omenti

when size and shape matter

An Omenti minipost

 

A reader sent sent a chart showing height vs weight for three major professional sports.  It's immediately obvious that some clustering is going on.  NFL football tends to favor taller and heavier players than soccer (football for most of the world) and NBA basketball strongly favors height.  While it's a nice example of how a specific sport will favor certain body types at the elite level, it's not as dramatic as photographic comparisons of Olympic athletes.  Taller and larger isn't always better - gymnasts and divers tend to be short, basketball and volleyball players tall, distance runners and soccer players are closer to average.  Sports involving pure strength, wrestling and weight lifting for example, have weight classes.  Why?

 

Height in volleyball and basketball seem pretty obvious and gymnasts are lighter so they can change direction more easily.  Away from elite levels it's possible to have some success in a sport if your size isn't optimal.  Some high schools have successful tall gymnasts and short basketball players, but as competition tightens having the right body type becomes an important factor.  Body size and shape have a large influence in how fast they came move their limbs and how strong they are for their weight. 

 

For the sake of argument imagine two athletes with the same body proportions but one is 60 inches tall and the other 70.  The ratio of their weights is the cube of the ratio of their heights (7/6)³    - the taller one would be about 1.6 times heavier.  Muscle power is proportional to the cross sectional area of the muscle - the length doesn't matter much.  Here the taller athlete would be (7/6)² or about 1.36 times stronger.    The big difference if you want to move your body quickly is the shorter athlete has a larger strength to weight ratio -  1.6/1.36  nearly 18% higher in this example.  This is critically important in gymnastics and diving.   As those sports became more specialized, elite athletes became smaller.  Simone Biles, arguably the best athlete in the world, stands four feet eight inches tall. 

 

Another factor is how easy it is to move a limb.  What is the limb's inertia. Inertia is usually defined as the resistance of a physical body to an change of velocity.  Something not moving just sits there and something moving, assuming no other forces like friction, just keeps moving at the same velocity.   Acceleration is just the change of velocity and this is where force equals mass times acceleration comes into play.  For many sports you need to consider rotational inertia.  Think of a volleyball player or gymnast swinging her arm. There's an inertia to the rotational motion - her arm muscles need to generate a torque to move the arm.  A physics 101 course will have the details, but for the power her muscles have to generate will be roughly proportional to the mass of her limb times the square of its length. Long limbs not only require more strength to move, but their mass increases as the cube of their length while the muscle strength only increases as the square.   It is very difficult for taller athletes to be as agile as shorter athletes.  To compensate volleyball and basketball players focus on building the muscles in their arms and legs while being lean.  

 

Sports like soccer require an optimal mixture of agility and height.  It turns out that an average stature is generally the best although goalies tend to be taller for obvious reasons. The best distance runners are a bit shorter than average and very lean. (heat dissipation is also very important and shorter athletes have an advantage).  In swimming upper body strength is more important than weight so tall athletes with long torsos are favored.  Rowing requires strength.  Added weight doesn't change the drag of the boat much so the best crew athletes are have lots of muscle cross section area. 

 

Beach volleyball is interesting as there are two specialized positions.  Height is favored for blocker at the net while defenders need great agility moving around the back court.  The best teams tend to have a tall blocker and a shorter defender, but  blockers need as much agility as possible and the defenders need some height, so it's a bit of a mix.  The best women's teams tend to average around six feet tall and the best men's teams about six feet five.  

 

It needs to be said again these height differences aren't that important if the competition isn't at an elite level as many other factors are involved.  Only the elite levels demand that you need most or all to win.  People should play whatever sport they enjoy and it's possible to have success if their body they don't look like a professional or Olympian. And consider the impact of certain rule changes in some sports.  Lower the basket a foot in basketball and the women's game suddenly sees a lot of dunking and the men's game would probably see somewhat shorter and more agile players.  Would either be more interesting?  Who knows - you would have to run the experiment for some time to see how those with the new right body types (arguably it might be the same women) would rise to the top.   It makes you wonder if and when some athletes will consider body modifications to compete.  We've already had a taste of that with running blades.

 

 

simple rocket science

Every now and again you hear someone say the way to get rid of nuclear waste is to send it into the Sun.  First the idea of putting seriously radioactive material on rockets that tend to explode every now and again is daft, but there's another problem - making it to the Sun.

 

Figuring out orbital motion, Newton used a simple thought experiment.  Imagine a special mountaintop cannon that can shoot balls as fast as you like.  You fire off a ball parallel to the horizon and watch as gravity pulls it down.  Now fire one faster .. it goes further before falling back to Earth.  Keep increasing the speed and it goes farther and farther until you make it all the way around about 88 minutes later.  The cannonball is now in orbit.. its velocity is high enough that it continually misses the Earth as it falls.. technically it's always in free fall.  

 

Astronauts in orbit never escape gravity - they're just in free fall.. the same you sometimes get in a roller coaster or an elevator when the cable suddenly breaks.

 

Now consider the Earth as it orbits the Sun.  Our orbit is reasonably close to circular with an average speed of about 30 kilometers per second.  If you want to send something into the Sun you have to burn off that speed - all of it.  the rocket would have to go 30 kilometers per second in the other direction.  It would then have an orbital velocity of zero and would fall directly into the Sun. Anything less and it would end up in some kind of orbit. 

 

Thirty kilometers per second is a tall order and impossible with chemically fueled rocket technology.  By comparison adding about 11 kilometers per second to Earth's orbital speed lets you escape the influence of Earth's gravity and head out into the outer solar system.  At about 16 kilometers per second you can entirely escape the solar system's influence and travel to the stars.  

 

It is much easier to build a rocket to go to the stars than to the Sun.

 

There's a trick if you don't mind taking the scenic route.  Circular orbital velocity is  ~ (GM/R)^.5, where G is the gravitational constant, M the mass you're orbiting around, and R the orbital radius.  Bodies orbiting close to the Sun move fast - Mercury is moving about 48 kilometers per second, while those farther out are slower - Neptune is just 5.4 kilometers per second.  If you send a rocket deeper into the solar system the amount of speed you need to burn off is lower.  Travel to the inner solar system becomes more practical and you could even send something into the Sun with current technology.  

 

The Parker Solar Probe is making a series of close approaches to the Sun - it uses this trick along with using Venus as a gravitational brake to move well within Mercury's orbit.  A most amazing mission ultimately coming within about 5.3 million kilometers of our star's surface and probably touching it's corona.

 

Finally a bit of gee whiz.  Standing on either of the Martian moons Phobos or Deimos, you could easily throw a baseball into orbit.  Most of you could probably throw a ball fast enough to reach escape velocity.  One of you could serve a volleyball fast enough.

 

 

 

 

a shoe-in mistake?

Imagine Sarah and Melissa up against Alix and April at the Tokyo Olympics this Summer.¹  The score is 20-19 in the second set of the Gold Medal match.   I doubt that anyone will say but what if Sarah was using the same sunscreen Alix uses? or what if they were only wearing another brand of bikini..   On the other hand F1 auto racing and 12 meter yacht racing represent a combination of athlete and machine and in the case of F1 the team strategist may be the most important element.  You have to ask what is important in sport?  What makes for fair competition and how do you compare results among events?  Convention and rules decide what is important and fair.  Sports make distinctions between male and female athletes.  Age classes are common throughout sport and a number have weight classes. Technology has become part of many sports, but generally it's heavily regulated.  

 

except in running

 

Recently the World Athletics, the body that governs many running events, ruled on a Nike shoe with a new rule that basically allows it.  I'm not a runner, but there's a lot of interesting physics and biomechanics going on.  In endurance sports the elites are judged by their athleticism - what are their VO2 max, COT and a few other measures?   VO2 max is roughly the maximum rate of oxygen consumption - think of it as directly related to the maximum amount of power you can generate.  The cost of transit or COT is calculated for about anything that moves.  You can think about it as your fuel economy.  

 

The graph shows what the cost of transit looks like for a person.  Everyone will be different, but the curve shapes are similar for people in reasonable physical condition.  Walking has a very narrow region of high efficiency or low COT. People are very good at finding their optimal walking speed and not straying from it  You can become more inefficient and burn more Calories by increasing your walking speed - it doesn't have to be by much - and get an additional benefit of a more intense exercise.

 

Running is different. Here COT is almost flat over a large speed range until you've reached your maximum comfortable speed.  Reducing your COT will improve your times. Doping generally buys you a two to five percent lower COT.  Of course that's dangerous and banned, but some do it anyway.

 

What if a piece of apparatus lowered your COT? What woud that mean for the sport? Would someone regulate it?

 

Variations of the Nike Vaporfly shoe have been around in development form for over four years. Early on it wasn't clear how much of a difference it made.  Then about two years ago it started to become clear there was a serious advantage using it.  The almost current shoe used in the two hour marathon assault effectively lowers COT by about four percent.  It does so by reducing the amount of energy lost to the ground.  The human foot acts a bit as a spring, storing energy as it hits the ground and releasing some as it rebounds.  It's not terribly efficient, which is one of the reasons you're faster on a bike than on foot. A shoe can increase this efficiency, but until recently the increases have been under one percent - less than the natural daily variation an athlete sees.  

 

It turns out World Athletics, the body that regulates running, basically hasn't regulated running shoes in over a decade until now. Nike uses a curved carbon fibre insert that adds a small amount of efficiency, but more importantly it has a very thick layer of a lightweight foam that acts as a spring.  The amount of energy it can store is proportional to the thickness - in this case about four centimeters.²  The carbon fibre insert gives stability to what would otherwise be a very unstable foam pillar.  Most conventional running shoes have less than a two centimeter platform which doesn't allow enough room for a curved carbon fibre insert .. that and the foam depth would be much lower reducing the spring effect in the process.

 

Tests so far indicate a four to six percent COT gain - this translates into two to four percent better times for a given athlete.   The shoes gives an increase similar to doping.   You might give everyone the same shoes, but there are a couple of issues. Nike patents heavily and not everyone runs for them ..  we have an uneven playing field until other shoe manufacturers can find their way around.  it's quite possible that medals might be determined by lawsuits.  Worse are indications that not everyone has the same COT response to the shoe.  The range appears to be zero to six percent with back strikers and very short contact times doing better. It also works bette for shorter runners as it increases their effective leg length faster than taller runners.  That's probably about an additional one percent effect. A number of potentially great athletes may have been eliminated from the podiums of the world.  Will be be looking at COT, VO2 max and Vaporfly responce as fundamental characteristics of a runner?

 

There are any number of access issues.  Many of the Div-I colleges have shoe sponsorships.  What if you're sponsor is the "wrong" company.  And for non-sponsored programs and amateurs can afford a more expensive shoe.  And the people impacted most - sponsored athletes - can't speak out one way or the other.

 

I don't follow athletics (track and field), but running seems like a rather pure sport.  Of course shoes make some difference, but it seems like that component should be minimized rather than maximized so we can see what the athlete can do rather than some combination.  A physicist might say something like just what is it the sport is trying to measure?  I would like to think it's who is the best athlete. 

 

So many questions.

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¹ Two of the best women's beach volleyball teams in the world. Sarah and Mel are Canadian and current world champions.  April and Alix are the best America has.  

² Hooke's Law.. the force needed to compress or stretch a spring varies linearly with distance.  Twice the distance, twice the force.