omenti

into the wind

You know it is really windy when you see pieces of tree flying overhead during the daily walk.  It wasn't easy keeping the normal pace going into the wind, but the trip back was easy.  Going back to sports it makes you think about the impact of wind on running and what the right strategy might be.  

 

A bit of physics will sort this out.  Consider a thought experiment where a runner starts off on a square course from leg 1 to 2 to 3 and finally to 4 that she runs at a constant speed s.  There is wind of velocity w that parallels two sides of the course and is perpendicular to the remaining two sides.  The amount of effort she has to spend to overcome wind resistance is proportional to the amount of power she must develop on each leg of the course.  I'll leave the physics to a footnote, but it turns out the power per lap is proportional to 4s( s² + w²).¹  Since w² is never negative, having any wind always forces her to deliver more power.  Her time in a single person race will always be slower if she is running at a maximum power level.

 

 

Now her strategy is clear.  When running with the wind at her back she should make sure she is running in clear air - that none of her trailing competitors can take advantage of her breaking the wind.  When she is running into the wind, she should be drafting faster runners to lower her apparently airspeed.

 

The reason we don't see dramatic difference in races with and without wind is that, at the speeds a human generates in a marathon, the power necessary to overcome air resistance is small - only a few percent that necessary to run.  It can make a difference comparing race times, but the disadvantage isn't enormous in most running events. 

 

Cycling is a different beast.  Since the power needed to overcome air resistance goes as the cube of your speed and cyclists are approximately not wind-cheating, racing benefits from any aerodynamic improvements.²  Improvements occurred over the years, but dramatic improvements came when experts in fluid dynamics began to study the problem.³

 

One area where you see an improvement large enough to make a difference in a race is in the design of the wheels.  Here is a high level paper from a state of the art wheel maker discussing why a racer would want to do this along with details of their design.  It isn't very technical, but it does give a sense of the amount of work that is done combining computer models and real world testing in low speed wind tunnels.  It shouldn't come as a surprise that such wheels can be very expensive. A few thousand dollars a pair is common and some will shrink the bank account by over six thousand dollars.

 

An important point is the computer tools are available.  Getting time in a wind tunnel is a different matter, but computer modeling has become important.  The important thing is you need engineers who are knowledgeable and can build accurate models.  Tools like this can give a false sense that you know what you are doing and it is possible to do more harm than good.  

 

Education and experience are critically important

 

Which brings us to the "Industrial Internet"

 

Recently several people asked me to comment on GE's announcement of their new initiative.  Here is the note I sent:

 

A few people have asked me about this since it was announced.  It turns out I have some deep experience as one of the designers of the mask lab information system project at Bell Labs in the late 1980s.  This is really hard to get right and hinges on success in several key areas.  It has and is being done by a few companies and requires a non-trivial effort (I've seen estimates that it consumes about 25-35% of the cost of building an IC fab line these days - of course they require it to make their process work as so much is at the leading edge of what the tools and process can do).

a bit of commentary...

GE has made a big deal about the "industrial internet".   I don't have deep knowledge of their specific program other than their PR documents (which are too high level and shallow) and high level articles like this one from  Technology Review 

http://www.technologyreview.com/news/509331/an-internet-for-manufacturing/

This sort of monitoring and analysis is not new.  Science has been doing it for a long time as fundamental part of understanding experiments.  Starting in the 60s this began to become computerized and it was common in particle physics from the mid 1970s.  I was involved with its adoption in integrated circuit manufacture in the mid to late 1980s.  Places like Intel, Bell Labs and IBM were trying to capture rich information from silicon processing.  It turned out to be an expensive task (the Bell Labs effort, which impacted mask making at two locations, involved a dozen people full time and probably $3-$4M a year for a five year period - the efforts at Intel and IBM were at least ten times that size, but one that was cost justified.  Many components were required to make it work: lots of sensors, a flexible database, good programmers, experimental scientists (physicists and chemists), mechanical and electrical engineers, and *really* good process engineers.  

Figuring out what was noise, understanding the sensors and finding good process engineers were the most difficult parts - along with finding people who were actually willing to change the process.  Even then there were many elements that couldn't be captured and leading edge places like Intel create carbon copies of fabrication lines to minimize variation in process.  

Hewlett Packard, Microsoft, Intel and others attempted to understand how to do this more generally to create a product that could be sold to manufacturers.  There were some large problems - many of which trace to understanding the process at a deep level. I'm aware of at least two approaches that involved anthropologists along with the physical scientists.

It was very clear you don't mix a network (of any kind), database and sensors and expect magic.

I hope GE does well, but there are a lot of issues genericizing this that range from computer science to mechanical and electrical engineering to process control and sociology and anthropology.  It is very easy to build a money sink if you don't get all of this right.

Experience has taught me there is a lot of experience that lives in the production lines that is largely untapped by the engineers and managers who created the processes in the first place. It needs to be underscored that sensors need to be understood deeply - I'm continually impressed with the lack of education in this area in most computer science courses.  The people who traditionally do these things are production engineers, but outside of a few areas the field is almost dead in the US.⁴  I find it exciting that GE is working in the area, but producing anything that is reasonably generic is will be a hard multidisciplinary problem.  Any organization that wants to tap the potential benefit needs to understand their process and measurement deeply - and that may not be a bad thing.

 

I'm at the end of my allotted time, but need to mention a wonderful development.  

The maker movement where people are building things that tend to lace computation with the real world is growing.  People are learning how to use sensors and microcontrollers and cheap computers such as the Raspberry Pi are accessible to kids in middle school.  

At the same time about a half dozen people have told me they intend to get their amateur radio license this year.  Understanding radio at a practical level is something I would recommend to anyone who wants to know a bit more about how the modern world works.  I'm going to hazard a guess that the average ham radio operator knows more about the fundamentals of radio than the average wireless executive.  

Perhaps we are at the beginning of something great. Maybe there is a natural hobby for many who can make contributions to the "Industrial Internet" and beyond as we move closer to the real world with sensors and computers.  And perhaps a few will even be instrumenting their sports and mixing that with a bit of critical thinking for a deeper undersanding.  It gives me a lot of hope - much more than using computer science and networking for selling things.

 

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¹ OK - a bit of physics.  First note that speed does not have a direction - velocity has a direction and magnitude, speed just a magnitude.  First consider an earlier post where I show the power needed to overcome air resistance is proportional to the the cube of the head wind.  The force of the wind goes as the square of its velocity, so power for the runner to overcome wind resistances goes as s * w² , where v and w are both vectors. In this case the wind direction has been chosen so we can ingore the vector nature, so s and w will just be the scalar components.

So running with the wind at her back, our runner needs to develop power proportional to s (s - w)²  and going into the wind her power needs to be s (s + w)². 

The crosswind case is a bit trickier.  The wind now comes in at an angle and the magnitude of the the resultant vector is  (s² + w²)^.5.  The magnitude of the force is the square so the power on each crosswind leg is s(s² + w²).  

Now we can add up the total power per lap.  It is proportional to s(2s² + 2w² + s² + w² + 2sw + s² + w² - 2sw) = 4s(s² + w²).  

 ² Cycling at commuting speeds has a cost, but it isn't significant until you face a headwind that exceeds 15 mph.  Commuters can comfortably pedal away in an upright position that would be impossible at 25 mph.  It is possible to dramatically improve the aerodynamics of a human powered vehicle by enclosing it in a shell.  These velomobiles can be pedaled by normal humans at 25 to 30 mph for long distances that would tax an Olympic cyclist on a conventional racing bicycle. 

³ The same can be said for swimming - remarkably the equations are similar.  Water is a fluid that is about 800 time denser than air.  

⁴ Production engineering is alive and well in Northern Europe, Japan and China.

 

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Reicpe Corner

 

The Super Bowl is in a few days.  Try to make some healthy snacks.  These are too simple.  You can roast almost any root vegetable like the first recipe and try other produce like sweet potatoes and even cauliflower (which is great when roasted with the same hot sauce you use for buffalo chicken wings -- something like Fred's hot sauce)

 

Roasted Carrots

 

° slice carrots into thin - say 1/4 to 3/8 inch thick slices and toss in olive oil and a bit of salt.  

° roast for 20 to 25 minutes at 400°F

 

 

Roasted Chickpeas

 

Ingredients

 

° 15 oz can of chickpeas

° 1 tbl olive oil

° 1 tbl curry powder

° 2 tsp cumin

° 1 tsp chilli powder

° 1 tsp coriander

° 1 tsp non-iodized sea salt

 

Technique

 

° Wash the chickpeas and dry off on a paper towel

° toss them with the oil and half of the salt

° roast at 400° F for 35 to 45 minutes until golden and borderline crunchy. Don't burn!

° let them cool to room temperature

° combine all of the spices in a large bowl and toss the chickpeas in with the spices

 

 

from lance to chimps via godzilla...

As I was taking a walk a peloton of perhaps 30 bikes whizzed by in relative silence.  Everyone was dressed in the lycra uniforms that cyclists seem to prefer and each bike probably cost well north of $5,000.  There are several groups of serious amateur cyclists around here.  You rarely see people commute on bikes, but there is a small racing culture.

 

The train wreak that is Lance Armstrong made me think of how cycling has changed over the years.  When I was young that's how kids got around - cheap transportation that offered freedom.  In college I took up riding to unwind on weekends along with commuting as I didn't have a car.  I joined a club that regularly took 100 mile rides - centuries - and found them to be an ideal way to unwind from the pressures of school.

 

There wasn't any lycra, helmets were rare and most of the bikes were inexpensive Schwinns.  The lack of proper kit didn't make any difference.  None of us followed racing.  Bicycles were simple transportation.

 

Somehow biking faded.  There was a resurgence for awhile as "mountain" bikes appeared, but it was a fad for most people.  But then this guy named Greg LeMond won the Tour de France.  Greg was an American - an American who managed to break down a barrier by winning a quintessentially European race.  People took notice and amateur athletes took up cycling.  Then a more remarkable series of events - Lance Armstrong came along winning several consecutive Tours.  His performance was nearly super-human with a power output in the mountain stages that was freakish - fewer than one in a billion people would have that sort of capability.  Not to mention he was a cancer surviver.

 

Amateur cycling in the US became a big thing.   Cycling for commuting and for the fun of it was still fading, but a visit to a bicycle store revealed serious exotica.

 

My cycling club in college had an interesting connection.  Paul MacCready had developed an interest.  Not in cycling, but in cyclists.  He was mounting a challenge to the Kremer Prize - £50,000 to the first person who could take off, stay at least ten feet above the ground and complete a figure eight around two pylons separated by a mile and a half.  Many had tried, but materials had changed and Paul happened to be a serious boffin when it came to aerodynamics and aircraft design.

 

Finding the right engine was important.  I can't quote the exact numbers, but something around 400 watts were needed for takeoff and perhaps 250 watts for cruising - assuming the pilot was *very* light.  Bryan Allen was an amateur cyclist who could develop enough power while not weighing much - probably under 130 pounds.  To cut a long story short they not only won the prize in August of 1977, but went on to cross the English Channel with an improved airplane.

 

If you've ever been around a group of world class cyclists you are struck by their size.  They are rarely over 5' 9 and tend to have amazing leg development while having very little muscle in their arms - not terribly surprising.  The rules of many sports conspire with physics and physiology to give world class athletes in a given event very similar body types and sizes.  A great luxury of just doing a sport for fun is hard work and passion can produce results that are good enough to keep you going, but as the level of competition increases there is a selection driven by genetics - you won't see 6' gymnasts or 5' 5 basketball players in Olympic competition.  Even with freakish athletic abilities physics gets in the way.

 

For some sports "bigger is better" doesn't hold.  Some sports favor the ability to change the direction your body - or part of it - is traveling.  Others require pure strength.  For those you either need the largest possible muscle or create special classes to allow athletes of a range of size to compete.

 

Here is where scaling comes in ..  if you scale up a body by some amount, how much does his or her strength change?

 

The strength of a muscle depends on how many muscle fibers are pulling together - strength increases as the cross sectional area of the muscle.  A person's cross sectional muscle area changes as the square of their height.  Their weight, on the other hand, increases as the cube of their height.¹  What is important to note is their strength to weight ratio changes as the square of their height divided by the cube of their height.  The chart shows a reasonably good correlation between the olympic records for the "clean and jerk" and the weight of the athlete to the two thirds power.   The smallest class of weight lifter can have lift three times his own weight while the largest class world record holder can only lift about 1.7 times his own weight.

 

There are some interesting consequences.  This limits the size of animals.  Scale up an animal and you reach a point where it is simply too heavy for its muscles to move around.  Scale down an animal and its strength to weight ratio increases dramatically. Godzilla wouldn't be able to move.²

 

Some sports like discus and hammer throwing don't have weight classes, so only pure strength is valued and the largest athletes have an enormous advantage.  Other sports, like cycling, have more complex interactions dictating ideal size and weight.³

 

This brings up back to the elite of the elites.  There are some sports where you need genetics that are one in a million or even one in ten million to compete at the highest level.  Someone like Lance Armstrong recorded such freakish performance racing in the mountains that it was more like one in a billion - or even rarer.  The problem with cycling is there are perhaps fifty cyclists at least one in hundreds of millions ... an indication of foul play.

 

Doping of one form or another exists in some sports.  Much of this is dangerous, but where do you draw the line?  Caffeine has been shown to enhance some types of performance as an example.  What is the acceptable normal for a human and what are we comfortable with kids emulating?⁴   Already we have seen debate over "handicapped" athletes like Oscar Pistorius in the London Olympics  We are nearing the point where an elite athlete might have an advantage by amputating limbs replacing them with artificial limbs that use exotic materials. There are advantages for runners as well as cyclists.  And we are on the verge of manipulating genes - some of the modifications may be unhealthy, others may prove to be neutral or even healthy.  It comes down to the fundamental question of what competition means and where we draw lines.  Many sports at the most elite levels have become entertainment with the potential for great financial reward.  We've seen many athletes trade the increased chance of a shortened life for short term rewards.  Watching the Lance train wreck play out and seeing if it changes cycling may be an indicator of what we tolerate - at least for the present.

 

The good news is most of those who play amateur and school sports are not playing at the elite level and don't need to be in order to be happy.  Doping and body modification, along with a need to be an Olympian, are just not important.  Short people can participate in sports that favor height and make up the difference with training and passion.  Tall or short people can cycle.... the list goes on and on.  

 

A few years ago I spoke with the athletic director of an academically elite school.  They require three semesters of physical education for all undergrads. They participate in N.C.A.A. Division III, and their record happens to be at the bottom of the barrel.  What impressed me was the school's attitude towards sport.  Their goal was to allow students to find physical activities that they liked well enough to continue on their own for life. The goal was to provide counterpoint to what was likely to be a sedentary work style and promote health over the long term.  They saw themselves as having a mission to act as a personal trainer.  Team sports and competition are a driver for some of their students, so they participate.⁵

 

And that leaves chimps.  An adult chimp is seriously stronger than any human - their strength to weight ratio is off-scale relative to ours.  This seems odd as they are close relatives sharing about 99% of their DNA with us.  The trick is they lack fine motor control - their muscle fibers are wired to contract in large groups where ours contract in much smaller groups and we can't contract the same percentage of muscle fibers as they can.   A chimp baseball player might have a wicked left hand, but their ball control would be seriously lacking and their handwriting would be awful.

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¹ Assuming their body shape and density remains the same.  A good first order assumption for very elite athletes in a given sport.  Area will increase as the square, volume as the cube.

Specifically if the length of an object with an area of a₁ changes from l₁ to l₂ the new area a₂ will be 

a₂ = a₁(l₂/l₁)²

double the length and the new area increases by a factor of four, triple it and it increases by a factor of nine. 

The volume will increase by the cube of the length.  

v₂ = v₁((l₂/l₁)³

Now doubling the length increases the volume by a factor of eight, tripling increases the volume by a factor of twenty seven. 

Since strength is proportional to the cross sectional area of a muscle and weight is proportional to their volume if everything is scaling uniformly, a person's strength to weight ratio changes as the square of their height divided by the cube of their height.  Or as their weight^2/3

It is important to stress that this ratio only holds if everything is scaled.  My friend Colleen, at 6'7, is about 23% taller than the average adult female.  Appling simple scaling, you would expect her to weight 86% more, but she is both thinner and more muscular and her ratio of leg length to height is much greater than the average female, so the rule doesn't hold.  Simple scaling breaks down when body proportions change and variation is common with extremely tall and short adults. What is true is she is quite a bit stronger and heavier and the length of her limbs means she can't accelerate them as quickly as a smaller person.  The rules of volleyball give her a great advantage in many positions, but less where quick movements are necessary.  This means she needs a teammate who is significantly smaller and capable of greater accelerations.  Woman's beach volleyball seems to favor those with a height of about 6'0 to 6'2 and a slim build.

² Not only would Godzilla not be able to move, but his bones wouldn't be able to support his weight.  Note that elephants have to have much thicker bones proportional to their size than smaller animals just to deal with the extra weight.  

³ It would be fascinating to make a composite representation of the measurements of the top ten athletes in every sport (accounting for specialists in team sports) and make a chart of the silhouettes ranging from the smallest gymnasts to basketball centers.  There is a lot of physics going on!  

⁴ I couldn't find the reference, but someone published the weights of line backers on top ranked high school football teams in Texas over the past fifty years.  The increase was greater than you might expect for recruiting very large boys and giving them enormous amounts of weight training.  There is a chance that doping is taking place.

⁵ The school is Caltech.  Oddly enough they managed to violate the N.C.A.A academic eligibility requirement. Very strange as Caltech may be the most selective school in the nation.

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Recipe Corner

 

I'm a big fan of garlic and of pressure cookers.  Why not use to pressure cooker to cook garlic?  You'll need a trivet for your pressure cooker and a small steamer basket.  Most pressure cookers come with trivets.

I'm still exploring my pressure cooker and am finding it extremely useful - you can save a lot of time and energy plus modern cookers are very safe.  I use a Kuhn Rikon - a bit spendy, but well-made and recommended by every experienced user I talked to.

 

Roasted Garlic

 

Ingredients

 

° 3 large garlic bulbs (see if that will fit in your steamer)

° a bit of high quality extra virgin olive oil

 

Technique

 

° chop the top quarter or so off the top of the garlic bulbs - keep the top section for your future garlic needs

° pour about a cup of water into your pressure cooker and place the bulbs cut side up in a steamer that sits on a trivet  

° cook for about 5 minutes on high pressure and then let the cooker come back to atmospheric pressure naturally - e.g. - just move it to a cold burner and let the pressure come down by itself

° remove the bulbs with tongs, place them in a heat-proof dish and drizzle the olive oil over them.  Broil on the top rack of your oven until they are nicely caramelized - about five minutes in my case.

° yum!

 

pulling your weight

It was 1900 at the Paris Olympics.  The Dutch pair of François Brandt and Roelof Klein had qualified in the coxed pairs, but had lost a race to a French pair.  They came to the conclusion Hermanus Brockmann, their 60 kg cox, was too heavy so they found a young boy in the crowd to do the duty.  The boy weighed 33 kilograms and was light enough that five kilograms of lead had to be attached to the shell to make the rudder properly set in the water.

 

The flying Dutchmen leapt to an early lead but couldn't keep their initial pace.  Halfway into the race the French started their move, but at the finish the Dutch were still ahead - but by less than a meter.  A dramatic race by any measure, but more curious is the fact that the cox disappeared into the crowd never to be awarded his gold medal.¹

 

How important is that dead weight?  In theory a cox aims the boat in the straightest possible line, gives pacing and coaching, and removes the effects of uneven thrust as much as possible.  But he or she also adds to the load. Just how important is that?

 

Before diving in,  I note that I'm going to give a sense of the sort of approximation that is common in the physical sciences during play.  One of my advisors said that a 13 year old kid who starts thinking about what miles per gallon means is left with the conclusion the measure is terrible as it doesn't work well in comparing vehicles (you really want the inverse - gallons per distance), you have someone who may well become a good engineer.  If, on the other hand, the 13 year old says "wow - I can express that as inverse acres!", the kid has physics potential.  

 

In doing very quick calculations to test ideas dimensional analysis is frequently invoked. The kid destined to be a natural scientist would look at the units and note that gallons is a volume or a mass.  Assuming you are using the same liquid in your comparisons - at least liquids of similar densities -  it doesn't matter ... take your pick.  Let's pick volume ..  the dimension of volume is a length cubed -  L³.  Miles are easy - just a length.  So miles per gallon is dimensionally L/L³ or 1/L² - an inverse area.  It could be inverse square meters, inverse square feet, or  ... hey .. inverse acres has a nice rural feel to it.^.2  

 

I needed to do a quick estimate for what is described next and rushed through it in about two minutes at the blackboard using this technique.  It is good enough to understand what is going on at a basic level and that is good enough to get started.  There have been complaints that some readers find my writing too technical.  It is ok to skip the next section and I'll color the skippable text in blue to make it easy, but I thought it might be interesting for some to see how I play.

 

So the question is how much does it cost for a racing skull to carry a cox?  Rather than a boat with two rowers let's consider the more general case with N rowers.  A four man boat has twice the power of a two man, but its weight is about twice as much.   Does having twice the engine and almost twice the weight help or hinder?

 

The power the rowers deliver mostly is used to overcome the drag on the hull.  It is

p = f_d * v

where p is power, f_d is the force of drag, and v is the boat's velocity relative to the water

The force of drag is reasonably complex and would require some careful measurements that depend on the shape of the hull and some other factors.  The important thing to realize it is proportional to the wetted area - something that goes as a length squared - and the square of the velocity.³   So 

f_d ∝ L² * v²

the power needed is 

p_d ∝ L² v² * v or L²v³ 

The power to overcome the drag is supplied by N rowers (assuming all are about equally strong).  A racing shell is pretty minimal, but its volume needs to increase to float with the heavier load.  The volume goes as L³ and also is proportional to N, so L ∝ N^1/3.  Getting tricky we substitute and now

p_d ∝ L²v³ ∝ N^2/3v³

getting to the end! ....  We know power supplied is proportional to N so 

N ∝ v³ N^2/3

solving for v we see

v ∝ N^1/9

 

The speed of the boat only increases slightly with an increasing number of rowers.  For those of you who have rejoined us it only increases at the one ninth power of the rowers or N^0.111.   The time is just to the inverse of the speed over similar distances so t ∝N^-1/9. If you look at world record times over similar distances this holds for one to four person coxless skulls reasonably well and is a good enough model for this purpose. 

 

The original question was what is the impact of the cox - the little guy or gal with the rudder and the microphone?  I did a similar analysis increasing the size of the boat, and thus its drag, by going to N + 1 crew members, but assuming only N are contributing to the power.  I won't go through the reasoning as it takes much more time to type than to think about it, but it is very similar.  The predicted time with a cox, t_cox is:

t_cox ∝ (N + 1)^2/9/N^1/3 

To get something that is easy to think about look at the ratio of cox and coxless times and apply a bit of rearranging

t_cox/t ∝ ((N + 1)/N)^2/9

(N + 1) is always bigger than N, so the cox always slows things down ...  not by a lot and the effect decreases with increasing N.  A two man boat should be about nine percent slower if the weight of the cox is similar to the rowers.  But it isn't.  The Dutch used a kid who was about a third the weight of each rower, so a reasonable guess would be about (2.33/2)^2/9 or something over two percent slower - probably several percent faster than an equal muscled crew with a cox that weighed as much as poor Hermanus Brockmann.

 

You can play with some numbers yourself - assuming the cox is just along for the ride the impact of having one decreases with crew number.   Since races are tight you don't want to race coxed vs uncoxed boats and you don't want a heavy cox.  Hopefully they add more value and perhaps you can get a sense of quantifying that value in real vs expected times.

 

A physics teacher usually doesn't do this sort of manipulation for non-major undergrads, but recommends checking answers by looking at the units - if you are calculating an energy it should have the dimensions of mass times the square of a velocity or ml²/t^{2  -} if your answer has different dimensions, there is no way the calculation can be correct. From there you can see if you have picked the right units.  It can be unfortunate to mix metric and Imperial units.⁴

 

Most of us use abstractions - frequently symbolic abstractions like art - to think about our fields.  They allow us to move quickly and play with the key concepts so we don't get lost in the forest of details.  When necessary it is often possible to do something much more detailed - at least we know how to do it in principle.

 

You could ask me what is the predicted time of a eight man coxed shell and I could give some rough approximations, but building an accurate model would rely on careful measurements.  But if you asked me for a ratio of times when the athletes and boat designs were roughly equivalent - then it is only a couple of minutes worth of calculating. You realize when all the tricky stuff drops out and the fundamental parts of the underlying physics are all readily available - in this case some analysis let us get down to just the number of power producing athletes.

 

You have probably seen Feynman diagrams.  They are really visual short hand abstractions of some very complex physics.  You can create and manipulate them with relative ease and make easy to calculate comparisons even though working through the underlying math can be extremely difficult.  They enable play and play and curiosity are two of the big drivers in the field.  Play greatly illuminates whatever you are working on and I encourage anyone to find the play component of their craft and hone it.

 

But in the experimental phase there has to be enormous caution and the analysis phase combines caution and self criticism.  It is still fun, but calculation short cuts don't apply as much as they did early on in the game.

 

But back to the game at hand.   What is the real value of a cox?  I had originally intended write about reducing the wiggle waggle in the shell's motion that is produced by the fact that there are uneven torques produced by the arrangement of the rowers when you have one oar per person.   Next time or the time after I'll write about suppressing the wiggle waggles.

 

And there is another really important issue in many sports.  Larger people tend to have more muscle, but they are also heavier.  Only a few sports adjust for this and the fact that many don't limits participation at elite levels in many sports to larger people.  But smaller people tend to have higher strength to weight ratios ... and you can't have a Godzilla.

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¹ I came across a brief reference to this reading about rowing history and tried to track down a bit more.  There are numerous references and a starting point is here.

² I don't mean to suggest natural scientists are better or worse than engineers.  You can have amazingly brilliant people in either.  The goals and nature of each of these sports attracts very different personalities and native inclinations.  In the end engineers do much better financially than physicists, so that is in their favor, but physics is great fun if that is your inclination.

³ Force has the units of mass * acceleration or mL/t².  Note that L² * v² is L² * L²/t² or L⁴/t², but m ∝ L³, so we can express the ball of wax as mL/t².  (I'm also using L capitalized as l is difficult to tell from the numeric value of one in this font.)

⁴ The Mars Climate Orbiter was lost at orbit insertion as the ground based computations assumed Imperial units for the retro-rocket thrusters ... specifically pound-seconds.  The spacecraft was constructed and the numeric values were tabulated using metric units of newton-seconds.  This destroyed the craft as it entered the atmosphere at a low altitude.  Nearly $700 million and a lot of potential science quickly went down the drain. 

A similar unit problem put a plane load of people at risk, but a pilot who knew a lot about sailplane flying was in the cockpit and the Gimli Glider became aviation legend.

 

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Recipe Corner

 

A really great snack from canned beans.  All measurements are approximate and don't matter much - just play around!

 

Roasted Garbanzo Beans

 

Ingredients

 

° a can of garbanzo beans

° a tablespoon or two of olive oil

° non-iodized salt

° spice blends - use your imagination.  I have a cajun seasoning that is very good.

Technique

 

° preheat oven to 400°F.

°  Drain the beans in a strainer and rinse with water .  Spread the beans on a paper towel and use another to absorb the excess water and roll the beans around to remove the skins. 

° put the beans on a baking sheet and drizzle olive oil over them making sure they are somewhat evenly coated. Roast for 30 to 45  minutes until the beans are a deep golden brown and crunchy and don't let 'em burn

°  season with salt and spice blend.

 

These are really addictive!  

how's that for wimping out with a quick recipe?  

 

 

dialing back gravity and where to stand for sport

When you jump into the air the height you reach is by how strong you are, how much you weight and gravity.  We don't have much control over gravity without a bit of serious travel, but what if we could dial it back?  Imagine travel to other worlds where the gravitational field is less - where you weigh less.  The gravitational acceleration depends on the radius of the world and its mass.¹  Relative to Earth the moon's surface gravity is about 0.17, Mercury is 0.38, Mars 0.38, and the tiny Martin moon of Phobos is only about 0.005.  

 

My vertical jump is approximately embarrassing, but Colleen is athletic and has trained hers and got to where she could raise her center of mass 31 inches.  She does this by converting energy from her muscles into a vertical velocity and reaches her peak height when that velocity has burned off - her initial energy = m_colleengh.  If you solve for h you note that if g is varied, her ultimate jump height varies as the inverse.  So her 31 inches on Earth becomes a bit over 15 feet on the Moon and 515 feet on Phobos!  Of course her weight on Phobos is only 14 ounces.

 

You can also calculate how long she would be above the ground.²  On Earth her flight is about four tenths of a second, but on the Moon it would increase to 5.7 seconds and Phobos gives a leisurely long trip of about 2 minutes and 40 seconds.

 

Imagine what sports would be like (assuming you could breathe, of course)!

 

Phobos would present some interesting challenges as the escape velocity is about 25 miles per hour.  It would be easy to throw a ball fast enough to leave the little moon and sail off into space.  You can also imagine constructing some not terribly cumbersome wings and flying around in an air filled room on our moon.  Any number of fantastic new sports could be created.    For fun let your imagination take flight and out a few numbers so you can invent some new sports for the Moon, Mars and beyond.  We appear to be wired to take delight in sport and I have no doubt this will happen some day even if it is largely impractical now.³

 

But we can move around on the Earth and find a bit of advantage for another reason...

 

The Earth spins about on its axis once every 24 hours.  There is a centripetal force from this spinning that tries to pull something off the surface. If you are on the equator the force of gravity plus the centripetal force makes you effectively a bit lighter.  At the poles the outwards force vanishes and you are a bit heavier.  A bit of physics and geometry gives the effective value for g is about 9.8061[1 - 0.00263cos(2Θ]), where Θ is your latitude in degrees.⁴  Plugging in the extremes of 0 and 90 degrees ... 

 

you weigh about 0.53% less at the equator than at the poles

 

There are a few other  terms -  one that depends on your height about sea level - you weigh about 0.11% less at 3,000 meters than at sea level....  and yet another smaller term that depends on the tides.⁵  The bottom line is that on a spherical rotating planet like the Earth with its variations in altitude there will be significant differences in the acceleration of a body due to gravity that depend on where you are.

 

If you want to lift the largest weight or jump as high as possible, you want to go as close to the poles as you can. Going to a higher altitude might hurt your athletic performance as there is less oxygen, and most Summer Olympic events seem to be held close to sea level these days. 

 

But the real world is a bit more complex.  Even if you include these corrections, very careful measurements of g show something else is lurking under the surface.  The big one is the shape of the Earth.  Our planet turns out to be far from spherical, but is rather a bumpy ellipsoid, so the altitude dependent terms needs correction.  Reference geoids are calculated and are an important component of the GPS system.  We also have high quality maps of the Moon and Mars...⁶

 

Under the surface are regions that vary in density - mountains and continents tend to be lighter material that "floats".  Maps of the distribution of mass under your feet changes depending where you are -  accurate gravitation maps have been tabulated by experimentation with satellite observations greatly increasing the accuracy of the models.  The value for g changes by about 0.2% within the boundaries of the lower 48 states.  Across the planet the difference can be as large as 0.8%.

 

Position is something you need to correct for if you care about precision weights and measures, but it is something that sport does not consider.  There are usually other factors that are larger in sports performance, so we can get away with ignoring it - but for some sports like weight lifting it may make a difference.  But if you really need to lose that extra pound and are into extreme travel ....

 

And some day we may be doing sport in spaceflight using simulated gravity (a rotating the spacecraft for example) or even on another planet or moon....  

 

... then things get fun!

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¹ The force of gravity is Gm₁m₂/r² where r is the distance between two bodies, m₁ and m₂ are their masses and G is a constant of nature.  We simply this on Earth by noting that force = mass times acceleration, so for a body on the Earth's surface the force of gravity is the mass of the object times the acceleration due to gravity.  A bit of algebra shows this is Gm_earth/r²_earth  It shows up in physics texts as g.  Your weight is the force that holds you to the planet and is just this acceleration times your mass.

The important thing to note is g depends on the radius and mass of the body you are standing on.  

² distance = gt²/2, so t = 2sqrt(2h/g) because it takes the same amount of time to go up as it does to fall.  Note that this neglects air resistance.  

³ This would be fertile ground for future completely immersive computer games where you senses can be altered - or at least a powerful enough simulation can give a sensation of very low gravitational accelerations.  

In the real universe a few astronauts managed to jump around on the moon and Alan Shepard even smuggled some golf balls and his six iron on Apollo 14 managing what was probably the more impressive shots ever

⁴ the centripetal force is mv² /R_earth where v is the speed the Earth's surface is moving at at a given latitude.  At the equator v is about 463 meters per second and it is 0 at the poles.  

⁵ At sea level g = Gm₁ /r² , so at altitude h, gh = Gm₁ /(r+h)² = Gm₁ /(r² + 2rh+h²). Noting h²/r² is extremely small and rearranging we get gh ~ g/(1+2h/r).  Note that the centripetal term changes a bit as the radius changes from r to r + h.   Plugging in the numbers this altitude dependent term where g at a given latitude decreases by about 3.92 *10^-7h, where h is the distance above sea level in meters.  It is straightforward to calculate the tidal term, but I won't in interesting of time.

⁶ Very accurate gravity maps can be made by carefully tracking the position of an orbiting satellite. The best are made using a pair of orbiting satellites flying in formation perhaps a hundred kilometers apart. They compare their relative positions to better than a millimeter.  Depending on what is directly under them, they speed up and slow down changing their separation a bit as they fly. One of the more impressive measurements in science.

 

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Recipe corner

 

Barbecued Okra

 

Okra has a bad reputation - largely from inappropriate cooking techniques. Getting it right is simple - just wash and carefully dry some fresh okra, string on a pair of bamboo skewers (don't run one through your finger!), brush with olive oil and a finishing salt like Maldon and throw on a hot grill for about 10 to 15 minutes turning a few times and brushing on more oil along the way.  

When experimenting with fresh produce it is often best to just try simple things and explore the flavors using various techniques rather than relying on many seasonings (other than salt) and other ingredients.

 

Rugbrød

 

Europeans usually have much better breads than Americans.  I'm a fan of the dark and dense ones - Danish rugbrød in particular.  Making it isn't easy and I can't find anything like it in bakeries (I keep trying - if you have a source, please let me know!).  I even wrote to the Danish embassy in Manhattan and had a reply lamenting the poor state of bread in the US.  They get deliveries from the motherland, but the staffer suggested I try a Swedish mix from Ikea.  

It turns out to work very well - look for Brödmix Flerkorn (Swedish for multi-grain bread mix). This is the old packaging.  Ikea has largely burned through that stock and has the same thing under their own brand with directions in English.  Making it is very very easy.  Just add some water to the milk carton-ish container, shake and pour into a baking pan.  You let the yeast do its thing for awhile and then bake.  It isn't the best rugbrød I've had, but it is still very good and a great basis for open face sandwiches.  Very healthy stuff too...

 

recommended!!

 

back to regular recipes soon...

there is a reason, turn, turn, turn ...

 A bit over 38 years ago a small band of dreamers used a bow and arrow to shoot a fishline between the then-unfinished World Trade Center towers and processed to draw larger lines back and forth until they finally managed to anchor a steel cable to both sides.   Early the next morning Philippe Petit stepped onto the cable from the South Tower at the 104^th floor level and spent the next 45 minutes stunning the city before a police helicopter threatened to pick him up and a rain began to fall.

 

Like most tightrope walkers, Petit used a large and quite heavy balancing pole.  Most people tend to think these are for lowering the walker's center of gravity to add a bit of stability, but they tend to raise the center of gravity a bit as the normal point is usually between the 51 or 54% height of a person.  The real reason turns out to be far more interesting and gets into some physics that explains a lot of Olympic sports and beyond. But before getting into that we first need a little trip in season and place, so if you can leave Mr Philppe on that thread between Earth and heaven let's go to a Wintery pond.

 

Imagine a nice frozen pond and a few skaters.   Imagine one of them knows her way around.  She is clearly used to smoothly gliding along the surface of the ice and settles into a spin with her arms stretched outwards.  She's spinning fairly quickly, but she pulls her arms in to her chest and her rate of spin increases dramatically even though the only thing she seems to be doing is moving her arms.

 

It turns out her spinning motion has a momentum - an angular momentum.  It is usually shown as L = Iω and is the rotational analog for momentum with I, the moment of inertia, acting like a mass and ω, the angular velocity acting like a velocity.¹  The important notion is this is a conserved quantity.  It takes energy to spin up a body, but once it is spinning the angular momentum doesn't change.  

 

The skater is able to alter her moment of inertia as it depends on the distribution of her mass.  It turns out it is greater when her arms are stretched out, so when she pulls them in her angular velocity must increase so her total angular momentum doesn't change.  And that is what makes Mr Petit's task a bit easier.  His long balancing pole is quite heavy and these things are often weighted towards the end.  His moment of inertia increases a lot and any tendency to rotate one way or the other is slowed - slow enough that his nervous system and muscles have time to compensate for instabilities from the vibrating wire, the wind and even slipping a bit in the rain.  It is a beautiful way to cheat just a bit.²

 

Many athletes use this - it is particularly important in sports where you are trying to rotate your body as you are flying through the air.  Subtle and not so subtle changes in the shape you wrap yourself into make dramatic changes in your spin and can even rotate you around different axes.  The reason why a diver straightens his body just before entering the water, aside from comfort, is the diver is supposed to stop his rotation - stretching like this does a dandy job.

 

You may notice a runner in a race on flat ground where acceleration is important keeps his arms fairly close to his body.  The reason has to do with angular acceleration.  Just as we have a linear form of kinetic energy there is an angular form that goes as Iω²/2 in the same way the linear form is mv²/2.   With the lower moment of inertia a runner can accelerate using less energy.  Now if you are running over unstable ground you want to extend your arms to give yourself some momentum to more easily move over these areas as well as give yourself additional stability.

 

A few posts ago I never got around to the cyclists.  It turns out I've been using mv²/2 as the kinetic energy for a bike throughout this blog but that is only an approximation.  I neglected the angular component for the wheels and the chain wheel, chain, cogs and spinning feet of the cyclist..  We can ignore everything but the contribution from the wheels. If we assume the wheels are the same it is Iω² , so the total kinetic energy of the bike is mv²/2 + Iω² . I, it turns out is related to the distribution of the mass in an object.  A rim that weighs the same has twice the moment of inertia as a uniform disk of the same mass and radius (in some units I_disk =  1/2 and I_rim = 1).

 

In a bike race it is important to spend most of your energy to accelerate the bike.  Lighter wheels are important as is a lower moment of inertia.  The best wheels for a bike have a light mass being careful to keep mass at the rim as low as possible.  Ideally you don't have to race with gusts of wind from the sides.  In a velodrome with no sidewind you can have solid disks for wheels as there is no wind to blow you over. This can be enormously imporatant for some events where burts of acceleration are required.   Outside of the calm velodrome a disk wheel is usually dangerously impractical.  The best you can do is to use exotic materials and buy or build the lightest wheel possible.³  Note that on off-road bikes it is often necessary to maintain momentum over uneven ground.  Here light wheels are not a great advantage, plus they need to be very strong.  

 

The impact of angular momentum and kinetic energy is felt throughout sport - any sport where you have to rotate or rapidly change direction.  Watch a soccer player and the position of his arms, the effort it takes in swinging a bat or someone doing any sort of throwing motion.  Notice the position of a leg below the knee as someone moves it forward when running - you make the leg as short as possible to avoid having to add energy.  It shows up almost everywhere and good technique follows physical principle.  

 

It even dictates likely partners in some team sports.  Beach volleyball is particularly interesting as there are only two players.  The amount of effort (torque) a player needs to develop to move part of her body through some arc is proportional to the square of the length of that body part.  Very tall people tend to accelerate more slowly.  Height is a great advantage for part of the beach game, but other parts demand rapid acceleration.  My friend Colleen at 6'7 had a lot of length to get moving.  Her 10% height difference over a six foot player translates into a 21% disadvantage in effort required move at the same angular velocity and even more over a smaller player.  A variety of rules seem to conspire to make the optimal height of a female volleyball player about six feet.  Colleen needed to balance her height with a very short partner - ideally someone about 5'6 and with lightning quick reflexes.⁴

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¹ I'm leaving out the its vector nature as well as the fact that the moment of inertia is really a tensor.  Lots of physics here that I'll just skip.  But it is important to note that ω is just the angle the body rotates through in a second it is usually expressed in degrees or radians per second. For something like a rotating wheel it is the linear velocity at an instant divided by the wheel's radius.  A small wheel turns at a fixed angular velocity covers less distance than a large wheel.

² I'm leaving out details that this applies to a particular axis of rotation as well as a calculation or two showing how much it slows him down.  

³ The best bike wheels can cost more than $7,000 a pair and weigh about a kilogram per pair.  To understand why some elite teams are willing to part with this money consider a bike where the wheels each have a mass m and the rest of the bike has a mass M.  The total energy of the bike in motion - the two wheels and the rest of the bike - is  (2m + M)v²/2 + 2(Iω²/2).   The inertia is Imr² for a wheel ..  for a thin rim I = 1, so it is must mr^2.. A bit of rearranging and remembering v= rω, we get (M + 2(2)m)v²/2  or(M + 4m)v²/2for the total energy.  Note that the radius of the wheel cancels out so you don't need smaller wheels unless they are lighter.  Also note a reduction in mass of the wheel is much more beneficial than weight in the rest of the bike - dropping a kilo from the wheels is like dropping four from the rest of the bike - and it turns out to be possible with exotic materials. Not to mention the bike is more responsive to acceleration.  No wonder they will pay so much.  And "they", in this case, is usually a professional team funded by someone other than the riders.  Some of these wheels are so close to the limit that they won't support a bike plus rider weight of over 80 kilograms - about 176 pounds.  Amateur racers use wheels that are a bit heavier and much less expensive - usually "a bargain" $2,000 or less a pair.  And the rest of us have bikes that cost less than half the price of a pair of good wheels and are perfectly happy.

⁴ Note that Karrie and Misty "balance" at a fraction under 6' and volleyball players make terrible gynmasts or divers.

 

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Recipe corner

 

Instead of the normal recipe a couple of items.  

 

The first is a discovery.  A friend is lactose intolerant and I've spent some time over the past year looking for a good enough ice cream alternative.  There are a lot of really awful products out there - and often at outrageous prices.  The best solution to date was a homemade coconut milk base that was churn frozen with liquid nitrogen to keep the ice crystals small enough to produce a good texture - I have been unable to get low enough temperatures with conventional technique.  Since that is difficult to do (I lost my easy source of liquid nitrogen and a dewar I could borrow for the asking),  I continued sampling commercial alternatives as they went on sale.  

 

Finally a winner!  It isn't cheap, but So Delicious makes a coconut "ice cream" that tastes good and has the closest texture and mouth feel to regular ice cream I've seen.  It isn't a substitute for the real thing and no one will be fooled comparing it to a super premium or quality homemade, but it is still pretty good.  I've sampled and can recommend the Cherry Amaretto, Passionate Mango and Mocha Almond Fudge flavors (I know - vanilla is the benchmark for really seeing how good it is, but I'm just looking for a substitute).  If you or a friend is lactose intolerant or a vegan, I can give this one a recommendation - even if it is spendy.  

 

I find I have to have a bit of an indulgence a few times a week to sustain my sanity during weight maintenance.  I'm in it for the long haul and you just can't deny yourself a few pleasures every now and again.  This means I can justify paying a lot for the occasional treat.

 

The other item is not food, but is an interesting paper from the Archives in Internal Medicine that may be great news if you want to have a healthy old age:

 

Midlife Fitness and the Development of Chronic Conditions in Later Life 

Benjamin L. Willis, MD, MPH; Ang Gao, MS; David Leonard, PhD; Laura F. DeFina, MD; Jarett D. Berry, MD, MS

 

Background  The association between cardiorespiratory fitness (fitness) and mortality is well described. However, the association between midlife fitness and the development of nonfatal chronic conditions in older age has not been studied.

Methods  To examine the association between midlife fitness and chronic disease outcomes in later life, participant data from the Cooper Center Longitudinal Study were linked with Medicare claims. We studied 18 670 healthy participants (21.1% women; median age, 49 years) who survived to receive Medicare coverage from January 1, 1999, to December 31, 2009. Fitness estimated by Balke treadmill time was analyzed as a continuous variable (in metabolic equivalents [METs]) and according to age- and sex-specific quintiles. Eight common chronic conditions were defined using validated algorithms, and associations between midlife fitness and the number of conditions were assessed using a modified Cox proportional hazards model that stratified the at-risk population by the number of conditions while adjusting for age, body mass index, blood pressure, cholesterol and glucose levels, alcohol use, and smoking.

Results  After 120 780 person-years of Medicare exposure with a median follow-up of 26 years, the highest quintile of fitness (quintile 5) was associated with a lower incidence of chronic conditions compared with the lowest quintile (quintile 1) in men (15.6 [95% CI, 15.0-16.2] vs 28.2 [27.4-29.0] per 100 person-years) and women (11.4 [10.5-12.3] vs 20.1 [18.7 vs 21.6] per 100 person-years). After multivariate adjustment, higher fitness (in METs) was associated with a lower risk of developing chronic conditions in men (hazard ratio, 0.95 [95% CI, 0.94-0.96] per MET) and women (0.94 [0.91-0.96] per MET). Among decedents (2406 [12.9%]), higher fitness was associated with lower risk of developing chronic conditions relative to survival (compression hazard ratio, 0.90 [95% CI, 0.88-0.92] per MET), suggesting morbidity compression.

Conclusions  In this cohort of healthy middle-aged adults, fitness was significantly associated with a lower risk of developing chronic disease outcomes during 26 years of follow-up. These findings suggest that higher midlife fitness may be associated with the compression of morbidity in older age.

Unfortunately it is behind their paywall.  The short version is regular exercise in midlife has a payoff as you age.  The awful chronic diseases are of much shorter duration and at the end of life - so your older years can be much better.  The relationship between midlife fitness and long term health has been suggested, but not carefully studied.  This study looks at 18,000 adults over 40 years and was able to focus on the final years of life.  

It isn't much of a surprise that heart disease and heart failure is reduced, but they found lower rates of diabetes, Alzheimer's disease, kidney disease, and a few others.

Modest levels seem to be sufficient - 150 minutes a week of moderate to vigorous physical activity is apparently sufficient - so swimming, jogging, cycling, etc...  My rowing would certainly qualify.  Perhaps this is why countries like Denmark and the Netherlands have lower rates of chronic disease in later life - a large percentage of the population is physically active as bicycles are regularly used for commuting and errands - a very cheap and nearly transparent way to get regular exercise.

As with many of these studies there are some caveats that came out in an interview and are probably in the paper - but it appears the underlying recommendation of getting some exercise is valid.

I find it fascinating that the Netherlands and Denmark both note correlations between cycling and lower healthcare costs.  I don't think they've performed this sort of study, but are probing the same thing.  They are able to calculate a cost/benefit ratio for building cycling infrastructure that saves medical expenses - since their governments build the infrastructure and offers universal healthcare (sigh - the civilized world), such justifications are easier to act upon.  The figure is something like a dollar spent on cycling infrastructure (bike lanes and roads, parking facilities, snow removal, and so on...) saves four dollars in healthcare costs.  This is one of the reasons why both countries are pushing for greater cycling use - overall fewer than half of their citizens regularly cycle (in the US it is about one percent of adults).

Adopting a regular exercise program can be tough as many of us are pressed for time.  I mined some of my evening "down" time - times when I would watch TV or listen to the radio.  Now I time shift with podcasts, audio books and online course lectures.  If you are selective the quality can be better than one gets sitting in front of the screen.  I generally do this first thing in the morning before starting into work.  I also had a period where I needed to lose weight and found it was essential to build my fitness level.  Now I'm in a weight maintenance mode, but the fitness component is essential.  This means I needed some coaching and motivation.  I recommend that approach - talk to someone who knows what they are doing. Some people like gyms as they get focus and equipment.  I find gyms are a pain to get to and expensive, so we have a home gym and I get coaching elsewhere.  

Experiment and find what works for you.  Perhaps it is jogging, swimming, cycling a team sport or even serious dancing ... there are many channels and all you need is to find one (perhaps even more than one) that you like and can sustain.  Here is a short piece on my weight loss and exercise program - different things may work better for you, but it may be a starting point.  I note that there are many immediate benefits from regular exercise - perhaps most impressive is the good feeling that persists for a few hours afterwards and what seems to be a somewhat greater cognitive capacity. (admittedly anecdotal)

I caught an audio stream with an author interview  - recommended listening. (about 10 minutes)

 

Midlifefitnessinterview

 

 

the costs of stop and go as well as spinning

If you are ever thinking about buying a rowing machine, we should talk.  I spend something north of six hours a week on one and have come to learn a fair amount about various approaches.   My main machine is a classic Concept II model B that was probably made in 1986.  It was the second generation of the first simulators that were good enough for serious rowing athletes to train on and you can learn a bit of good technique with them.  It is also built extremely well.  You pull a handle attached to a chain that spins a racketed sprocket that is, in turn, attached to a flywheel with some turbine blades cut into its face.  Most of your work goes into swirling the air.  The immediate vicinity of the machine is mostly dust free as a result.

 

This year I added a second machine as something of a splurge.  Nice as the model B is, and there are several newer models but it seems unlikely this one will wear out in my lifetime,  it doesn't go far enough to reproducing the motion of a rower in a scull and you miss some important bits of form as a result.  Most important is the fact that your feet are stationary and your trunk moves back and forth.  Some serious rowing enthusiasts mount their machines on nearly frictionless sliding rails.  Doing this sort of works, but is expensive and takes a lot of room.

 

The folks who make the Concept II machines (they also built most of the racing oars used in competition), came up with a newer design with a clever mechanical system that allows your butt to stay mostly fixed and more closely encourages proper technique.  I splurged and bought one. Lovely and recommended if you intend to also use a proper scull, but overkill for regular exercise.

 

Why I mention it is that it has a similar flywheel, but adds a shroud with louvers that allow you to control the amount of air the blades can swirl.  This allows you to carefully tailor your training load.  When wide open the air drag is much greater than what the model B produces - as you stop rowing the flywheel comes to a stop much faster than the old design.  One thing you notice right away is that if your strokes are poorly timed or of unequal effort, you end up wasting a good deal of energy.  While this may be ok for exercise, it would be deadly when you are  racing.  There are advantages to a constant speed.

 

Which takes us to the bicycle track.  If you watched the indoor track bike racing you many have wondered about the fact the riders often travel very slowly and then suddenly burst into wild acceleration as they race to the finish.  You also may have noticed the unusual disk wheels in some events.  Why?

 

It turns out rules get involved in some events, basically indoor racing is in still air and the wheels have a bit less air resistance.  They also have a lower moment of inertia than a spoked wheel which gives them a great advantage when accelerating.  

 

When you are riding a bike you have to supply some work to get it up to speed.  Once it is moving there are a couple of forces that try to slow you down - one is friction against the road and the other is air resistance.  At bicyclish speeds the road friction is pretty low - particularly if you are using extremely narrow high pressure track bike tires and pales in comparison to air resistance.  If you stop pedaling and just coast on level ground, you slow and eventually come to a rest.   You can also supply some work to counteract the air resistance (and road friction) and move along at a constant speed.  Most of us have experienced both of these techniques on bicycles (it happens to anything that moves in a fluid, but I happen to love examples that you feel with your own physical exertion).

 

strap in - time for a deeper look

 

To set this up let's look at the energy required to get up to some speed, let's call that v.  Let's call the mass m - in the case of a bike it would be the rider plus her bike, for a runner it is just the person.  You start out with no kinetic energy and end up with E_k = mv²/2.  When you stop you lose all of that energy - mostly in the form of heat.¹  The rate of energy loss (technically power) is just E_k/t, where t is the time it takes to stop.  

 

Let's look at the case where you travel some distance d at a constant speed v and then quickly stop.  You can talk about the average energy loss for that distance as well as the average power loss.  It is just Ek divided by d/v  (d/v is the time it takes to go the distance at a constant velocity).  Substituting you get mv³/2d.  A couple of things to look at ...  this is large when the distance is small and it also grows rapidly with velocity.  So far so good...

 

The other drain is air resistance.  A runner (you can do this for anything moving through a fluid) presents an area towards the wind - let's call that A, and over some time t it sweeps out a volume of air that is just A times the distance she travels or Avt.2  You are pushing a mass of air in front of you away.  The mass is just the density of the air times its volume or m_air = pAvt where p is the density of air (about 1.3 kg/m³ at sea level and average air pressure). ³  When you move through the air the energy you have to supply just moves and swirls the air.  It is just m_airv²/2 or pAtv³/2. Divide by t to get the average rate and t drops out leaving you with pAv³/2.

 

Now it is time to compare the rate of energy loss from braking to the energy loss from air resistance. The ratio is useful:  m/pAd.   If the mass of the runner or vehicle is greater than the mass of the air in the volume tracked out, more energy is lost to braking rather than air resistance.  Another way of looking at it is if this ratio is greater than 1.0 more energy is lost in braking than is spent overcoming air resistance at speed.

 

This is significant.  It tells us when starting and stopping doesn't make sense and can even tell you when an aerodynamic car or bike makes more sense than one that is light weight.  The threshold is just 1 = m/pAd or d = m/pA.  

 

Plugging in a few numbers you get d ~ 120 meters for a runner, 250 m for a cyclist, and 1,100m for the car.⁴  A useful result.  If you drive with lots of stops and starts it makes sense to get a light weight car and not worry so much about aerodynamics.  If you have a lot of highway driving the weight is not as important as aerodynamics.  Also a cyclist or runner who can easily accelerate (say they are lighter or have more white muscle) can fatigue the competition by setting pace and varying their speed.   

 

Drat - I'm ten minutes over my allotted hour and there isn't time to talk about the inertia in bike wheels.  I'll stop here and pick up there soon.  It adds a bit of complexity, but is quite beautiful and the general concept applies to figure skating, gymnastics, diving and even volleyball.

 

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¹ Two points.  There is another form of energy that goes into spinning the wheels if you have a bike, car or some other wheeled transport.  We'll touch on that later, but I want to keep the argument simple at this point.  Also stopping something can go into sound, flexing a muscle and so on ... but heat is usually the largest sink.

² A point I'm glossing over.  Here "A" is an effective area that takes into account how aerodynamic the moving body is.  It is the product of a coefficient of drag, a measurable quantity that varies for different shapes - a jetliner or sailplane has a much lower drag coefficient than a runner, bike rider, brick or piano.  So when I say A, I really mean aC_d, where C_d is the drag coefficient and a is the measured cross sectional area you present to the air.  Likewise I should point out that v is the relative air velocity when you are talking about air resistance and the velocity relative to the ground where you are talking about the runner's, biker's or car's kinetic energy.  So we'll just assume there is a perfect calm to keep the equations simple.

³ Rather than track down the html for the greek letter rho, I'll just use p which sort of looks like a rho:-)

⁴ I assume the runner has a mass of 70kg and an effective area A (aC_d) of 0.45m², the rider plus bike has a mass of 80kg and an effective area of 0.25m², and the car and driver have a mass of 1,500kg and an effective area of 1m².

 

 

 

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Recipe corner - two quick tricks

 

Dealing with too much bread

We have a lot of bread from a bit of over experimentation and some of it is getting old.  Rather than talk about making something to begin with, here is my favorite thing to do with slightly older bread (it works on fresh bread too) as long as it still has a bit of moisture.  If the bread is getting really dry, put it in a plastic bag, flit in a bit of water and seal the bag.  In a couple of hours it should be in much better shape unless it is really over the hill.

Cut the bread into half inch thick slices, lay them on a baking sheet and brush one side wit a fair amount of olive oil.  I like using a thyme infused olive oil and, lacking that, I just chop a small bit of fresh thyme into some olive oil awhile before brushing it for a similar effect.  But I love thyme so your mileage may vary.

Pop the pan into a 350°F oven for about five minutes until the bread is slightly toasted and browned - the wonderful Maillard reaction browns the bread and creates dozens of fantastic flavor compounds.  Remove the bread and while it is still warm take a peeled clove of garlic and rub each piece of bread with it as hard as you can without crunching the bread to spread some of the garlicy goodness into a few of the cracks.  Have at it and put as much down as your love of garlic dictates.  Let it them to room temperature. 

I bet you can't eat just one:-)  There are so many possibilities for variations on the theme, so have fun!

 

The simplest "ice cream"

Really simple, really good and not bad for your health either.  The kids can make it too.

Take a few bananas and freeze them.  Break them into smaller pieces and put into a food processor with the standard metal blade.  Switch on and let it run a few minutes stopping every now and again to scrape down the sides.  At some point there will be a neat little phase transition of sorts and it will turn into a semi-frozen mass with the consistency of soft ice cream.  At that point just scoop it out and enjoy it or add some flavorings and spin it for another thirty seconds or so.  I really like throwing in some peanut butter and then adding broken bits of semisweet chocolate afterwards along with some crushed nuts.  Adding a few tablespoons of chocolate syrup is good too.

It turns out bananas have a boatload of pectin.  Pectin is concentrated in the walls of the plant cells and the mechanical action of the blades breaks the cell walls and allows the pectin to form into lovely pectin chains which form the basis for the gel that has the nice ice creamy texture.

 

why lift and separation is important

I was struck by this Louis Vuitton ad with Michael Phelps and Larisa Latynina - two remarkable athletes in the service of formal clothing and quite a shift from the standard attire as well as depiction of athletes from the original ancient games.  

 

Modern athletes wear a wide range of clothing appropriate to the sport.  Some is protective, some only has minor functionality other than basic modest and offering sponsors billboard space for television, but some athletic clothing offers competitive advantage.

 

Running offers some interesting examples.  If you run fast enough you can feel a considerable amount of wind resistance.  You want to reduce that force against you as much as possible.  Basically you are moving the air in front of you as you run.  About a year ago I wrote a post with a quick derivation of the power you have to develop to deal with that force.  The force turns out to be  half of the coefficient of drag for your body * the area you present as you run * the density of the air *  the square of your velocity relative to the air.¹  The important bits that you can control are your velocity, your frontal cross sectional area, and your coefficient of drag.  A cyclist can adapt a posture to minimize her frontal area while running generally makes that impossible.  Cyclists use a lot of aerodynamic trick with their bikes and runners can play with their clothing.  

 

To understand running attire it is useful to consider golf.

 

Sports balls are fascinating objects.  Apart from ping pong balls, few are smooth and spherical.  The shape gives them unusual properties that makes playing with them more interesting.  Balls tend to evolve with a sport and then, at some point, standardize so everyone can play on even terms.  

 

Early golf balls were mostly spherical hardwood.  It was noticed at the time that some balls were better than others, specifically some that we beaten up a bit would go further on a drive, but other beaten up balls performed worse.  Progression eventually led to a realization that small surface imperfections were important for good performance and the modern dimpled ball emerged.

 

The physics is pretty neat.  Two things are going on - one is caused by the spin on the ball and the other is related to the airstream immediately around it.²  The second is the larger effect, so I'll only consider it for the time being.

 

There are two basic types of airflow - laminar and turbulent.  Laminar flow is smooth (think of laminations), while turbulent flow is rough and choppy.  Laminar flow tends to take place at "low" speeds and turbulence becomes dominant as airspeed increases. 

A smooth ball generates a large wake as it pushes air molecules aside. Immediately behind the ball the air molecules are further apart compared to the air around and in front of the ball. A region of low pressure forms just behind the ball sucking it backwards and slowing it in the process. The air immediately around the ball is the boundary layer and one worries about where it separates from the ball - having it separate further behind the ball produces a smaller amount of total separation and the pressure drop behind the ball is smaller.  

. The dimpled ball separates the air less and has a smaller wake. The air behind the ball does not differ in air pressure as much as with the smooth ball so the dimpled ball has a smaller pressure drag and can travel further.

 

If you look at the airflow very close to the dimpled ball you notice they are roughing up the flow a bit and generating a bit of turbulence.  This makes the air stick a bit more to the ball.  It generate a bit of drag, but that turns out to be completely washed out by the fact the boundary layer sticks around a bit longer.  

 

Sweet   Dimpled balls are just better and have been around for a long time, but the effort was mostly trial and error - these days it has been possible to show what is taking place.  

 

But what does this have to do with running?

 

As it happens we create boundary layers when we run.  Our size and speed mean that if we're wearing something smooth - like a lycra bodysuit - the airflow is mostly laminar and there is an early and largish boundary separation that creates a low pressure area behind us.  One can imagine a diet of beans might help, but only for brief moments and the impact wouldn't be that great anyway, so it makes much more sense to make sure the boundary layer doesn't detach as quickly.

 

It turns out the trick is a tight fitting almost smooth body suit (you don't want a loose fit as the flapping fabric would present extra area creating even more drag) covered with a thin ribbing - about a half millimeter high and just enough to rough up the air and get the boundary layer to hang around a bit longer.  The C_d drops and the runner can put more of her power into moving herself rather than wasting it on moving air.  The effect can be dramatic.  The effect is more important as the airspeed goes up and at the very high speeds seen in the 100 meter event such suits are worth as much as a tenth of a second.³  At slower speeds air resistance is much less important (remember the force goes as the square of the relative airspeed and therefore the necessary power required to overcome it goes as the cube).

 

Hair, it turns out, is less of a problem than you might think.  There was a period when sprinters wore hoods, but the heat generated around their heads became excessive.  The head is only about 7% of your total body area and the impact of air resistance is about 3% of the total effort a sprinter must create at top speed.  Seven percent of three percent is under a hundredth of a second and the impact of heat buildup renders that counterproductive.

 

Talk of the Olympics and specialized suits brings up the Speedo LRZ swimsuits see prior to the 2008 competition.  Of all of Olympic sport, more science has probably been devoted to swimming than anything else.  Lowering the drag from moving through water is a big thing - after all - water is nearly 800 times denser than air and the underlying physics is well understood (although the calculations can be very difficult).  Speedo came up with a seamless and wrinkle-free shell of a suit and its shape stayed smooth throughout the swimming stroke. There was also a thin layer of a foamy material that had very small gas pockets that made the swimmer more buoyant.  They rode higher in the water and produced less drag.  

 

The overall effect was pretty dramatic - a 5% to 8% reduction in overall drag - but the cost was high.  The suits were very expensive ($500), took a half hour to put on and only lasted a race or two.  Since their impact was about the same on the top swimmers the decision was made to ban them and records set using them are noted separately.

 

There are many more examples - it turns out shoes are a fascinating area, but it would take pages and pages to describe the current understanding of shoes vs no barefoot as well as the difference between shoes.  So that's it for today.

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¹ The area for this is what only what the oncoming air sees and is often called the frontal cross sectional area.  Also note that the relative velocity is important.  If you are running at 10 mph with a 10 mph tailwind, the effective velocity is 0 - you don't have to move the air that is in your path.  Tailwinds are even better and records have strict limit on how big they can be.

The coefficient of drag, or C_d, is a quantity that represents how easily a shape moves through a fluid.  At a given speed the frontal area times the C_d will tell you the force you have to generate to move the air column before you aside - double the area or C_d and you need twice the force (or power).  C_d range from well under 0.1 for a sailplane, about 0.20 to 0.30 for many sports cars,  0.7 for a cyclist, 1.0 for a runner, 1.4 for the Empire State Building, 1.9 for the Eiffel Tower, and 2.1 for a brick.

² A spinning ball produces lift through the Magnus effect.  I won't go into it, but ping me if you are interested.  I've worked it out for volleyballs and found an interesting result that explains part of the ball's trajectory ..,

³ In his world record 100 meter run Usain Bolt was moving at 12.27 meters per second at the 65 meter point - about 27.3 mph!  He was producing about 3,000 watts of power at the time - about twice what a stove top electric burner consumes.  This is near the human limit for burst power production and can only be maintained for a short amount of time. The body can't sweat out this extra heat immediately and the core body temperature of a sprinter increases rapidly.  If their muscles could be powered a bit longer the increase in body temperature would kill them.

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Recipe corner.

First a technique from shesimmers for making sticky rice that doesn't require much kit.  I just tried it and had excellent results.  recommended!

 

There are a variety of tiger salads.  I don't know where this one originated, but we tried it last night and found it deliciousSim as well as easy to make.

 

Simple Tiger Salad 

 

Ingredients

 

° 1 large bunch cilantro, with the thick stems removed, cut into 3-inch lengths (about 5 cups, loosely packed)

° 1 green bell pepper stemmed, seeded and slivered (cucumber would do nicely too)

° 1 fresh chili pepper, stemmed, seeded and slivered

° 2 scallions, slivered

° 2 tsp vegetable oil

° 1/4 teaspoon salt

° sesame oil and white vinegar, to taste

° a handful of chopped peanuts (optional)

 

Technique

 

° In a bowl, combine cilantro, green pepper, chili pepper and scallions. Add vegetable oil and salt; toss lightly.

° Add peanuts if you like and a few drops of sesame oil, vinegar and more salt to taste; toss again. Pile on a plate and serve immediately as it wilts quickly

 

cheating gravity

My Dad has this recurring dream...  He is running impossibly fast and comes on a smooth lake...  "Why not?" - and he starts running across it almost effortlessly getting only the bottom of his feet wet.  He can run for miles like this and wakes up happy and exhilarated.

 

I have flying dreams and a different sort of running dream.  I'm running very fast with longer and longer strides.  I begin to increase the length of my strikes and start to pull my legs up a bit as I'm heading back towards the ground on each so the strides seem longer and longer.  At some point I'm totally avoiding the ground.  

 

Such dreams are probably common, but what about some athletes like basketball players who appear to float in the air for awhile? It can look particularly impressive as part of a slam dunk I've also seen it in soccer, er, football and volleyball.  A volleyball playing friend told me sometimes she does it at the net so to keep herself well positioned to put together a block.  She can touch a bit over 11 feet, so the ability to linger for a few tenths of a second at a slightly lower level can give an advantage.  Plus "it feels neat!"  

 

But the real masters are probably ballet dancers.  

 

There seems to be something a bit wrong here - after all - high school physics teaches us that someone jumping will propel themselves in a parabolic arc.  That is still true for a complicated object like a human body.  The trick is that the its center of mass follows the parabolic path.  You can move the rest of your body into any position you can muster while this is taking place.  The physics is all very simple even though the motion of any of the given points can be very confusing.¹  As its motion slows near the top of the trajectory the dancer can move her limbs so as to keep some of her body in a stationary vertical position.  Adjustments are constantly made as her vertical speed slows, stops and then begins to increase in the other direction. As some point her center of mass is moving too quickly to compensate.  

 

I watched a video of a dancer performing a grand jeté.   In it she raises her legs into a nearly horizontal position and raises her arms above her head dropping the level of her head relative to her center of mass as it rises.  She reverses the process as she begins to fall earthward again.  I timed it at 0.44 seconds - a very long illusion.  I also timed a basketball player in a slam dunk contest at about 0.3 seconds.  In theory he could probably do it longer with his longer limbs, but he lacked her technique and 0.3s still looks startling and even beautiful to the audience.  In volleyball it is more on the order of basketball.  I'm sure it must feel wonderful when probably executed.

 

Using the fine print and the fact that we notice heads a lot to "cheat" gravity.

 

There is another use of this in sport.   If you are standing normally, your center of mass is about 55% of your height from the ground and inside your body. If you bend forward at your hips your center of mass moves forward.  It is possible to move it outside your body.²  A high jumper can arrange for his body to move so that it completely soars above the bar even though the trajectory of his center of mass might pass under the bar (or somehow cause some of him to collide with it).  Dick Fosbury perfected the technique in the late 60s and revolutionized a sport - the Fosbury Flop.

 

Our sense of time is finely tuned to the environment we live in and that includes possible motions of our bodies.  We can discern individual bits of motion down to about three hundreds of a second - our world is viewed at roughly video rate.  A really fast tennis serve is a bit north of 65 meters per second.  Air resistance quickly drops that, but the ball initially is travels about 2 meters before we can take in the next frame³ The receiving player must make a lot of assumptions about where the ball is going to go based on subtle information before the ball is hit.  Clearly a lot of experience in understanding the biomechanics of how the trajectory of a tennis ball is created is built into any experienced player.  The same can be said for many other sports - baseball, even though the ball's speed coming off the bat is somewhat lower than that of a tennis ball, is more dramatic as the ball has enough mass that it does not slow down as quickly..  

 

Athletes are really good at Newtonian physics!

 

I'm better than Colleen sitting down with equations and working something out, but she has a much better ability to execute a series of those equations - equations that can be way to difficult for me to solve analytically - and not only come up with answers in real time, but convert the answers to values her muscles can use adjusting for real time position information of her own body.  Even more impressive is the fact that her senses notice where her body was rather than where it is at any given time.  We all have a neural time lag. Since she is very tall, she lives a bit more in the past than I do making the feat even more impressive.⁴

 

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¹ Take a hammer, or something else with an uneven mass distribution, and toss it with a bit of spin.  (hopefully away from anything that can be damaged)  The tends will form a tumbling pair of paths, but if you carefully watch the motion of the center of mass near its head. That will trace out a smooth parabolic trajectory.  

² You may have tried this as a student trying to pick up a chair with your head against a wall.  Women tend to have lower centers of mass relative to their height than men - the net result can be the men are unable to pick up the chair, but the women can.

³ There is additional time used to register an event, but ignore that and assume you are watching the ball.

⁴ Neural impulses travel at speeds that are slower than you may think anywhere from a few to about 120 meters per second.  Touch generally moves about 50 meters per second and pain much more slowly (hammer your finger and you notice you've done something really stupid fairly quickly, but the pain takes about a second to register - this is really useful to making an unencumbered choice when something really goes wrong)

The body tends to aggregate a few types of perception - touch your nose.  You "feel" the touch with your finger tip and the tip of your nose even though the time delay on the path from your nose to your brain is much less (up to a few tenths of a second).  People with longer bodies and longer neural path lengths perceive reality a bit later than shorter people.  Colleen lives a few hundredths of a second more in the past than I do (probably about 0.05s or so - certainly more than a perceived image frame) and has to adjust the motion of her body appropriately. Of course we never notice any of that, but it is a fascinating new layer of complexity.

 

Anyway - you can probably figure out that I woke up after one of those wonderful dreams where I can adjust my stride so as to rarely touch the ground.  Of course you might actually do that if you could dial back the force of gravity.  For some fun, think about Olympic events on the moon where the force of gravity is about a sixth that of Earth (assume you are in a big stadium that has an atmosphere to make it a bit more interesting) ... what would the record book look like?  And note that your reaction time is suddenly improved relative to how events transpire in some (not all!) sports...

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recipe corner

 

This was really good the other night. Heirloom tomatoes are wonderful now and it  that roasting them might be just wonderful.  Some corn was lurking along with a very flavorful vegetable stock - enough to spark a soup.  The quantities shown are very approximate - use your intuition and don't follow exactly.

 

Corn and Tomato Summer Soup

 

Ingredients

 

° 4 large very ripe heirloom tomatoes

° 2 ears of corn- cut off the kernels

° 4 cloves of garlic minced

° a small yellow onion

° a swish of olive oil 

° a small chili finely chopped (I'll leave it up to you how hot or not, so pick your poison - you can leave it out)

° 700g or so of vegetable stock (about 3 cups)

° salt and pepper

° plain greek yogurt (I like Fage 2%, or the full test if you dare)

 

Technique

 

° Preheat your oven to 400°F

° Heat the olive oil in a large pan over a medium low heat .

° Add the onions, garlic, chili and some salt and sweat the onions (cook them 'til translucent - about 4 or 5 minutes for me)

° In another pot heat the stock

° Slice the tomatoes in half and cut out the cores, drizzle some olive oil on their flat sides and place them flat side down on a cookie sheet.  Roast until they just start to caramelize, but don't let them burn (about 10 minutes for me)

° Dump the tomatoes into the pot with the onion and garlic.  Pour a bit of the stock onto the yummy browned pan scrapings and scrape all of that into the pot.

° Cook on a medium heat for about 5 or 10 minutes until it starts to dry out a bit (depending on how much stock you have ladled onto it)

° Add the corn kernels and cook for another few minutes (maybe 3 or 4)

° Add the stock, bring to a boil and reduce to a simmer and cover. Let it cook "enough" - about 45 minutes for me.

° Put it into a food processor or use an immersion blender (much less dangerous).  Strain off the debris 

° Season to taste.  You will need pepper and possibly more salt.  Some herbs may be appropriate.

° Serve with a bit of yogurt and a drizzle of olive oil on each bowl. I added some chopped basil, but use your imagination.

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Yesterday it was pointed out that it was "eat ice cream all day day" ..  I decided to make something and picked up some heavy cream in the evening and then searched the pantry for inspiration.  I ended up with a tried a true vanilla with some additions.  Recommended.  But try to get pasteurized heavy cream rather than the ultra pasteurized variety if you can (it isn't easy).  Also use pasteurized eggs for safety as this is an uncooked method.

Lots of room for experimentation here!

 

Chocolate, Bing Cherry and Pecan Ice Cream

 

Ingredients

° 2 large pasteurized eggs 

° 185g (about 3/4 cup) granulated white sugar

° 2 cups heavy cream (pasteurized rather than ultrapasteurized if possible)

° 1 cup whole milk 

° half vanilla bean (optional)

° about 50g coarsely chopped semisweet chocolate (a mixture of chocolate types would be great!)

° about 50g bing cherries, pitted and cut into quarters

° about 30g coarsely chopped pecans

 

Technique

 

° chill the chocolate, cherries and nuts in separate bowls and get as close to freezing as you can

° whisk eggs until light and fluffy - a couple of minutes usually

° whisk in the sugar a bit at a time and then completely bend.  Pour in the milk and cream and continue to blend.  

° split and scrape the vanilla bean - mix in the goodstuff  (I didn't have a bean and it worked out, but I think it would be better with)

° add to your ice cream freezer and start freezing

° a minute or so before it is ready add the nuts, chocolate and cherries

 

 

flying through the water

Fifteen feet across and thirty inches deep,  old vinyl swimming pool wasn't terribly useful for swimming.  I was twelve and its novelty had worn off.  The obvious uses were floating or just trying to stay cool in the Summer, but it turned out to make a lovely wind tunnel and general piece of experimental apparatus.

 

My Dad liked ice cream enough that he found five gallon cartons that our freezer could barely hold.  These were very sturdy and the empties were useful.  It turns out you probably don't want to try it, but I though I could launch a model rocket from under water by covering the top with something the rocket could fly through.¹   But somehow the idea of moving through water - flying through water - caught my fancy.

 

Plastic model airplanes were common back then and I had the idea that I might be able to fly once of them.  After all, the better ones had a bit of an airfoil molded into the wing.  What I didn't know at the time was this was a good idea.  Water and air are both fluids and the motion of a body through them is governed by the same fluid dynamics.  The difference is water is about 800 times denser than air.  It took quite a bit of experimentation, but finally I had a nice "wind tunnel" that replaced air with water.²

 

You've probably done the same with your hand out the car's window. The airflow against your hand creates quite a bit of drag, but you can change the shape of your hand by cupping it a bit to resemble an airplane's airfoil and something wonderful happens. There is lift - the same sort of lift that allows flight under the right conditions - enough, depending on the angle of attack, to make it challenging to hold in place when the car is at highway speeds.³   This same airfoil can be used underwater as a hydrofoil when we swim and gives a neat window to examine of some the Olympic swimming events as well as how those of us who are less skilled and athletic manage.

 

Brynne suggested swimming as the next Olympic topic and Jean triggered something about airfoils.  A nice topic as there has been an enormous amount of research into swimming since the 70s.  Computational fluid dynamics, a discipline fueled by the aerospace industry, had advanced to the point where it was possible to study the basics of a human moving through water and competitive swimming has been revolutionized mostly through improvements in technique.⁴  After all - things moving through water behave very much like things moving through really dense air - the sort of thing I was learned from that little vinyl wind tunnel, er, swimming pool when I was twelve.⁵

 

While runners and cyclists go forward by pushing off of solid surfaces, swimmers move forward by pushing against the fluid they are flying through.  You cup your hand a bit and control the angle it makes with the water.  Just like an airfoil there is gravity, drag, lift and propulsion - the propulsion is from the lift pointing mostly forward.  Fortunately the human body has almost the same density as water, so very little work has to be done to support yourself against gravity.

 

There are three basic types of drag that try to hold a swimmer back - friction, pressure and waves.  The first type - friction of the body against the water - varies with the speed and shape of the swimmer.  This is what you feel and have to pay attention to as a recreational swimmer as it is important at all speeds.  For the same body shape it scales linearly with your cross sectional area to the direction of motion and the square of your speed relative to that of the water - just like running or biking through the air.  The power required to counteract this resistive force goes as the cube of your speed.  It takes a lot of muscle and effort to go just a bit faster.

 

As you swim there is a pressure difference between the water immediately in front and behind you - the pressure being higher in front.  This creates another type of drag and one that becomes increasingly important as you move faster.  Most recreational swimmers don't go fast enough for it to dominate, but if you're moving quickly it becomes a real issue in a hurry.

 

Near the surface of the water you have to plow through the waves.  You create your own and have to deal with those of others even in an otherwise perfectly still pool.  As you move faster both their amplitude and their wavelength - the peak to peak distance between swells - increase. If you are going fast enough that the wavelength is a bit longer than your height you can get caught in your own trough which is a natural practical speed limit.  A taller swimmer will have a longer wavelength to break and has a higher speed limit than someone who is shorter.  

 

The amplitude of the waves you generate can be changed with technique and great progress has been made with computational analysis and the application of newly discovered techniques.  Likewise a lot of work has gone into basic swimming technique to supply more thrust.

 

This wave interaction has an interesting story.  If you can swim underwater you don't have to deal with it.  A fast freestyle swimmer will stay submerged as long as they can after a start or when they turn.  In 2010 an American swimmer broke the world record in the 50 meter backstroke by staying underwater the whole time using a dolphin kick and a few other tricks.  In the end he was disqualified and the rules were changed to limit the distance a swimmer can remain submerged.  It is important to come as close to this limit if you can if you want to win at the highest levels as wave drag at high speeds can account for more than half the total drag.

 

World class swimmers tend to have long torsos, very long and powerful arms and relatively short legs with large flippers - er - feet.  Mike Phelps and Missy Franklin are both relatively tall with very long torsos and wingspans greater than their heights - they also have great lungs and an insane ability to capacity to use oxygen - a great VO₂ max .  Both have very large feet and have great arm muscles and big hands.  They were made to swim fast.  Usain Both is very tall, with a short torso and very long legs, an enormous percentage of white muscle, and a very short achilles tendon.  He was made to run fast.  Of course, beyond the genetic gifts there is an enormous amount of dedication and excellent training and coaching...  

 

...but at what level of sport are genetic gifts required?

 

For average k12 and recreational sports I doubt that genetic gifts are required to do well and enjoy yourself.  You should do what you enjoy. I've seen really good 5'7" high school basketball players do very well. Perhaps at state tournaments or in very competitive leagues height starts to be necessary, but you can do a lot with hard work and a love of the game.  Exceptions may be people who have dramatically different red to white muscle ratios.  There are people who just can't jump, but can run forever (that runs in my family) I suspect, for these people as well as for the natural sprinter/jumpers, you will gravitate to sports that seem right to you.  

 

But at the highest level of sport you need everything as well as some luck.  Colleen, at 6'7 and extremely long legs and arms, is one of these people.  Long limbs are good for some sports, but you pay a price when you need to rotate your body.  When she was a pre-teen she really wanted to dive well, but a 6'1 11 year old just can't rotate her body quickly enough.  It would be fascinating to make a silhouette of the a composite average of the top few in the world for each sport and create a poster - gymnasts on one end and basketball players on the other.  It is remarkable that world class bike riders are about the same height and the same is true of distance runners.  But so few of us will compete at these levels that the best advice is undoubtedly what the ad suggests - pick whatever sport you like and - 

 

Just Do It!

 

__________

¹ I tried three or four different materials for a breakable windows the rocket could puncture.  Unfortunately materials strong enough to submerge to a satisfying depth kept the rocket inside usually resulting in a delayed rupture with a lot of acrid smoke belching to the surface and a water damaged rocket.

² I built a little underwater tow track with a couple of pulleys, a crank and a small scale for making measurements.  I didn't realize that the airfoils on the models weren't terribly accurate, but I was able to "fly" some of the aircraft and even rig them for climbing and banking by bending little control surfaces I added with a bit of tape. 

³ There are four basic forces on an airplane in flight - gravity trying to pull it down, lift counteracting gravity, drag trying to slow the aircraft and thrust from an engine pulling it forward (of course unpowered gliding is possible too and then you just out three forces).  If you carefully examine an airfoil the top surface has a concave surface and the bottom surface usually has a flat or cave surface.  Air meeting the airfoil either goes above it or below it.  The air that travels across the top has a longer path to take and, since the same amount that starts out just in front of  the airfoil has to be the same as that just behind it, the air pressure on top is lower and the pressure on the bottom higher. The net result is an upward lift.  As the aircraft increases its speed relative to the air it is moving through the lift increases.  At some point the lift force exceeds that of gravity and we have flight.

⁴ Checking the records for the men's 100 meter freestyle the progression has been from 52.9s in 1964 to 4.9s today.  The women have gone from 58.9s to 52.1s.  Swimming is about four times slower than running for many events so compare this to the 400m track event which has gone from 44.9s to 42.2s for men and 51s to 47.6s for women - a much smaller rate of progression.  Technique turns out to be much more important than the exotic and very expensive swimsuits seen during the last Olympics.  In sport there is a level where relatively tiny improvements can give an enormous advantage.

⁵ If you want to motivate a teen to learn a bit about math getting them fascinated by aerodynamics and fluid flow is an outstanding gateway drug.  The Navier-Stokes equations are a beautiful way to address fluid dynamics.  Non-linear partial differential equations and a bit of fundamental bedrock of mathematical literacy for the physical, and even some of the biological, sciences.  A motivated teenager can learn quite a bit if there is a strong motivation.

__________

Recipe corner

 

I love a good granola bar and this chocolate cherry one is a winner.  This is good with a scoop of a rich vanilla ice cream on top or just by themselves.

 

Chocolate Cherry Almond Bars

 

Ingredients

 

° 150g (1-2/3 c) rolled oats

° 115g honey (1/3 c) I like Tupelo these days)

° 40g (1/3 c) whole wheat flour

° 1/2 tsp salt

° 50g (about 2 oz) chocolate bar crushed (about 70% cocoa)

° 75g (1/2 c) dried cherries

° 75g (1/2 c) slivered almonds 

° 1 tsp good vanilla extract

° 55g (1/4 c) butter (you can use coconut or olive oil)

° 50g (1/4 c) dark brown sugar (I have used 1/2 brown sugar, 1/2 molasses too)

 

Technique

 

° set oven to 350° F

° combine everything in a large bowl and mix well

° spread onto a baking sheet and pat down until it is about a half inch thick - cover exposed edges with a bit of foil so they don't get too brown

° bake until the top is golden brown - maybe 25 minutes

° cool and cut into whatever bar shape pleases

 

The second recipe - after all, I didn't post one with the last post, is something I will make in the near future to honor a breakthrough Jean made a few days ago. (isn't it wonderful to celebrate friends like this?).  I've made the vanilla and it is one of my best vanillas ever.  I've also done the fudge and will make the modification I've suggested.  It will be a slam dunk, I'm sure.  I'll leave everything in old units as this is from old notes before I began to weigh ingredients.   If you don't make your own ice cream try this with a super premium vanilla softened, a good fudge and some peanut butter and peanut butter cups.  It should be excellent too:-)

 

Peanut Butter Chocolate Ribbon Ice Cream

 

Ingredients

ice cream

° 1 cup whole milk

° 2/3 cup white sugar

° 2 cups heavy cream in two separate cups - try to get just pasteurized rather than ultrapasteurized if you can

° a bit of salt

° 6 egg yolks from large eggs (odd that large is the standard egg size, isn't it?)

° 2 tsp vanilla extract - highest quality you have

° the scrapings of one vanilla bean

° a couple of handfuls of the smallest peanut butter cups chopped coarsely.  I'm guessing about 5 or 6 ounces.

fudge ribbon

° 1/2 cup white sugar

° 1/3 cup light corn syrup

° 1/2 cup water

° 6 tbl Dutch-process cocoa powder (some of the high end cocoa powers aren't and won't work well here)

° 1/2 tsp vanilla

for the peanut butter ribbon

° 1/3 cup smooth peanut butter (I think the stuff without sugar will be best - but stir it well)

° a bit of whole milk - maybe a couple of tbl

 

Technique

 

° Heat the milk, sugar, 1 cup heavy cream and a pinch of salt in a sauce pan - just warm it

° in another bowl whisk the egg yolks while slowly adding some of the heated mixture

° As the mixture heats to somewhat warm, put the yolk mixture into the sauce pan

° stir constantly over a medium heat until the mixture thickens.  The gold standard is when it coats the spatula - now you have custard

° pour throw a strainer over another bowl you have cleverly pre-positioned and stir in the remaining cup of heavy cream

° stir in the vanilla extract and bean scrapings 

° stir it every now and again until it cools and then chill in the fridge for a few hours

now onto the fudge - 

° mix the water, sugar, corn syrup and cocoa over a medium heat until bubbles just start to form - then boil for a minute or so stirring constantly and remove from the heat.

° stir in the vanilla extract and let cool.  You can pour it into a jar and store it.  Make sure it is chilled before you use it!

now for the ice cream making!

° churn freeze the custard mixture as per the instructions of your ice cream machine

° as this happens whisk the milk and peanut butter together

° when the machine begins to slow add the chopped chocolate peanut butter cups and let it run another minute or so.  

° move some (a third?) of the ice cream to a storage container and drizzle a third of the fudge and the peanut butter/milk mixture and repeat the process until you have have added all of the layers.  

° finish by throwing it in your freezer for a few hours.  I suspect I'll break in well before that as I frequently act my shoe size and I happen to be the "adult supervision" here

 

 

it's a drag...

OK - I've been spending way too much time watching the Olympics.  The fact that all of the events are being streamed has had an impact on the amount of work I've been able to accomplish, so I'm writing off some of this as vacation time.  

 

I tend to be interested in sports I've had some involvement with - either by participation (and never at a terribly athletic level), through the involvement of a friend or relative, or by getting involved in the science behind a sport.¹  

 

I had asked for suggestions of science of sport questions people might have and a few people responded.  Ted asked about the remarkable long jump record set by Bob Beamon.  According to the always infallible Wikipedia, he came to the event as a favorite with a personal best of 8.33 meters - very close to the world record at the time.   Somehow he managed 8.90 meters - 29 feet 2.5 inches - over 21 inches longer than the world record at the time.  This was such a huge increase over everyone else in the world - and himself - that it stood out and remained the record until 1991 when Mike Powell jumped a 8.95 meters.  Beamon still has the second longest jump in history, although a few have approached it.

 

Ted asked about what might be going on - after all - records were falling for jumping and sprinting events, while distance events saw terrible performance.

 

Mexico City is 2,240 meters above sea level and oxygen absorption by the human body is only about 90% what the athlete can manage at sea level.  Athletes who had spent time training at altitude were able to absorb somewhat more than athletes who weren't acclimatized with the distance events being dominated by runners from high altitudes, although the times were not fast compared with sea level performances.  Sprinting events, on the other hand, saw a lot of new records.

 

It turns out oxygen absorption isn't very important in sprinting events.  During the burst of speed of a flat out sprint, the muscles are converting chemical to mechanical energy by anaerobic metabolism.²  In other words it makes sense that anaerobic events shouldn't be degraded, while aerobic events will.

 

The atmosphere has a lower density at greater altitude above sea level.  At  20° C air density is 1.23 kilograms per cubic meter at sea level, but Mexico City is down to 0.98.  Although the density is only 80% of sea level, you will only see a 0.1% drop in your sprint time, while many of the winning sprinters saw improvements in the 1 to 2% range.³  Further analysis suggests the real culprit was the wind.

 

The winds at Mexico City were largely behind the athletes for the 100 and 200 meter events and were high - bordering on, and possibly exceeding, the 2.0 meter per second limit requirement for official Olympic records.   Precise weather data was not recorded and it is impossible to make absolute statements, but tail winds of this speed turn out to be enough to account for the improvements several athletes saw and there was a suspicion that they may have much stronger at times.⁴

 

For all endurance events athletes who had trained at altitude had a big advantage over those who did not.  Since'68 some athletes train at altitude as the body learns to absorb more oxygen at the lower air pressure.  The effect is short-lived and needs to be properly timed for best effect.  Probably more common these days is sleeping in oxygen tents that simulate high altitudes.

 

The wind does have an impact on many events though - and perhaps technique should vary to take it into account.  Imagine a longer race with a windspeed of w and runners pushing along at a constant speed v.  For sake of argument think of them as running a square lap with legs that have a north, west, south and east alignment and have the wind coming from the north.  When a runner is going north she will have an effective windspeed of v+w and when she is going south v-w.  The force she feels will be proportional to (v+w)² on the north leg (v-w)² on the south and just v² on the east and west portions.  As long as the magnitude of v is greater than that of w, the total force for the race will be greater than it would be if the conditions were calm - she has to work harder to keep up the same pace. 

 

Fortunately this is fine and dandy if all of the runners are experiencing the same conditions.  And there are some tricks you can play.  If you run directly behind another runner your effective airspeed, and thus air resistance, is less than that of an exposed runner.  Runners and cyclists often bunch in packs to take advantage of this and the leader is at a big disadvantage.  

 

But what if there is a trailing wind?  I rarely see athletes take advantage of this and I've mentioned it to a couple of Olympic coaches.  The runner (or cyclist) with the most wind at their back has an advantage, but those in the pack no longer benefit from the trailing wind.  A better strategy would seem to be to break out of the pack.  I was told the athletes don't know the wind velocity at any moment and windspeeds in these races is usually too low from them to take chances.  

 

But what about Bob's miracle record-smashing jump? I found a few papers on the subject.  The greater speed from the tail wind he probably had was probably enough to account for about half the extra distance.  The rest probably came from his athleticism and perhaps a variation on his techniques.  The fact that another person was able to better it in a calm shows that the record was humanly possible - he was able to muster the magic of doing it 23 years earlier than improvements in training and technique would suggest.  

 

This is the beauty of sport - when someone manages to tap what seems impossible and astound the world.

__________

¹ I'm very slow, but can have a bit of endurance.  When I actively cycled centuries (100 mile rides) were no big deal.  My niece Magi also is a red muscle (slow twitch) person, but she is a genuine athlete.  She does marathons and is a nationally ranked ultra-marathon runner, racing in the mountains.  Ultra-marathons usually start at 50 miles - yikes!

Pip and Dave - and probably others among you - have run marathons and Jheri is a "purely for the fun of it" runner who knocked off a 2:58 marathon the first time she tried one.  

Colleen is exceptionally athletic having been a Division 1 All American in volleyball when she was in college and then moving on to pro indoor volleyball in Europe and finally pro beach volleyball.  She taught me a lot about the sport and it is one of the main Olympic attractions for me.

² It is a bit beyond a short post, but there are two types of anaerobic (without oxygen) metabolism.  Both provide mechanical energy that greatly exceeds what aerobic metabolism can provide.  Different muscle types are specialized for one or the other.  White muscle is good for anaerobic metabolism, while red muscle (it looks red due to the oxygenated blood in it) is better suited for the long haul.  Most people have 50:50 mixtures - but people good at endurance running can have as much as 80% red muscle, and 100 yard dash specialists can have about 75% white muscle. Usain Bolt could never run a marathon - at least not with a credible amateur time.  This leads to a lot of interesting questions about body type and genetics in sport at the amateur, pro and world class levels.

A note on sub 10 second 100 meter races.  The runners produce power at 2,500 to 3,000 watts.  This is above and beyond the normal 70 or so watts used to keep the body functioning, but not physically moving.  There is no way this heat can be immediately removed (for comparison the electric element on a stovetop is about 1,500 watts) and the internal body temperature soars.  If the race was as long as 20 seconds at that level most of the runners would probably die from heat effects. Fortunately muscles can only function at this level for about 10 seconds.  The 200 meter races are very different from 100 meters, even though both are sprints.

³ Offered without derivation - there is quite a bit of physics behind this number. 

⁴ Again more physics, but a 2 meter/s following wind gives approximately a 0.12 second improvement for a 100 meter dash about twice that for 200 meters.