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 104th 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. 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 usually 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 Idisk = 1/2 and Irim = 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 important for some events where bursts 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 mr2.. 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 Kerri and Misty "balance" at a fraction under 6' and volleyball players make terrible gymnasts 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
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)
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