about science, is that one thing can be

related to unexpected phenomena. And you can describe

it all using math. Very cool. Thank you so much for

watching this video. And happy physics-ing.