Does height matter in sports?


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.

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